TSTP Solution File: ITP048^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP048^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 : Thu Aug 31 03:17:46 EDT 2023
% Result : Theorem 1.05s 1.26s
% Output : Proof 1.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.16 % Problem : ITP048^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.17 % Command : do_cvc5 %s %d
% 0.17/0.38 % Computer : n006.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun Aug 27 11:34:52 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.23/0.55 %----Proving TH0
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 % File : ITP048^1 : TPTP v8.1.2. Released v7.5.0.
% 0.23/0.55 % Domain : Interactive Theorem Proving
% 0.23/0.55 % Problem : Sledgehammer EdmondsKarp_Termination_Abstract problem prob_146__7582994_1
% 0.23/0.55 % Version : Especial.
% 0.23/0.55 % English :
% 0.23/0.55
% 0.23/0.55 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.23/0.55 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.23/0.55 % Source : [Des21]
% 0.23/0.55 % Names : EdmondsKarp_Termination_Abstract/prob_146__7582994_1 [Des21]
% 0.23/0.55
% 0.23/0.55 % Status : Theorem
% 0.23/0.55 % Rating : 0.38 v8.1.0, 0.36 v7.5.0
% 0.23/0.55 % Syntax : Number of formulae : 315 ( 110 unt; 41 typ; 0 def)
% 0.23/0.55 % Number of atoms : 715 ( 188 equ; 0 cnn)
% 0.23/0.55 % Maximal formula atoms : 12 ( 2 avg)
% 0.23/0.55 % Number of connectives : 2319 ( 60 ~; 10 |; 41 &;1894 @)
% 0.23/0.55 % ( 0 <=>; 314 =>; 0 <=; 0 <~>)
% 0.23/0.55 % Maximal formula depth : 16 ( 7 avg)
% 0.23/0.55 % Number of types : 7 ( 6 usr)
% 0.23/0.55 % Number of type conns : 160 ( 160 >; 0 *; 0 +; 0 <<)
% 0.23/0.55 % Number of symbols : 36 ( 35 usr; 12 con; 0-4 aty)
% 0.23/0.55 % Number of variables : 826 ( 87 ^; 705 !; 34 ?; 826 :)
% 0.23/0.55 % SPC : TH0_THM_EQU_NAR
% 0.23/0.55
% 0.23/0.55 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:24.947
% 0.23/0.55 %------------------------------------------------------------------------------
% 0.23/0.55 % Could-be-implicit typings (6)
% 0.23/0.55 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.23/0.55 list_P559422087at_nat: $tType ).
% 0.23/0.55
% 0.23/0.55 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.23/0.55 product_prod_nat_nat: $tType ).
% 0.23/0.55
% 0.23/0.55 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.23/0.55 set_nat: $tType ).
% 0.23/0.55
% 0.23/0.55 thf(ty_n_tf__capacity,type,
% 0.23/0.55 capacity: $tType ).
% 0.23/0.55
% 0.23/0.55 thf(ty_n_t__Nat__Onat,type,
% 0.23/0.55 nat: $tType ).
% 0.23/0.55
% 0.23/0.55 thf(ty_n_tf__a,type,
% 0.23/0.55 a: $tType ).
% 0.23/0.55
% 0.23/0.55 % Explicit typings (35)
% 0.23/0.55 thf(sy_c_Graph_OGraph_Oconnected_001tf__a,type,
% 0.23/0.55 connected_a: ( product_prod_nat_nat > a ) > nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_Oconnected_001tf__capacity,type,
% 0.23/0.55 connected_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_Odist_001tf__a,type,
% 0.23/0.55 dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_Odist_001tf__capacity,type,
% 0.23/0.55 dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_OisPath_001tf__a,type,
% 0.23/0.55 isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_OisPath_001tf__capacity,type,
% 0.23/0.55 isPath_capacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__a,type,
% 0.23/0.55 isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_OisShortestPath_001tf__capacity,type,
% 0.23/0.55 isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_OisSimplePath_001tf__a,type,
% 0.23/0.55 isSimplePath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_OisSimplePath_001tf__capacity,type,
% 0.23/0.55 isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_Omin__dist_001tf__a,type,
% 0.23/0.55 min_dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_Omin__dist_001tf__capacity,type,
% 0.23/0.55 min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_OreachableNodes_001tf__a,type,
% 0.23/0.55 reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Graph_OGraph_OreachableNodes_001tf__capacity,type,
% 0.23/0.55 reacha1693770334pacity: ( product_prod_nat_nat > capacity ) > nat > set_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.23/0.55 plus_plus_nat: nat > nat > nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.23/0.55 size_s1990949619at_nat: list_P559422087at_nat > nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
% 0.23/0.55 ord_Least_nat: ( nat > $o ) > nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.23/0.55 ord_less_nat: nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.23/0.55 ord_less_eq_nat: nat > nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.23/0.55 collect_nat: ( nat > $o ) > set_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_c_member_001t__Nat__Onat,type,
% 0.23/0.55 member_nat: nat > set_nat > $o ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_c,type,
% 0.23/0.55 c: product_prod_nat_nat > capacity ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_c_H,type,
% 0.23/0.55 c2: product_prod_nat_nat > a ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_p,type,
% 0.23/0.55 p: list_P559422087at_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_p1____,type,
% 0.23/0.55 p1: list_P559422087at_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_p1a____,type,
% 0.23/0.55 p1a: list_P559422087at_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_p2_H____,type,
% 0.23/0.55 p2: list_P559422087at_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_p2_Ha____,type,
% 0.23/0.55 p2_a: list_P559422087at_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_p_H,type,
% 0.23/0.55 p3: list_P559422087at_nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_s,type,
% 0.23/0.55 s: nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_t,type,
% 0.23/0.55 t: nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_u____,type,
% 0.23/0.55 u: nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_ua____,type,
% 0.23/0.55 ua: nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_v____,type,
% 0.23/0.55 v: nat ).
% 0.23/0.55
% 0.23/0.55 thf(sy_v_va____,type,
% 0.23/0.55 va: nat ).
% 0.23/0.55
% 0.23/0.55 % Relevant facts (273)
% 0.23/0.55 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,
% 0.23/0.55 ( ( min_dist_capacity @ c @ s @ t )
% 0.23/0.55 = ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % \<open>min_dist s t = min_dist s u + min_dist u t\<close>
% 0.23/0.55 thf(fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062,axiom,
% 0.23/0.55 ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ) ).
% 0.23/0.55
% 0.23/0.55 % \<open>min_dist s u < length p1\<close>
% 0.23/0.55 thf(fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062,axiom,
% 0.23/0.55 ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ) ).
% 0.23/0.55
% 0.23/0.55 % \<open>min_dist u t \<le> length p2'\<close>
% 0.23/0.55 thf(fact_3_nat__add__left__cancel__less,axiom,
% 0.23/0.55 ! [K: nat,M: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.23/0.55 = ( ord_less_nat @ M @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % nat_add_left_cancel_less
% 0.23/0.55 thf(fact_4_add__less__cancel__left,axiom,
% 0.23/0.55 ! [C: nat,A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.23/0.55 = ( ord_less_nat @ A @ B ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_less_cancel_left
% 0.23/0.55 thf(fact_5_add__less__cancel__right,axiom,
% 0.23/0.55 ! [A: nat,C: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.23/0.55 = ( ord_less_nat @ A @ B ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_less_cancel_right
% 0.23/0.55 thf(fact_6__C1_Oprems_C_I2_J,axiom,
% 0.23/0.55 isPath_capacity @ c @ s @ p1a @ va ).
% 0.23/0.55
% 0.23/0.55 % "1.prems"(2)
% 0.23/0.55 thf(fact_7_SP,axiom,
% 0.23/0.55 isShor1936442771pacity @ c @ s @ p @ t ).
% 0.23/0.55
% 0.23/0.55 % SP
% 0.23/0.55 thf(fact_8_min__dist__split_I2_J,axiom,
% 0.23/0.55 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ U @ D1 @ W )
% 0.23/0.55 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 0.23/0.55 => ( ( ( min_dist_capacity @ c @ U @ V )
% 0.23/0.55 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.23/0.55 => ( ( min_dist_capacity @ c @ W @ V )
% 0.23/0.55 = D2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % min_dist_split(2)
% 0.23/0.55 thf(fact_9_min__dist__split_I1_J,axiom,
% 0.23/0.55 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ U @ D1 @ W )
% 0.23/0.55 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 0.23/0.55 => ( ( ( min_dist_capacity @ c @ U @ V )
% 0.23/0.55 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.23/0.55 => ( ( min_dist_capacity @ c @ U @ W )
% 0.23/0.55 = D1 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % min_dist_split(1)
% 0.23/0.55 thf(fact_10_min__dist__less,axiom,
% 0.23/0.55 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 0.23/0.55 ( ( connected_capacity @ c @ Src @ V )
% 0.23/0.55 => ( ( ( min_dist_capacity @ c @ Src @ V )
% 0.23/0.55 = D )
% 0.23/0.55 => ( ( ord_less_nat @ D3 @ D )
% 0.23/0.55 => ? [V2: nat] :
% 0.23/0.55 ( ( connected_capacity @ c @ Src @ V2 )
% 0.23/0.55 & ( ( min_dist_capacity @ c @ Src @ V2 )
% 0.23/0.55 = D3 ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % min_dist_less
% 0.23/0.55 thf(fact_11_add__left__cancel,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ( plus_plus_nat @ A @ B )
% 0.23/0.55 = ( plus_plus_nat @ A @ C ) )
% 0.23/0.55 = ( B = C ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_left_cancel
% 0.23/0.55 thf(fact_12_add__right__cancel,axiom,
% 0.23/0.55 ! [B: nat,A: nat,C: nat] :
% 0.23/0.55 ( ( ( plus_plus_nat @ B @ A )
% 0.23/0.55 = ( plus_plus_nat @ C @ A ) )
% 0.23/0.55 = ( B = C ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_right_cancel
% 0.23/0.55 thf(fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062,axiom,
% 0.23/0.55 isPath_capacity @ c @ ua @ p2_a @ t ).
% 0.23/0.55
% 0.23/0.55 % \<open>isPath u p2' t\<close>
% 0.23/0.55 thf(fact_14_dist__trans,axiom,
% 0.23/0.55 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ U @ D1 @ W )
% 0.23/0.55 => ( ( dist_capacity @ c @ W @ D2 @ V )
% 0.23/0.55 => ( dist_capacity @ c @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dist_trans
% 0.23/0.55 thf(fact_15_connected__def,axiom,
% 0.23/0.55 ! [U: nat,V: nat] :
% 0.23/0.55 ( ( connected_capacity @ c @ U @ V )
% 0.23/0.55 = ( ? [P: list_P559422087at_nat] : ( isPath_capacity @ c @ U @ P @ V ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % connected_def
% 0.23/0.55 thf(fact_16_shortestPath__is__path,axiom,
% 0.23/0.55 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.55 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 0.23/0.55 => ( isPath_capacity @ c @ U @ P2 @ V ) ) ).
% 0.23/0.55
% 0.23/0.55 % shortestPath_is_path
% 0.23/0.55 thf(fact_17_connected__by__dist,axiom,
% 0.23/0.55 ! [V: nat,V3: nat] :
% 0.23/0.55 ( ( connected_capacity @ c @ V @ V3 )
% 0.23/0.55 = ( ? [D4: nat] : ( dist_capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % connected_by_dist
% 0.23/0.55 thf(fact_18_obtain__shortest__path,axiom,
% 0.23/0.55 ! [U: nat,V: nat] :
% 0.23/0.55 ( ( connected_capacity @ c @ U @ V )
% 0.23/0.55 => ~ ! [P3: list_P559422087at_nat] :
% 0.23/0.55 ~ ( isShor1936442771pacity @ c @ U @ P3 @ V ) ) ).
% 0.23/0.55
% 0.23/0.55 % obtain_shortest_path
% 0.23/0.55 thf(fact_19_min__dist__le,axiom,
% 0.23/0.55 ! [Src: nat,V: nat,D3: nat] :
% 0.23/0.55 ( ( connected_capacity @ c @ Src @ V )
% 0.23/0.55 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_capacity @ c @ Src @ V ) )
% 0.23/0.55 => ? [V2: nat] :
% 0.23/0.55 ( ( connected_capacity @ c @ Src @ V2 )
% 0.23/0.55 & ( ( min_dist_capacity @ c @ Src @ V2 )
% 0.23/0.55 = D3 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % min_dist_le
% 0.23/0.55 thf(fact_20_min__dist__minD,axiom,
% 0.23/0.55 ! [V: nat,D: nat,V3: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ V @ D @ V3 )
% 0.23/0.55 => ( ord_less_eq_nat @ ( min_dist_capacity @ c @ V @ V3 ) @ D ) ) ).
% 0.23/0.55
% 0.23/0.55 % min_dist_minD
% 0.23/0.55 thf(fact_21_min__distI__eq,axiom,
% 0.23/0.55 ! [V: nat,D: nat,V3: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ V @ D @ V3 )
% 0.23/0.55 => ( ! [D5: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ V @ D5 @ V3 )
% 0.23/0.55 => ( ord_less_eq_nat @ D @ D5 ) )
% 0.23/0.55 => ( ( min_dist_capacity @ c @ V @ V3 )
% 0.23/0.55 = D ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % min_distI_eq
% 0.23/0.55 thf(fact_22_isPath__distD,axiom,
% 0.23/0.55 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.55 ( ( isPath_capacity @ c @ U @ P2 @ V )
% 0.23/0.55 => ( dist_capacity @ c @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 0.23/0.55
% 0.23/0.55 % isPath_distD
% 0.23/0.55 thf(fact_23_dist__def,axiom,
% 0.23/0.55 ! [V: nat,D: nat,V3: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ V @ D @ V3 )
% 0.23/0.55 = ( ? [P: list_P559422087at_nat] :
% 0.23/0.55 ( ( isPath_capacity @ c @ V @ P @ V3 )
% 0.23/0.55 & ( ( size_s1990949619at_nat @ P )
% 0.23/0.55 = D ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dist_def
% 0.23/0.55 thf(fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062,axiom,
% 0.23/0.55 isPath_capacity @ c @ s @ p1 @ v ).
% 0.23/0.55
% 0.23/0.55 % \<open>isPath s p1__ v__\<close>
% 0.23/0.55 thf(fact_25_min__dist__is__dist,axiom,
% 0.23/0.55 ! [V: nat,V3: nat] :
% 0.23/0.55 ( ( connected_capacity @ c @ V @ V3 )
% 0.23/0.55 => ( dist_capacity @ c @ V @ ( min_dist_capacity @ c @ V @ V3 ) @ V3 ) ) ).
% 0.23/0.55
% 0.23/0.55 % min_dist_is_dist
% 0.23/0.55 thf(fact_26_isShortestPath__def,axiom,
% 0.23/0.55 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.55 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 0.23/0.55 = ( ( isPath_capacity @ c @ U @ P2 @ V )
% 0.23/0.55 & ! [P4: list_P559422087at_nat] :
% 0.23/0.55 ( ( isPath_capacity @ c @ U @ P4 @ V )
% 0.23/0.55 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % isShortestPath_def
% 0.23/0.55 thf(fact_27_min__distI2,axiom,
% 0.23/0.55 ! [V: nat,V3: nat,Q: nat > $o] :
% 0.23/0.55 ( ( connected_capacity @ c @ V @ V3 )
% 0.23/0.55 => ( ! [D6: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ V @ D6 @ V3 )
% 0.23/0.55 => ( ! [D7: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ V @ D7 @ V3 )
% 0.23/0.55 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 0.23/0.55 => ( Q @ D6 ) ) )
% 0.23/0.55 => ( Q @ ( min_dist_capacity @ c @ V @ V3 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % min_distI2
% 0.23/0.55 thf(fact_28_isShortestPath__min__dist__def,axiom,
% 0.23/0.55 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.55 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 0.23/0.55 = ( ( isPath_capacity @ c @ U @ P2 @ V )
% 0.23/0.55 & ( ( size_s1990949619at_nat @ P2 )
% 0.23/0.55 = ( min_dist_capacity @ c @ U @ V ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % isShortestPath_min_dist_def
% 0.23/0.55 thf(fact_29__092_060open_062connected_As_Au_092_060close_062,axiom,
% 0.23/0.55 connected_capacity @ c @ s @ ua ).
% 0.23/0.55
% 0.23/0.55 % \<open>connected s u\<close>
% 0.23/0.55 thf(fact_30_add__le__cancel__right,axiom,
% 0.23/0.55 ! [A: nat,C: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.23/0.55 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_le_cancel_right
% 0.23/0.55 thf(fact_31_add__le__cancel__left,axiom,
% 0.23/0.55 ! [C: nat,A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.23/0.55 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_le_cancel_left
% 0.23/0.55 thf(fact_32_nat__add__left__cancel__le,axiom,
% 0.23/0.55 ! [K: nat,M: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.23/0.55 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % nat_add_left_cancel_le
% 0.23/0.55 thf(fact_33_P1,axiom,
% 0.23/0.55 isPath_capacity @ c @ s @ p1a @ va ).
% 0.23/0.55
% 0.23/0.55 % P1
% 0.23/0.55 thf(fact_34_connected__refl,axiom,
% 0.23/0.55 ! [V: nat] : ( connected_capacity @ c @ V @ V ) ).
% 0.23/0.55
% 0.23/0.55 % connected_refl
% 0.23/0.55 thf(fact_35_connected__distI,axiom,
% 0.23/0.55 ! [V: nat,D: nat,V3: nat] :
% 0.23/0.55 ( ( dist_capacity @ c @ V @ D @ V3 )
% 0.23/0.55 => ( connected_capacity @ c @ V @ V3 ) ) ).
% 0.23/0.55
% 0.23/0.55 % connected_distI
% 0.23/0.55 thf(fact_36_le__refl,axiom,
% 0.23/0.55 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.23/0.55
% 0.23/0.55 % le_refl
% 0.23/0.55 thf(fact_37_le__trans,axiom,
% 0.23/0.55 ! [I: nat,J: nat,K: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.55 => ( ( ord_less_eq_nat @ J @ K )
% 0.23/0.55 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_trans
% 0.23/0.55 thf(fact_38_eq__imp__le,axiom,
% 0.23/0.55 ! [M: nat,N: nat] :
% 0.23/0.55 ( ( M = N )
% 0.23/0.55 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % eq_imp_le
% 0.23/0.55 thf(fact_39_le__antisym,axiom,
% 0.23/0.55 ! [M: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.55 => ( ( ord_less_eq_nat @ N @ M )
% 0.23/0.55 => ( M = N ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_antisym
% 0.23/0.55 thf(fact_40_nat__le__linear,axiom,
% 0.23/0.55 ! [M: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.55 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.23/0.55
% 0.23/0.55 % nat_le_linear
% 0.23/0.55 thf(fact_41_Nat_Oex__has__greatest__nat,axiom,
% 0.23/0.55 ! [P5: nat > $o,K: nat,B: nat] :
% 0.23/0.55 ( ( P5 @ K )
% 0.23/0.55 => ( ! [Y: nat] :
% 0.23/0.55 ( ( P5 @ Y )
% 0.23/0.55 => ( ord_less_eq_nat @ Y @ B ) )
% 0.23/0.55 => ? [X: nat] :
% 0.23/0.55 ( ( P5 @ X )
% 0.23/0.55 & ! [Y2: nat] :
% 0.23/0.55 ( ( P5 @ Y2 )
% 0.23/0.55 => ( ord_less_eq_nat @ Y2 @ X ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % Nat.ex_has_greatest_nat
% 0.23/0.55 thf(fact_42_add__le__imp__le__right,axiom,
% 0.23/0.55 ! [A: nat,C: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.23/0.55 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_le_imp_le_right
% 0.23/0.55 thf(fact_43_add__le__imp__le__left,axiom,
% 0.23/0.55 ! [C: nat,A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.23/0.55 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_le_imp_le_left
% 0.23/0.55 thf(fact_44_le__iff__add,axiom,
% 0.23/0.55 ( ord_less_eq_nat
% 0.23/0.55 = ( ^ [A2: nat,B2: nat] :
% 0.23/0.55 ? [C2: nat] :
% 0.23/0.55 ( B2
% 0.23/0.55 = ( plus_plus_nat @ A2 @ C2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_iff_add
% 0.23/0.55 thf(fact_45_mem__Collect__eq,axiom,
% 0.23/0.55 ! [A: nat,P5: nat > $o] :
% 0.23/0.55 ( ( member_nat @ A @ ( collect_nat @ P5 ) )
% 0.23/0.55 = ( P5 @ A ) ) ).
% 0.23/0.55
% 0.23/0.55 % mem_Collect_eq
% 0.23/0.55 thf(fact_46_Collect__mem__eq,axiom,
% 0.23/0.55 ! [A3: set_nat] :
% 0.23/0.55 ( ( collect_nat
% 0.23/0.55 @ ^ [X2: nat] : ( member_nat @ X2 @ A3 ) )
% 0.23/0.55 = A3 ) ).
% 0.23/0.55
% 0.23/0.55 % Collect_mem_eq
% 0.23/0.55 thf(fact_47_Collect__cong,axiom,
% 0.23/0.55 ! [P5: nat > $o,Q: nat > $o] :
% 0.23/0.55 ( ! [X: nat] :
% 0.23/0.55 ( ( P5 @ X )
% 0.23/0.55 = ( Q @ X ) )
% 0.23/0.55 => ( ( collect_nat @ P5 )
% 0.23/0.55 = ( collect_nat @ Q ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % Collect_cong
% 0.23/0.55 thf(fact_48_add__right__mono,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_right_mono
% 0.23/0.55 thf(fact_49_less__eqE,axiom,
% 0.23/0.55 ! [A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ~ ! [C3: nat] :
% 0.23/0.55 ( B
% 0.23/0.55 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_eqE
% 0.23/0.55 thf(fact_50_add__left__mono,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_left_mono
% 0.23/0.55 thf(fact_51_add__mono,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_eq_nat @ C @ D )
% 0.23/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_mono
% 0.23/0.55 thf(fact_52_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.23/0.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.55 ( ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.55 & ( ord_less_eq_nat @ K @ L ) )
% 0.23/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_mono_thms_linordered_semiring(1)
% 0.23/0.55 thf(fact_53_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.23/0.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.55 ( ( ( I = J )
% 0.23/0.55 & ( ord_less_eq_nat @ K @ L ) )
% 0.23/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_mono_thms_linordered_semiring(2)
% 0.23/0.55 thf(fact_54_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.23/0.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.55 ( ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.55 & ( K = L ) )
% 0.23/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_mono_thms_linordered_semiring(3)
% 0.23/0.55 thf(fact_55_less__mono__imp__le__mono,axiom,
% 0.23/0.55 ! [F: nat > nat,I: nat,J: nat] :
% 0.23/0.55 ( ! [I2: nat,J2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I2 @ J2 )
% 0.23/0.55 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.23/0.55 => ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_mono_imp_le_mono
% 0.23/0.55 thf(fact_56_le__neq__implies__less,axiom,
% 0.23/0.55 ! [M: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.55 => ( ( M != N )
% 0.23/0.55 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_neq_implies_less
% 0.23/0.55 thf(fact_57_less__or__eq__imp__le,axiom,
% 0.23/0.55 ! [M: nat,N: nat] :
% 0.23/0.55 ( ( ( ord_less_nat @ M @ N )
% 0.23/0.55 | ( M = N ) )
% 0.23/0.55 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_or_eq_imp_le
% 0.23/0.55 thf(fact_58_le__eq__less__or__eq,axiom,
% 0.23/0.55 ( ord_less_eq_nat
% 0.23/0.55 = ( ^ [M2: nat,N2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ M2 @ N2 )
% 0.23/0.55 | ( M2 = N2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_eq_less_or_eq
% 0.23/0.55 thf(fact_59_less__imp__le__nat,axiom,
% 0.23/0.55 ! [M: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_nat @ M @ N )
% 0.23/0.55 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_imp_le_nat
% 0.23/0.55 thf(fact_60_nat__less__le,axiom,
% 0.23/0.55 ( ord_less_nat
% 0.23/0.55 = ( ^ [M2: nat,N2: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.23/0.55 & ( M2 != N2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % nat_less_le
% 0.23/0.55 thf(fact_61_nat__le__iff__add,axiom,
% 0.23/0.55 ( ord_less_eq_nat
% 0.23/0.55 = ( ^ [M2: nat,N2: nat] :
% 0.23/0.55 ? [K2: nat] :
% 0.23/0.55 ( N2
% 0.23/0.55 = ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % nat_le_iff_add
% 0.23/0.55 thf(fact_62_trans__le__add2,axiom,
% 0.23/0.55 ! [I: nat,J: nat,M: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.55 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % trans_le_add2
% 0.23/0.55 thf(fact_63_trans__le__add1,axiom,
% 0.23/0.55 ! [I: nat,J: nat,M: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.55 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % trans_le_add1
% 0.23/0.55 thf(fact_64_add__le__mono1,axiom,
% 0.23/0.55 ! [I: nat,J: nat,K: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_le_mono1
% 0.23/0.55 thf(fact_65_add__le__mono,axiom,
% 0.23/0.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.55 => ( ( ord_less_eq_nat @ K @ L )
% 0.23/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_le_mono
% 0.23/0.55 thf(fact_66_le__Suc__ex,axiom,
% 0.23/0.55 ! [K: nat,L: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ K @ L )
% 0.23/0.55 => ? [N3: nat] :
% 0.23/0.55 ( L
% 0.23/0.55 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_Suc_ex
% 0.23/0.55 thf(fact_67_add__leD2,axiom,
% 0.23/0.55 ! [M: nat,K: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.23/0.55 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_leD2
% 0.23/0.55 thf(fact_68_add__leD1,axiom,
% 0.23/0.55 ! [M: nat,K: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.23/0.55 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_leD1
% 0.23/0.55 thf(fact_69_le__add2,axiom,
% 0.23/0.55 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_add2
% 0.23/0.55 thf(fact_70_le__add1,axiom,
% 0.23/0.55 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_add1
% 0.23/0.55 thf(fact_71_add__leE,axiom,
% 0.23/0.55 ! [M: nat,K: nat,N: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.23/0.55 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.55 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_leE
% 0.23/0.55 thf(fact_72_add__right__imp__eq,axiom,
% 0.23/0.55 ! [B: nat,A: nat,C: nat] :
% 0.23/0.55 ( ( ( plus_plus_nat @ B @ A )
% 0.23/0.55 = ( plus_plus_nat @ C @ A ) )
% 0.23/0.55 => ( B = C ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_right_imp_eq
% 0.23/0.55 thf(fact_73_add__left__imp__eq,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ( plus_plus_nat @ A @ B )
% 0.23/0.55 = ( plus_plus_nat @ A @ C ) )
% 0.23/0.55 => ( B = C ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_left_imp_eq
% 0.23/0.55 thf(fact_74_add_Oleft__commute,axiom,
% 0.23/0.55 ! [B: nat,A: nat,C: nat] :
% 0.23/0.55 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.23/0.55 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add.left_commute
% 0.23/0.55 thf(fact_75_add_Ocommute,axiom,
% 0.23/0.55 ( plus_plus_nat
% 0.23/0.55 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add.commute
% 0.23/0.55 thf(fact_76_add_Oassoc,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.23/0.55 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add.assoc
% 0.23/0.55 thf(fact_77_group__cancel_Oadd2,axiom,
% 0.23/0.55 ! [B3: nat,K: nat,B: nat,A: nat] :
% 0.23/0.55 ( ( B3
% 0.23/0.55 = ( plus_plus_nat @ K @ B ) )
% 0.23/0.55 => ( ( plus_plus_nat @ A @ B3 )
% 0.23/0.55 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % group_cancel.add2
% 0.23/0.55 thf(fact_78_group__cancel_Oadd1,axiom,
% 0.23/0.55 ! [A3: nat,K: nat,A: nat,B: nat] :
% 0.23/0.55 ( ( A3
% 0.23/0.55 = ( plus_plus_nat @ K @ A ) )
% 0.23/0.55 => ( ( plus_plus_nat @ A3 @ B )
% 0.23/0.55 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % group_cancel.add1
% 0.23/0.55 thf(fact_79_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.23/0.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.55 ( ( ( I = J )
% 0.23/0.55 & ( K = L ) )
% 0.23/0.55 => ( ( plus_plus_nat @ I @ K )
% 0.23/0.55 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % add_mono_thms_linordered_semiring(4)
% 0.23/0.55 thf(fact_80_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.23/0.55 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ab_semigroup_add_class.add_ac(1)
% 0.23/0.55 thf(fact_81_linorder__neqE__nat,axiom,
% 0.23/0.55 ! [X3: nat,Y3: nat] :
% 0.23/0.55 ( ( X3 != Y3 )
% 0.23/0.55 => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.55 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % linorder_neqE_nat
% 0.23/0.55 thf(fact_82_infinite__descent,axiom,
% 0.23/0.55 ! [P5: nat > $o,N: nat] :
% 0.23/0.55 ( ! [N3: nat] :
% 0.23/0.55 ( ~ ( P5 @ N3 )
% 0.23/0.55 => ? [M3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ M3 @ N3 )
% 0.23/0.55 & ~ ( P5 @ M3 ) ) )
% 0.23/0.55 => ( P5 @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % infinite_descent
% 0.23/0.55 thf(fact_83_nat__less__induct,axiom,
% 0.23/0.55 ! [P5: nat > $o,N: nat] :
% 0.23/0.55 ( ! [N3: nat] :
% 0.23/0.55 ( ! [M3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ M3 @ N3 )
% 0.23/0.55 => ( P5 @ M3 ) )
% 0.23/0.55 => ( P5 @ N3 ) )
% 0.23/0.55 => ( P5 @ N ) ) ).
% 0.23/0.55
% 0.23/0.55 % nat_less_induct
% 0.23/0.55 thf(fact_84_less__irrefl__nat,axiom,
% 0.23/0.55 ! [N: nat] :
% 0.23/0.55 ~ ( ord_less_nat @ N @ N ) ).
% 0.23/0.55
% 0.23/0.55 % less_irrefl_nat
% 0.23/0.55 thf(fact_85_less__not__refl3,axiom,
% 0.23/0.55 ! [S: nat,T: nat] :
% 0.23/0.55 ( ( ord_less_nat @ S @ T )
% 0.23/0.55 => ( S != T ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_not_refl3
% 0.23/0.55 thf(fact_86_less__not__refl2,axiom,
% 0.23/0.55 ! [N: nat,M: nat] :
% 0.23/0.55 ( ( ord_less_nat @ N @ M )
% 0.23/0.55 => ( M != N ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_not_refl2
% 0.23/0.55 thf(fact_87_less__not__refl,axiom,
% 0.23/0.55 ! [N: nat] :
% 0.23/0.55 ~ ( ord_less_nat @ N @ N ) ).
% 0.23/0.55
% 0.23/0.55 % less_not_refl
% 0.23/0.55 thf(fact_88_nat__neq__iff,axiom,
% 0.23/0.55 ! [M: nat,N: nat] :
% 0.23/0.55 ( ( M != N )
% 0.23/0.55 = ( ( ord_less_nat @ M @ N )
% 0.23/0.55 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % nat_neq_iff
% 0.23/0.55 thf(fact_89_size__neq__size__imp__neq,axiom,
% 0.23/0.55 ! [X3: list_P559422087at_nat,Y3: list_P559422087at_nat] :
% 0.23/0.55 ( ( ( size_s1990949619at_nat @ X3 )
% 0.23/0.55 != ( size_s1990949619at_nat @ Y3 ) )
% 0.23/0.55 => ( X3 != Y3 ) ) ).
% 0.23/0.55
% 0.23/0.55 % size_neq_size_imp_neq
% 0.23/0.55 thf(fact_90_add__less__le__mono,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( ( ord_less_eq_nat @ C @ D )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_less_le_mono
% 0.23/0.56 thf(fact_91_add__le__less__mono,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.56 => ( ( ord_less_nat @ C @ D )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_le_less_mono
% 0.23/0.56 thf(fact_92_add__mono__thms__linordered__field_I3_J,axiom,
% 0.23/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.56 ( ( ( ord_less_nat @ I @ J )
% 0.23/0.56 & ( ord_less_eq_nat @ K @ L ) )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_mono_thms_linordered_field(3)
% 0.23/0.56 thf(fact_93_add__mono__thms__linordered__field_I4_J,axiom,
% 0.23/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.56 ( ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.56 & ( ord_less_nat @ K @ L ) )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_mono_thms_linordered_field(4)
% 0.23/0.56 thf(fact_94_mono__nat__linear__lb,axiom,
% 0.23/0.56 ! [F: nat > nat,M: nat,K: nat] :
% 0.23/0.56 ( ! [M4: nat,N3: nat] :
% 0.23/0.56 ( ( ord_less_nat @ M4 @ N3 )
% 0.23/0.56 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 0.23/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % mono_nat_linear_lb
% 0.23/0.56 thf(fact_95_add__less__imp__less__right,axiom,
% 0.23/0.56 ! [A: nat,C: nat,B: nat] :
% 0.23/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.23/0.56 => ( ord_less_nat @ A @ B ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_less_imp_less_right
% 0.23/0.56 thf(fact_96_add__less__imp__less__left,axiom,
% 0.23/0.56 ! [C: nat,A: nat,B: nat] :
% 0.23/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.23/0.56 => ( ord_less_nat @ A @ B ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_less_imp_less_left
% 0.23/0.56 thf(fact_97_add__strict__right__mono,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_strict_right_mono
% 0.23/0.56 thf(fact_98_add__strict__left__mono,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_strict_left_mono
% 0.23/0.56 thf(fact_99_add__strict__mono,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( ( ord_less_nat @ C @ D )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_strict_mono
% 0.23/0.56 thf(fact_100_add__mono__thms__linordered__field_I1_J,axiom,
% 0.23/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.56 ( ( ( ord_less_nat @ I @ J )
% 0.23/0.56 & ( K = L ) )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_mono_thms_linordered_field(1)
% 0.23/0.56 thf(fact_101_add__mono__thms__linordered__field_I2_J,axiom,
% 0.23/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.56 ( ( ( I = J )
% 0.23/0.56 & ( ord_less_nat @ K @ L ) )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_mono_thms_linordered_field(2)
% 0.23/0.56 thf(fact_102_add__mono__thms__linordered__field_I5_J,axiom,
% 0.23/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.56 ( ( ( ord_less_nat @ I @ J )
% 0.23/0.56 & ( ord_less_nat @ K @ L ) )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_mono_thms_linordered_field(5)
% 0.23/0.56 thf(fact_103_less__add__eq__less,axiom,
% 0.23/0.56 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.23/0.56 ( ( ord_less_nat @ K @ L )
% 0.23/0.56 => ( ( ( plus_plus_nat @ M @ L )
% 0.23/0.56 = ( plus_plus_nat @ K @ N ) )
% 0.23/0.56 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_add_eq_less
% 0.23/0.56 thf(fact_104_trans__less__add2,axiom,
% 0.23/0.56 ! [I: nat,J: nat,M: nat] :
% 0.23/0.56 ( ( ord_less_nat @ I @ J )
% 0.23/0.56 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % trans_less_add2
% 0.23/0.56 thf(fact_105_trans__less__add1,axiom,
% 0.23/0.56 ! [I: nat,J: nat,M: nat] :
% 0.23/0.56 ( ( ord_less_nat @ I @ J )
% 0.23/0.56 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % trans_less_add1
% 0.23/0.56 thf(fact_106_add__less__mono1,axiom,
% 0.23/0.56 ! [I: nat,J: nat,K: nat] :
% 0.23/0.56 ( ( ord_less_nat @ I @ J )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_less_mono1
% 0.23/0.56 thf(fact_107_not__add__less2,axiom,
% 0.23/0.56 ! [J: nat,I: nat] :
% 0.23/0.56 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.23/0.56
% 0.23/0.56 % not_add_less2
% 0.23/0.56 thf(fact_108_not__add__less1,axiom,
% 0.23/0.56 ! [I: nat,J: nat] :
% 0.23/0.56 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.23/0.56
% 0.23/0.56 % not_add_less1
% 0.23/0.56 thf(fact_109_add__less__mono,axiom,
% 0.23/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.23/0.56 ( ( ord_less_nat @ I @ J )
% 0.23/0.56 => ( ( ord_less_nat @ K @ L )
% 0.23/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_less_mono
% 0.23/0.56 thf(fact_110_add__lessD1,axiom,
% 0.23/0.56 ! [I: nat,J: nat,K: nat] :
% 0.23/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.23/0.56 => ( ord_less_nat @ I @ K ) ) ).
% 0.23/0.56
% 0.23/0.56 % add_lessD1
% 0.23/0.56 thf(fact_111_reachableNodes__def,axiom,
% 0.23/0.56 ! [U: nat] :
% 0.23/0.56 ( ( reacha1693770334pacity @ c @ U )
% 0.23/0.56 = ( collect_nat @ ( connected_capacity @ c @ U ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % reachableNodes_def
% 0.23/0.56 thf(fact_112_min__dist__def,axiom,
% 0.23/0.56 ! [V: nat,V3: nat] :
% 0.23/0.56 ( ( min_dist_capacity @ c @ V @ V3 )
% 0.23/0.56 = ( ord_Least_nat
% 0.23/0.56 @ ^ [D4: nat] : ( dist_capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % min_dist_def
% 0.23/0.56 thf(fact_113_Graph_OisShortestPath__min__dist__def,axiom,
% 0.23/0.56 ( isShor1936442771pacity
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.23/0.56 ( ( isPath_capacity @ C2 @ U2 @ P @ V4 )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P )
% 0.23/0.56 = ( min_dist_capacity @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isShortestPath_min_dist_def
% 0.23/0.56 thf(fact_114_Graph_OisShortestPath__min__dist__def,axiom,
% 0.23/0.56 ( isShortestPath_a
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.23/0.56 ( ( isPath_a @ C2 @ U2 @ P @ V4 )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P )
% 0.23/0.56 = ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isShortestPath_min_dist_def
% 0.23/0.56 thf(fact_115_Graph_OisShortestPath__def,axiom,
% 0.23/0.56 ( isShor1936442771pacity
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.23/0.56 ( ( isPath_capacity @ C2 @ U2 @ P @ V4 )
% 0.23/0.56 & ! [P4: list_P559422087at_nat] :
% 0.23/0.56 ( ( isPath_capacity @ C2 @ U2 @ P4 @ V4 )
% 0.23/0.56 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isShortestPath_def
% 0.23/0.56 thf(fact_116_Graph_OisShortestPath__def,axiom,
% 0.23/0.56 ( isShortestPath_a
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.23/0.56 ( ( isPath_a @ C2 @ U2 @ P @ V4 )
% 0.23/0.56 & ! [P4: list_P559422087at_nat] :
% 0.23/0.56 ( ( isPath_a @ C2 @ U2 @ P4 @ V4 )
% 0.23/0.56 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isShortestPath_def
% 0.23/0.56 thf(fact_117_Graph_Omin__distI2,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,V: nat,V3: nat,Q: nat > $o] :
% 0.23/0.56 ( ( connected_capacity @ C @ V @ V3 )
% 0.23/0.56 => ( ! [D6: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ V @ D6 @ V3 )
% 0.23/0.56 => ( ! [D7: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ V @ D7 @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 0.23/0.56 => ( Q @ D6 ) ) )
% 0.23/0.56 => ( Q @ ( min_dist_capacity @ C @ V @ V3 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_distI2
% 0.23/0.56 thf(fact_118_Graph_Omin__distI2,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,V: nat,V3: nat,Q: nat > $o] :
% 0.23/0.56 ( ( connected_a @ C @ V @ V3 )
% 0.23/0.56 => ( ! [D6: nat] :
% 0.23/0.56 ( ( dist_a @ C @ V @ D6 @ V3 )
% 0.23/0.56 => ( ! [D7: nat] :
% 0.23/0.56 ( ( dist_a @ C @ V @ D7 @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 0.23/0.56 => ( Q @ D6 ) ) )
% 0.23/0.56 => ( Q @ ( min_dist_a @ C @ V @ V3 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_distI2
% 0.23/0.56 thf(fact_119_isShortestPath__alt,axiom,
% 0.23/0.56 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isShor1936442771pacity @ c @ U @ P2 @ V )
% 0.23/0.56 = ( ( isSimp1359852763pacity @ c @ U @ P2 @ V )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P2 )
% 0.23/0.56 = ( min_dist_capacity @ c @ U @ V ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % isShortestPath_alt
% 0.23/0.56 thf(fact_120_Graph_Odist__def,axiom,
% 0.23/0.56 ( dist_capacity
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,D4: nat,V5: nat] :
% 0.23/0.56 ? [P: list_P559422087at_nat] :
% 0.23/0.56 ( ( isPath_capacity @ C2 @ V4 @ P @ V5 )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P )
% 0.23/0.56 = D4 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.dist_def
% 0.23/0.56 thf(fact_121_Graph_Odist__def,axiom,
% 0.23/0.56 ( dist_a
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,D4: nat,V5: nat] :
% 0.23/0.56 ? [P: list_P559422087at_nat] :
% 0.23/0.56 ( ( isPath_a @ C2 @ V4 @ P @ V5 )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P )
% 0.23/0.56 = D4 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.dist_def
% 0.23/0.56 thf(fact_122_Graph_OisPath__distD,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isPath_capacity @ C @ U @ P2 @ V )
% 0.23/0.56 => ( dist_capacity @ C @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isPath_distD
% 0.23/0.56 thf(fact_123_Graph_OisPath__distD,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isPath_a @ C @ U @ P2 @ V )
% 0.23/0.56 => ( dist_a @ C @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isPath_distD
% 0.23/0.56 thf(fact_124_Graph_Omin__dist__is__dist,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,V: nat,V3: nat] :
% 0.23/0.56 ( ( connected_capacity @ C @ V @ V3 )
% 0.23/0.56 => ( dist_capacity @ C @ V @ ( min_dist_capacity @ C @ V @ V3 ) @ V3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_is_dist
% 0.23/0.56 thf(fact_125_Graph_Omin__dist__is__dist,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,V: nat,V3: nat] :
% 0.23/0.56 ( ( connected_a @ C @ V @ V3 )
% 0.23/0.56 => ( dist_a @ C @ V @ ( min_dist_a @ C @ V @ V3 ) @ V3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_is_dist
% 0.23/0.56 thf(fact_126_Graph_Omin__dist__split_I1_J,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 0.23/0.56 => ( ( ( min_dist_capacity @ C @ U @ V )
% 0.23/0.56 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.23/0.56 => ( ( min_dist_capacity @ C @ U @ W )
% 0.23/0.56 = D1 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_split(1)
% 0.23/0.56 thf(fact_127_Graph_Omin__dist__split_I1_J,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_a @ C @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_a @ C @ W @ D2 @ V )
% 0.23/0.56 => ( ( ( min_dist_a @ C @ U @ V )
% 0.23/0.56 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.23/0.56 => ( ( min_dist_a @ C @ U @ W )
% 0.23/0.56 = D1 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_split(1)
% 0.23/0.56 thf(fact_128_isSPath__pathLE,axiom,
% 0.23/0.56 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.23/0.56 ( ( isPath_capacity @ c @ S @ P2 @ T )
% 0.23/0.56 => ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ c @ S @ P6 @ T ) ) ).
% 0.23/0.56
% 0.23/0.56 % isSPath_pathLE
% 0.23/0.56 thf(fact_129_shortestPath__is__simple,axiom,
% 0.23/0.56 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.23/0.56 ( ( isShor1936442771pacity @ c @ S @ P2 @ T )
% 0.23/0.56 => ( isSimp1359852763pacity @ c @ S @ P2 @ T ) ) ).
% 0.23/0.56
% 0.23/0.56 % shortestPath_is_simple
% 0.23/0.56 thf(fact_130_Graph_OreachableNodes_Ocong,axiom,
% 0.23/0.56 reacha1693770334pacity = reacha1693770334pacity ).
% 0.23/0.56
% 0.23/0.56 % Graph.reachableNodes.cong
% 0.23/0.56 thf(fact_131_Graph_OreachableNodes_Ocong,axiom,
% 0.23/0.56 reachableNodes_a = reachableNodes_a ).
% 0.23/0.56
% 0.23/0.56 % Graph.reachableNodes.cong
% 0.23/0.56 thf(fact_132_Graph_OisSimplePath_Ocong,axiom,
% 0.23/0.56 isSimp1359852763pacity = isSimp1359852763pacity ).
% 0.23/0.56
% 0.23/0.56 % Graph.isSimplePath.cong
% 0.23/0.56 thf(fact_133_Graph_OisSimplePath_Ocong,axiom,
% 0.23/0.56 isSimplePath_a = isSimplePath_a ).
% 0.23/0.56
% 0.23/0.56 % Graph.isSimplePath.cong
% 0.23/0.56 thf(fact_134_Graph_OisSPath__pathLE,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.23/0.56 ( ( isPath_capacity @ C @ S @ P2 @ T )
% 0.23/0.56 => ? [P6: list_P559422087at_nat] : ( isSimp1359852763pacity @ C @ S @ P6 @ T ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isSPath_pathLE
% 0.23/0.56 thf(fact_135_Graph_OisSPath__pathLE,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.23/0.56 ( ( isPath_a @ C @ S @ P2 @ T )
% 0.23/0.56 => ? [P6: list_P559422087at_nat] : ( isSimplePath_a @ C @ S @ P6 @ T ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isSPath_pathLE
% 0.23/0.56 thf(fact_136_Graph_OshortestPath__is__simple,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.23/0.56 ( ( isShor1936442771pacity @ C @ S @ P2 @ T )
% 0.23/0.56 => ( isSimp1359852763pacity @ C @ S @ P2 @ T ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.shortestPath_is_simple
% 0.23/0.56 thf(fact_137_Graph_OshortestPath__is__simple,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.23/0.56 ( ( isShortestPath_a @ C @ S @ P2 @ T )
% 0.23/0.56 => ( isSimplePath_a @ C @ S @ P2 @ T ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.shortestPath_is_simple
% 0.23/0.56 thf(fact_138_Graph_OreachableNodes__def,axiom,
% 0.23/0.56 ( reacha1693770334pacity
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat] : ( collect_nat @ ( connected_capacity @ C2 @ U2 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.reachableNodes_def
% 0.23/0.56 thf(fact_139_Graph_OreachableNodes__def,axiom,
% 0.23/0.56 ( reachableNodes_a
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > a,U2: nat] : ( collect_nat @ ( connected_a @ C2 @ U2 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.reachableNodes_def
% 0.23/0.56 thf(fact_140_Graph_Omin__dist__def,axiom,
% 0.23/0.56 ( min_dist_capacity
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,V5: nat] :
% 0.23/0.56 ( ord_Least_nat
% 0.23/0.56 @ ^ [D4: nat] : ( dist_capacity @ C2 @ V4 @ D4 @ V5 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_def
% 0.23/0.56 thf(fact_141_Graph_Omin__dist__def,axiom,
% 0.23/0.56 ( min_dist_a
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
% 0.23/0.56 ( ord_Least_nat
% 0.23/0.56 @ ^ [D4: nat] : ( dist_a @ C2 @ V4 @ D4 @ V5 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_def
% 0.23/0.56 thf(fact_142_Graph_OisShortestPath__alt,axiom,
% 0.23/0.56 ( isShor1936442771pacity
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.23/0.56 ( ( isSimp1359852763pacity @ C2 @ U2 @ P @ V4 )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P )
% 0.23/0.56 = ( min_dist_capacity @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isShortestPath_alt
% 0.23/0.56 thf(fact_143_Graph_OisShortestPath__alt,axiom,
% 0.23/0.56 ( isShortestPath_a
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,P: list_P559422087at_nat,V4: nat] :
% 0.23/0.56 ( ( isSimplePath_a @ C2 @ U2 @ P @ V4 )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P )
% 0.23/0.56 = ( min_dist_a @ C2 @ U2 @ V4 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.isShortestPath_alt
% 0.23/0.56 thf(fact_144_Graph_OisPath_Ocong,axiom,
% 0.23/0.56 isPath_capacity = isPath_capacity ).
% 0.23/0.56
% 0.23/0.56 % Graph.isPath.cong
% 0.23/0.56 thf(fact_145_Graph_OisPath_Ocong,axiom,
% 0.23/0.56 isPath_a = isPath_a ).
% 0.23/0.56
% 0.23/0.56 % Graph.isPath.cong
% 0.23/0.56 thf(fact_146_Graph_Omin__dist_Ocong,axiom,
% 0.23/0.56 min_dist_capacity = min_dist_capacity ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist.cong
% 0.23/0.56 thf(fact_147_Graph_Omin__dist_Ocong,axiom,
% 0.23/0.56 min_dist_a = min_dist_a ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist.cong
% 0.23/0.56 thf(fact_148_Graph_Oconnected__refl,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,V: nat] : ( connected_capacity @ C @ V @ V ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected_refl
% 0.23/0.56 thf(fact_149_Graph_Oconnected__refl,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,V: nat] : ( connected_a @ C @ V @ V ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected_refl
% 0.23/0.56 thf(fact_150_Graph_Oconnected_Ocong,axiom,
% 0.23/0.56 connected_capacity = connected_capacity ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected.cong
% 0.23/0.56 thf(fact_151_Graph_Oconnected_Ocong,axiom,
% 0.23/0.56 connected_a = connected_a ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected.cong
% 0.23/0.56 thf(fact_152_Graph_Odist_Ocong,axiom,
% 0.23/0.56 dist_capacity = dist_capacity ).
% 0.23/0.56
% 0.23/0.56 % Graph.dist.cong
% 0.23/0.56 thf(fact_153_Graph_Odist_Ocong,axiom,
% 0.23/0.56 dist_a = dist_a ).
% 0.23/0.56
% 0.23/0.56 % Graph.dist.cong
% 0.23/0.56 thf(fact_154_Graph_OisShortestPath_Ocong,axiom,
% 0.23/0.56 isShor1936442771pacity = isShor1936442771pacity ).
% 0.23/0.56
% 0.23/0.56 % Graph.isShortestPath.cong
% 0.23/0.56 thf(fact_155_Graph_OisShortestPath_Ocong,axiom,
% 0.23/0.56 isShortestPath_a = isShortestPath_a ).
% 0.23/0.56
% 0.23/0.56 % Graph.isShortestPath.cong
% 0.23/0.56 thf(fact_156_Graph_Odist__trans,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 0.23/0.56 => ( dist_capacity @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.dist_trans
% 0.23/0.56 thf(fact_157_Graph_Odist__trans,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_a @ C @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_a @ C @ W @ D2 @ V )
% 0.23/0.56 => ( dist_a @ C @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.dist_trans
% 0.23/0.56 thf(fact_158_Graph_Oconnected__def,axiom,
% 0.23/0.56 ( connected_capacity
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > capacity,U2: nat,V4: nat] :
% 0.23/0.56 ? [P: list_P559422087at_nat] : ( isPath_capacity @ C2 @ U2 @ P @ V4 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected_def
% 0.23/0.56 thf(fact_159_Graph_Oconnected__def,axiom,
% 0.23/0.56 ( connected_a
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > a,U2: nat,V4: nat] :
% 0.23/0.56 ? [P: list_P559422087at_nat] : ( isPath_a @ C2 @ U2 @ P @ V4 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected_def
% 0.23/0.56 thf(fact_160_Graph_OshortestPath__is__path,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isShor1936442771pacity @ C @ U @ P2 @ V )
% 0.23/0.56 => ( isPath_capacity @ C @ U @ P2 @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.shortestPath_is_path
% 0.23/0.56 thf(fact_161_Graph_OshortestPath__is__path,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isShortestPath_a @ C @ U @ P2 @ V )
% 0.23/0.56 => ( isPath_a @ C @ U @ P2 @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.shortestPath_is_path
% 0.23/0.56 thf(fact_162_Graph_Oconnected__by__dist,axiom,
% 0.23/0.56 ( connected_capacity
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > capacity,V4: nat,V5: nat] :
% 0.23/0.56 ? [D4: nat] : ( dist_capacity @ C2 @ V4 @ D4 @ V5 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected_by_dist
% 0.23/0.56 thf(fact_163_Graph_Oconnected__by__dist,axiom,
% 0.23/0.56 ( connected_a
% 0.23/0.56 = ( ^ [C2: product_prod_nat_nat > a,V4: nat,V5: nat] :
% 0.23/0.56 ? [D4: nat] : ( dist_a @ C2 @ V4 @ D4 @ V5 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected_by_dist
% 0.23/0.56 thf(fact_164_Graph_Oconnected__distI,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ V @ D @ V3 )
% 0.23/0.56 => ( connected_capacity @ C @ V @ V3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected_distI
% 0.23/0.56 thf(fact_165_Graph_Oconnected__distI,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_a @ C @ V @ D @ V3 )
% 0.23/0.56 => ( connected_a @ C @ V @ V3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.connected_distI
% 0.23/0.56 thf(fact_166_Graph_Oobtain__shortest__path,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,U: nat,V: nat] :
% 0.23/0.56 ( ( connected_capacity @ C @ U @ V )
% 0.23/0.56 => ~ ! [P3: list_P559422087at_nat] :
% 0.23/0.56 ~ ( isShor1936442771pacity @ C @ U @ P3 @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.obtain_shortest_path
% 0.23/0.56 thf(fact_167_Graph_Oobtain__shortest__path,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,U: nat,V: nat] :
% 0.23/0.56 ( ( connected_a @ C @ U @ V )
% 0.23/0.56 => ~ ! [P3: list_P559422087at_nat] :
% 0.23/0.56 ~ ( isShortestPath_a @ C @ U @ P3 @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.obtain_shortest_path
% 0.23/0.56 thf(fact_168_Graph_Omin__dist__less,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D: nat,D3: nat] :
% 0.23/0.56 ( ( connected_capacity @ C @ Src @ V )
% 0.23/0.56 => ( ( ( min_dist_capacity @ C @ Src @ V )
% 0.23/0.56 = D )
% 0.23/0.56 => ( ( ord_less_nat @ D3 @ D )
% 0.23/0.56 => ? [V2: nat] :
% 0.23/0.56 ( ( connected_capacity @ C @ Src @ V2 )
% 0.23/0.56 & ( ( min_dist_capacity @ C @ Src @ V2 )
% 0.23/0.56 = D3 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_less
% 0.23/0.56 thf(fact_169_Graph_Omin__dist__less,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D: nat,D3: nat] :
% 0.23/0.56 ( ( connected_a @ C @ Src @ V )
% 0.23/0.56 => ( ( ( min_dist_a @ C @ Src @ V )
% 0.23/0.56 = D )
% 0.23/0.56 => ( ( ord_less_nat @ D3 @ D )
% 0.23/0.56 => ? [V2: nat] :
% 0.23/0.56 ( ( connected_a @ C @ Src @ V2 )
% 0.23/0.56 & ( ( min_dist_a @ C @ Src @ V2 )
% 0.23/0.56 = D3 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_less
% 0.23/0.56 thf(fact_170_Graph_Omin__dist__le,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,Src: nat,V: nat,D3: nat] :
% 0.23/0.56 ( ( connected_capacity @ C @ Src @ V )
% 0.23/0.56 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_capacity @ C @ Src @ V ) )
% 0.23/0.56 => ? [V2: nat] :
% 0.23/0.56 ( ( connected_capacity @ C @ Src @ V2 )
% 0.23/0.56 & ( ( min_dist_capacity @ C @ Src @ V2 )
% 0.23/0.56 = D3 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_le
% 0.23/0.56 thf(fact_171_Graph_Omin__dist__le,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,Src: nat,V: nat,D3: nat] :
% 0.23/0.56 ( ( connected_a @ C @ Src @ V )
% 0.23/0.56 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_a @ C @ Src @ V ) )
% 0.23/0.56 => ? [V2: nat] :
% 0.23/0.56 ( ( connected_a @ C @ Src @ V2 )
% 0.23/0.56 & ( ( min_dist_a @ C @ Src @ V2 )
% 0.23/0.56 = D3 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_le
% 0.23/0.56 thf(fact_172_Graph_Omin__distI__eq,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ V @ D @ V3 )
% 0.23/0.56 => ( ! [D5: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ V @ D5 @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ D @ D5 ) )
% 0.23/0.56 => ( ( min_dist_capacity @ C @ V @ V3 )
% 0.23/0.56 = D ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_distI_eq
% 0.23/0.56 thf(fact_173_Graph_Omin__distI__eq,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_a @ C @ V @ D @ V3 )
% 0.23/0.56 => ( ! [D5: nat] :
% 0.23/0.56 ( ( dist_a @ C @ V @ D5 @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ D @ D5 ) )
% 0.23/0.56 => ( ( min_dist_a @ C @ V @ V3 )
% 0.23/0.56 = D ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_distI_eq
% 0.23/0.56 thf(fact_174_Graph_Omin__dist__minD,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ V @ D @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ ( min_dist_capacity @ C @ V @ V3 ) @ D ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_minD
% 0.23/0.56 thf(fact_175_Graph_Omin__dist__minD,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_a @ C @ V @ D @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ ( min_dist_a @ C @ V @ V3 ) @ D ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_minD
% 0.23/0.56 thf(fact_176_Graph_Omin__dist__split_I2_J,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_capacity @ C @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_capacity @ C @ W @ D2 @ V )
% 0.23/0.56 => ( ( ( min_dist_capacity @ C @ U @ V )
% 0.23/0.56 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.23/0.56 => ( ( min_dist_capacity @ C @ W @ V )
% 0.23/0.56 = D2 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_split(2)
% 0.23/0.56 thf(fact_177_Graph_Omin__dist__split_I2_J,axiom,
% 0.23/0.56 ! [C: product_prod_nat_nat > a,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_a @ C @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_a @ C @ W @ D2 @ V )
% 0.23/0.56 => ( ( ( min_dist_a @ C @ U @ V )
% 0.23/0.56 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.23/0.56 => ( ( min_dist_a @ C @ W @ V )
% 0.23/0.56 = D2 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % Graph.min_dist_split(2)
% 0.23/0.56 thf(fact_178__C1_Oprems_C_I3_J,axiom,
% 0.23/0.56 isPath_a @ c2 @ ua @ p2_a @ t ).
% 0.23/0.56
% 0.23/0.56 % "1.prems"(3)
% 0.23/0.56 thf(fact_179_not__less__Least,axiom,
% 0.23/0.56 ! [K: nat,P5: nat > $o] :
% 0.23/0.56 ( ( ord_less_nat @ K @ ( ord_Least_nat @ P5 ) )
% 0.23/0.56 => ~ ( P5 @ K ) ) ).
% 0.23/0.56
% 0.23/0.56 % not_less_Least
% 0.23/0.56 thf(fact_180_Least__le,axiom,
% 0.23/0.56 ! [P5: nat > $o,K: nat] :
% 0.23/0.56 ( ( P5 @ K )
% 0.23/0.56 => ( ord_less_eq_nat @ ( ord_Least_nat @ P5 ) @ K ) ) ).
% 0.23/0.56
% 0.23/0.56 % Least_le
% 0.23/0.56 thf(fact_181_g_H_Oconnected__by__dist,axiom,
% 0.23/0.56 ! [V: nat,V3: nat] :
% 0.23/0.56 ( ( connected_a @ c2 @ V @ V3 )
% 0.23/0.56 = ( ? [D4: nat] : ( dist_a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.connected_by_dist
% 0.23/0.56 thf(fact_182_g_H_Omin__dist__is__dist,axiom,
% 0.23/0.56 ! [V: nat,V3: nat] :
% 0.23/0.56 ( ( connected_a @ c2 @ V @ V3 )
% 0.23/0.56 => ( dist_a @ c2 @ V @ ( min_dist_a @ c2 @ V @ V3 ) @ V3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_dist_is_dist
% 0.23/0.56 thf(fact_183_g_H_Oobtain__shortest__path,axiom,
% 0.23/0.56 ! [U: nat,V: nat] :
% 0.23/0.56 ( ( connected_a @ c2 @ U @ V )
% 0.23/0.56 => ~ ! [P3: list_P559422087at_nat] :
% 0.23/0.56 ~ ( isShortestPath_a @ c2 @ U @ P3 @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.obtain_shortest_path
% 0.23/0.56 thf(fact_184_g_H_OshortestPath__is__simple,axiom,
% 0.23/0.56 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.23/0.56 ( ( isShortestPath_a @ c2 @ S @ P2 @ T )
% 0.23/0.56 => ( isSimplePath_a @ c2 @ S @ P2 @ T ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.shortestPath_is_simple
% 0.23/0.56 thf(fact_185_g_H_OreachableNodes__def,axiom,
% 0.23/0.56 ! [U: nat] :
% 0.23/0.56 ( ( reachableNodes_a @ c2 @ U )
% 0.23/0.56 = ( collect_nat @ ( connected_a @ c2 @ U ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.reachableNodes_def
% 0.23/0.56 thf(fact_186_g_H_Omin__dist__less,axiom,
% 0.23/0.56 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 0.23/0.56 ( ( connected_a @ c2 @ Src @ V )
% 0.23/0.56 => ( ( ( min_dist_a @ c2 @ Src @ V )
% 0.23/0.56 = D )
% 0.23/0.56 => ( ( ord_less_nat @ D3 @ D )
% 0.23/0.56 => ? [V2: nat] :
% 0.23/0.56 ( ( connected_a @ c2 @ Src @ V2 )
% 0.23/0.56 & ( ( min_dist_a @ c2 @ Src @ V2 )
% 0.23/0.56 = D3 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_dist_less
% 0.23/0.56 thf(fact_187_g_H_Omin__distI2,axiom,
% 0.23/0.56 ! [V: nat,V3: nat,Q: nat > $o] :
% 0.23/0.56 ( ( connected_a @ c2 @ V @ V3 )
% 0.23/0.56 => ( ! [D6: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ V @ D6 @ V3 )
% 0.23/0.56 => ( ! [D7: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ V @ D7 @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ D6 @ D7 ) )
% 0.23/0.56 => ( Q @ D6 ) ) )
% 0.23/0.56 => ( Q @ ( min_dist_a @ c2 @ V @ V3 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_distI2
% 0.23/0.56 thf(fact_188_g_H_Omin__distI__eq,axiom,
% 0.23/0.56 ! [V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ V @ D @ V3 )
% 0.23/0.56 => ( ! [D5: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ V @ D5 @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ D @ D5 ) )
% 0.23/0.56 => ( ( min_dist_a @ c2 @ V @ V3 )
% 0.23/0.56 = D ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_distI_eq
% 0.23/0.56 thf(fact_189_g_H_Omin__dist__le,axiom,
% 0.23/0.56 ! [Src: nat,V: nat,D3: nat] :
% 0.23/0.56 ( ( connected_a @ c2 @ Src @ V )
% 0.23/0.56 => ( ( ord_less_eq_nat @ D3 @ ( min_dist_a @ c2 @ Src @ V ) )
% 0.23/0.56 => ? [V2: nat] :
% 0.23/0.56 ( ( connected_a @ c2 @ Src @ V2 )
% 0.23/0.56 & ( ( min_dist_a @ c2 @ Src @ V2 )
% 0.23/0.56 = D3 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_dist_le
% 0.23/0.56 thf(fact_190_g_H_Omin__dist__minD,axiom,
% 0.23/0.56 ! [V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ V @ D @ V3 )
% 0.23/0.56 => ( ord_less_eq_nat @ ( min_dist_a @ c2 @ V @ V3 ) @ D ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_dist_minD
% 0.23/0.56 thf(fact_191_g_H_Omin__dist__split_I2_J,axiom,
% 0.23/0.56 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 0.23/0.56 => ( ( ( min_dist_a @ c2 @ U @ V )
% 0.23/0.56 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.23/0.56 => ( ( min_dist_a @ c2 @ W @ V )
% 0.23/0.56 = D2 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_dist_split(2)
% 0.23/0.56 thf(fact_192_g_H_Omin__dist__split_I1_J,axiom,
% 0.23/0.56 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 0.23/0.56 => ( ( ( min_dist_a @ c2 @ U @ V )
% 0.23/0.56 = ( plus_plus_nat @ D1 @ D2 ) )
% 0.23/0.56 => ( ( min_dist_a @ c2 @ U @ W )
% 0.23/0.56 = D1 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_dist_split(1)
% 0.23/0.56 thf(fact_193_g_H_Odist__trans,axiom,
% 0.23/0.56 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ U @ D1 @ W )
% 0.23/0.56 => ( ( dist_a @ c2 @ W @ D2 @ V )
% 0.23/0.56 => ( dist_a @ c2 @ U @ ( plus_plus_nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.dist_trans
% 0.23/0.56 thf(fact_194_g_H_Oconnected__def,axiom,
% 0.23/0.56 ! [U: nat,V: nat] :
% 0.23/0.56 ( ( connected_a @ c2 @ U @ V )
% 0.23/0.56 = ( ? [P: list_P559422087at_nat] : ( isPath_a @ c2 @ U @ P @ V ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.connected_def
% 0.23/0.56 thf(fact_195_g_H_OisSPath__pathLE,axiom,
% 0.23/0.56 ! [S: nat,P2: list_P559422087at_nat,T: nat] :
% 0.23/0.56 ( ( isPath_a @ c2 @ S @ P2 @ T )
% 0.23/0.56 => ? [P6: list_P559422087at_nat] : ( isSimplePath_a @ c2 @ S @ P6 @ T ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.isSPath_pathLE
% 0.23/0.56 thf(fact_196_g_H_OshortestPath__is__path,axiom,
% 0.23/0.56 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 0.23/0.56 => ( isPath_a @ c2 @ U @ P2 @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.shortestPath_is_path
% 0.23/0.56 thf(fact_197_g_H_OisShortestPath__alt,axiom,
% 0.23/0.56 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 0.23/0.56 = ( ( isSimplePath_a @ c2 @ U @ P2 @ V )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P2 )
% 0.23/0.56 = ( min_dist_a @ c2 @ U @ V ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.isShortestPath_alt
% 0.23/0.56 thf(fact_198_g_H_Omin__dist__def,axiom,
% 0.23/0.56 ! [V: nat,V3: nat] :
% 0.23/0.56 ( ( min_dist_a @ c2 @ V @ V3 )
% 0.23/0.56 = ( ord_Least_nat
% 0.23/0.56 @ ^ [D4: nat] : ( dist_a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.min_dist_def
% 0.23/0.56 thf(fact_199_g_H_Odist__def,axiom,
% 0.23/0.56 ! [V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ V @ D @ V3 )
% 0.23/0.56 = ( ? [P: list_P559422087at_nat] :
% 0.23/0.56 ( ( isPath_a @ c2 @ V @ P @ V3 )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P )
% 0.23/0.56 = D ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.dist_def
% 0.23/0.56 thf(fact_200_g_H_OisPath__distD,axiom,
% 0.23/0.56 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isPath_a @ c2 @ U @ P2 @ V )
% 0.23/0.56 => ( dist_a @ c2 @ U @ ( size_s1990949619at_nat @ P2 ) @ V ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.isPath_distD
% 0.23/0.56 thf(fact_201_g_H_OisShortestPath__min__dist__def,axiom,
% 0.23/0.56 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 0.23/0.56 = ( ( isPath_a @ c2 @ U @ P2 @ V )
% 0.23/0.56 & ( ( size_s1990949619at_nat @ P2 )
% 0.23/0.56 = ( min_dist_a @ c2 @ U @ V ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.isShortestPath_min_dist_def
% 0.23/0.56 thf(fact_202_order__refl,axiom,
% 0.23/0.56 ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 0.23/0.56
% 0.23/0.56 % order_refl
% 0.23/0.56 thf(fact_203_g_H_OisShortestPath__def,axiom,
% 0.23/0.56 ! [U: nat,P2: list_P559422087at_nat,V: nat] :
% 0.23/0.56 ( ( isShortestPath_a @ c2 @ U @ P2 @ V )
% 0.23/0.56 = ( ( isPath_a @ c2 @ U @ P2 @ V )
% 0.23/0.56 & ! [P4: list_P559422087at_nat] :
% 0.23/0.56 ( ( isPath_a @ c2 @ U @ P4 @ V )
% 0.23/0.56 => ( ord_less_eq_nat @ ( size_s1990949619at_nat @ P2 ) @ ( size_s1990949619at_nat @ P4 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.isShortestPath_def
% 0.23/0.56 thf(fact_204_assms_I5_J,axiom,
% 0.23/0.56 isPath_a @ c2 @ s @ p3 @ t ).
% 0.23/0.56
% 0.23/0.56 % assms(5)
% 0.23/0.56 thf(fact_205__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062,axiom,
% 0.23/0.56 isPath_a @ c2 @ u @ p2 @ t ).
% 0.23/0.56
% 0.23/0.56 % \<open>g'.isPath u__ p2'__ t\<close>
% 0.23/0.56 thf(fact_206_g_H_Oconnected__distI,axiom,
% 0.23/0.56 ! [V: nat,D: nat,V3: nat] :
% 0.23/0.56 ( ( dist_a @ c2 @ V @ D @ V3 )
% 0.23/0.56 => ( connected_a @ c2 @ V @ V3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % g'.connected_distI
% 0.23/0.56 thf(fact_207_g_H_Oconnected__refl,axiom,
% 0.23/0.56 ! [V: nat] : ( connected_a @ c2 @ V @ V ) ).
% 0.23/0.56
% 0.23/0.56 % g'.connected_refl
% 0.23/0.56 thf(fact_208_P2_H,axiom,
% 0.23/0.56 isPath_a @ c2 @ ua @ p2_a @ t ).
% 0.23/0.56
% 0.23/0.56 % P2'
% 0.23/0.56 thf(fact_209_order__subst1,axiom,
% 0.23/0.56 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.23/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.56 => ( ! [X: nat,Y: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.23/0.56 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order_subst1
% 0.23/0.56 thf(fact_210_order__subst2,axiom,
% 0.23/0.56 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.56 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.23/0.56 => ( ! [X: nat,Y: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.23/0.56 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order_subst2
% 0.23/0.56 thf(fact_211_ord__eq__le__subst,axiom,
% 0.23/0.56 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.56 ( ( A
% 0.23/0.56 = ( F @ B ) )
% 0.23/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.56 => ( ! [X: nat,Y: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.23/0.56 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % ord_eq_le_subst
% 0.23/0.56 thf(fact_212_ord__le__eq__subst,axiom,
% 0.23/0.56 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.56 => ( ( ( F @ B )
% 0.23/0.56 = C )
% 0.23/0.56 => ( ! [X: nat,Y: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.56 => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.23/0.56 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % ord_le_eq_subst
% 0.23/0.56 thf(fact_213_eq__iff,axiom,
% 0.23/0.56 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.23/0.56 = ( ^ [X2: nat,Y5: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ X2 @ Y5 )
% 0.23/0.56 & ( ord_less_eq_nat @ Y5 @ X2 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % eq_iff
% 0.23/0.56 thf(fact_214_antisym,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.56 => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.23/0.56 => ( X3 = Y3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % antisym
% 0.23/0.56 thf(fact_215_linear,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.56 | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % linear
% 0.23/0.56 thf(fact_216_eq__refl,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( X3 = Y3 )
% 0.23/0.56 => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % eq_refl
% 0.23/0.56 thf(fact_217_le__cases,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.56 => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % le_cases
% 0.23/0.56 thf(fact_218_order_Otrans,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.56 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order.trans
% 0.23/0.56 thf(fact_219_le__cases3,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.23/0.56 ( ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.56 => ~ ( ord_less_eq_nat @ Y3 @ Z2 ) )
% 0.23/0.56 => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.23/0.56 => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 0.23/0.56 => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 0.23/0.56 => ~ ( ord_less_eq_nat @ Z2 @ Y3 ) )
% 0.23/0.56 => ( ( ( ord_less_eq_nat @ Z2 @ Y3 )
% 0.23/0.56 => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
% 0.23/0.56 => ( ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 0.23/0.56 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 0.23/0.56 => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 0.23/0.56 => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % le_cases3
% 0.23/0.56 thf(fact_220_antisym__conv,axiom,
% 0.23/0.56 ! [Y3: nat,X3: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.23/0.56 => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.56 = ( X3 = Y3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % antisym_conv
% 0.23/0.56 thf(fact_221_order__class_Oorder_Oeq__iff,axiom,
% 0.23/0.56 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.23/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.23/0.56 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order_class.order.eq_iff
% 0.23/0.56 thf(fact_222_ord__eq__le__trans,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat] :
% 0.23/0.56 ( ( A = B )
% 0.23/0.56 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.56 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % ord_eq_le_trans
% 0.23/0.56 thf(fact_223_ord__le__eq__trans,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.56 => ( ( B = C )
% 0.23/0.56 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % ord_le_eq_trans
% 0.23/0.56 thf(fact_224_order__class_Oorder_Oantisym,axiom,
% 0.23/0.56 ! [A: nat,B: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.56 => ( ( ord_less_eq_nat @ B @ A )
% 0.23/0.56 => ( A = B ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order_class.order.antisym
% 0.23/0.56 thf(fact_225_order__trans,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.23/0.56 => ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 0.23/0.56 => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order_trans
% 0.23/0.56 thf(fact_226_dual__order_Orefl,axiom,
% 0.23/0.56 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.23/0.56
% 0.23/0.56 % dual_order.refl
% 0.23/0.56 thf(fact_227_linorder__wlog,axiom,
% 0.23/0.56 ! [P5: nat > nat > $o,A: nat,B: nat] :
% 0.23/0.56 ( ! [A4: nat,B4: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ A4 @ B4 )
% 0.23/0.56 => ( P5 @ A4 @ B4 ) )
% 0.23/0.56 => ( ! [A4: nat,B4: nat] :
% 0.23/0.56 ( ( P5 @ B4 @ A4 )
% 0.23/0.56 => ( P5 @ A4 @ B4 ) )
% 0.23/0.56 => ( P5 @ A @ B ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % linorder_wlog
% 0.23/0.56 thf(fact_228_dual__order_Otrans,axiom,
% 0.23/0.56 ! [B: nat,A: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ B @ A )
% 0.23/0.56 => ( ( ord_less_eq_nat @ C @ B )
% 0.23/0.56 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % dual_order.trans
% 0.23/0.56 thf(fact_229_dual__order_Oeq__iff,axiom,
% 0.23/0.56 ( ( ^ [Y4: nat,Z: nat] : ( Y4 = Z ) )
% 0.23/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.23/0.56 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % dual_order.eq_iff
% 0.23/0.56 thf(fact_230_dual__order_Oantisym,axiom,
% 0.23/0.56 ! [B: nat,A: nat] :
% 0.23/0.56 ( ( ord_less_eq_nat @ B @ A )
% 0.23/0.56 => ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.56 => ( A = B ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % dual_order.antisym
% 0.23/0.56 thf(fact_231_dual__order_Ostrict__implies__not__eq,axiom,
% 0.23/0.56 ! [B: nat,A: nat] :
% 0.23/0.56 ( ( ord_less_nat @ B @ A )
% 0.23/0.56 => ( A != B ) ) ).
% 0.23/0.56
% 0.23/0.56 % dual_order.strict_implies_not_eq
% 0.23/0.56 thf(fact_232_order_Ostrict__implies__not__eq,axiom,
% 0.23/0.56 ! [A: nat,B: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( A != B ) ) ).
% 0.23/0.56
% 0.23/0.56 % order.strict_implies_not_eq
% 0.23/0.56 thf(fact_233_not__less__iff__gr__or__eq,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 0.23/0.56 = ( ( ord_less_nat @ Y3 @ X3 )
% 0.23/0.56 | ( X3 = Y3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % not_less_iff_gr_or_eq
% 0.23/0.56 thf(fact_234_dual__order_Ostrict__trans,axiom,
% 0.23/0.56 ! [B: nat,A: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_nat @ B @ A )
% 0.23/0.56 => ( ( ord_less_nat @ C @ B )
% 0.23/0.56 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % dual_order.strict_trans
% 0.23/0.56 thf(fact_235_linorder__less__wlog,axiom,
% 0.23/0.56 ! [P5: nat > nat > $o,A: nat,B: nat] :
% 0.23/0.56 ( ! [A4: nat,B4: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A4 @ B4 )
% 0.23/0.56 => ( P5 @ A4 @ B4 ) )
% 0.23/0.56 => ( ! [A4: nat] : ( P5 @ A4 @ A4 )
% 0.23/0.56 => ( ! [A4: nat,B4: nat] :
% 0.23/0.56 ( ( P5 @ B4 @ A4 )
% 0.23/0.56 => ( P5 @ A4 @ B4 ) )
% 0.23/0.56 => ( P5 @ A @ B ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % linorder_less_wlog
% 0.23/0.56 thf(fact_236_exists__least__iff,axiom,
% 0.23/0.56 ( ( ^ [P7: nat > $o] :
% 0.23/0.56 ? [X4: nat] : ( P7 @ X4 ) )
% 0.23/0.56 = ( ^ [P8: nat > $o] :
% 0.23/0.56 ? [N2: nat] :
% 0.23/0.56 ( ( P8 @ N2 )
% 0.23/0.56 & ! [M2: nat] :
% 0.23/0.56 ( ( ord_less_nat @ M2 @ N2 )
% 0.23/0.56 => ~ ( P8 @ M2 ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % exists_least_iff
% 0.23/0.56 thf(fact_237_less__imp__not__less,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_imp_not_less
% 0.23/0.56 thf(fact_238_order_Ostrict__trans,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( ( ord_less_nat @ B @ C )
% 0.23/0.56 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order.strict_trans
% 0.23/0.56 thf(fact_239_dual__order_Oirrefl,axiom,
% 0.23/0.56 ! [A: nat] :
% 0.23/0.56 ~ ( ord_less_nat @ A @ A ) ).
% 0.23/0.56
% 0.23/0.56 % dual_order.irrefl
% 0.23/0.56 thf(fact_240_linorder__cases,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ( ( X3 != Y3 )
% 0.23/0.56 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % linorder_cases
% 0.23/0.56 thf(fact_241_less__imp__triv,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat,P5: $o] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ( ( ord_less_nat @ Y3 @ X3 )
% 0.23/0.56 => P5 ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_imp_triv
% 0.23/0.56 thf(fact_242_less__imp__not__eq2,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ( Y3 != X3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_imp_not_eq2
% 0.23/0.56 thf(fact_243_antisym__conv3,axiom,
% 0.23/0.56 ! [Y3: nat,X3: nat] :
% 0.23/0.56 ( ~ ( ord_less_nat @ Y3 @ X3 )
% 0.23/0.56 => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
% 0.23/0.56 = ( X3 = Y3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % antisym_conv3
% 0.23/0.56 thf(fact_244_less__induct,axiom,
% 0.23/0.56 ! [P5: nat > $o,A: nat] :
% 0.23/0.56 ( ! [X: nat] :
% 0.23/0.56 ( ! [Y2: nat] :
% 0.23/0.56 ( ( ord_less_nat @ Y2 @ X )
% 0.23/0.56 => ( P5 @ Y2 ) )
% 0.23/0.56 => ( P5 @ X ) )
% 0.23/0.56 => ( P5 @ A ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_induct
% 0.23/0.56 thf(fact_245_less__not__sym,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_not_sym
% 0.23/0.56 thf(fact_246_less__imp__not__eq,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ( X3 != Y3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_imp_not_eq
% 0.23/0.56 thf(fact_247_dual__order_Oasym,axiom,
% 0.23/0.56 ! [B: nat,A: nat] :
% 0.23/0.56 ( ( ord_less_nat @ B @ A )
% 0.23/0.56 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.23/0.56
% 0.23/0.56 % dual_order.asym
% 0.23/0.56 thf(fact_248_ord__less__eq__trans,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( ( B = C )
% 0.23/0.56 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % ord_less_eq_trans
% 0.23/0.56 thf(fact_249_ord__eq__less__trans,axiom,
% 0.23/0.56 ! [A: nat,B: nat,C: nat] :
% 0.23/0.56 ( ( A = B )
% 0.23/0.56 => ( ( ord_less_nat @ B @ C )
% 0.23/0.56 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % ord_eq_less_trans
% 0.23/0.56 thf(fact_250_less__irrefl,axiom,
% 0.23/0.56 ! [X3: nat] :
% 0.23/0.56 ~ ( ord_less_nat @ X3 @ X3 ) ).
% 0.23/0.56
% 0.23/0.56 % less_irrefl
% 0.23/0.56 thf(fact_251_less__linear,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 | ( X3 = Y3 )
% 0.23/0.56 | ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_linear
% 0.23/0.56 thf(fact_252_less__trans,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ( ( ord_less_nat @ Y3 @ Z2 )
% 0.23/0.56 => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_trans
% 0.23/0.56 thf(fact_253_less__asym_H,axiom,
% 0.23/0.56 ! [A: nat,B: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_asym'
% 0.23/0.56 thf(fact_254_less__asym,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_asym
% 0.23/0.56 thf(fact_255_less__imp__neq,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ( X3 != Y3 ) ) ).
% 0.23/0.56
% 0.23/0.56 % less_imp_neq
% 0.23/0.56 thf(fact_256_order_Oasym,axiom,
% 0.23/0.56 ! [A: nat,B: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.23/0.56
% 0.23/0.56 % order.asym
% 0.23/0.56 thf(fact_257_neq__iff,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( X3 != Y3 )
% 0.23/0.56 = ( ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 | ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % neq_iff
% 0.23/0.56 thf(fact_258_neqE,axiom,
% 0.23/0.56 ! [X3: nat,Y3: nat] :
% 0.23/0.56 ( ( X3 != Y3 )
% 0.23/0.56 => ( ~ ( ord_less_nat @ X3 @ Y3 )
% 0.23/0.56 => ( ord_less_nat @ Y3 @ X3 ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % neqE
% 0.23/0.56 thf(fact_259_gt__ex,axiom,
% 0.23/0.56 ! [X3: nat] :
% 0.23/0.56 ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 0.23/0.56
% 0.23/0.56 % gt_ex
% 0.23/0.56 thf(fact_260_order__less__subst2,axiom,
% 0.23/0.56 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.23/0.56 => ( ! [X: nat,Y: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X @ Y )
% 0.23/0.56 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.23/0.56 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order_less_subst2
% 0.23/0.56 thf(fact_261_order__less__subst1,axiom,
% 0.23/0.56 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.23/0.56 => ( ( ord_less_nat @ B @ C )
% 0.23/0.56 => ( ! [X: nat,Y: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X @ Y )
% 0.23/0.56 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.23/0.56 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % order_less_subst1
% 0.23/0.56 thf(fact_262_ord__less__eq__subst,axiom,
% 0.23/0.56 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.56 ( ( ord_less_nat @ A @ B )
% 0.23/0.56 => ( ( ( F @ B )
% 0.23/0.56 = C )
% 0.23/0.56 => ( ! [X: nat,Y: nat] :
% 0.23/0.56 ( ( ord_less_nat @ X @ Y )
% 0.23/0.56 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.23/0.56 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.56
% 0.23/0.56 % ord_less_eq_subst
% 0.23/0.56 thf(fact_263_ord__eq__less__subst,axiom,
% 0.23/0.62 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.62 ( ( A
% 0.23/0.62 = ( F @ B ) )
% 0.23/0.62 => ( ( ord_less_nat @ B @ C )
% 0.23/0.62 => ( ! [X: nat,Y: nat] :
% 0.23/0.62 ( ( ord_less_nat @ X @ Y )
% 0.23/0.62 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) )
% 0.23/0.62 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.62
% 0.23/0.62 % ord_eq_less_subst
% 0.23/0.62 thf(fact_264_LeastI2,axiom,
% 0.23/0.62 ! [P5: nat > $o,A: nat,Q: nat > $o] :
% 0.23/0.62 ( ( P5 @ A )
% 0.23/0.62 => ( ! [X: nat] :
% 0.23/0.62 ( ( P5 @ X )
% 0.23/0.62 => ( Q @ X ) )
% 0.23/0.62 => ( Q @ ( ord_Least_nat @ P5 ) ) ) ) ).
% 0.23/0.62
% 0.23/0.62 % LeastI2
% 0.23/0.62 thf(fact_265_LeastI__ex,axiom,
% 0.23/0.62 ! [P5: nat > $o] :
% 0.23/0.62 ( ? [X_12: nat] : ( P5 @ X_12 )
% 0.23/0.62 => ( P5 @ ( ord_Least_nat @ P5 ) ) ) ).
% 0.23/0.62
% 0.23/0.62 % LeastI_ex
% 0.23/0.62 thf(fact_266_LeastI2__ex,axiom,
% 0.23/0.62 ! [P5: nat > $o,Q: nat > $o] :
% 0.23/0.62 ( ? [X_12: nat] : ( P5 @ X_12 )
% 0.23/0.62 => ( ! [X: nat] :
% 0.23/0.62 ( ( P5 @ X )
% 0.23/0.62 => ( Q @ X ) )
% 0.23/0.62 => ( Q @ ( ord_Least_nat @ P5 ) ) ) ) ).
% 0.23/0.62
% 0.23/0.62 % LeastI2_ex
% 0.23/0.62 thf(fact_267_LeastI,axiom,
% 0.23/0.62 ! [P5: nat > $o,K: nat] :
% 0.23/0.62 ( ( P5 @ K )
% 0.23/0.62 => ( P5 @ ( ord_Least_nat @ P5 ) ) ) ).
% 0.23/0.62
% 0.23/0.62 % LeastI
% 0.23/0.62 thf(fact_268_order_Onot__eq__order__implies__strict,axiom,
% 0.23/0.62 ! [A: nat,B: nat] :
% 0.23/0.62 ( ( A != B )
% 0.23/0.62 => ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.62 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.23/0.62
% 0.23/0.62 % order.not_eq_order_implies_strict
% 0.23/0.62 thf(fact_269_dual__order_Ostrict__implies__order,axiom,
% 0.23/0.62 ! [B: nat,A: nat] :
% 0.23/0.62 ( ( ord_less_nat @ B @ A )
% 0.23/0.62 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.23/0.62
% 0.23/0.62 % dual_order.strict_implies_order
% 0.23/0.62 thf(fact_270_dual__order_Ostrict__iff__order,axiom,
% 0.23/0.62 ( ord_less_nat
% 0.23/0.62 = ( ^ [B2: nat,A2: nat] :
% 0.23/0.62 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.23/0.62 & ( A2 != B2 ) ) ) ) ).
% 0.23/0.62
% 0.23/0.62 % dual_order.strict_iff_order
% 0.23/0.62 thf(fact_271_dual__order_Oorder__iff__strict,axiom,
% 0.23/0.62 ( ord_less_eq_nat
% 0.23/0.62 = ( ^ [B2: nat,A2: nat] :
% 0.23/0.62 ( ( ord_less_nat @ B2 @ A2 )
% 0.23/0.62 | ( A2 = B2 ) ) ) ) ).
% 0.23/0.62
% 0.23/0.62 % dual_order.order_iff_strict
% 0.23/0.62 thf(fact_272_order_Ostrict__implies__order,axiom,
% 0.23/0.62 ! [A: nat,B: nat] :
% 0.23/0.62 ( ( ord_less_nat @ A @ B )
% 0.23/0.62 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.23/0.62
% 0.23/0.62 % order.strict_implies_order
% 0.23/0.62
% 0.23/0.62 % Conjectures (1)
% 0.23/0.62 thf(conj_0,conjecture,
% 0.23/0.62 ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ).
% 0.23/0.62
% 0.23/0.62 %------------------------------------------------------------------------------
% 0.23/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.n8KNEa8Z5C/cvc5---1.0.5_22049.p...
% 0.23/0.62 (declare-sort $$unsorted 0)
% 0.23/0.62 (declare-sort tptp.list_P559422087at_nat 0)
% 0.23/0.62 (declare-sort tptp.product_prod_nat_nat 0)
% 0.23/0.62 (declare-sort tptp.set_nat 0)
% 0.23/0.62 (declare-sort tptp.capacity 0)
% 0.23/0.62 (declare-sort tptp.nat 0)
% 0.23/0.62 (declare-sort tptp.a 0)
% 0.23/0.62 (declare-fun tptp.connected_a ((-> tptp.product_prod_nat_nat tptp.a) tptp.nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.connected_capacity ((-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.dist_a ((-> tptp.product_prod_nat_nat tptp.a) tptp.nat tptp.nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.dist_capacity ((-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.isPath_a ((-> tptp.product_prod_nat_nat tptp.a) tptp.nat tptp.list_P559422087at_nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.isPath_capacity ((-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.list_P559422087at_nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.isShortestPath_a ((-> tptp.product_prod_nat_nat tptp.a) tptp.nat tptp.list_P559422087at_nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.isShor1936442771pacity ((-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.list_P559422087at_nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.isSimplePath_a ((-> tptp.product_prod_nat_nat tptp.a) tptp.nat tptp.list_P559422087at_nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.isSimp1359852763pacity ((-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.list_P559422087at_nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.min_dist_a ((-> tptp.product_prod_nat_nat tptp.a) tptp.nat tptp.nat) tptp.nat)
% 0.23/0.62 (declare-fun tptp.min_dist_capacity ((-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat) tptp.nat)
% 0.23/0.62 (declare-fun tptp.reachableNodes_a ((-> tptp.product_prod_nat_nat tptp.a) tptp.nat) tptp.set_nat)
% 0.23/0.62 (declare-fun tptp.reacha1693770334pacity ((-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat) tptp.set_nat)
% 0.23/0.62 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.23/0.62 (declare-fun tptp.size_s1990949619at_nat (tptp.list_P559422087at_nat) tptp.nat)
% 0.23/0.62 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.23/0.62 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.23/0.62 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.23/0.62 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.23/0.62 (declare-fun tptp.c (tptp.product_prod_nat_nat) tptp.capacity)
% 0.23/0.62 (declare-fun tptp.c2 (tptp.product_prod_nat_nat) tptp.a)
% 0.23/0.62 (declare-fun tptp.p () tptp.list_P559422087at_nat)
% 0.23/0.62 (declare-fun tptp.p1 () tptp.list_P559422087at_nat)
% 0.23/0.62 (declare-fun tptp.p1a () tptp.list_P559422087at_nat)
% 0.23/0.62 (declare-fun tptp.p2 () tptp.list_P559422087at_nat)
% 0.23/0.62 (declare-fun tptp.p2_a () tptp.list_P559422087at_nat)
% 0.23/0.62 (declare-fun tptp.p3 () tptp.list_P559422087at_nat)
% 0.23/0.62 (declare-fun tptp.s () tptp.nat)
% 0.23/0.62 (declare-fun tptp.t () tptp.nat)
% 0.23/0.62 (declare-fun tptp.u () tptp.nat)
% 0.23/0.62 (declare-fun tptp.ua () tptp.nat)
% 0.23/0.62 (declare-fun tptp.v () tptp.nat)
% 0.23/0.62 (declare-fun tptp.va () tptp.nat)
% 0.23/0.62 (assert (let ((_let_1 (@ tptp.min_dist_capacity tptp.c))) (let ((_let_2 (@ _let_1 tptp.s))) (= (@ _let_2 tptp.t) (@ (@ tptp.plus_plus_nat (@ _let_2 tptp.ua)) (@ (@ _let_1 tptp.ua) tptp.t))))))
% 0.23/0.62 (assert (@ (@ tptp.ord_less_nat (@ (@ (@ tptp.min_dist_capacity tptp.c) tptp.s) tptp.ua)) (@ tptp.size_s1990949619at_nat tptp.p1a)))
% 0.23/0.62 (assert (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_capacity tptp.c) tptp.ua) tptp.t)) (@ tptp.size_s1990949619at_nat tptp.p2_a)))
% 0.23/0.62 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.23/0.62 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.s) tptp.p1a) tptp.va))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) tptp.s) tptp.p) tptp.t))
% 0.23/0.62 (assert (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.min_dist_capacity tptp.c))) (let ((_let_2 (@ tptp.dist_capacity tptp.c))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ (@ _let_1 U) V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ (@ _let_1 W) V) D2))))))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.min_dist_capacity tptp.c) U))) (let ((_let_2 (@ tptp.dist_capacity tptp.c))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ _let_1 V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ _let_1 W) D1))))))))
% 0.23/0.62 (assert (forall ((Src tptp.nat) (V tptp.nat) (D tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity tptp.c) Src) V) (=> (= (@ (@ (@ tptp.min_dist_capacity tptp.c) Src) V) D) (=> (@ (@ tptp.ord_less_nat D3) D) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_capacity tptp.c) Src) V2) (= (@ (@ (@ tptp.min_dist_capacity tptp.c) Src) V2) D3))))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.ua) tptp.p2_a) tptp.t))
% 0.23/0.62 (assert (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.dist_capacity tptp.c))) (let ((_let_2 (@ _let_1 U))) (=> (@ (@ _let_2 D1) W) (=> (@ (@ (@ _let_1 W) D2) V) (@ (@ _let_2 (@ (@ tptp.plus_plus_nat D1) D2)) V)))))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (V tptp.nat)) (= (@ (@ (@ tptp.connected_capacity tptp.c) U) V) (exists ((P tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P) V)))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P2) V) (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P2) V))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ tptp.connected_capacity tptp.c) V) V3) (exists ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D4) V3)))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (V tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity tptp.c) U) V) (not (forall ((P3 tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P3) V)))))))
% 0.23/0.62 (assert (forall ((Src tptp.nat) (V tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity tptp.c) Src) V) (=> (@ (@ tptp.ord_less_eq_nat D3) (@ (@ (@ tptp.min_dist_capacity tptp.c) Src) V)) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_capacity tptp.c) Src) V2) (= (@ (@ (@ tptp.min_dist_capacity tptp.c) Src) V2) D3)))))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D) V3) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3)) D))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D) V3) (=> (forall ((D5 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D5) V3) (@ (@ tptp.ord_less_eq_nat D) D5))) (= (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3) D)))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P2) V) (@ (@ (@ (@ tptp.dist_capacity tptp.c) U) (@ tptp.size_s1990949619at_nat P2)) V))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D) V3) (exists ((P tptp.list_P559422087at_nat)) (and (@ (@ (@ (@ tptp.isPath_capacity tptp.c) V) P) V3) (= (@ tptp.size_s1990949619at_nat P) D))))))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.s) tptp.p1) tptp.v))
% 0.23/0.62 (assert (forall ((V tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity tptp.c) V) V3) (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3)) V3))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P2) V) (and (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P2) V) (forall ((P4 tptp.list_P559422087at_nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P4) V) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1990949619at_nat P2)) (@ tptp.size_s1990949619at_nat P4))))))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (V3 tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.connected_capacity tptp.c) V) V3) (=> (forall ((D6 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D6) V3) (=> (forall ((D7 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D7) V3) (@ (@ tptp.ord_less_eq_nat D6) D7))) (@ Q D6)))) (@ Q (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3))))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P2) V) (and (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P2) V) (= (@ tptp.size_s1990949619at_nat P2) (@ (@ (@ tptp.min_dist_capacity tptp.c) U) V))))))
% 0.23/0.62 (assert (@ (@ (@ tptp.connected_capacity tptp.c) tptp.s) tptp.ua))
% 0.23/0.62 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.23/0.62 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 0.23/0.62 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.s) tptp.p1a) tptp.va))
% 0.23/0.62 (assert (forall ((V tptp.nat)) (@ (@ (@ tptp.connected_capacity tptp.c) V) V)))
% 0.23/0.62 (assert (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D) V3) (@ (@ (@ tptp.connected_capacity tptp.c) V) V3))))
% 0.23/0.62 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P5 K) (=> (forall ((Y tptp.nat)) (=> (@ P5 Y) (@ (@ tptp.ord_less_eq_nat Y) B))) (exists ((X tptp.nat)) (and (@ P5 X) (forall ((Y2 tptp.nat)) (=> (@ P5 Y2) (@ (@ tptp.ord_less_eq_nat Y2) X)))))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.23/0.62 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 0.23/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (exists ((C2 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A2) C2))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (P5 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P5)) (@ P5 A))))
% 0.23/0.62 (assert (forall ((A3 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A3))) A3)))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X tptp.nat)) (= (@ P5 X) (@ Q X))) (= (@ tptp.collect_nat P5) (@ tptp.collect_nat Q)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.62 (assert (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (not (= M2 N2))))))
% 0.23/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (exists ((K2 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M2) K2))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.23/0.62 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N3))))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.62 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 0.23/0.62 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.23/0.62 (assert (= tptp.plus_plus_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A2))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 0.23/0.62 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 0.23/0.62 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A3) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (= X3 Y3)) (=> (not (@ (@ tptp.ord_less_nat X3) Y3)) (@ (@ tptp.ord_less_nat Y3) X3)))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P5 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P5 M3)))))) (@ P5 N))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P5 M3))) (@ P5 N3))) (@ P5 N))))
% 0.23/0.62 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.23/0.62 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.23/0.62 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.23/0.62 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.23/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.23/0.62 (assert (forall ((X3 tptp.list_P559422087at_nat) (Y3 tptp.list_P559422087at_nat)) (=> (not (= (@ tptp.size_s1990949619at_nat X3) (@ tptp.size_s1990949619at_nat Y3))) (not (= X3 Y3)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 0.23/0.62 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.23/0.62 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.23/0.62 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.23/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 0.23/0.62 (assert (forall ((U tptp.nat)) (= (@ (@ tptp.reacha1693770334pacity tptp.c) U) (@ tptp.collect_nat (@ (@ tptp.connected_capacity tptp.c) U)))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D4) V3))))))
% 0.23/0.62 (assert (= tptp.isShor1936442771pacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isPath_capacity C2) U2) P) V4) (= (@ tptp.size_s1990949619at_nat P) (@ (@ (@ tptp.min_dist_capacity C2) U2) V4))))))
% 0.23/0.62 (assert (= tptp.isShortestPath_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isPath_a C2) U2) P) V4) (= (@ tptp.size_s1990949619at_nat P) (@ (@ (@ tptp.min_dist_a C2) U2) V4))))))
% 0.23/0.62 (assert (= tptp.isShor1936442771pacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isPath_capacity C2) U2) P) V4) (forall ((P4 tptp.list_P559422087at_nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity C2) U2) P4) V4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1990949619at_nat P)) (@ tptp.size_s1990949619at_nat P4))))))))
% 0.23/0.62 (assert (= tptp.isShortestPath_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isPath_a C2) U2) P) V4) (forall ((P4 tptp.list_P559422087at_nat)) (=> (@ (@ (@ (@ tptp.isPath_a C2) U2) P4) V4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1990949619at_nat P)) (@ tptp.size_s1990949619at_nat P4))))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (V3 tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.connected_capacity C) V) V3) (=> (forall ((D6 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D6) V3) (=> (forall ((D7 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D7) V3) (@ (@ tptp.ord_less_eq_nat D6) D7))) (@ Q D6)))) (@ Q (@ (@ (@ tptp.min_dist_capacity C) V) V3))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (V3 tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.connected_a C) V) V3) (=> (forall ((D6 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D6) V3) (=> (forall ((D7 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D7) V3) (@ (@ tptp.ord_less_eq_nat D6) D7))) (@ Q D6)))) (@ Q (@ (@ (@ tptp.min_dist_a C) V) V3))))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P2) V) (and (@ (@ (@ (@ tptp.isSimp1359852763pacity tptp.c) U) P2) V) (= (@ tptp.size_s1990949619at_nat P2) (@ (@ (@ tptp.min_dist_capacity tptp.c) U) V))))))
% 0.23/0.62 (assert (= tptp.dist_capacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (V4 tptp.nat) (D4 tptp.nat) (V5 tptp.nat)) (exists ((P tptp.list_P559422087at_nat)) (and (@ (@ (@ (@ tptp.isPath_capacity C2) V4) P) V5) (= (@ tptp.size_s1990949619at_nat P) D4))))))
% 0.23/0.62 (assert (= tptp.dist_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (V4 tptp.nat) (D4 tptp.nat) (V5 tptp.nat)) (exists ((P tptp.list_P559422087at_nat)) (and (@ (@ (@ (@ tptp.isPath_a C2) V4) P) V5) (= (@ tptp.size_s1990949619at_nat P) D4))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity C) U) P2) V) (@ (@ (@ (@ tptp.dist_capacity C) U) (@ tptp.size_s1990949619at_nat P2)) V))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_a C) U) P2) V) (@ (@ (@ (@ tptp.dist_a C) U) (@ tptp.size_s1990949619at_nat P2)) V))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity C) V) V3) (@ (@ (@ (@ tptp.dist_capacity C) V) (@ (@ (@ tptp.min_dist_capacity C) V) V3)) V3))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a C) V) V3) (@ (@ (@ (@ tptp.dist_a C) V) (@ (@ (@ tptp.min_dist_a C) V) V3)) V3))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.min_dist_capacity C) U))) (let ((_let_2 (@ tptp.dist_capacity C))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ _let_1 V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ _let_1 W) D1))))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.min_dist_a C) U))) (let ((_let_2 (@ tptp.dist_a C))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ _let_1 V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ _let_1 W) D1))))))))
% 0.23/0.62 (assert (forall ((S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity tptp.c) S) P2) T) (exists ((P6 tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isSimp1359852763pacity tptp.c) S) P6) T)))))
% 0.23/0.62 (assert (forall ((S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) S) P2) T) (@ (@ (@ (@ tptp.isSimp1359852763pacity tptp.c) S) P2) T))))
% 0.23/0.62 (assert (= tptp.reacha1693770334pacity tptp.reacha1693770334pacity))
% 0.23/0.62 (assert (= tptp.reachableNodes_a tptp.reachableNodes_a))
% 0.23/0.62 (assert (= tptp.isSimp1359852763pacity tptp.isSimp1359852763pacity))
% 0.23/0.62 (assert (= tptp.isSimplePath_a tptp.isSimplePath_a))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity C) S) P2) T) (exists ((P6 tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isSimp1359852763pacity C) S) P6) T)))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_a C) S) P2) T) (exists ((P6 tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isSimplePath_a C) S) P6) T)))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isShor1936442771pacity C) S) P2) T) (@ (@ (@ (@ tptp.isSimp1359852763pacity C) S) P2) T))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isShortestPath_a C) S) P2) T) (@ (@ (@ (@ tptp.isSimplePath_a C) S) P2) T))))
% 0.23/0.62 (assert (= tptp.reacha1693770334pacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat)) (@ tptp.collect_nat (@ (@ tptp.connected_capacity C2) U2)))))
% 0.23/0.62 (assert (= tptp.reachableNodes_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat)) (@ tptp.collect_nat (@ (@ tptp.connected_a C2) U2)))))
% 0.23/0.62 (assert (= tptp.min_dist_capacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (V4 tptp.nat) (V5 tptp.nat)) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_capacity C2) V4) D4) V5))))))
% 0.23/0.62 (assert (= tptp.min_dist_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (V4 tptp.nat) (V5 tptp.nat)) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_a C2) V4) D4) V5))))))
% 0.23/0.62 (assert (= tptp.isShor1936442771pacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isSimp1359852763pacity C2) U2) P) V4) (= (@ tptp.size_s1990949619at_nat P) (@ (@ (@ tptp.min_dist_capacity C2) U2) V4))))))
% 0.23/0.62 (assert (= tptp.isShortestPath_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isSimplePath_a C2) U2) P) V4) (= (@ tptp.size_s1990949619at_nat P) (@ (@ (@ tptp.min_dist_a C2) U2) V4))))))
% 0.23/0.62 (assert (= tptp.isPath_capacity tptp.isPath_capacity))
% 0.23/0.62 (assert (= tptp.isPath_a tptp.isPath_a))
% 0.23/0.62 (assert (= tptp.min_dist_capacity tptp.min_dist_capacity))
% 0.23/0.62 (assert (= tptp.min_dist_a tptp.min_dist_a))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat)) (@ (@ (@ tptp.connected_capacity C) V) V)))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat)) (@ (@ (@ tptp.connected_a C) V) V)))
% 0.23/0.62 (assert (= tptp.connected_capacity tptp.connected_capacity))
% 0.23/0.62 (assert (= tptp.connected_a tptp.connected_a))
% 0.23/0.62 (assert (= tptp.dist_capacity tptp.dist_capacity))
% 0.23/0.62 (assert (= tptp.dist_a tptp.dist_a))
% 0.23/0.62 (assert (= tptp.isShor1936442771pacity tptp.isShor1936442771pacity))
% 0.23/0.62 (assert (= tptp.isShortestPath_a tptp.isShortestPath_a))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.dist_capacity C))) (let ((_let_2 (@ _let_1 U))) (=> (@ (@ _let_2 D1) W) (=> (@ (@ (@ _let_1 W) D2) V) (@ (@ _let_2 (@ (@ tptp.plus_plus_nat D1) D2)) V)))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.dist_a C))) (let ((_let_2 (@ _let_1 U))) (=> (@ (@ _let_2 D1) W) (=> (@ (@ (@ _let_1 W) D2) V) (@ (@ _let_2 (@ (@ tptp.plus_plus_nat D1) D2)) V)))))))
% 0.23/0.62 (assert (= tptp.connected_capacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat) (V4 tptp.nat)) (exists ((P tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isPath_capacity C2) U2) P) V4)))))
% 0.23/0.62 (assert (= tptp.connected_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat) (V4 tptp.nat)) (exists ((P tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isPath_a C2) U2) P) V4)))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isShor1936442771pacity C) U) P2) V) (@ (@ (@ (@ tptp.isPath_capacity C) U) P2) V))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isShortestPath_a C) U) P2) V) (@ (@ (@ (@ tptp.isPath_a C) U) P2) V))))
% 0.23/0.62 (assert (= tptp.connected_capacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (V4 tptp.nat) (V5 tptp.nat)) (exists ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_capacity C2) V4) D4) V5)))))
% 0.23/0.62 (assert (= tptp.connected_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (V4 tptp.nat) (V5 tptp.nat)) (exists ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_a C2) V4) D4) V5)))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D) V3) (@ (@ (@ tptp.connected_capacity C) V) V3))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D) V3) (@ (@ (@ tptp.connected_a C) V) V3))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (V tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity C) U) V) (not (forall ((P3 tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isShor1936442771pacity C) U) P3) V)))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (V tptp.nat)) (=> (@ (@ (@ tptp.connected_a C) U) V) (not (forall ((P3 tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isShortestPath_a C) U) P3) V)))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (Src tptp.nat) (V tptp.nat) (D tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity C) Src) V) (=> (= (@ (@ (@ tptp.min_dist_capacity C) Src) V) D) (=> (@ (@ tptp.ord_less_nat D3) D) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_capacity C) Src) V2) (= (@ (@ (@ tptp.min_dist_capacity C) Src) V2) D3))))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (Src tptp.nat) (V tptp.nat) (D tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a C) Src) V) (=> (= (@ (@ (@ tptp.min_dist_a C) Src) V) D) (=> (@ (@ tptp.ord_less_nat D3) D) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_a C) Src) V2) (= (@ (@ (@ tptp.min_dist_a C) Src) V2) D3))))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (Src tptp.nat) (V tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity C) Src) V) (=> (@ (@ tptp.ord_less_eq_nat D3) (@ (@ (@ tptp.min_dist_capacity C) Src) V)) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_capacity C) Src) V2) (= (@ (@ (@ tptp.min_dist_capacity C) Src) V2) D3)))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (Src tptp.nat) (V tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a C) Src) V) (=> (@ (@ tptp.ord_less_eq_nat D3) (@ (@ (@ tptp.min_dist_a C) Src) V)) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_a C) Src) V2) (= (@ (@ (@ tptp.min_dist_a C) Src) V2) D3)))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D) V3) (=> (forall ((D5 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D5) V3) (@ (@ tptp.ord_less_eq_nat D) D5))) (= (@ (@ (@ tptp.min_dist_capacity C) V) V3) D)))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D) V3) (=> (forall ((D5 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D5) V3) (@ (@ tptp.ord_less_eq_nat D) D5))) (= (@ (@ (@ tptp.min_dist_a C) V) V3) D)))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D) V3) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_capacity C) V) V3)) D))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D) V3) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_a C) V) V3)) D))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.min_dist_capacity C))) (let ((_let_2 (@ tptp.dist_capacity C))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ (@ _let_1 U) V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ (@ _let_1 W) V) D2))))))))
% 0.23/0.62 (assert (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.min_dist_a C))) (let ((_let_2 (@ tptp.dist_a C))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ (@ _let_1 U) V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ (@ _let_1 W) V) D2))))))))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isPath_a tptp.c2) tptp.ua) tptp.p2_a) tptp.t))
% 0.23/0.62 (assert (forall ((K tptp.nat) (P5 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat K) (@ tptp.ord_Least_nat P5)) (not (@ P5 K)))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P5 K) (@ (@ tptp.ord_less_eq_nat (@ tptp.ord_Least_nat P5)) K))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ tptp.connected_a tptp.c2) V) V3) (exists ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D4) V3)))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a tptp.c2) V) V3) (@ (@ (@ (@ tptp.dist_a tptp.c2) V) (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3)) V3))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (V tptp.nat)) (=> (@ (@ (@ tptp.connected_a tptp.c2) U) V) (not (forall ((P3 tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P3) V)))))))
% 0.23/0.62 (assert (forall ((S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) S) P2) T) (@ (@ (@ (@ tptp.isSimplePath_a tptp.c2) S) P2) T))))
% 0.23/0.62 (assert (forall ((U tptp.nat)) (= (@ (@ tptp.reachableNodes_a tptp.c2) U) (@ tptp.collect_nat (@ (@ tptp.connected_a tptp.c2) U)))))
% 0.23/0.62 (assert (forall ((Src tptp.nat) (V tptp.nat) (D tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a tptp.c2) Src) V) (=> (= (@ (@ (@ tptp.min_dist_a tptp.c2) Src) V) D) (=> (@ (@ tptp.ord_less_nat D3) D) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_a tptp.c2) Src) V2) (= (@ (@ (@ tptp.min_dist_a tptp.c2) Src) V2) D3))))))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (V3 tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.connected_a tptp.c2) V) V3) (=> (forall ((D6 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D6) V3) (=> (forall ((D7 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D7) V3) (@ (@ tptp.ord_less_eq_nat D6) D7))) (@ Q D6)))) (@ Q (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3))))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D) V3) (=> (forall ((D5 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D5) V3) (@ (@ tptp.ord_less_eq_nat D) D5))) (= (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3) D)))))
% 0.23/0.62 (assert (forall ((Src tptp.nat) (V tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a tptp.c2) Src) V) (=> (@ (@ tptp.ord_less_eq_nat D3) (@ (@ (@ tptp.min_dist_a tptp.c2) Src) V)) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_a tptp.c2) Src) V2) (= (@ (@ (@ tptp.min_dist_a tptp.c2) Src) V2) D3)))))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D) V3) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3)) D))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.min_dist_a tptp.c2))) (let ((_let_2 (@ tptp.dist_a tptp.c2))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ (@ _let_1 U) V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ (@ _let_1 W) V) D2))))))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.min_dist_a tptp.c2) U))) (let ((_let_2 (@ tptp.dist_a tptp.c2))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ _let_1 V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ _let_1 W) D1))))))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.dist_a tptp.c2))) (let ((_let_2 (@ _let_1 U))) (=> (@ (@ _let_2 D1) W) (=> (@ (@ (@ _let_1 W) D2) V) (@ (@ _let_2 (@ (@ tptp.plus_plus_nat D1) D2)) V)))))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (V tptp.nat)) (= (@ (@ (@ tptp.connected_a tptp.c2) U) V) (exists ((P tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P) V)))))
% 0.23/0.62 (assert (forall ((S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_a tptp.c2) S) P2) T) (exists ((P6 tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isSimplePath_a tptp.c2) S) P6) T)))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P2) V) (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P2) V))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P2) V) (and (@ (@ (@ (@ tptp.isSimplePath_a tptp.c2) U) P2) V) (= (@ tptp.size_s1990949619at_nat P2) (@ (@ (@ tptp.min_dist_a tptp.c2) U) V))))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D4) V3))))))
% 0.23/0.62 (assert (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D) V3) (exists ((P tptp.list_P559422087at_nat)) (and (@ (@ (@ (@ tptp.isPath_a tptp.c2) V) P) V3) (= (@ tptp.size_s1990949619at_nat P) D))))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P2) V) (@ (@ (@ (@ tptp.dist_a tptp.c2) U) (@ tptp.size_s1990949619at_nat P2)) V))))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P2) V) (and (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P2) V) (= (@ tptp.size_s1990949619at_nat P2) (@ (@ (@ tptp.min_dist_a tptp.c2) U) V))))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) X3)))
% 0.23/0.62 (assert (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P2) V) (and (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P2) V) (forall ((P4 tptp.list_P559422087at_nat)) (=> (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P4) V) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1990949619at_nat P2)) (@ tptp.size_s1990949619at_nat P4))))))))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isPath_a tptp.c2) tptp.s) tptp.p3) tptp.t))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isPath_a tptp.c2) tptp.u) tptp.p2) tptp.t))
% 0.23/0.62 (assert (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D) V3) (@ (@ (@ tptp.connected_a tptp.c2) V) V3))))
% 0.23/0.62 (assert (forall ((V tptp.nat)) (@ (@ (@ tptp.connected_a tptp.c2) V) V)))
% 0.23/0.62 (assert (@ (@ (@ (@ tptp.isPath_a tptp.c2) tptp.ua) tptp.p2_a) tptp.t))
% 0.23/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 0.23/0.62 (assert (= (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X2)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (= X3 Y3)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X3))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= X3 Y3) (@ (@ tptp.ord_less_eq_nat X3) Y3))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X3) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X3))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y3))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X3))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.23/0.62 (assert (forall ((Y3 tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (= (@ (@ tptp.ord_less_eq_nat X3) Y3) (= X3 Y3)))))
% 0.23/0.62 (assert (= (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) A2)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z2) (@ _let_1 Z2))))))
% 0.23/0.62 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P5 A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P5 B4) A4) (@ (@ P5 A4) B4))) (@ (@ P5 A) B)))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.23/0.62 (assert (= (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X3) Y3)) (or (@ (@ tptp.ord_less_nat Y3) X3) (= X3 Y3)))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (@ (@ P5 A4) B4))) (=> (forall ((A4 tptp.nat)) (@ (@ P5 A4) A4)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P5 B4) A4) (@ (@ P5 A4) B4))) (@ (@ P5 A) B))))))
% 0.23/0.62 (assert (= (lambda ((P7 (-> tptp.nat Bool))) (exists ((X4 tptp.nat)) (@ P7 X4))) (lambda ((P8 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P8 N2) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ P8 M2)))))))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (@ (@ tptp.ord_less_nat Y3) X3)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 0.23/0.62 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y3)) (=> (not (= X3 Y3)) (@ (@ tptp.ord_less_nat Y3) X3)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (P5 Bool)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (=> (@ (@ tptp.ord_less_nat Y3) X3) P5))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (= Y3 X3)))))
% 0.23/0.62 (assert (forall ((Y3 tptp.nat) (X3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y3) X3)) (= (not (@ (@ tptp.ord_less_nat X3) Y3)) (= X3 Y3)))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y2) X) (@ P5 Y2))) (@ P5 X))) (@ P5 A))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (@ (@ tptp.ord_less_nat Y3) X3)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (= X3 Y3)))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat)) (not (@ (@ tptp.ord_less_nat X3) X3))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y3) (= X3 Y3) (@ (@ tptp.ord_less_nat Y3) X3))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_nat Y3) Z2) (@ _let_1 Z2))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (@ (@ tptp.ord_less_nat Y3) X3)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (= X3 Y3)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (not (= X3 Y3)) (or (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_nat Y3) X3)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (= X3 Y3)) (=> (not (@ (@ tptp.ord_less_nat X3) Y3)) (@ (@ tptp.ord_less_nat Y3) X3)))))
% 0.23/0.62 (assert (forall ((X3 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X3) X_1))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (A tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ P5 A) (=> (forall ((X tptp.nat)) (=> (@ P5 X) (@ Q X))) (@ Q (@ tptp.ord_Least_nat P5))))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool))) (=> (exists ((X_12 tptp.nat)) (@ P5 X_12)) (@ P5 (@ tptp.ord_Least_nat P5)))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (exists ((X_12 tptp.nat)) (@ P5 X_12)) (=> (forall ((X tptp.nat)) (=> (@ P5 X) (@ Q X))) (@ Q (@ tptp.ord_Least_nat P5))))))
% 0.23/0.62 (assert (forall ((P5 (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P5 K) (@ P5 (@ tptp.ord_Least_nat P5)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 0.23/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 0.23/0.62 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (not (= A2 B2))))))
% 0.23/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A2) (= A2 B2)))))
% 0.23/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.23/0.62 (assert (not (@ (@ tptp.ord_less_nat (@ (@ (@ tptp.min_dist_capacity tptp.c) tptp.s) tptp.t)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1990949619at_nat tptp.p1a)) (@ tptp.size_s1990949619at_nat tptp.p2_a)))))
% 0.23/0.62 (set-info :filename cvc5---1.0.5_22049)
% 0.23/0.62 (check-sat-assuming ( true ))
% 0.23/0.62 ------- get file name : TPTP file name is ITP048^1
% 0.23/0.62 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22049.smt2...
% 1.05/1.26 --- Run --ho-elim --full-saturate-quant at 10...
% 1.05/1.26 % SZS status Theorem for ITP048^1
% 1.05/1.26 % SZS output start Proof for ITP048^1
% 1.05/1.26 (
% 1.05/1.26 (let ((_let_1 (@ tptp.size_s1990949619at_nat tptp.p2_a))) (let ((_let_2 (@ tptp.size_s1990949619at_nat tptp.p1a))) (let ((_let_3 (@ (@ tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.min_dist_capacity tptp.c))) (let ((_let_5 (@ _let_4 tptp.s))) (let ((_let_6 (@ _let_5 tptp.t))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat _let_6) _let_3)))) (let ((_let_8 (@ tptp.isPath_a tptp.c2))) (let ((_let_9 (@ (@ (@ _let_8 tptp.ua) tptp.p2_a) tptp.t))) (let ((_let_10 (= tptp.connected_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat) (V4 tptp.nat)) (exists ((P tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isPath_a C2) U2) P) V4)))))) (let ((_let_11 (= tptp.connected_capacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat) (V4 tptp.nat)) (exists ((P tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isPath_capacity C2) U2) P) V4)))))) (let ((_let_12 (= tptp.min_dist_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (V4 tptp.nat) (V5 tptp.nat)) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_a C2) V4) D4) V5))))))) (let ((_let_13 (= tptp.min_dist_capacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (V4 tptp.nat) (V5 tptp.nat)) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_capacity C2) V4) D4) V5))))))) (let ((_let_14 (= tptp.reachableNodes_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat)) (@ tptp.collect_nat (@ (@ tptp.connected_a C2) U2)))))) (let ((_let_15 (= tptp.reacha1693770334pacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat)) (@ tptp.collect_nat (@ (@ tptp.connected_capacity C2) U2)))))) (let ((_let_16 (= tptp.dist_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (V4 tptp.nat) (D4 tptp.nat) (V5 tptp.nat)) (exists ((P tptp.list_P559422087at_nat)) (and (@ (@ (@ (@ tptp.isPath_a C2) V4) P) V5) (= (@ tptp.size_s1990949619at_nat P) D4))))))) (let ((_let_17 (= tptp.dist_capacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (V4 tptp.nat) (D4 tptp.nat) (V5 tptp.nat)) (exists ((P tptp.list_P559422087at_nat)) (and (@ (@ (@ (@ tptp.isPath_capacity C2) V4) P) V5) (= (@ tptp.size_s1990949619at_nat P) D4))))))) (let ((_let_18 (= tptp.isShortestPath_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isPath_a C2) U2) P) V4) (= (@ tptp.size_s1990949619at_nat P) (@ (@ (@ tptp.min_dist_a C2) U2) V4))))))) (let ((_let_19 (= tptp.isShor1936442771pacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isPath_capacity C2) U2) P) V4) (= (@ tptp.size_s1990949619at_nat P) (@ (@ (@ tptp.min_dist_capacity C2) U2) V4))))))) (let ((_let_20 (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))) (let ((_let_21 (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (not (= M2 N2))))))) (let ((_let_22 (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (exists ((C2 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A2) C2))))))) (let ((_let_23 (@ tptp.isPath_capacity tptp.c))) (let ((_let_24 (@ _let_23 tptp.s))) (let ((_let_25 (@ (@ _let_24 tptp.p1a) tptp.va))) (let ((_let_26 (@ (@ _let_4 tptp.ua) tptp.t))) (let ((_let_27 (@ (@ tptp.ord_less_eq_nat _let_26) _let_1))) (let ((_let_28 (@ _let_5 tptp.ua))) (let ((_let_29 (@ (@ tptp.ord_less_nat _let_28) _let_2))) (let ((_let_30 (= _let_6 (@ (@ tptp.plus_plus_nat _let_28) _let_26)))) (let ((_let_31 (ho_179 k_178 k_228))) (let ((_let_32 (ho_179 k_178 k_227))) (let ((_let_33 (ho_120 k_119 _let_32))) (let ((_let_34 (ho_121 _let_33 _let_31))) (let ((_let_35 (ho_179 k_178 k_226))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (ho_121 _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_231))) (let ((_let_38 (ho_106 k_105 tptp.p1a))) (let ((_let_39 (= _let_38 _let_37))) (let ((_let_40 (ho_121 (ho_120 k_119 _let_31) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_232))) (let ((_let_41 (ho_106 k_105 tptp.p2_a))) (let ((_let_42 (= _let_41 _let_40))) (let ((_let_43 (ho_121 (ho_120 k_119 _let_34) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_322))) (let ((_let_44 (ho_121 (ho_120 k_119 _let_37) _let_40))) (let ((_let_45 (= _let_44 _let_43))) (let ((_let_46 (ho_121 (ho_120 k_119 _let_38) _let_41))) (let ((_let_47 (= _let_46 (ho_121 (ho_120 k_119 _let_35) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_322)))) (let ((_let_48 (0))) (let ((_let_49 (forall ((u |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|) (i |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (= (ho_115 v ii) (ite (= i ii) e (ho_115 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.nat tptp.nat Bool)|) (i |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat tptp.nat Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (e tptp.capacity) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_111 v ii) (ite (= i ii) e (ho_111 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (y |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_55 (forall ((u |u_(-> tptp.list_P559422087at_nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.list_P559422087at_nat)) (not (forall ((v |u_(-> tptp.list_P559422087at_nat tptp.nat Bool)|)) (not (forall ((ii tptp.list_P559422087at_nat)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_56 (forall ((x |u_(-> tptp.list_P559422087at_nat tptp.nat Bool)|) (y |u_(-> tptp.list_P559422087at_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.list_P559422087at_nat)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_57 (forall ((u |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|) (i |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (= (ho_108 v ii) (ite (= i ii) e (ho_108 u ii)))))))))) (let ((_let_58 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_59 (forall ((u |u_(-> tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|) (e |u_(-> tptp.list_P559422087at_nat tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_60 (forall ((x |u_(-> tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_61 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_62 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_63 (forall ((u |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.nat Bool)|) (i |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (= (ho_163 v ii) (ite (= i ii) e (ho_163 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (= (ho_163 x z) (ho_163 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> tptp.list_P559422087at_nat tptp.nat)|) (e tptp.nat) (i tptp.list_P559422087at_nat)) (not (forall ((v |u_(-> tptp.list_P559422087at_nat tptp.nat)|)) (not (forall ((ii tptp.list_P559422087at_nat)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> tptp.list_P559422087at_nat tptp.nat)|) (y |u_(-> tptp.list_P559422087at_nat tptp.nat)|)) (or (not (forall ((z tptp.list_P559422087at_nat)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_67 (forall ((u |u_(-> tptp.set_nat Bool)|) (e Bool) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_211 v ii) (ite (= i ii) e (ho_211 u ii)))))))))) (let ((_let_68 (forall ((x |u_(-> tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_211 x z) (ho_211 y z)))) (= x y))))) (let ((_let_69 (forall ((u |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.nat tptp.nat Bool)|) (i |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat tptp.nat Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_70 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_71 (forall ((u |u_(-> tptp.product_prod_nat_nat tptp.a)|) (e tptp.a) (i tptp.product_prod_nat_nat)) (not (forall ((v |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (not (forall ((ii tptp.product_prod_nat_nat)) (= (ho_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_72 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.a)|) (y |u_(-> tptp.product_prod_nat_nat tptp.a)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_73 (forall ((u |u_(-> tptp.nat _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|) (e |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_74 (forall ((x |u_(-> tptp.nat _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_75 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_76 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_79 (forall ((u |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat tptp.nat Bool)|) (i |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|)) (not (forall ((ii |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (= (ho_167 v ii) (ite (= i ii) e (ho_167 u ii)))))))))) (let ((_let_80 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.capacity)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.capacity)|)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_121 v ii) (ite (= i ii) e (ho_121 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> tptp.set_nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_208 v ii) (ite (= i ii) e (ho_208 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_87 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_88 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|) (e tptp.set_nat) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_230 v ii) (ite (= i ii) e (ho_230 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_230 x z) (ho_230 y z)))) (= x y))))) (let ((_let_91 (forall ((u |u_(-> tptp.nat _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|) (e |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_92 (forall ((x |u_(-> tptp.nat _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.product_prod_nat_nat tptp.a)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat)|) (e tptp.nat) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_179 v ii) (ite (= i ii) e (ho_179 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> tptp.nat tptp.set_nat Bool)|) (e |u_(-> tptp.set_nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_210 v ii) (ite (= i ii) e (ho_210 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_210 x z) (ho_210 y z)))) (= x y))))) (let ((_let_97 (forall ((BOUND_VARIABLE_27271 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_27024 tptp.nat) (BOUND_VARIABLE_27025 tptp.nat) (BOUND_VARIABLE_27026 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_100 BOUND_VARIABLE_27271) BOUND_VARIABLE_27024) BOUND_VARIABLE_27025) BOUND_VARIABLE_27026) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_27271) BOUND_VARIABLE_27024) P) BOUND_VARIABLE_27025)) (not (= BOUND_VARIABLE_27026 (ho_106 k_105 P)))))))))) (let ((_let_98 (forall ((BOUND_VARIABLE_27326 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_27006 tptp.nat) (BOUND_VARIABLE_27007 tptp.nat) (BOUND_VARIABLE_27008 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_112 BOUND_VARIABLE_27326) BOUND_VARIABLE_27006) BOUND_VARIABLE_27007) BOUND_VARIABLE_27008) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_27326) BOUND_VARIABLE_27006) P) BOUND_VARIABLE_27007)) (not (= BOUND_VARIABLE_27008 (ho_106 k_105 P)))))))))) (let ((_let_99 (forall ((BOUND_VARIABLE_27361 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26988 tptp.nat) (BOUND_VARIABLE_26989 tptp.nat) (BOUND_VARIABLE_26990 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_116 BOUND_VARIABLE_27361) BOUND_VARIABLE_26988) BOUND_VARIABLE_26989) BOUND_VARIABLE_26990) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_27361) BOUND_VARIABLE_26988) P) BOUND_VARIABLE_26989)) (not (= BOUND_VARIABLE_26990 (ho_106 k_105 P)))))))))) (let ((_let_100 (forall ((BOUND_VARIABLE_27384 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26970 tptp.nat) (BOUND_VARIABLE_26971 tptp.nat) (BOUND_VARIABLE_26972 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_117 BOUND_VARIABLE_27384) BOUND_VARIABLE_26970) BOUND_VARIABLE_26971) BOUND_VARIABLE_26972) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_27384) BOUND_VARIABLE_26970) P) BOUND_VARIABLE_26971)) (not (= BOUND_VARIABLE_26972 (ho_106 k_105 P)))))))))) (let ((_let_101 (forall ((BOUND_VARIABLE_26953 tptp.nat) (BOUND_VARIABLE_26954 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_26953 BOUND_VARIABLE_26954))) (= (ho_104 (ho_103 k_118 BOUND_VARIABLE_26953) BOUND_VARIABLE_26954) (or (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26954 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26953) C2))))) (not _let_1)) _let_1)))))) (let ((_let_102 (forall ((BOUND_VARIABLE_26938 tptp.nat) (BOUND_VARIABLE_26939 tptp.nat)) (= (ho_104 (ho_103 k_122 BOUND_VARIABLE_26938) BOUND_VARIABLE_26939) (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26939 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26938) C2))))) (not (= BOUND_VARIABLE_26938 BOUND_VARIABLE_26939))))))) (let ((_let_103 (forall ((BOUND_VARIABLE_26923 tptp.nat) (BOUND_VARIABLE_26924 tptp.nat)) (= (ho_104 (ho_103 k_123 BOUND_VARIABLE_26923) BOUND_VARIABLE_26924) (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26924 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26923) C2))))) (not (= BOUND_VARIABLE_26923 BOUND_VARIABLE_26924))))))) (let ((_let_104 (forall ((BOUND_VARIABLE_27454 |u_(-> tptp.nat Bool)|)) (= (ho_125 k_124 BOUND_VARIABLE_27454) (not (forall ((X4 tptp.nat)) (not (ho_104 BOUND_VARIABLE_27454 X4)))))))) (let ((_let_105 (forall ((BOUND_VARIABLE_27469 |u_(-> tptp.nat Bool)|)) (= (ho_125 k_126 BOUND_VARIABLE_27469) (not (forall ((N2 tptp.nat)) (or (not (ho_104 BOUND_VARIABLE_27469 N2)) (not (forall ((M2 tptp.nat) (BOUND_VARIABLE_17356 tptp.nat)) (or (not (= N2 (ho_121 (ho_120 k_119 M2) BOUND_VARIABLE_17356))) (= N2 M2) (not (ho_104 BOUND_VARIABLE_27469 M2)))))))))))) (let ((_let_106 (forall ((BOUND_VARIABLE_26892 tptp.nat) (BOUND_VARIABLE_26893 tptp.nat)) (= (= BOUND_VARIABLE_26892 BOUND_VARIABLE_26893) (ho_104 (ho_103 k_127 BOUND_VARIABLE_26892) BOUND_VARIABLE_26893))))) (let ((_let_107 (forall ((BOUND_VARIABLE_26873 tptp.nat) (BOUND_VARIABLE_26874 tptp.nat)) (= (ho_104 (ho_103 k_128 BOUND_VARIABLE_26873) BOUND_VARIABLE_26874) (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26873 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26874) C2))))) (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26874 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26873) C2)))))))))) (let ((_let_108 (forall ((BOUND_VARIABLE_26866 tptp.nat) (BOUND_VARIABLE_26867 tptp.nat)) (= (= BOUND_VARIABLE_26866 BOUND_VARIABLE_26867) (ho_104 (ho_103 k_129 BOUND_VARIABLE_26866) BOUND_VARIABLE_26867))))) (let ((_let_109 (forall ((BOUND_VARIABLE_26847 tptp.nat) (BOUND_VARIABLE_26848 tptp.nat)) (= (ho_104 (ho_103 k_130 BOUND_VARIABLE_26847) BOUND_VARIABLE_26848) (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26848 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26847) C2))))) (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26847 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26848) C2)))))))))) (let ((_let_110 (forall ((BOUND_VARIABLE_26840 tptp.nat) (BOUND_VARIABLE_26841 tptp.nat)) (= (= BOUND_VARIABLE_26840 BOUND_VARIABLE_26841) (ho_104 (ho_103 k_131 BOUND_VARIABLE_26840) BOUND_VARIABLE_26841))))) (let ((_let_111 (forall ((BOUND_VARIABLE_26821 tptp.nat) (BOUND_VARIABLE_26822 tptp.nat)) (= (ho_104 (ho_103 k_132 BOUND_VARIABLE_26821) BOUND_VARIABLE_26822) (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26822 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26821) C2))))) (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26821 (ho_121 (ho_120 k_119 BOUND_VARIABLE_26822) C2)))))))))) (let ((_let_112 (forall ((BOUND_VARIABLE_26805 tptp.nat) (BOUND_VARIABLE_26806 tptp.nat) (BOUND_VARIABLE_26807 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_133 BOUND_VARIABLE_26805) BOUND_VARIABLE_26806) BOUND_VARIABLE_26807) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26805) P) BOUND_VARIABLE_26806)) (not (= BOUND_VARIABLE_26807 (ho_106 k_105 P)))))))))) (let ((_let_113 (forall ((BOUND_VARIABLE_26789 tptp.nat) (BOUND_VARIABLE_26790 tptp.nat) (BOUND_VARIABLE_26791 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_135 BOUND_VARIABLE_26789) BOUND_VARIABLE_26790) BOUND_VARIABLE_26791) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26789) P) BOUND_VARIABLE_26790)) (not (= BOUND_VARIABLE_26791 (ho_106 k_105 P)))))))))) (let ((_let_114 (forall ((BOUND_VARIABLE_26773 tptp.nat) (BOUND_VARIABLE_26774 tptp.nat) (BOUND_VARIABLE_26775 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_136 BOUND_VARIABLE_26773) BOUND_VARIABLE_26774) BOUND_VARIABLE_26775) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26773) P) BOUND_VARIABLE_26774)) (not (= BOUND_VARIABLE_26775 (ho_106 k_105 P)))))))))) (let ((_let_115 (forall ((BOUND_VARIABLE_26757 tptp.nat) (BOUND_VARIABLE_26758 tptp.nat) (BOUND_VARIABLE_26759 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_137 BOUND_VARIABLE_26757) BOUND_VARIABLE_26758) BOUND_VARIABLE_26759) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26757) P) BOUND_VARIABLE_26758)) (not (= BOUND_VARIABLE_26759 (ho_106 k_105 P)))))))))) (let ((_let_116 (forall ((BOUND_VARIABLE_26741 tptp.nat) (BOUND_VARIABLE_26742 tptp.nat) (BOUND_VARIABLE_26743 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_138 BOUND_VARIABLE_26741) BOUND_VARIABLE_26742) BOUND_VARIABLE_26743) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26741) P) BOUND_VARIABLE_26742)) (not (= BOUND_VARIABLE_26743 (ho_106 k_105 P)))))))))) (let ((_let_117 (forall ((BOUND_VARIABLE_26725 tptp.nat) (BOUND_VARIABLE_26726 tptp.nat) (BOUND_VARIABLE_26727 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_139 BOUND_VARIABLE_26725) BOUND_VARIABLE_26726) BOUND_VARIABLE_26727) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26725) P) BOUND_VARIABLE_26726)) (not (= BOUND_VARIABLE_26727 (ho_106 k_105 P)))))))))) (let ((_let_118 (forall ((BOUND_VARIABLE_26709 tptp.nat) (BOUND_VARIABLE_26710 tptp.nat) (BOUND_VARIABLE_26711 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_140 BOUND_VARIABLE_26709) BOUND_VARIABLE_26710) BOUND_VARIABLE_26711) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26709) P) BOUND_VARIABLE_26710)) (not (= BOUND_VARIABLE_26711 (ho_106 k_105 P)))))))))) (let ((_let_119 (forall ((BOUND_VARIABLE_26693 tptp.nat) (BOUND_VARIABLE_26694 tptp.nat) (BOUND_VARIABLE_26695 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_141 BOUND_VARIABLE_26693) BOUND_VARIABLE_26694) BOUND_VARIABLE_26695) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26693) P) BOUND_VARIABLE_26694)) (not (= BOUND_VARIABLE_26695 (ho_106 k_105 P)))))))))) (let ((_let_120 (forall ((BOUND_VARIABLE_26677 tptp.nat) (BOUND_VARIABLE_26678 tptp.nat) (BOUND_VARIABLE_26679 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_142 BOUND_VARIABLE_26677) BOUND_VARIABLE_26678) BOUND_VARIABLE_26679) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26677) P) BOUND_VARIABLE_26678)) (not (= BOUND_VARIABLE_26679 (ho_106 k_105 P)))))))))) (let ((_let_121 (forall ((BOUND_VARIABLE_26661 tptp.nat) (BOUND_VARIABLE_26662 tptp.nat) (BOUND_VARIABLE_26663 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_143 BOUND_VARIABLE_26661) BOUND_VARIABLE_26662) BOUND_VARIABLE_26663) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26661) P) BOUND_VARIABLE_26662)) (not (= BOUND_VARIABLE_26663 (ho_106 k_105 P)))))))))) (let ((_let_122 (forall ((BOUND_VARIABLE_26645 tptp.nat) (BOUND_VARIABLE_26646 tptp.nat) (BOUND_VARIABLE_26647 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_144 BOUND_VARIABLE_26645) BOUND_VARIABLE_26646) BOUND_VARIABLE_26647) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26645) P) BOUND_VARIABLE_26646)) (not (= BOUND_VARIABLE_26647 (ho_106 k_105 P)))))))))) (let ((_let_123 (forall ((BOUND_VARIABLE_26629 tptp.nat) (BOUND_VARIABLE_26630 tptp.nat) (BOUND_VARIABLE_26631 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_145 BOUND_VARIABLE_26629) BOUND_VARIABLE_26630) BOUND_VARIABLE_26631) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26629) P) BOUND_VARIABLE_26630)) (not (= BOUND_VARIABLE_26631 (ho_106 k_105 P)))))))))) (let ((_let_124 (forall ((BOUND_VARIABLE_26613 tptp.nat) (BOUND_VARIABLE_26614 tptp.nat) (BOUND_VARIABLE_26615 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_146 BOUND_VARIABLE_26613) BOUND_VARIABLE_26614) BOUND_VARIABLE_26615) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26613) P) BOUND_VARIABLE_26614)) (not (= BOUND_VARIABLE_26615 (ho_106 k_105 P)))))))))) (let ((_let_125 (forall ((BOUND_VARIABLE_26597 tptp.nat) (BOUND_VARIABLE_26598 tptp.nat) (BOUND_VARIABLE_26599 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_147 BOUND_VARIABLE_26597) BOUND_VARIABLE_26598) BOUND_VARIABLE_26599) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26597) P) BOUND_VARIABLE_26598)) (not (= BOUND_VARIABLE_26599 (ho_106 k_105 P)))))))))) (let ((_let_126 (forall ((BOUND_VARIABLE_26581 tptp.nat) (BOUND_VARIABLE_26582 tptp.nat) (BOUND_VARIABLE_26583 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_148 BOUND_VARIABLE_26581) BOUND_VARIABLE_26582) BOUND_VARIABLE_26583) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26581) P) BOUND_VARIABLE_26582)) (not (= BOUND_VARIABLE_26583 (ho_106 k_105 P)))))))))) (let ((_let_127 (forall ((BOUND_VARIABLE_26565 tptp.nat) (BOUND_VARIABLE_26566 tptp.nat) (BOUND_VARIABLE_26567 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_149 BOUND_VARIABLE_26565) BOUND_VARIABLE_26566) BOUND_VARIABLE_26567) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26565) P) BOUND_VARIABLE_26566)) (not (= BOUND_VARIABLE_26567 (ho_106 k_105 P)))))))))) (let ((_let_128 (forall ((BOUND_VARIABLE_26549 tptp.nat) (BOUND_VARIABLE_26550 tptp.nat) (BOUND_VARIABLE_26551 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_150 BOUND_VARIABLE_26549) BOUND_VARIABLE_26550) BOUND_VARIABLE_26551) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26549) P) BOUND_VARIABLE_26550)) (not (= BOUND_VARIABLE_26551 (ho_106 k_105 P)))))))))) (let ((_let_129 (forall ((BOUND_VARIABLE_26533 tptp.nat) (BOUND_VARIABLE_26534 tptp.nat) (BOUND_VARIABLE_26535 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_151 BOUND_VARIABLE_26533) BOUND_VARIABLE_26534) BOUND_VARIABLE_26535) (not (forall ((BOUND_VARIABLE_13752 tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 k_134) BOUND_VARIABLE_26533) BOUND_VARIABLE_13752) BOUND_VARIABLE_26534)) (not (= BOUND_VARIABLE_26535 (ho_106 k_105 BOUND_VARIABLE_13752)))))))))) (let ((_let_130 (forall ((BOUND_VARIABLE_27901 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26516 tptp.nat) (BOUND_VARIABLE_26517 tptp.nat) (BOUND_VARIABLE_26518 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_152 BOUND_VARIABLE_27901) BOUND_VARIABLE_26516) BOUND_VARIABLE_26517) BOUND_VARIABLE_26518) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_27901) BOUND_VARIABLE_26516) P) BOUND_VARIABLE_26517)) (not (= BOUND_VARIABLE_26518 (ho_106 k_105 P)))))))))) (let ((_let_131 (forall ((BOUND_VARIABLE_27924 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26498 tptp.nat) (BOUND_VARIABLE_26499 tptp.nat) (BOUND_VARIABLE_26500 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_153 BOUND_VARIABLE_27924) BOUND_VARIABLE_26498) BOUND_VARIABLE_26499) BOUND_VARIABLE_26500) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_27924) BOUND_VARIABLE_26498) P) BOUND_VARIABLE_26499)) (not (= BOUND_VARIABLE_26500 (ho_106 k_105 P)))))))))) (let ((_let_132 (forall ((BOUND_VARIABLE_27947 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26480 tptp.nat) (BOUND_VARIABLE_26481 tptp.nat) (BOUND_VARIABLE_26482 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_154 BOUND_VARIABLE_27947) BOUND_VARIABLE_26480) BOUND_VARIABLE_26481) BOUND_VARIABLE_26482) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_27947) BOUND_VARIABLE_26480) P) BOUND_VARIABLE_26481)) (not (= BOUND_VARIABLE_26482 (ho_106 k_105 P)))))))))) (let ((_let_133 (forall ((BOUND_VARIABLE_27970 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26462 tptp.nat) (BOUND_VARIABLE_26463 tptp.nat) (BOUND_VARIABLE_26464 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_155 BOUND_VARIABLE_27970) BOUND_VARIABLE_26462) BOUND_VARIABLE_26463) BOUND_VARIABLE_26464) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_27970) BOUND_VARIABLE_26462) P) BOUND_VARIABLE_26463)) (not (= BOUND_VARIABLE_26464 (ho_106 k_105 P)))))))))) (let ((_let_134 (forall ((BOUND_VARIABLE_27993 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26444 tptp.nat) (BOUND_VARIABLE_26445 tptp.nat) (BOUND_VARIABLE_26446 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_156 BOUND_VARIABLE_27993) BOUND_VARIABLE_26444) BOUND_VARIABLE_26445) BOUND_VARIABLE_26446) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_27993) BOUND_VARIABLE_26444) P) BOUND_VARIABLE_26445)) (not (= BOUND_VARIABLE_26446 (ho_106 k_105 P)))))))))) (let ((_let_135 (forall ((BOUND_VARIABLE_28016 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26426 tptp.nat) (BOUND_VARIABLE_26427 tptp.nat) (BOUND_VARIABLE_26428 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_157 BOUND_VARIABLE_28016) BOUND_VARIABLE_26426) BOUND_VARIABLE_26427) BOUND_VARIABLE_26428) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28016) BOUND_VARIABLE_26426) P) BOUND_VARIABLE_26427)) (not (= BOUND_VARIABLE_26428 (ho_106 k_105 P)))))))))) (let ((_let_136 (forall ((BOUND_VARIABLE_28039 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26408 tptp.nat) (BOUND_VARIABLE_26409 tptp.nat) (BOUND_VARIABLE_26410 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_158 BOUND_VARIABLE_28039) BOUND_VARIABLE_26408) BOUND_VARIABLE_26409) BOUND_VARIABLE_26410) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28039) BOUND_VARIABLE_26408) P) BOUND_VARIABLE_26409)) (not (= BOUND_VARIABLE_26410 (ho_106 k_105 P)))))))))) (let ((_let_137 (forall ((BOUND_VARIABLE_28062 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26390 tptp.nat) (BOUND_VARIABLE_26391 tptp.nat) (BOUND_VARIABLE_26392 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_159 BOUND_VARIABLE_28062) BOUND_VARIABLE_26390) BOUND_VARIABLE_26391) BOUND_VARIABLE_26392) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28062) BOUND_VARIABLE_26390) P) BOUND_VARIABLE_26391)) (not (= BOUND_VARIABLE_26392 (ho_106 k_105 P)))))))))) (let ((_let_138 (forall ((BOUND_VARIABLE_28085 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26372 tptp.nat) (BOUND_VARIABLE_26373 tptp.nat) (BOUND_VARIABLE_26374 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_160 BOUND_VARIABLE_28085) BOUND_VARIABLE_26372) BOUND_VARIABLE_26373) BOUND_VARIABLE_26374) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28085) BOUND_VARIABLE_26372) P) BOUND_VARIABLE_26373)) (not (= BOUND_VARIABLE_26374 (ho_106 k_105 P)))))))))) (let ((_let_139 (forall ((BOUND_VARIABLE_26353 tptp.nat) (BOUND_VARIABLE_28108 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26355 tptp.nat) (BOUND_VARIABLE_26356 tptp.nat)) (= (ho_104 (ho_103 (ho_163 (ho_162 k_161 BOUND_VARIABLE_26353) BOUND_VARIABLE_28108) BOUND_VARIABLE_26355) BOUND_VARIABLE_26356) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28108) BOUND_VARIABLE_26353) P) BOUND_VARIABLE_26355)) (not (= BOUND_VARIABLE_26356 (ho_106 k_105 P)))))))))) (let ((_let_140 (forall ((BOUND_VARIABLE_28139 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26336 tptp.nat) (BOUND_VARIABLE_26337 tptp.nat) (BOUND_VARIABLE_26338 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_164 BOUND_VARIABLE_28139) BOUND_VARIABLE_26336) BOUND_VARIABLE_26337) BOUND_VARIABLE_26338) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28139) BOUND_VARIABLE_26336) P) BOUND_VARIABLE_26337)) (not (= BOUND_VARIABLE_26338 (ho_106 k_105 P)))))))))) (let ((_let_141 (forall ((BOUND_VARIABLE_26317 tptp.nat) (BOUND_VARIABLE_28162 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26319 tptp.nat) (BOUND_VARIABLE_26320 tptp.nat)) (= (ho_104 (ho_103 (ho_167 (ho_166 k_165 BOUND_VARIABLE_26317) BOUND_VARIABLE_28162) BOUND_VARIABLE_26319) BOUND_VARIABLE_26320) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28162) BOUND_VARIABLE_26317) P) BOUND_VARIABLE_26319)) (not (= BOUND_VARIABLE_26320 (ho_106 k_105 P)))))))))) (let ((_let_142 (forall ((BOUND_VARIABLE_28193 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26300 tptp.nat) (BOUND_VARIABLE_26301 tptp.nat) (BOUND_VARIABLE_26302 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_168 BOUND_VARIABLE_28193) BOUND_VARIABLE_26300) BOUND_VARIABLE_26301) BOUND_VARIABLE_26302) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28193) BOUND_VARIABLE_26300) P) BOUND_VARIABLE_26301)) (not (= BOUND_VARIABLE_26302 (ho_106 k_105 P)))))))))) (let ((_let_143 (forall ((BOUND_VARIABLE_28216 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26282 tptp.nat) (BOUND_VARIABLE_26283 tptp.nat) (BOUND_VARIABLE_26284 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_169 BOUND_VARIABLE_28216) BOUND_VARIABLE_26282) BOUND_VARIABLE_26283) BOUND_VARIABLE_26284) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28216) BOUND_VARIABLE_26282) P) BOUND_VARIABLE_26283)) (not (= BOUND_VARIABLE_26284 (ho_106 k_105 P)))))))))) (let ((_let_144 (forall ((BOUND_VARIABLE_28239 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26264 tptp.nat) (BOUND_VARIABLE_26265 tptp.nat) (BOUND_VARIABLE_26266 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_170 BOUND_VARIABLE_28239) BOUND_VARIABLE_26264) BOUND_VARIABLE_26265) BOUND_VARIABLE_26266) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28239) BOUND_VARIABLE_26264) P) BOUND_VARIABLE_26265)) (not (= BOUND_VARIABLE_26266 (ho_106 k_105 P)))))))))) (let ((_let_145 (forall ((BOUND_VARIABLE_28262 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26246 tptp.nat) (BOUND_VARIABLE_26247 tptp.nat) (BOUND_VARIABLE_26248 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_171 BOUND_VARIABLE_28262) BOUND_VARIABLE_26246) BOUND_VARIABLE_26247) BOUND_VARIABLE_26248) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28262) BOUND_VARIABLE_26246) P) BOUND_VARIABLE_26247)) (not (= BOUND_VARIABLE_26248 (ho_106 k_105 P)))))))))) (let ((_let_146 (forall ((BOUND_VARIABLE_28285 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26228 tptp.nat) (BOUND_VARIABLE_26229 tptp.nat) (BOUND_VARIABLE_26230 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_172 BOUND_VARIABLE_28285) BOUND_VARIABLE_26228) BOUND_VARIABLE_26229) BOUND_VARIABLE_26230) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28285) BOUND_VARIABLE_26228) P) BOUND_VARIABLE_26229)) (not (= BOUND_VARIABLE_26230 (ho_106 k_105 P)))))))))) (let ((_let_147 (forall ((BOUND_VARIABLE_28308 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26210 tptp.nat) (BOUND_VARIABLE_26211 tptp.nat) (BOUND_VARIABLE_26212 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_173 BOUND_VARIABLE_28308) BOUND_VARIABLE_26210) BOUND_VARIABLE_26211) BOUND_VARIABLE_26212) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28308) BOUND_VARIABLE_26210) P) BOUND_VARIABLE_26211)) (not (= BOUND_VARIABLE_26212 (ho_106 k_105 P)))))))))) (let ((_let_148 (forall ((BOUND_VARIABLE_28330 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26196 tptp.nat) (BOUND_VARIABLE_26197 tptp.nat)) (= (ho_104 (ho_103 (ho_163 k_174 BOUND_VARIABLE_28330) BOUND_VARIABLE_26196) BOUND_VARIABLE_26197) (not (forall ((P tptp.list_P559422087at_nat)) (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28330) BOUND_VARIABLE_26196) P) BOUND_VARIABLE_26197)))))))) (let ((_let_149 (forall ((BOUND_VARIABLE_28348 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26182 tptp.nat) (BOUND_VARIABLE_26183 tptp.nat)) (= (ho_104 (ho_103 (ho_163 k_175 BOUND_VARIABLE_28348) BOUND_VARIABLE_26182) BOUND_VARIABLE_26183) (not (forall ((P tptp.list_P559422087at_nat)) (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28348) BOUND_VARIABLE_26182) P) BOUND_VARIABLE_26183)))))))) (let ((_let_150 (forall ((BOUND_VARIABLE_28366 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26168 tptp.nat) (BOUND_VARIABLE_26169 tptp.nat)) (= (ho_104 (ho_103 (ho_167 k_176 BOUND_VARIABLE_28366) BOUND_VARIABLE_26168) BOUND_VARIABLE_26169) (not (forall ((P tptp.list_P559422087at_nat)) (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28366) BOUND_VARIABLE_26168) P) BOUND_VARIABLE_26169)))))))) (let ((_let_151 (forall ((BOUND_VARIABLE_28384 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26154 tptp.nat) (BOUND_VARIABLE_26155 tptp.nat)) (= (ho_104 (ho_103 (ho_167 k_177 BOUND_VARIABLE_28384) BOUND_VARIABLE_26154) BOUND_VARIABLE_26155) (not (forall ((P tptp.list_P559422087at_nat)) (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28384) BOUND_VARIABLE_26154) P) BOUND_VARIABLE_26155)))))))) (let ((_let_152 (forall ((BOUND_VARIABLE_28399 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26107 tptp.nat) (BOUND_VARIABLE_26108 tptp.list_P559422087at_nat) (BOUND_VARIABLE_26109 tptp.nat)) (= (ho_104 (ho_110 (ho_109 (ho_108 k_181 BOUND_VARIABLE_28399) BOUND_VARIABLE_26107) BOUND_VARIABLE_26108) BOUND_VARIABLE_26109) (and (ho_104 (ho_110 (ho_109 (ho_108 k_180 BOUND_VARIABLE_28399) BOUND_VARIABLE_26107) BOUND_VARIABLE_26108) BOUND_VARIABLE_26109) (= (ho_179 k_178 (ho_103 (ho_102 (ho_101 k_100 BOUND_VARIABLE_28399) BOUND_VARIABLE_26107) BOUND_VARIABLE_26109)) (ho_106 k_105 BOUND_VARIABLE_26108))))))) (let ((_let_153 (forall ((BOUND_VARIABLE_28429 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26060 tptp.nat) (BOUND_VARIABLE_26061 tptp.list_P559422087at_nat) (BOUND_VARIABLE_26062 tptp.nat)) (= (ho_104 (ho_110 (ho_109 (ho_115 k_183 BOUND_VARIABLE_28429) BOUND_VARIABLE_26060) BOUND_VARIABLE_26061) BOUND_VARIABLE_26062) (and (ho_104 (ho_110 (ho_109 (ho_115 k_182 BOUND_VARIABLE_28429) BOUND_VARIABLE_26060) BOUND_VARIABLE_26061) BOUND_VARIABLE_26062) (= (ho_179 k_178 (ho_103 (ho_102 (ho_113 k_112 BOUND_VARIABLE_28429) BOUND_VARIABLE_26060) BOUND_VARIABLE_26062)) (ho_106 k_105 BOUND_VARIABLE_26061))))))) (let ((_let_154 (forall ((BOUND_VARIABLE_28458 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_26042 tptp.nat) (BOUND_VARIABLE_26043 tptp.nat) (BOUND_VARIABLE_26044 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_184 BOUND_VARIABLE_28458) BOUND_VARIABLE_26042) BOUND_VARIABLE_26043) BOUND_VARIABLE_26044) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28458) BOUND_VARIABLE_26042) P) BOUND_VARIABLE_26043)) (not (= BOUND_VARIABLE_26044 (ho_106 k_105 P)))))))))) (let ((_let_155 (forall ((BOUND_VARIABLE_28481 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_26024 tptp.nat) (BOUND_VARIABLE_26025 tptp.nat) (BOUND_VARIABLE_26026 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_185 BOUND_VARIABLE_28481) BOUND_VARIABLE_26024) BOUND_VARIABLE_26025) BOUND_VARIABLE_26026) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28481) BOUND_VARIABLE_26024) P) BOUND_VARIABLE_26025)) (not (= BOUND_VARIABLE_26026 (ho_106 k_105 P)))))))))) (let ((_let_156 (forall ((BOUND_VARIABLE_26007 tptp.nat) (BOUND_VARIABLE_26008 tptp.nat) (BOUND_VARIABLE_26009 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_186 BOUND_VARIABLE_26007) BOUND_VARIABLE_26008) BOUND_VARIABLE_26009) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_26007) P) BOUND_VARIABLE_26008)) (not (= BOUND_VARIABLE_26009 (ho_106 k_105 P)))))))))) (let ((_let_157 (forall ((BOUND_VARIABLE_28524 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_25990 tptp.nat) (BOUND_VARIABLE_25991 tptp.nat) (BOUND_VARIABLE_25992 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_188 BOUND_VARIABLE_28524) BOUND_VARIABLE_25990) BOUND_VARIABLE_25991) BOUND_VARIABLE_25992) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28524) BOUND_VARIABLE_25990) P) BOUND_VARIABLE_25991)) (not (= BOUND_VARIABLE_25992 (ho_106 k_105 P)))))))))) (let ((_let_158 (forall ((BOUND_VARIABLE_28547 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_25972 tptp.nat) (BOUND_VARIABLE_25973 tptp.nat) (BOUND_VARIABLE_25974 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_189 BOUND_VARIABLE_28547) BOUND_VARIABLE_25972) BOUND_VARIABLE_25973) BOUND_VARIABLE_25974) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28547) BOUND_VARIABLE_25972) P) BOUND_VARIABLE_25973)) (not (= BOUND_VARIABLE_25974 (ho_106 k_105 P)))))))))) (let ((_let_159 (forall ((BOUND_VARIABLE_28570 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_25954 tptp.nat) (BOUND_VARIABLE_25955 tptp.nat) (BOUND_VARIABLE_25956 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_190 BOUND_VARIABLE_28570) BOUND_VARIABLE_25954) BOUND_VARIABLE_25955) BOUND_VARIABLE_25956) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28570) BOUND_VARIABLE_25954) P) BOUND_VARIABLE_25955)) (not (= BOUND_VARIABLE_25956 (ho_106 k_105 P)))))))))) (let ((_let_160 (forall ((BOUND_VARIABLE_28593 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_25936 tptp.nat) (BOUND_VARIABLE_25937 tptp.nat) (BOUND_VARIABLE_25938 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_191 BOUND_VARIABLE_28593) BOUND_VARIABLE_25936) BOUND_VARIABLE_25937) BOUND_VARIABLE_25938) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28593) BOUND_VARIABLE_25936) P) BOUND_VARIABLE_25937)) (not (= BOUND_VARIABLE_25938 (ho_106 k_105 P)))))))))) (let ((_let_161 (forall ((BOUND_VARIABLE_28615 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_25918 tptp.nat) (BOUND_VARIABLE_25919 tptp.nat) (BOUND_VARIABLE_25920 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_192 BOUND_VARIABLE_28615) BOUND_VARIABLE_25918) BOUND_VARIABLE_25919) BOUND_VARIABLE_25920) (not (forall ((BOUND_VARIABLE_23305 tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28615) BOUND_VARIABLE_25918) BOUND_VARIABLE_23305) BOUND_VARIABLE_25919)) (not (= BOUND_VARIABLE_25920 (ho_106 k_105 BOUND_VARIABLE_23305)))))))))) (let ((_let_162 (forall ((BOUND_VARIABLE_28639 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_25900 tptp.nat) (BOUND_VARIABLE_25901 tptp.nat) (BOUND_VARIABLE_25902 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_193 BOUND_VARIABLE_28639) BOUND_VARIABLE_25900) BOUND_VARIABLE_25901) BOUND_VARIABLE_25902) (not (forall ((BOUND_VARIABLE_23190 tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28639) BOUND_VARIABLE_25900) BOUND_VARIABLE_23190) BOUND_VARIABLE_25901)) (not (= BOUND_VARIABLE_25902 (ho_106 k_105 BOUND_VARIABLE_23190)))))))))) (let ((_let_163 (forall ((BOUND_VARIABLE_25883 tptp.nat) (BOUND_VARIABLE_25884 tptp.nat) (BOUND_VARIABLE_25885 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_194 BOUND_VARIABLE_25883) BOUND_VARIABLE_25884) BOUND_VARIABLE_25885) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25883) P) BOUND_VARIABLE_25884)) (not (= BOUND_VARIABLE_25885 (ho_106 k_105 P)))))))))) (let ((_let_164 (forall ((BOUND_VARIABLE_28682 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_25866 tptp.nat) (BOUND_VARIABLE_25867 tptp.nat) (BOUND_VARIABLE_25868 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_101 k_195 BOUND_VARIABLE_28682) BOUND_VARIABLE_25866) BOUND_VARIABLE_25867) BOUND_VARIABLE_25868) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28682) BOUND_VARIABLE_25866) P) BOUND_VARIABLE_25867)) (not (= BOUND_VARIABLE_25868 (ho_106 k_105 P)))))))))) (let ((_let_165 (forall ((BOUND_VARIABLE_28705 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_25848 tptp.nat) (BOUND_VARIABLE_25849 tptp.nat) (BOUND_VARIABLE_25850 tptp.nat)) (= (ho_104 (ho_103 (ho_102 (ho_113 k_196 BOUND_VARIABLE_28705) BOUND_VARIABLE_25848) BOUND_VARIABLE_25849) BOUND_VARIABLE_25850) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28705) BOUND_VARIABLE_25848) P) BOUND_VARIABLE_25849)) (not (= BOUND_VARIABLE_25850 (ho_106 k_105 P)))))))))) (let ((_let_166 (forall ((BOUND_VARIABLE_28728 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_25823 tptp.nat) (BOUND_VARIABLE_25824 tptp.list_P559422087at_nat) (BOUND_VARIABLE_25825 tptp.nat)) (= (ho_104 (ho_110 (ho_109 (ho_108 k_197 BOUND_VARIABLE_28728) BOUND_VARIABLE_25823) BOUND_VARIABLE_25824) BOUND_VARIABLE_25825) (and (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28728) BOUND_VARIABLE_25823) BOUND_VARIABLE_25824) BOUND_VARIABLE_25825) (forall ((P4 tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28728) BOUND_VARIABLE_25823) P4) BOUND_VARIABLE_25825)) (not (forall ((C2 tptp.nat)) (not (= (ho_121 (ho_120 k_119 (ho_106 k_105 BOUND_VARIABLE_25824)) C2) (ho_106 k_105 P4)))))))))))) (let ((_let_167 (forall ((BOUND_VARIABLE_28755 |u_(-> tptp.product_prod_nat_nat tptp.a)|) (BOUND_VARIABLE_25778 tptp.nat) (BOUND_VARIABLE_25779 tptp.list_P559422087at_nat) (BOUND_VARIABLE_25780 tptp.nat)) (= (ho_104 (ho_110 (ho_109 (ho_108 k_198 BOUND_VARIABLE_28755) BOUND_VARIABLE_25778) BOUND_VARIABLE_25779) BOUND_VARIABLE_25780) (and (ho_104 (ho_110 (ho_109 (ho_108 k_107 BOUND_VARIABLE_28755) BOUND_VARIABLE_25778) BOUND_VARIABLE_25779) BOUND_VARIABLE_25780) (= (ho_179 k_178 (ho_103 (ho_102 (ho_101 k_116 BOUND_VARIABLE_28755) BOUND_VARIABLE_25778) BOUND_VARIABLE_25780)) (ho_106 k_105 BOUND_VARIABLE_25779))))))) (let ((_let_168 (forall ((BOUND_VARIABLE_28783 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_25753 tptp.nat) (BOUND_VARIABLE_25754 tptp.list_P559422087at_nat) (BOUND_VARIABLE_25755 tptp.nat)) (= (ho_104 (ho_110 (ho_109 (ho_115 k_199 BOUND_VARIABLE_28783) BOUND_VARIABLE_25753) BOUND_VARIABLE_25754) BOUND_VARIABLE_25755) (and (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28783) BOUND_VARIABLE_25753) BOUND_VARIABLE_25754) BOUND_VARIABLE_25755) (forall ((P4 tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28783) BOUND_VARIABLE_25753) P4) BOUND_VARIABLE_25755)) (not (forall ((C2 tptp.nat)) (not (= (ho_121 (ho_120 k_119 (ho_106 k_105 BOUND_VARIABLE_25754)) C2) (ho_106 k_105 P4)))))))))))) (let ((_let_169 (forall ((BOUND_VARIABLE_28810 |u_(-> tptp.product_prod_nat_nat tptp.capacity)|) (BOUND_VARIABLE_25708 tptp.nat) (BOUND_VARIABLE_25709 tptp.list_P559422087at_nat) (BOUND_VARIABLE_25710 tptp.nat)) (= (ho_104 (ho_110 (ho_109 (ho_115 k_200 BOUND_VARIABLE_28810) BOUND_VARIABLE_25708) BOUND_VARIABLE_25709) BOUND_VARIABLE_25710) (and (ho_104 (ho_110 (ho_109 (ho_115 k_114 BOUND_VARIABLE_28810) BOUND_VARIABLE_25708) BOUND_VARIABLE_25709) BOUND_VARIABLE_25710) (= (ho_179 k_178 (ho_103 (ho_102 (ho_113 k_117 BOUND_VARIABLE_28810) BOUND_VARIABLE_25708) BOUND_VARIABLE_25710)) (ho_106 k_105 BOUND_VARIABLE_25709))))))) (let ((_let_170 (forall ((BOUND_VARIABLE_25691 tptp.nat) (BOUND_VARIABLE_25692 tptp.nat) (BOUND_VARIABLE_25693 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_201 BOUND_VARIABLE_25691) BOUND_VARIABLE_25692) BOUND_VARIABLE_25693) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25691) P) BOUND_VARIABLE_25692)) (not (= BOUND_VARIABLE_25693 (ho_106 k_105 P)))))))))) (let ((_let_171 (forall ((BOUND_VARIABLE_25675 tptp.nat) (BOUND_VARIABLE_25676 tptp.nat) (BOUND_VARIABLE_25677 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_202 BOUND_VARIABLE_25675) BOUND_VARIABLE_25676) BOUND_VARIABLE_25677) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25675) P) BOUND_VARIABLE_25676)) (not (= BOUND_VARIABLE_25677 (ho_106 k_105 P)))))))))) (let ((_let_172 (forall ((BOUND_VARIABLE_25667 tptp.nat) (BOUND_VARIABLE_25668 tptp.nat)) (= (ho_121 (ho_120 k_203 BOUND_VARIABLE_25667) BOUND_VARIABLE_25668) (ho_121 (ho_120 k_119 BOUND_VARIABLE_25668) BOUND_VARIABLE_25667))))) (let ((_let_173 (forall ((BOUND_VARIABLE_25655 tptp.nat) (BOUND_VARIABLE_25656 tptp.nat)) (= (ho_104 (ho_103 k_204 BOUND_VARIABLE_25655) BOUND_VARIABLE_25656) (not (forall ((K2 tptp.nat)) (not (= BOUND_VARIABLE_25656 (ho_121 (ho_120 k_119 BOUND_VARIABLE_25655) K2))))))))) (let ((_let_174 (forall ((BOUND_VARIABLE_25643 tptp.nat) (BOUND_VARIABLE_25644 tptp.nat)) (= (ho_104 (ho_103 k_205 BOUND_VARIABLE_25643) BOUND_VARIABLE_25644) (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_25644 (ho_121 (ho_120 k_119 BOUND_VARIABLE_25643) C2))))))))) (let ((_let_175 (forall ((BOUND_VARIABLE_25627 tptp.nat) (BOUND_VARIABLE_25628 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_25627 BOUND_VARIABLE_25628))) (= (ho_104 (ho_103 k_206 BOUND_VARIABLE_25627) BOUND_VARIABLE_25628) (or (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_25628 (ho_121 (ho_120 k_119 BOUND_VARIABLE_25627) C2))))) (not _let_1)) _let_1)))))) (let ((_let_176 (forall ((BOUND_VARIABLE_25619 tptp.set_nat) (BOUND_VARIABLE_25620 tptp.nat)) (= (ho_104 (ho_208 k_207 BOUND_VARIABLE_25619) BOUND_VARIABLE_25620) (ho_211 (ho_210 k_209 BOUND_VARIABLE_25620) BOUND_VARIABLE_25619))))) (let ((_let_177 (forall ((BOUND_VARIABLE_25603 tptp.nat) (BOUND_VARIABLE_25604 tptp.nat) (BOUND_VARIABLE_25605 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_212 BOUND_VARIABLE_25603) BOUND_VARIABLE_25604) BOUND_VARIABLE_25605) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25603) P) BOUND_VARIABLE_25604)) (not (= BOUND_VARIABLE_25605 (ho_106 k_105 P)))))))))) (let ((_let_178 (forall ((BOUND_VARIABLE_25587 tptp.nat) (BOUND_VARIABLE_25588 tptp.nat) (BOUND_VARIABLE_25589 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_213 BOUND_VARIABLE_25587) BOUND_VARIABLE_25588) BOUND_VARIABLE_25589) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25587) P) BOUND_VARIABLE_25588)) (not (= BOUND_VARIABLE_25589 (ho_106 k_105 P)))))))))) (let ((_let_179 (forall ((BOUND_VARIABLE_25571 tptp.nat) (BOUND_VARIABLE_25572 tptp.nat) (BOUND_VARIABLE_25573 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_214 BOUND_VARIABLE_25571) BOUND_VARIABLE_25572) BOUND_VARIABLE_25573) (not (forall ((BOUND_VARIABLE_21408 tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25571) BOUND_VARIABLE_21408) BOUND_VARIABLE_25572)) (not (= BOUND_VARIABLE_25573 (ho_106 k_105 BOUND_VARIABLE_21408)))))))))) (let ((_let_180 (forall ((BOUND_VARIABLE_25555 tptp.nat) (BOUND_VARIABLE_25556 tptp.nat) (BOUND_VARIABLE_25557 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_215 BOUND_VARIABLE_25555) BOUND_VARIABLE_25556) BOUND_VARIABLE_25557) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25555) P) BOUND_VARIABLE_25556)) (not (= BOUND_VARIABLE_25557 (ho_106 k_105 P)))))))))) (let ((_let_181 (forall ((BOUND_VARIABLE_25539 tptp.nat) (BOUND_VARIABLE_25540 tptp.nat) (BOUND_VARIABLE_25541 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_216 BOUND_VARIABLE_25539) BOUND_VARIABLE_25540) BOUND_VARIABLE_25541) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25539) P) BOUND_VARIABLE_25540)) (not (= BOUND_VARIABLE_25541 (ho_106 k_105 P)))))))))) (let ((_let_182 (forall ((BOUND_VARIABLE_25523 tptp.nat) (BOUND_VARIABLE_25524 tptp.nat) (BOUND_VARIABLE_25525 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_217 BOUND_VARIABLE_25523) BOUND_VARIABLE_25524) BOUND_VARIABLE_25525) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25523) P) BOUND_VARIABLE_25524)) (not (= BOUND_VARIABLE_25525 (ho_106 k_105 P)))))))))) (let ((_let_183 (forall ((BOUND_VARIABLE_25507 tptp.nat) (BOUND_VARIABLE_25508 tptp.nat) (BOUND_VARIABLE_25509 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_218 BOUND_VARIABLE_25507) BOUND_VARIABLE_25508) BOUND_VARIABLE_25509) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25507) P) BOUND_VARIABLE_25508)) (not (= BOUND_VARIABLE_25509 (ho_106 k_105 P)))))))))) (let ((_let_184 (forall ((BOUND_VARIABLE_25491 tptp.nat) (BOUND_VARIABLE_25492 tptp.nat) (BOUND_VARIABLE_25493 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_219 BOUND_VARIABLE_25491) BOUND_VARIABLE_25492) BOUND_VARIABLE_25493) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25491) P) BOUND_VARIABLE_25492)) (not (= BOUND_VARIABLE_25493 (ho_106 k_105 P)))))))))) (let ((_let_185 (forall ((BOUND_VARIABLE_25475 tptp.nat) (BOUND_VARIABLE_25476 tptp.nat) (BOUND_VARIABLE_25477 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_220 BOUND_VARIABLE_25475) BOUND_VARIABLE_25476) BOUND_VARIABLE_25477) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25475) P) BOUND_VARIABLE_25476)) (not (= BOUND_VARIABLE_25477 (ho_106 k_105 P)))))))))) (let ((_let_186 (forall ((BOUND_VARIABLE_25459 tptp.nat) (BOUND_VARIABLE_25460 tptp.nat) (BOUND_VARIABLE_25461 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_221 BOUND_VARIABLE_25459) BOUND_VARIABLE_25460) BOUND_VARIABLE_25461) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25459) P) BOUND_VARIABLE_25460)) (not (= BOUND_VARIABLE_25461 (ho_106 k_105 P)))))))))) (let ((_let_187 (forall ((BOUND_VARIABLE_25443 tptp.nat) (BOUND_VARIABLE_25444 tptp.nat) (BOUND_VARIABLE_25445 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_222 BOUND_VARIABLE_25443) BOUND_VARIABLE_25444) BOUND_VARIABLE_25445) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25443) P) BOUND_VARIABLE_25444)) (not (= BOUND_VARIABLE_25445 (ho_106 k_105 P)))))))))) (let ((_let_188 (forall ((BOUND_VARIABLE_25427 tptp.nat) (BOUND_VARIABLE_25428 tptp.nat) (BOUND_VARIABLE_25429 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_223 BOUND_VARIABLE_25427) BOUND_VARIABLE_25428) BOUND_VARIABLE_25429) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25427) P) BOUND_VARIABLE_25428)) (not (= BOUND_VARIABLE_25429 (ho_106 k_105 P)))))))))) (let ((_let_189 (forall ((BOUND_VARIABLE_25411 tptp.nat) (BOUND_VARIABLE_25412 tptp.nat) (BOUND_VARIABLE_25413 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_224 BOUND_VARIABLE_25411) BOUND_VARIABLE_25412) BOUND_VARIABLE_25413) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25411) P) BOUND_VARIABLE_25412)) (not (= BOUND_VARIABLE_25413 (ho_106 k_105 P)))))))))) (let ((_let_190 (forall ((BOUND_VARIABLE_25395 tptp.nat) (BOUND_VARIABLE_25396 tptp.nat) (BOUND_VARIABLE_25397 tptp.nat)) (= (ho_104 (ho_103 (ho_102 k_225 BOUND_VARIABLE_25395) BOUND_VARIABLE_25396) BOUND_VARIABLE_25397) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) BOUND_VARIABLE_25395) P) BOUND_VARIABLE_25396)) (not (= BOUND_VARIABLE_25397 (ho_106 k_105 P)))))))))) (let ((_let_191 (forall ((BOUND_VARIABLE_25385 tptp.nat)) (= (ho_104 k_226 BOUND_VARIABLE_25385) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) tptp.s) P) tptp.t)) (not (= BOUND_VARIABLE_25385 (ho_106 k_105 P)))))))))) (let ((_let_192 (forall ((BOUND_VARIABLE_25375 tptp.nat)) (= (ho_104 k_227 BOUND_VARIABLE_25375) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) tptp.s) P) tptp.ua)) (not (= BOUND_VARIABLE_25375 (ho_106 k_105 P)))))))))) (let ((_let_193 (forall ((BOUND_VARIABLE_25365 tptp.nat)) (= (ho_104 k_228 BOUND_VARIABLE_25365) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (ho_104 (ho_110 (ho_109 (ho_115 k_114 k_187) tptp.ua) P) tptp.t)) (not (= BOUND_VARIABLE_25365 (ho_106 k_105 P)))))))))) (let ((_let_194 (forall ((BOUND_VARIABLE_27023 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_27024 tptp.nat) (BOUND_VARIABLE_27025 tptp.nat) (BOUND_VARIABLE_27026 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_27023) BOUND_VARIABLE_27024) P) BOUND_VARIABLE_27025)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_27026))))) (ll_98 BOUND_VARIABLE_27023 BOUND_VARIABLE_27024 BOUND_VARIABLE_27025 BOUND_VARIABLE_27026))))) (let ((_let_195 (forall ((BOUND_VARIABLE_27005 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_27006 tptp.nat) (BOUND_VARIABLE_27007 tptp.nat) (BOUND_VARIABLE_27008 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_27005) BOUND_VARIABLE_27006) P) BOUND_VARIABLE_27007)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_27008))))) (ll_97 BOUND_VARIABLE_27005 BOUND_VARIABLE_27006 BOUND_VARIABLE_27007 BOUND_VARIABLE_27008))))) (let ((_let_196 (forall ((BOUND_VARIABLE_26987 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26988 tptp.nat) (BOUND_VARIABLE_26989 tptp.nat) (BOUND_VARIABLE_26990 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26987) BOUND_VARIABLE_26988) P) BOUND_VARIABLE_26989)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26990))))) (ll_96 BOUND_VARIABLE_26987 BOUND_VARIABLE_26988 BOUND_VARIABLE_26989 BOUND_VARIABLE_26990))))) (let ((_let_197 (forall ((BOUND_VARIABLE_26969 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26970 tptp.nat) (BOUND_VARIABLE_26971 tptp.nat) (BOUND_VARIABLE_26972 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26969) BOUND_VARIABLE_26970) P) BOUND_VARIABLE_26971)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26972))))) (ll_95 BOUND_VARIABLE_26969 BOUND_VARIABLE_26970 BOUND_VARIABLE_26971 BOUND_VARIABLE_26972))))) (let ((_let_198 (forall ((BOUND_VARIABLE_26953 tptp.nat) (BOUND_VARIABLE_26954 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_26953 BOUND_VARIABLE_26954))) (= (or (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26954 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26953) C2))))) (not _let_1)) _let_1) (ll_94 BOUND_VARIABLE_26953 BOUND_VARIABLE_26954)))))) (let ((_let_199 (forall ((BOUND_VARIABLE_26938 tptp.nat) (BOUND_VARIABLE_26939 tptp.nat)) (= (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26939 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26938) C2))))) (not (= BOUND_VARIABLE_26938 BOUND_VARIABLE_26939))) (ll_93 BOUND_VARIABLE_26938 BOUND_VARIABLE_26939))))) (let ((_let_200 (forall ((BOUND_VARIABLE_26923 tptp.nat) (BOUND_VARIABLE_26924 tptp.nat)) (= (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26924 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26923) C2))))) (not (= BOUND_VARIABLE_26923 BOUND_VARIABLE_26924))) (ll_92 BOUND_VARIABLE_26923 BOUND_VARIABLE_26924))))) (let ((_let_201 (forall ((BOUND_VARIABLE_26914 (-> tptp.nat Bool))) (= (not (forall ((X4 tptp.nat)) (not (@ BOUND_VARIABLE_26914 X4)))) (ll_91 BOUND_VARIABLE_26914))))) (let ((_let_202 (forall ((BOUND_VARIABLE_26899 (-> tptp.nat Bool))) (= (not (forall ((N2 tptp.nat)) (or (not (@ BOUND_VARIABLE_26899 N2)) (not (forall ((M2 tptp.nat) (BOUND_VARIABLE_17356 tptp.nat)) (or (not (= N2 (@ (@ tptp.plus_plus_nat M2) BOUND_VARIABLE_17356))) (= N2 M2) (not (@ BOUND_VARIABLE_26899 M2)))))))) (ll_90 BOUND_VARIABLE_26899))))) (let ((_let_203 (forall ((BOUND_VARIABLE_26892 tptp.nat) (BOUND_VARIABLE_26893 tptp.nat)) (= (= BOUND_VARIABLE_26892 BOUND_VARIABLE_26893) (ll_89 BOUND_VARIABLE_26892 BOUND_VARIABLE_26893))))) (let ((_let_204 (forall ((BOUND_VARIABLE_26873 tptp.nat) (BOUND_VARIABLE_26874 tptp.nat)) (= (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26873 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26874) C2))))) (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26874 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26873) C2)))))) (ll_88 BOUND_VARIABLE_26873 BOUND_VARIABLE_26874))))) (let ((_let_205 (forall ((BOUND_VARIABLE_26866 tptp.nat) (BOUND_VARIABLE_26867 tptp.nat)) (= (= BOUND_VARIABLE_26866 BOUND_VARIABLE_26867) (ll_87 BOUND_VARIABLE_26866 BOUND_VARIABLE_26867))))) (let ((_let_206 (forall ((BOUND_VARIABLE_26847 tptp.nat) (BOUND_VARIABLE_26848 tptp.nat)) (= (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26848 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26847) C2))))) (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26847 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26848) C2)))))) (ll_86 BOUND_VARIABLE_26847 BOUND_VARIABLE_26848))))) (let ((_let_207 (forall ((BOUND_VARIABLE_26840 tptp.nat) (BOUND_VARIABLE_26841 tptp.nat)) (= (= BOUND_VARIABLE_26840 BOUND_VARIABLE_26841) (ll_85 BOUND_VARIABLE_26840 BOUND_VARIABLE_26841))))) (let ((_let_208 (forall ((BOUND_VARIABLE_26821 tptp.nat) (BOUND_VARIABLE_26822 tptp.nat)) (= (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26822 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26821) C2))))) (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_26821 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_26822) C2)))))) (ll_84 BOUND_VARIABLE_26821 BOUND_VARIABLE_26822))))) (let ((_let_209 (forall ((BOUND_VARIABLE_26805 tptp.nat) (BOUND_VARIABLE_26806 tptp.nat) (BOUND_VARIABLE_26807 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26805) P) BOUND_VARIABLE_26806)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26807))))) (ll_83 BOUND_VARIABLE_26805 BOUND_VARIABLE_26806 BOUND_VARIABLE_26807))))) (let ((_let_210 (forall ((BOUND_VARIABLE_26789 tptp.nat) (BOUND_VARIABLE_26790 tptp.nat) (BOUND_VARIABLE_26791 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26789) P) BOUND_VARIABLE_26790)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26791))))) (ll_82 BOUND_VARIABLE_26789 BOUND_VARIABLE_26790 BOUND_VARIABLE_26791))))) (let ((_let_211 (forall ((BOUND_VARIABLE_26773 tptp.nat) (BOUND_VARIABLE_26774 tptp.nat) (BOUND_VARIABLE_26775 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26773) P) BOUND_VARIABLE_26774)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26775))))) (ll_81 BOUND_VARIABLE_26773 BOUND_VARIABLE_26774 BOUND_VARIABLE_26775))))) (let ((_let_212 (forall ((BOUND_VARIABLE_26757 tptp.nat) (BOUND_VARIABLE_26758 tptp.nat) (BOUND_VARIABLE_26759 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26757) P) BOUND_VARIABLE_26758)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26759))))) (ll_80 BOUND_VARIABLE_26757 BOUND_VARIABLE_26758 BOUND_VARIABLE_26759))))) (let ((_let_213 (forall ((BOUND_VARIABLE_26741 tptp.nat) (BOUND_VARIABLE_26742 tptp.nat) (BOUND_VARIABLE_26743 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26741) P) BOUND_VARIABLE_26742)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26743))))) (ll_79 BOUND_VARIABLE_26741 BOUND_VARIABLE_26742 BOUND_VARIABLE_26743))))) (let ((_let_214 (forall ((BOUND_VARIABLE_26725 tptp.nat) (BOUND_VARIABLE_26726 tptp.nat) (BOUND_VARIABLE_26727 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26725) P) BOUND_VARIABLE_26726)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26727))))) (ll_78 BOUND_VARIABLE_26725 BOUND_VARIABLE_26726 BOUND_VARIABLE_26727))))) (let ((_let_215 (forall ((BOUND_VARIABLE_26709 tptp.nat) (BOUND_VARIABLE_26710 tptp.nat) (BOUND_VARIABLE_26711 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26709) P) BOUND_VARIABLE_26710)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26711))))) (ll_77 BOUND_VARIABLE_26709 BOUND_VARIABLE_26710 BOUND_VARIABLE_26711))))) (let ((_let_216 (forall ((BOUND_VARIABLE_26693 tptp.nat) (BOUND_VARIABLE_26694 tptp.nat) (BOUND_VARIABLE_26695 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26693) P) BOUND_VARIABLE_26694)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26695))))) (ll_76 BOUND_VARIABLE_26693 BOUND_VARIABLE_26694 BOUND_VARIABLE_26695))))) (let ((_let_217 (forall ((BOUND_VARIABLE_26677 tptp.nat) (BOUND_VARIABLE_26678 tptp.nat) (BOUND_VARIABLE_26679 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26677) P) BOUND_VARIABLE_26678)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26679))))) (ll_75 BOUND_VARIABLE_26677 BOUND_VARIABLE_26678 BOUND_VARIABLE_26679))))) (let ((_let_218 (forall ((BOUND_VARIABLE_26661 tptp.nat) (BOUND_VARIABLE_26662 tptp.nat) (BOUND_VARIABLE_26663 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26661) P) BOUND_VARIABLE_26662)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26663))))) (ll_74 BOUND_VARIABLE_26661 BOUND_VARIABLE_26662 BOUND_VARIABLE_26663))))) (let ((_let_219 (forall ((BOUND_VARIABLE_26645 tptp.nat) (BOUND_VARIABLE_26646 tptp.nat) (BOUND_VARIABLE_26647 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26645) P) BOUND_VARIABLE_26646)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26647))))) (ll_73 BOUND_VARIABLE_26645 BOUND_VARIABLE_26646 BOUND_VARIABLE_26647))))) (let ((_let_220 (forall ((BOUND_VARIABLE_26629 tptp.nat) (BOUND_VARIABLE_26630 tptp.nat) (BOUND_VARIABLE_26631 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26629) P) BOUND_VARIABLE_26630)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26631))))) (ll_72 BOUND_VARIABLE_26629 BOUND_VARIABLE_26630 BOUND_VARIABLE_26631))))) (let ((_let_221 (forall ((BOUND_VARIABLE_26613 tptp.nat) (BOUND_VARIABLE_26614 tptp.nat) (BOUND_VARIABLE_26615 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26613) P) BOUND_VARIABLE_26614)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26615))))) (ll_71 BOUND_VARIABLE_26613 BOUND_VARIABLE_26614 BOUND_VARIABLE_26615))))) (let ((_let_222 (forall ((BOUND_VARIABLE_26597 tptp.nat) (BOUND_VARIABLE_26598 tptp.nat) (BOUND_VARIABLE_26599 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26597) P) BOUND_VARIABLE_26598)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26599))))) (ll_70 BOUND_VARIABLE_26597 BOUND_VARIABLE_26598 BOUND_VARIABLE_26599))))) (let ((_let_223 (forall ((BOUND_VARIABLE_26581 tptp.nat) (BOUND_VARIABLE_26582 tptp.nat) (BOUND_VARIABLE_26583 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26581) P) BOUND_VARIABLE_26582)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26583))))) (ll_69 BOUND_VARIABLE_26581 BOUND_VARIABLE_26582 BOUND_VARIABLE_26583))))) (let ((_let_224 (forall ((BOUND_VARIABLE_26565 tptp.nat) (BOUND_VARIABLE_26566 tptp.nat) (BOUND_VARIABLE_26567 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26565) P) BOUND_VARIABLE_26566)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26567))))) (ll_68 BOUND_VARIABLE_26565 BOUND_VARIABLE_26566 BOUND_VARIABLE_26567))))) (let ((_let_225 (forall ((BOUND_VARIABLE_26549 tptp.nat) (BOUND_VARIABLE_26550 tptp.nat) (BOUND_VARIABLE_26551 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26549) P) BOUND_VARIABLE_26550)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26551))))) (ll_67 BOUND_VARIABLE_26549 BOUND_VARIABLE_26550 BOUND_VARIABLE_26551))))) (let ((_let_226 (forall ((BOUND_VARIABLE_26533 tptp.nat) (BOUND_VARIABLE_26534 tptp.nat) (BOUND_VARIABLE_26535 tptp.nat)) (= (ll_66 BOUND_VARIABLE_26533 BOUND_VARIABLE_26534 BOUND_VARIABLE_26535) (not (forall ((BOUND_VARIABLE_13752 tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a tptp.c2) BOUND_VARIABLE_26533) BOUND_VARIABLE_13752) BOUND_VARIABLE_26534)) (not (= (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_13752) BOUND_VARIABLE_26535))))))))) (let ((_let_227 (forall ((BOUND_VARIABLE_26515 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26516 tptp.nat) (BOUND_VARIABLE_26517 tptp.nat) (BOUND_VARIABLE_26518 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26515) BOUND_VARIABLE_26516) P) BOUND_VARIABLE_26517)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26518))))) (ll_65 BOUND_VARIABLE_26515 BOUND_VARIABLE_26516 BOUND_VARIABLE_26517 BOUND_VARIABLE_26518))))) (let ((_let_228 (forall ((BOUND_VARIABLE_26497 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26498 tptp.nat) (BOUND_VARIABLE_26499 tptp.nat) (BOUND_VARIABLE_26500 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26497) BOUND_VARIABLE_26498) P) BOUND_VARIABLE_26499)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26500))))) (ll_64 BOUND_VARIABLE_26497 BOUND_VARIABLE_26498 BOUND_VARIABLE_26499 BOUND_VARIABLE_26500))))) (let ((_let_229 (forall ((BOUND_VARIABLE_26479 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26480 tptp.nat) (BOUND_VARIABLE_26481 tptp.nat) (BOUND_VARIABLE_26482 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26479) BOUND_VARIABLE_26480) P) BOUND_VARIABLE_26481)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26482))))) (ll_63 BOUND_VARIABLE_26479 BOUND_VARIABLE_26480 BOUND_VARIABLE_26481 BOUND_VARIABLE_26482))))) (let ((_let_230 (forall ((BOUND_VARIABLE_26461 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26462 tptp.nat) (BOUND_VARIABLE_26463 tptp.nat) (BOUND_VARIABLE_26464 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26461) BOUND_VARIABLE_26462) P) BOUND_VARIABLE_26463)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26464))))) (ll_62 BOUND_VARIABLE_26461 BOUND_VARIABLE_26462 BOUND_VARIABLE_26463 BOUND_VARIABLE_26464))))) (let ((_let_231 (forall ((BOUND_VARIABLE_26443 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26444 tptp.nat) (BOUND_VARIABLE_26445 tptp.nat) (BOUND_VARIABLE_26446 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26443) BOUND_VARIABLE_26444) P) BOUND_VARIABLE_26445)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26446))))) (ll_61 BOUND_VARIABLE_26443 BOUND_VARIABLE_26444 BOUND_VARIABLE_26445 BOUND_VARIABLE_26446))))) (let ((_let_232 (forall ((BOUND_VARIABLE_26425 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26426 tptp.nat) (BOUND_VARIABLE_26427 tptp.nat) (BOUND_VARIABLE_26428 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26425) BOUND_VARIABLE_26426) P) BOUND_VARIABLE_26427)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26428))))) (ll_60 BOUND_VARIABLE_26425 BOUND_VARIABLE_26426 BOUND_VARIABLE_26427 BOUND_VARIABLE_26428))))) (let ((_let_233 (forall ((BOUND_VARIABLE_26407 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26408 tptp.nat) (BOUND_VARIABLE_26409 tptp.nat) (BOUND_VARIABLE_26410 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26407) BOUND_VARIABLE_26408) P) BOUND_VARIABLE_26409)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26410))))) (ll_59 BOUND_VARIABLE_26407 BOUND_VARIABLE_26408 BOUND_VARIABLE_26409 BOUND_VARIABLE_26410))))) (let ((_let_234 (forall ((BOUND_VARIABLE_26389 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26390 tptp.nat) (BOUND_VARIABLE_26391 tptp.nat) (BOUND_VARIABLE_26392 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26389) BOUND_VARIABLE_26390) P) BOUND_VARIABLE_26391)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26392))))) (ll_58 BOUND_VARIABLE_26389 BOUND_VARIABLE_26390 BOUND_VARIABLE_26391 BOUND_VARIABLE_26392))))) (let ((_let_235 (forall ((BOUND_VARIABLE_26371 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26372 tptp.nat) (BOUND_VARIABLE_26373 tptp.nat) (BOUND_VARIABLE_26374 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26371) BOUND_VARIABLE_26372) P) BOUND_VARIABLE_26373)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26374))))) (ll_57 BOUND_VARIABLE_26371 BOUND_VARIABLE_26372 BOUND_VARIABLE_26373 BOUND_VARIABLE_26374))))) (let ((_let_236 (forall ((BOUND_VARIABLE_26353 tptp.nat) (BOUND_VARIABLE_26354 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26355 tptp.nat) (BOUND_VARIABLE_26356 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26354) BOUND_VARIABLE_26353) P) BOUND_VARIABLE_26355)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26356))))) (ll_56 BOUND_VARIABLE_26353 BOUND_VARIABLE_26354 BOUND_VARIABLE_26355 BOUND_VARIABLE_26356))))) (let ((_let_237 (forall ((BOUND_VARIABLE_26335 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26336 tptp.nat) (BOUND_VARIABLE_26337 tptp.nat) (BOUND_VARIABLE_26338 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26335) BOUND_VARIABLE_26336) P) BOUND_VARIABLE_26337)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26338))))) (ll_55 BOUND_VARIABLE_26335 BOUND_VARIABLE_26336 BOUND_VARIABLE_26337 BOUND_VARIABLE_26338))))) (let ((_let_238 (forall ((BOUND_VARIABLE_26317 tptp.nat) (BOUND_VARIABLE_26318 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26319 tptp.nat) (BOUND_VARIABLE_26320 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26318) BOUND_VARIABLE_26317) P) BOUND_VARIABLE_26319)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26320))))) (ll_54 BOUND_VARIABLE_26317 BOUND_VARIABLE_26318 BOUND_VARIABLE_26319 BOUND_VARIABLE_26320))))) (let ((_let_239 (forall ((BOUND_VARIABLE_26299 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26300 tptp.nat) (BOUND_VARIABLE_26301 tptp.nat) (BOUND_VARIABLE_26302 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26299) BOUND_VARIABLE_26300) P) BOUND_VARIABLE_26301)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26302))))) (ll_53 BOUND_VARIABLE_26299 BOUND_VARIABLE_26300 BOUND_VARIABLE_26301 BOUND_VARIABLE_26302))))) (let ((_let_240 (forall ((BOUND_VARIABLE_26281 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26282 tptp.nat) (BOUND_VARIABLE_26283 tptp.nat) (BOUND_VARIABLE_26284 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26281) BOUND_VARIABLE_26282) P) BOUND_VARIABLE_26283)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26284))))) (ll_52 BOUND_VARIABLE_26281 BOUND_VARIABLE_26282 BOUND_VARIABLE_26283 BOUND_VARIABLE_26284))))) (let ((_let_241 (forall ((BOUND_VARIABLE_26263 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26264 tptp.nat) (BOUND_VARIABLE_26265 tptp.nat) (BOUND_VARIABLE_26266 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26263) BOUND_VARIABLE_26264) P) BOUND_VARIABLE_26265)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26266))))) (ll_51 BOUND_VARIABLE_26263 BOUND_VARIABLE_26264 BOUND_VARIABLE_26265 BOUND_VARIABLE_26266))))) (let ((_let_242 (forall ((BOUND_VARIABLE_26245 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26246 tptp.nat) (BOUND_VARIABLE_26247 tptp.nat) (BOUND_VARIABLE_26248 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26245) BOUND_VARIABLE_26246) P) BOUND_VARIABLE_26247)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26248))))) (ll_50 BOUND_VARIABLE_26245 BOUND_VARIABLE_26246 BOUND_VARIABLE_26247 BOUND_VARIABLE_26248))))) (let ((_let_243 (forall ((BOUND_VARIABLE_26227 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26228 tptp.nat) (BOUND_VARIABLE_26229 tptp.nat) (BOUND_VARIABLE_26230 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26227) BOUND_VARIABLE_26228) P) BOUND_VARIABLE_26229)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26230))))) (ll_49 BOUND_VARIABLE_26227 BOUND_VARIABLE_26228 BOUND_VARIABLE_26229 BOUND_VARIABLE_26230))))) (let ((_let_244 (forall ((BOUND_VARIABLE_26209 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26210 tptp.nat) (BOUND_VARIABLE_26211 tptp.nat) (BOUND_VARIABLE_26212 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26209) BOUND_VARIABLE_26210) P) BOUND_VARIABLE_26211)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26212))))) (ll_48 BOUND_VARIABLE_26209 BOUND_VARIABLE_26210 BOUND_VARIABLE_26211 BOUND_VARIABLE_26212))))) (let ((_let_245 (forall ((BOUND_VARIABLE_26195 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26196 tptp.nat) (BOUND_VARIABLE_26197 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26195) BOUND_VARIABLE_26196) P) BOUND_VARIABLE_26197)))) (ll_47 BOUND_VARIABLE_26195 BOUND_VARIABLE_26196 BOUND_VARIABLE_26197))))) (let ((_let_246 (forall ((BOUND_VARIABLE_26181 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26182 tptp.nat) (BOUND_VARIABLE_26183 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26181) BOUND_VARIABLE_26182) P) BOUND_VARIABLE_26183)))) (ll_46 BOUND_VARIABLE_26181 BOUND_VARIABLE_26182 BOUND_VARIABLE_26183))))) (let ((_let_247 (forall ((BOUND_VARIABLE_26167 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26168 tptp.nat) (BOUND_VARIABLE_26169 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26167) BOUND_VARIABLE_26168) P) BOUND_VARIABLE_26169)))) (ll_45 BOUND_VARIABLE_26167 BOUND_VARIABLE_26168 BOUND_VARIABLE_26169))))) (let ((_let_248 (forall ((BOUND_VARIABLE_26153 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26154 tptp.nat) (BOUND_VARIABLE_26155 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26153) BOUND_VARIABLE_26154) P) BOUND_VARIABLE_26155)))) (ll_44 BOUND_VARIABLE_26153 BOUND_VARIABLE_26154 BOUND_VARIABLE_26155))))) (let ((_let_249 (forall ((BOUND_VARIABLE_26106 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26107 tptp.nat) (BOUND_VARIABLE_26108 tptp.list_P559422087at_nat) (BOUND_VARIABLE_26109 tptp.nat)) (= (ll_43 BOUND_VARIABLE_26106 BOUND_VARIABLE_26107 BOUND_VARIABLE_26108 BOUND_VARIABLE_26109) (and (@ (@ (@ (@ tptp.isSimplePath_a BOUND_VARIABLE_26106) BOUND_VARIABLE_26107) BOUND_VARIABLE_26108) BOUND_VARIABLE_26109) (= (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_26108) (@ tptp.ord_Least_nat (@ (@ (@ ll_98 BOUND_VARIABLE_26106) BOUND_VARIABLE_26107) BOUND_VARIABLE_26109)))))))) (let ((_let_250 (forall ((BOUND_VARIABLE_26059 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26060 tptp.nat) (BOUND_VARIABLE_26061 tptp.list_P559422087at_nat) (BOUND_VARIABLE_26062 tptp.nat)) (= (ll_42 BOUND_VARIABLE_26059 BOUND_VARIABLE_26060 BOUND_VARIABLE_26061 BOUND_VARIABLE_26062) (and (@ (@ (@ (@ tptp.isSimp1359852763pacity BOUND_VARIABLE_26059) BOUND_VARIABLE_26060) BOUND_VARIABLE_26061) BOUND_VARIABLE_26062) (= (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_26061) (@ tptp.ord_Least_nat (@ (@ (@ ll_97 BOUND_VARIABLE_26059) BOUND_VARIABLE_26060) BOUND_VARIABLE_26062)))))))) (let ((_let_251 (forall ((BOUND_VARIABLE_26041 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_26042 tptp.nat) (BOUND_VARIABLE_26043 tptp.nat) (BOUND_VARIABLE_26044 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_26041) BOUND_VARIABLE_26042) P) BOUND_VARIABLE_26043)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26044))))) (ll_41 BOUND_VARIABLE_26041 BOUND_VARIABLE_26042 BOUND_VARIABLE_26043 BOUND_VARIABLE_26044))))) (let ((_let_252 (forall ((BOUND_VARIABLE_26023 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_26024 tptp.nat) (BOUND_VARIABLE_26025 tptp.nat) (BOUND_VARIABLE_26026 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_26023) BOUND_VARIABLE_26024) P) BOUND_VARIABLE_26025)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26026))))) (ll_40 BOUND_VARIABLE_26023 BOUND_VARIABLE_26024 BOUND_VARIABLE_26025 BOUND_VARIABLE_26026))))) (let ((_let_253 (forall ((BOUND_VARIABLE_26007 tptp.nat) (BOUND_VARIABLE_26008 tptp.nat) (BOUND_VARIABLE_26009 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_26007) P) BOUND_VARIABLE_26008)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_26009))))) (ll_39 BOUND_VARIABLE_26007 BOUND_VARIABLE_26008 BOUND_VARIABLE_26009))))) (let ((_let_254 (forall ((BOUND_VARIABLE_25989 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_25990 tptp.nat) (BOUND_VARIABLE_25991 tptp.nat) (BOUND_VARIABLE_25992 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_25989) BOUND_VARIABLE_25990) P) BOUND_VARIABLE_25991)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25992))))) (ll_38 BOUND_VARIABLE_25989 BOUND_VARIABLE_25990 BOUND_VARIABLE_25991 BOUND_VARIABLE_25992))))) (let ((_let_255 (forall ((BOUND_VARIABLE_25971 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_25972 tptp.nat) (BOUND_VARIABLE_25973 tptp.nat) (BOUND_VARIABLE_25974 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_25971) BOUND_VARIABLE_25972) P) BOUND_VARIABLE_25973)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25974))))) (ll_37 BOUND_VARIABLE_25971 BOUND_VARIABLE_25972 BOUND_VARIABLE_25973 BOUND_VARIABLE_25974))))) (let ((_let_256 (forall ((BOUND_VARIABLE_25953 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_25954 tptp.nat) (BOUND_VARIABLE_25955 tptp.nat) (BOUND_VARIABLE_25956 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_25953) BOUND_VARIABLE_25954) P) BOUND_VARIABLE_25955)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25956))))) (ll_36 BOUND_VARIABLE_25953 BOUND_VARIABLE_25954 BOUND_VARIABLE_25955 BOUND_VARIABLE_25956))))) (let ((_let_257 (forall ((BOUND_VARIABLE_25935 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_25936 tptp.nat) (BOUND_VARIABLE_25937 tptp.nat) (BOUND_VARIABLE_25938 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_25935) BOUND_VARIABLE_25936) P) BOUND_VARIABLE_25937)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25938))))) (ll_35 BOUND_VARIABLE_25935 BOUND_VARIABLE_25936 BOUND_VARIABLE_25937 BOUND_VARIABLE_25938))))) (let ((_let_258 (forall ((BOUND_VARIABLE_25917 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_25918 tptp.nat) (BOUND_VARIABLE_25919 tptp.nat) (BOUND_VARIABLE_25920 tptp.nat)) (= (ll_34 BOUND_VARIABLE_25917 BOUND_VARIABLE_25918 BOUND_VARIABLE_25919 BOUND_VARIABLE_25920) (not (forall ((BOUND_VARIABLE_23305 tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_25917) BOUND_VARIABLE_25918) BOUND_VARIABLE_23305) BOUND_VARIABLE_25919)) (not (= (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_23305) BOUND_VARIABLE_25920))))))))) (let ((_let_259 (forall ((BOUND_VARIABLE_25899 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_25900 tptp.nat) (BOUND_VARIABLE_25901 tptp.nat) (BOUND_VARIABLE_25902 tptp.nat)) (= (ll_33 BOUND_VARIABLE_25899 BOUND_VARIABLE_25900 BOUND_VARIABLE_25901 BOUND_VARIABLE_25902) (not (forall ((BOUND_VARIABLE_23190 tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_25899) BOUND_VARIABLE_25900) BOUND_VARIABLE_23190) BOUND_VARIABLE_25901)) (not (= (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_23190) BOUND_VARIABLE_25902))))))))) (let ((_let_260 (forall ((BOUND_VARIABLE_25883 tptp.nat) (BOUND_VARIABLE_25884 tptp.nat) (BOUND_VARIABLE_25885 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25883) P) BOUND_VARIABLE_25884)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25885))))) (ll_32 BOUND_VARIABLE_25883 BOUND_VARIABLE_25884 BOUND_VARIABLE_25885))))) (let ((_let_261 (forall ((BOUND_VARIABLE_25865 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_25866 tptp.nat) (BOUND_VARIABLE_25867 tptp.nat) (BOUND_VARIABLE_25868 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_25865) BOUND_VARIABLE_25866) P) BOUND_VARIABLE_25867)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25868))))) (ll_31 BOUND_VARIABLE_25865 BOUND_VARIABLE_25866 BOUND_VARIABLE_25867 BOUND_VARIABLE_25868))))) (let ((_let_262 (forall ((BOUND_VARIABLE_25847 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_25848 tptp.nat) (BOUND_VARIABLE_25849 tptp.nat) (BOUND_VARIABLE_25850 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_25847) BOUND_VARIABLE_25848) P) BOUND_VARIABLE_25849)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25850))))) (ll_30 BOUND_VARIABLE_25847 BOUND_VARIABLE_25848 BOUND_VARIABLE_25849 BOUND_VARIABLE_25850))))) (let ((_let_263 (forall ((BOUND_VARIABLE_25822 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_25823 tptp.nat) (BOUND_VARIABLE_25824 tptp.list_P559422087at_nat) (BOUND_VARIABLE_25825 tptp.nat)) (= (and (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_25822) BOUND_VARIABLE_25823) BOUND_VARIABLE_25824) BOUND_VARIABLE_25825) (forall ((P4 tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_25822) BOUND_VARIABLE_25823) P4) BOUND_VARIABLE_25825)) (not (forall ((C2 tptp.nat)) (not (= (@ tptp.size_s1990949619at_nat P4) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_25824)) C2)))))))) (ll_29 BOUND_VARIABLE_25822 BOUND_VARIABLE_25823 BOUND_VARIABLE_25824 BOUND_VARIABLE_25825))))) (let ((_let_264 (forall ((BOUND_VARIABLE_25777 (-> tptp.product_prod_nat_nat tptp.a)) (BOUND_VARIABLE_25778 tptp.nat) (BOUND_VARIABLE_25779 tptp.list_P559422087at_nat) (BOUND_VARIABLE_25780 tptp.nat)) (= (ll_28 BOUND_VARIABLE_25777 BOUND_VARIABLE_25778 BOUND_VARIABLE_25779 BOUND_VARIABLE_25780) (and (@ (@ (@ (@ tptp.isPath_a BOUND_VARIABLE_25777) BOUND_VARIABLE_25778) BOUND_VARIABLE_25779) BOUND_VARIABLE_25780) (= (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_25779) (@ tptp.ord_Least_nat (@ (@ (@ ll_96 BOUND_VARIABLE_25777) BOUND_VARIABLE_25778) BOUND_VARIABLE_25780)))))))) (let ((_let_265 (forall ((BOUND_VARIABLE_25752 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_25753 tptp.nat) (BOUND_VARIABLE_25754 tptp.list_P559422087at_nat) (BOUND_VARIABLE_25755 tptp.nat)) (= (and (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_25752) BOUND_VARIABLE_25753) BOUND_VARIABLE_25754) BOUND_VARIABLE_25755) (forall ((P4 tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_25752) BOUND_VARIABLE_25753) P4) BOUND_VARIABLE_25755)) (not (forall ((C2 tptp.nat)) (not (= (@ tptp.size_s1990949619at_nat P4) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_25754)) C2)))))))) (ll_27 BOUND_VARIABLE_25752 BOUND_VARIABLE_25753 BOUND_VARIABLE_25754 BOUND_VARIABLE_25755))))) (let ((_let_266 (forall ((BOUND_VARIABLE_25707 (-> tptp.product_prod_nat_nat tptp.capacity)) (BOUND_VARIABLE_25708 tptp.nat) (BOUND_VARIABLE_25709 tptp.list_P559422087at_nat) (BOUND_VARIABLE_25710 tptp.nat)) (= (ll_26 BOUND_VARIABLE_25707 BOUND_VARIABLE_25708 BOUND_VARIABLE_25709 BOUND_VARIABLE_25710) (and (@ (@ (@ (@ tptp.isPath_capacity BOUND_VARIABLE_25707) BOUND_VARIABLE_25708) BOUND_VARIABLE_25709) BOUND_VARIABLE_25710) (= (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_25709) (@ tptp.ord_Least_nat (@ (@ (@ ll_95 BOUND_VARIABLE_25707) BOUND_VARIABLE_25708) BOUND_VARIABLE_25710)))))))) (let ((_let_267 (forall ((BOUND_VARIABLE_25691 tptp.nat) (BOUND_VARIABLE_25692 tptp.nat) (BOUND_VARIABLE_25693 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25691) P) BOUND_VARIABLE_25692)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25693))))) (ll_25 BOUND_VARIABLE_25691 BOUND_VARIABLE_25692 BOUND_VARIABLE_25693))))) (let ((_let_268 (forall ((BOUND_VARIABLE_25675 tptp.nat) (BOUND_VARIABLE_25676 tptp.nat) (BOUND_VARIABLE_25677 tptp.nat)) (= (ll_24 BOUND_VARIABLE_25675 BOUND_VARIABLE_25676 BOUND_VARIABLE_25677) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25675) P) BOUND_VARIABLE_25676)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25677))))))))) (let ((_let_269 (forall ((BOUND_VARIABLE_25667 tptp.nat) (BOUND_VARIABLE_25668 tptp.nat)) (= (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_25668) BOUND_VARIABLE_25667) (ll_23 BOUND_VARIABLE_25667 BOUND_VARIABLE_25668))))) (let ((_let_270 (forall ((BOUND_VARIABLE_25655 tptp.nat) (BOUND_VARIABLE_25656 tptp.nat)) (= (not (forall ((K2 tptp.nat)) (not (= BOUND_VARIABLE_25656 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_25655) K2))))) (ll_22 BOUND_VARIABLE_25655 BOUND_VARIABLE_25656))))) (let ((_let_271 (forall ((BOUND_VARIABLE_25643 tptp.nat) (BOUND_VARIABLE_25644 tptp.nat)) (= (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_25644 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_25643) C2))))) (ll_21 BOUND_VARIABLE_25643 BOUND_VARIABLE_25644))))) (let ((_let_272 (forall ((BOUND_VARIABLE_25627 tptp.nat) (BOUND_VARIABLE_25628 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_25627 BOUND_VARIABLE_25628))) (= (or (and (not (forall ((C2 tptp.nat)) (not (= BOUND_VARIABLE_25628 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_25627) C2))))) (not _let_1)) _let_1) (ll_20 BOUND_VARIABLE_25627 BOUND_VARIABLE_25628)))))) (let ((_let_273 (forall ((BOUND_VARIABLE_25619 tptp.set_nat) (BOUND_VARIABLE_25620 tptp.nat)) (= (@ (@ tptp.member_nat BOUND_VARIABLE_25620) BOUND_VARIABLE_25619) (ll_19 BOUND_VARIABLE_25619 BOUND_VARIABLE_25620))))) (let ((_let_274 (forall ((BOUND_VARIABLE_25603 tptp.nat) (BOUND_VARIABLE_25604 tptp.nat) (BOUND_VARIABLE_25605 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25603) P) BOUND_VARIABLE_25604)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25605))))) (ll_18 BOUND_VARIABLE_25603 BOUND_VARIABLE_25604 BOUND_VARIABLE_25605))))) (let ((_let_275 (forall ((BOUND_VARIABLE_25587 tptp.nat) (BOUND_VARIABLE_25588 tptp.nat) (BOUND_VARIABLE_25589 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25587) P) BOUND_VARIABLE_25588)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25589))))) (ll_17 BOUND_VARIABLE_25587 BOUND_VARIABLE_25588 BOUND_VARIABLE_25589))))) (let ((_let_276 (forall ((BOUND_VARIABLE_25571 tptp.nat) (BOUND_VARIABLE_25572 tptp.nat) (BOUND_VARIABLE_25573 tptp.nat)) (= (ll_16 BOUND_VARIABLE_25571 BOUND_VARIABLE_25572 BOUND_VARIABLE_25573) (not (forall ((BOUND_VARIABLE_21408 tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25571) BOUND_VARIABLE_21408) BOUND_VARIABLE_25572)) (not (= (@ tptp.size_s1990949619at_nat BOUND_VARIABLE_21408) BOUND_VARIABLE_25573))))))))) (let ((_let_277 (forall ((BOUND_VARIABLE_25555 tptp.nat) (BOUND_VARIABLE_25556 tptp.nat) (BOUND_VARIABLE_25557 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25555) P) BOUND_VARIABLE_25556)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25557))))) (ll_15 BOUND_VARIABLE_25555 BOUND_VARIABLE_25556 BOUND_VARIABLE_25557))))) (let ((_let_278 (forall ((BOUND_VARIABLE_25539 tptp.nat) (BOUND_VARIABLE_25540 tptp.nat) (BOUND_VARIABLE_25541 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25539) P) BOUND_VARIABLE_25540)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25541))))) (ll_14 BOUND_VARIABLE_25539 BOUND_VARIABLE_25540 BOUND_VARIABLE_25541))))) (let ((_let_279 (forall ((BOUND_VARIABLE_25523 tptp.nat) (BOUND_VARIABLE_25524 tptp.nat) (BOUND_VARIABLE_25525 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25523) P) BOUND_VARIABLE_25524)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25525))))) (ll_13 BOUND_VARIABLE_25523 BOUND_VARIABLE_25524 BOUND_VARIABLE_25525))))) (let ((_let_280 (forall ((BOUND_VARIABLE_25507 tptp.nat) (BOUND_VARIABLE_25508 tptp.nat) (BOUND_VARIABLE_25509 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25507) P) BOUND_VARIABLE_25508)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25509))))) (ll_12 BOUND_VARIABLE_25507 BOUND_VARIABLE_25508 BOUND_VARIABLE_25509))))) (let ((_let_281 (forall ((BOUND_VARIABLE_25491 tptp.nat) (BOUND_VARIABLE_25492 tptp.nat) (BOUND_VARIABLE_25493 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25491) P) BOUND_VARIABLE_25492)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25493))))) (ll_11 BOUND_VARIABLE_25491 BOUND_VARIABLE_25492 BOUND_VARIABLE_25493))))) (let ((_let_282 (forall ((BOUND_VARIABLE_25475 tptp.nat) (BOUND_VARIABLE_25476 tptp.nat) (BOUND_VARIABLE_25477 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25475) P) BOUND_VARIABLE_25476)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25477))))) (ll_10 BOUND_VARIABLE_25475 BOUND_VARIABLE_25476 BOUND_VARIABLE_25477))))) (let ((_let_283 (forall ((BOUND_VARIABLE_25459 tptp.nat) (BOUND_VARIABLE_25460 tptp.nat) (BOUND_VARIABLE_25461 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25459) P) BOUND_VARIABLE_25460)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25461))))) (ll_9 BOUND_VARIABLE_25459 BOUND_VARIABLE_25460 BOUND_VARIABLE_25461))))) (let ((_let_284 (forall ((BOUND_VARIABLE_25443 tptp.nat) (BOUND_VARIABLE_25444 tptp.nat) (BOUND_VARIABLE_25445 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25443) P) BOUND_VARIABLE_25444)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25445))))) (ll_8 BOUND_VARIABLE_25443 BOUND_VARIABLE_25444 BOUND_VARIABLE_25445))))) (let ((_let_285 (forall ((BOUND_VARIABLE_25427 tptp.nat) (BOUND_VARIABLE_25428 tptp.nat) (BOUND_VARIABLE_25429 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25427) P) BOUND_VARIABLE_25428)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25429))))) (ll_7 BOUND_VARIABLE_25427 BOUND_VARIABLE_25428 BOUND_VARIABLE_25429))))) (let ((_let_286 (forall ((BOUND_VARIABLE_25411 tptp.nat) (BOUND_VARIABLE_25412 tptp.nat) (BOUND_VARIABLE_25413 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25411) P) BOUND_VARIABLE_25412)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25413))))) (ll_6 BOUND_VARIABLE_25411 BOUND_VARIABLE_25412 BOUND_VARIABLE_25413))))) (let ((_let_287 (forall ((BOUND_VARIABLE_25395 tptp.nat) (BOUND_VARIABLE_25396 tptp.nat) (BOUND_VARIABLE_25397 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) BOUND_VARIABLE_25395) P) BOUND_VARIABLE_25396)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25397))))) (ll_5 BOUND_VARIABLE_25395 BOUND_VARIABLE_25396 BOUND_VARIABLE_25397))))) (let ((_let_288 (forall ((BOUND_VARIABLE_25385 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.s) P) tptp.t)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25385))))) (ll_4 BOUND_VARIABLE_25385))))) (let ((_let_289 (forall ((BOUND_VARIABLE_25375 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.s) P) tptp.ua)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25375))))) (ll_3 BOUND_VARIABLE_25375))))) (let ((_let_290 (forall ((BOUND_VARIABLE_25365 tptp.nat)) (= (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.ua) P) tptp.t)) (not (= (@ tptp.size_s1990949619at_nat P) BOUND_VARIABLE_25365))))) (ll_2 BOUND_VARIABLE_25365))))) (let ((_let_291 (@ tptp.ord_Least_nat ll_4))) (let ((_let_292 (@ tptp.ord_Least_nat ll_3))) (let ((_let_293 (= (@ (@ tptp.plus_plus_nat _let_292) (@ tptp.ord_Least_nat ll_2)) _let_291))) (let ((_let_294 (and _let_293 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194))) (let ((_let_295 (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.s) P) tptp.ua)) (not (= (@ tptp.size_s1990949619at_nat P) D4))))))))) (let ((_let_296 (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.s) P) tptp.t)) (not (= (@ tptp.size_s1990949619at_nat P) D4))))))))) (let ((_let_297 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_298 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO _let_297 :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_299 (ASSUME :args (_let_19)))) (let ((_let_300 (ASSUME :args (_let_18)))) (let ((_let_301 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_302 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_303 (ASSUME :args (_let_15)))) (let ((_let_304 (ASSUME :args (_let_14)))) (let ((_let_305 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_306 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297))) (let ((_let_307 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_30)) (TRANS (MACRO_SR_EQ_INTRO _let_306 :args (_let_30 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_296 (@ (@ tptp.plus_plus_nat _let_295) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (not (forall ((P tptp.list_P559422087at_nat)) (or (not (@ (@ (@ (@ tptp.isPath_capacity tptp.c) tptp.ua) P) tptp.t)) (not (= (@ tptp.size_s1990949619at_nat P) D4))))))))) _let_293))))) (PREPROCESS :args ((and _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194)))) :args (_let_294)) (PREPROCESS :args ((= _let_294 (and _let_36 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97))))) (PREPROCESS :args ((and _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49)))) :args ((and _let_36 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49))) :args _let_48))) (let ((_let_308 (forall ((C2 tptp.nat)) (not (= (ho_106 k_105 tptp.p1a) (ho_121 (ho_120 k_119 (ho_179 k_178 k_227)) C2)))))) (let ((_let_309 (= _let_32 _let_38))) (let ((_let_310 (not _let_309))) (let ((_let_311 (not _let_308))) (let ((_let_312 (and (not (forall ((C2 tptp.nat)) (not (= (@ tptp.size_s1990949619at_nat tptp.p1a) (@ (@ tptp.plus_plus_nat (@ tptp.ord_Least_nat ll_3)) C2))))) (not (= _let_2 _let_292))))) (let ((_let_313 (EQ_RESOLVE (ASSUME :args (_let_29)) 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tptp.connected_capacity tptp.c) V) V3) (exists ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D4) V3)))) (forall ((U tptp.nat) (V tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity tptp.c) U) V) (not (forall ((P3 tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P3) V)))))) (forall ((Src tptp.nat) (V tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity tptp.c) Src) V) (=> (@ (@ tptp.ord_less_eq_nat D3) (@ (@ (@ tptp.min_dist_capacity tptp.c) Src) V)) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_capacity tptp.c) Src) V2) (= (@ (@ (@ tptp.min_dist_capacity tptp.c) Src) V2) D3)))))) (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D) V3) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3)) D))) (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D) V3) (=> (forall ((D5 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D5) V3) (@ (@ tptp.ord_less_eq_nat D) D5))) (= (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3) D)))) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P2) V) (@ (@ (@ (@ tptp.dist_capacity tptp.c) U) (@ tptp.size_s1990949619at_nat P2)) V))) (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D) V3) (exists ((P tptp.list_P559422087at_nat)) (and (@ (@ (@ (@ tptp.isPath_capacity tptp.c) V) P) V3) (= (@ tptp.size_s1990949619at_nat P) D))))) (@ (@ _let_24 tptp.p1) tptp.v) (forall ((V tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity tptp.c) V) V3) (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3)) V3))) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P2) V) (and (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P2) V) (forall ((P4 tptp.list_P559422087at_nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P4) V) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1990949619at_nat P2)) (@ tptp.size_s1990949619at_nat P4))))))) (forall ((V tptp.nat) (V3 tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.connected_capacity tptp.c) V) V3) (=> (forall ((D6 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D6) V3) (=> (forall ((D7 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D7) V3) (@ (@ tptp.ord_less_eq_nat D6) D7))) (@ Q D6)))) (@ Q (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3))))) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P2) V) (and (@ (@ (@ (@ tptp.isPath_capacity tptp.c) U) P2) V) (= (@ tptp.size_s1990949619at_nat P2) (@ (@ (@ tptp.min_dist_capacity tptp.c) U) V))))) (@ (@ (@ tptp.connected_capacity tptp.c) tptp.s) tptp.ua) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))) _let_25 (forall ((V tptp.nat)) (@ (@ (@ tptp.connected_capacity tptp.c) V) V)) (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D) V3) (@ (@ (@ tptp.connected_capacity tptp.c) V) V3))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((P5 (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P5 K) (=> (forall ((Y tptp.nat)) (=> (@ P5 Y) (@ (@ tptp.ord_less_eq_nat Y) B))) (exists ((X tptp.nat)) (and (@ P5 X) (forall ((Y2 tptp.nat)) (=> (@ P5 Y2) (@ (@ tptp.ord_less_eq_nat Y2) X)))))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))) _let_22 (forall ((A tptp.nat) (P5 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P5)) (@ P5 A))) (forall ((A3 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A3))) A3)) (forall ((P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X tptp.nat)) (= (@ P5 X) (@ Q X))) (= (@ tptp.collect_nat P5) (@ tptp.collect_nat Q)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))) _let_21 (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (exists ((K2 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M2) K2))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N3))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.plus_plus_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A2))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))) (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))) (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A3) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (= X3 Y3)) (=> (not (@ (@ tptp.ord_less_nat X3) Y3)) (@ (@ tptp.ord_less_nat Y3) X3)))) (forall ((P5 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P5 N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P5 M3)))))) (@ P5 N))) (forall ((P5 (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P5 M3))) (@ P5 N3))) (@ P5 N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))) (forall ((X3 tptp.list_P559422087at_nat) (Y3 tptp.list_P559422087at_nat)) (=> (not (= (@ tptp.size_s1990949619at_nat X3) (@ tptp.size_s1990949619at_nat Y3))) (not (= X3 Y3)))) _let_20 (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))) (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))) (forall ((U tptp.nat)) (= (@ (@ tptp.reacha1693770334pacity tptp.c) U) (@ tptp.collect_nat (@ (@ tptp.connected_capacity tptp.c) U)))) (forall ((V tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ tptp.min_dist_capacity tptp.c) V) V3) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_capacity tptp.c) V) D4) V3))))) _let_19 _let_18 (= tptp.isShor1936442771pacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isPath_capacity C2) U2) P) V4) (forall ((P4 tptp.list_P559422087at_nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity C2) U2) P4) V4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1990949619at_nat P)) (@ tptp.size_s1990949619at_nat P4))))))) (= tptp.isShortestPath_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isPath_a C2) U2) P) V4) (forall ((P4 tptp.list_P559422087at_nat)) (=> (@ (@ (@ (@ tptp.isPath_a C2) U2) P4) V4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1990949619at_nat P)) (@ tptp.size_s1990949619at_nat P4))))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (V3 tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.connected_capacity C) V) V3) (=> (forall ((D6 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D6) V3) (=> (forall ((D7 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D7) V3) (@ (@ tptp.ord_less_eq_nat D6) D7))) (@ Q D6)))) (@ Q (@ (@ (@ tptp.min_dist_capacity C) V) V3))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (V3 tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.connected_a C) V) V3) (=> (forall ((D6 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D6) V3) (=> (forall ((D7 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D7) V3) (@ (@ tptp.ord_less_eq_nat D6) D7))) (@ Q D6)))) (@ Q (@ (@ (@ tptp.min_dist_a C) V) V3))))) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) U) P2) V) (and (@ (@ (@ (@ tptp.isSimp1359852763pacity tptp.c) U) P2) V) (= (@ tptp.size_s1990949619at_nat P2) (@ (@ (@ tptp.min_dist_capacity tptp.c) U) V))))) _let_17 _let_16 (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity C) U) P2) V) (@ (@ (@ (@ tptp.dist_capacity C) U) (@ tptp.size_s1990949619at_nat P2)) V))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_a C) U) P2) V) (@ (@ (@ (@ tptp.dist_a C) U) (@ tptp.size_s1990949619at_nat P2)) V))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity C) V) V3) (@ (@ (@ (@ tptp.dist_capacity C) V) (@ (@ (@ tptp.min_dist_capacity C) V) V3)) V3))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a C) V) V3) (@ (@ (@ (@ tptp.dist_a C) V) (@ (@ (@ tptp.min_dist_a C) V) V3)) V3))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.min_dist_capacity C) U))) (let ((_let_2 (@ tptp.dist_capacity C))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ _let_1 V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ _let_1 W) D1))))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.min_dist_a C) U))) (let ((_let_2 (@ tptp.dist_a C))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ _let_1 V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ _let_1 W) D1))))))) (forall ((S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity tptp.c) S) P2) T) (exists ((P6 tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isSimp1359852763pacity tptp.c) S) P6) T)))) (forall ((S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isShor1936442771pacity tptp.c) S) P2) T) (@ (@ (@ (@ tptp.isSimp1359852763pacity tptp.c) S) P2) T))) (= tptp.reacha1693770334pacity tptp.reacha1693770334pacity) (= tptp.reachableNodes_a tptp.reachableNodes_a) (= tptp.isSimp1359852763pacity tptp.isSimp1359852763pacity) (= tptp.isSimplePath_a tptp.isSimplePath_a) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_capacity C) S) P2) T) (exists ((P6 tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isSimp1359852763pacity C) S) P6) T)))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_a C) S) P2) T) (exists ((P6 tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isSimplePath_a C) S) P6) T)))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isShor1936442771pacity C) S) P2) T) (@ (@ (@ (@ tptp.isSimp1359852763pacity C) S) P2) T))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isShortestPath_a C) S) P2) T) (@ (@ (@ (@ tptp.isSimplePath_a C) S) P2) T))) _let_15 _let_14 _let_13 _let_12 (= tptp.isShor1936442771pacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isSimp1359852763pacity C2) U2) P) V4) (= (@ tptp.size_s1990949619at_nat P) (@ (@ (@ tptp.min_dist_capacity C2) U2) V4))))) (= tptp.isShortestPath_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (U2 tptp.nat) (P tptp.list_P559422087at_nat) (V4 tptp.nat)) (and (@ (@ (@ (@ tptp.isSimplePath_a C2) U2) P) V4) (= (@ tptp.size_s1990949619at_nat P) (@ (@ (@ tptp.min_dist_a C2) U2) V4))))) (= tptp.isPath_capacity tptp.isPath_capacity) (= tptp.isPath_a tptp.isPath_a) (= tptp.min_dist_capacity tptp.min_dist_capacity) (= tptp.min_dist_a tptp.min_dist_a) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat)) (@ (@ (@ tptp.connected_capacity C) V) V)) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat)) (@ (@ (@ tptp.connected_a C) V) V)) (= tptp.connected_capacity tptp.connected_capacity) (= tptp.connected_a tptp.connected_a) (= tptp.dist_capacity tptp.dist_capacity) (= tptp.dist_a tptp.dist_a) (= tptp.isShor1936442771pacity tptp.isShor1936442771pacity) (= tptp.isShortestPath_a tptp.isShortestPath_a) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.dist_capacity C))) (let ((_let_2 (@ _let_1 U))) (=> (@ (@ _let_2 D1) W) (=> (@ (@ (@ _let_1 W) D2) V) (@ (@ _let_2 (@ (@ tptp.plus_plus_nat D1) D2)) V)))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.dist_a C))) (let ((_let_2 (@ _let_1 U))) (=> (@ (@ _let_2 D1) W) (=> (@ (@ (@ _let_1 W) D2) V) (@ (@ _let_2 (@ (@ tptp.plus_plus_nat D1) D2)) V)))))) _let_11 _let_10 (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isShor1936442771pacity C) U) P2) V) (@ (@ (@ (@ tptp.isPath_capacity C) U) P2) V))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isShortestPath_a C) U) P2) V) (@ (@ (@ (@ tptp.isPath_a C) U) P2) V))) (= tptp.connected_capacity (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.capacity)) (V4 tptp.nat) (V5 tptp.nat)) (exists ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_capacity C2) V4) D4) V5)))) (= tptp.connected_a (lambda ((C2 (-> tptp.product_prod_nat_nat tptp.a)) (V4 tptp.nat) (V5 tptp.nat)) (exists ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_a C2) V4) D4) V5)))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D) V3) (@ (@ (@ tptp.connected_capacity C) V) V3))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D) V3) (@ (@ (@ tptp.connected_a C) V) V3))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (V tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity C) U) V) (not (forall ((P3 tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isShor1936442771pacity C) U) P3) V)))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (V tptp.nat)) (=> (@ (@ (@ tptp.connected_a C) U) V) (not (forall ((P3 tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isShortestPath_a C) U) P3) V)))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (Src tptp.nat) (V tptp.nat) (D tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity C) Src) V) (=> (= (@ (@ (@ tptp.min_dist_capacity C) Src) V) D) (=> (@ (@ tptp.ord_less_nat D3) D) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_capacity C) Src) V2) (= (@ (@ (@ tptp.min_dist_capacity C) Src) V2) D3))))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (Src tptp.nat) (V tptp.nat) (D tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a C) Src) V) (=> (= (@ (@ (@ tptp.min_dist_a C) Src) V) D) (=> (@ (@ tptp.ord_less_nat D3) D) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_a C) Src) V2) (= (@ (@ (@ tptp.min_dist_a C) Src) V2) D3))))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (Src tptp.nat) (V tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_capacity C) Src) V) (=> (@ (@ tptp.ord_less_eq_nat D3) (@ (@ (@ tptp.min_dist_capacity C) Src) V)) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_capacity C) Src) V2) (= (@ (@ (@ tptp.min_dist_capacity C) Src) V2) D3)))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (Src tptp.nat) (V tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a C) Src) V) (=> (@ (@ tptp.ord_less_eq_nat D3) (@ (@ (@ tptp.min_dist_a C) Src) V)) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_a C) Src) V2) (= (@ (@ (@ tptp.min_dist_a C) Src) V2) D3)))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D) V3) (=> (forall ((D5 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D5) V3) (@ (@ tptp.ord_less_eq_nat D) D5))) (= (@ (@ (@ tptp.min_dist_capacity C) V) V3) D)))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D) V3) (=> (forall ((D5 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D5) V3) (@ (@ tptp.ord_less_eq_nat D) D5))) (= (@ (@ (@ tptp.min_dist_a C) V) V3) D)))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_capacity C) V) D) V3) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_capacity C) V) V3)) D))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a C) V) D) V3) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_a C) V) V3)) D))) (forall ((C (-> tptp.product_prod_nat_nat tptp.capacity)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.min_dist_capacity C))) (let ((_let_2 (@ tptp.dist_capacity C))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ (@ _let_1 U) V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ (@ _let_1 W) V) D2))))))) (forall ((C (-> tptp.product_prod_nat_nat tptp.a)) (U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.min_dist_a C))) (let ((_let_2 (@ tptp.dist_a C))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ (@ _let_1 U) V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ (@ _let_1 W) V) D2))))))) _let_9 (forall ((K tptp.nat) (P5 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat K) (@ tptp.ord_Least_nat P5)) (not (@ P5 K)))) (forall ((P5 (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P5 K) (@ (@ tptp.ord_less_eq_nat (@ tptp.ord_Least_nat P5)) K))) (forall ((V tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ tptp.connected_a tptp.c2) V) V3) (exists ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D4) V3)))) (forall ((V tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a tptp.c2) V) V3) (@ (@ (@ (@ tptp.dist_a tptp.c2) V) (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3)) V3))) (forall ((U tptp.nat) (V tptp.nat)) (=> (@ (@ (@ tptp.connected_a tptp.c2) U) V) (not (forall ((P3 tptp.list_P559422087at_nat)) (not (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P3) V)))))) (forall ((S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) S) P2) T) (@ (@ (@ (@ tptp.isSimplePath_a tptp.c2) S) P2) T))) (forall ((U tptp.nat)) (= (@ (@ tptp.reachableNodes_a tptp.c2) U) (@ tptp.collect_nat (@ (@ tptp.connected_a tptp.c2) U)))) (forall ((Src tptp.nat) (V tptp.nat) (D tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a tptp.c2) Src) V) (=> (= (@ (@ (@ tptp.min_dist_a tptp.c2) Src) V) D) (=> (@ (@ tptp.ord_less_nat D3) D) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_a tptp.c2) Src) V2) (= (@ (@ (@ tptp.min_dist_a tptp.c2) Src) V2) D3))))))) (forall ((V tptp.nat) (V3 tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.connected_a tptp.c2) V) V3) (=> (forall ((D6 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D6) V3) (=> (forall ((D7 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D7) V3) (@ (@ tptp.ord_less_eq_nat D6) D7))) (@ Q D6)))) (@ Q (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3))))) (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D) V3) (=> (forall ((D5 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D5) V3) (@ (@ tptp.ord_less_eq_nat D) D5))) (= (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3) D)))) (forall ((Src tptp.nat) (V tptp.nat) (D3 tptp.nat)) (=> (@ (@ (@ tptp.connected_a tptp.c2) Src) V) (=> (@ (@ tptp.ord_less_eq_nat D3) (@ (@ (@ tptp.min_dist_a tptp.c2) Src) V)) (exists ((V2 tptp.nat)) (and (@ (@ (@ tptp.connected_a tptp.c2) Src) V2) (= (@ (@ (@ tptp.min_dist_a tptp.c2) Src) V2) D3)))))) (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D) V3) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3)) D))) (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.min_dist_a tptp.c2))) (let ((_let_2 (@ tptp.dist_a tptp.c2))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ (@ _let_1 U) V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ (@ _let_1 W) V) D2))))))) (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.min_dist_a tptp.c2) U))) (let ((_let_2 (@ tptp.dist_a tptp.c2))) (=> (@ (@ (@ _let_2 U) D1) W) (=> (@ (@ (@ _let_2 W) D2) V) (=> (= (@ _let_1 V) (@ (@ tptp.plus_plus_nat D1) D2)) (= (@ _let_1 W) D1))))))) (forall ((U tptp.nat) (D1 tptp.nat) (W tptp.nat) (D2 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.dist_a tptp.c2))) (let ((_let_2 (@ _let_1 U))) (=> (@ (@ _let_2 D1) W) (=> (@ (@ (@ _let_1 W) D2) V) (@ (@ _let_2 (@ (@ tptp.plus_plus_nat D1) D2)) V)))))) (forall ((U tptp.nat) (V tptp.nat)) (= (@ (@ (@ tptp.connected_a tptp.c2) U) V) (exists ((P tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P) V)))) (forall ((S tptp.nat) (P2 tptp.list_P559422087at_nat) (T tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_a tptp.c2) S) P2) T) (exists ((P6 tptp.list_P559422087at_nat)) (@ (@ (@ (@ tptp.isSimplePath_a tptp.c2) S) P6) T)))) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P2) V) (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P2) V))) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P2) V) (and (@ (@ (@ (@ tptp.isSimplePath_a tptp.c2) U) P2) V) (= (@ tptp.size_s1990949619at_nat P2) (@ (@ (@ tptp.min_dist_a tptp.c2) U) V))))) (forall ((V tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ tptp.min_dist_a tptp.c2) V) V3) (@ tptp.ord_Least_nat (lambda ((D4 tptp.nat)) (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D4) V3))))) (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (= (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D) V3) (exists ((P tptp.list_P559422087at_nat)) (and (@ (@ (@ (@ tptp.isPath_a tptp.c2) V) P) V3) (= (@ tptp.size_s1990949619at_nat P) D))))) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (=> (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P2) V) (@ (@ (@ (@ tptp.dist_a tptp.c2) U) (@ tptp.size_s1990949619at_nat P2)) V))) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P2) V) (and (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P2) V) (= (@ tptp.size_s1990949619at_nat P2) (@ (@ (@ tptp.min_dist_a tptp.c2) U) V))))) (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) X3)) (forall ((U tptp.nat) (P2 tptp.list_P559422087at_nat) (V tptp.nat)) (= (@ (@ (@ (@ tptp.isShortestPath_a tptp.c2) U) P2) V) (and (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P2) V) (forall ((P4 tptp.list_P559422087at_nat)) (=> (@ (@ (@ (@ tptp.isPath_a tptp.c2) U) P4) V) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1990949619at_nat P2)) (@ tptp.size_s1990949619at_nat P4))))))) (@ (@ (@ _let_8 tptp.s) tptp.p3) tptp.t) (@ (@ (@ _let_8 tptp.u) tptp.p2) tptp.t) (forall ((V tptp.nat) (D tptp.nat) (V3 tptp.nat)) (=> (@ (@ (@ (@ tptp.dist_a tptp.c2) V) D) V3) (@ (@ (@ tptp.connected_a tptp.c2) V) V3))) (forall ((V tptp.nat)) (@ (@ (@ tptp.connected_a tptp.c2) V) V)) _let_9 (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (= (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)) (lambda ((X2 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X2)))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (= X3 Y3)))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X3))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= X3 Y3) (@ (@ tptp.ord_less_eq_nat X3) Y3))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X3) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X3))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))) (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X3))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y3))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X3))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((Y3 tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (= (@ (@ tptp.ord_less_eq_nat X3) Y3) (= X3 Y3)))) (= (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) A2)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))) (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z2) (@ _let_1 Z2))))) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)) (forall ((P5 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P5 A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P5 B4) A4) (@ (@ P5 A4) B4))) (@ (@ P5 A) B)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (= (lambda ((Y4 tptp.nat) (Z tptp.nat)) (= Y4 Z)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat A2) B2)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X3) Y3)) (or (@ (@ tptp.ord_less_nat Y3) X3) (= X3 Y3)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((P5 (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (@ (@ P5 A4) B4))) (=> (forall ((A4 tptp.nat)) (@ (@ P5 A4) A4)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P5 B4) A4) (@ (@ P5 A4) B4))) (@ (@ P5 A) B))))) (= (lambda ((P7 (-> tptp.nat Bool))) (exists ((X4 tptp.nat)) (@ P7 X4))) (lambda ((P8 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P8 N2) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ P8 M2)))))))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (@ (@ tptp.ord_less_nat Y3) X3)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X3) Y3)) (=> (not (= X3 Y3)) (@ (@ tptp.ord_less_nat Y3) X3)))) (forall ((X3 tptp.nat) (Y3 tptp.nat) (P5 Bool)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (=> (@ (@ tptp.ord_less_nat Y3) X3) P5))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (= Y3 X3)))) (forall ((Y3 tptp.nat) (X3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y3) X3)) (= (not (@ (@ tptp.ord_less_nat X3) Y3)) (= X3 Y3)))) (forall ((P5 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y2) X) (@ P5 Y2))) (@ P5 X))) (@ P5 A))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (@ (@ tptp.ord_less_nat Y3) X3)))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (= X3 Y3)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((X3 tptp.nat)) (not (@ (@ tptp.ord_less_nat X3) X3))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y3) (= X3 Y3) (@ (@ tptp.ord_less_nat Y3) X3))) (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_nat Y3) Z2) (@ _let_1 Z2))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (@ (@ tptp.ord_less_nat Y3) X3)))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (not (= X3 Y3)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (not (= X3 Y3)) (or (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_nat Y3) X3)))) (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (not (= X3 Y3)) (=> (not (@ (@ tptp.ord_less_nat X3) Y3)) (@ (@ tptp.ord_less_nat Y3) X3)))) (forall ((X3 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X3) X_1))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((P5 (-> tptp.nat Bool)) (A tptp.nat) (Q (-> tptp.nat Bool))) (=> (@ P5 A) (=> (forall ((X tptp.nat)) (=> (@ P5 X) (@ Q X))) (@ Q (@ tptp.ord_Least_nat P5))))) (forall ((P5 (-> tptp.nat Bool))) (=> (exists ((X_12 tptp.nat)) (@ P5 X_12)) (@ P5 (@ tptp.ord_Least_nat P5)))) (forall ((P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (exists ((X_12 tptp.nat)) (@ P5 X_12)) (=> (forall ((X tptp.nat)) (=> (@ P5 X) (@ Q X))) (@ Q (@ tptp.ord_Least_nat P5))))) (forall ((P5 (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P5 K) (@ P5 (@ tptp.ord_Least_nat P5)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))) (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (not (= A2 B2))))) (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A2) (= A2 B2)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))) _let_7 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.05/1.27 )
% 1.05/1.27 % SZS output end Proof for ITP048^1
% 1.05/1.27 % cvc5---1.0.5 exiting
% 1.05/1.27 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------