TSTP Solution File: ITP052^1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP052^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 : Tue May 7 07:47:25 EDT 2024
% Result : Theorem 15.50s 4.84s
% Output : Refutation 16.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 329
% Syntax : Number of formulae : 606 ( 226 unt; 54 typ; 0 def)
% Number of atoms : 1426 ( 379 equ; 12 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 4893 ( 124 ~; 4 |; 70 &;4109 @)
% ( 0 <=>; 586 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 480 ( 480 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 9 con; 0-5 aty)
% Number of variables : 1568 ( 96 ^1420 !; 52 ?;1568 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_P559422087at_nat_type,type,
list_P559422087at_nat: $tType ).
thf(set_Pr1986765409at_nat_type,type,
set_Pr1986765409at_nat: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(capacity_type,type,
capacity: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(augmen887209518pacity_type,type,
augmen887209518pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(augmen72931474pacity_type,type,
augmen72931474pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > product_prod_nat_nat > capacity ).
thf(augmen1090971539pacity_type,type,
augmen1090971539pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > $o ).
thf(augmen68920357pacity_type,type,
augmen68920357pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > capacity ).
thf(finite217307323pacity_type,type,
finite217307323pacity: ( product_prod_nat_nat > capacity ) > $o ).
thf(isShor1936442771pacity_type,type,
isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(isSimp1359852763pacity_type,type,
isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(plus_plus_capacity_type,type,
plus_plus_capacity: capacity > capacity > capacity ).
thf(zero_zero_capacity_type,type,
zero_zero_capacity: capacity ).
thf(inf_in2138576462_nat_o_type,type,
inf_in2138576462_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(inf_in586391887at_nat_type,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(set_Pr2131844118at_nat_type,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(finite1387368318pacity_type,type,
finite1387368318pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(flow_capacity_type,type,
flow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(val_capacity_type,type,
val_capacity: ( product_prod_nat_nat > capacity ) > nat > ( product_prod_nat_nat > capacity ) > capacity ).
thf(nCut_capacity_type,type,
nCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
thf(cap_capacity_type,type,
cap_capacity: ( product_prod_nat_nat > capacity ) > set_nat > capacity ).
thf(nFlow_capacity_type,type,
nFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(nPreflow_capacity_type,type,
nPreflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(network_capacity_type,type,
network_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
thf(excess_capacity_type,type,
excess_capacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > nat > capacity ).
thf(isMaxFlow_capacity_type,type,
isMaxFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(is_max2144541363pacity_type,type,
is_max2144541363pacity: ( product_prod_nat_nat > capacity ) > nat > nat > capacity > $o ).
thf(preflow_capacity_type,type,
preflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(isMinCut_capacity_type,type,
isMinCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
thf(bot_bo513358416_nat_o_type,type,
bot_bo513358416_nat_o: product_prod_nat_nat > $o ).
thf(bot_bot_o_type,type,
bot_bot_o: $o ).
thf(bot_bo2130386637at_nat_type,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(ord_le1015898640_nat_o_type,type,
ord_le1015898640_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(ord_le116442893at_nat_type,type,
ord_le116442893at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(ord_less_capacity_type,type,
ord_less_capacity: capacity > capacity > $o ).
thf(ord_le1039616028_nat_o_type,type,
ord_le1039616028_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(ord_le841296385at_nat_type,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(ord_less_eq_capacity_type,type,
ord_less_eq_capacity: capacity > capacity > $o ).
thf(product_Pair_nat_nat_type,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(product_swap_nat_nat_type,type,
product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(converse_nat_nat_type,type,
converse_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(residu1549650759pacity_type,type,
residu1549650759pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(residu800046103pacity_type,type,
residu800046103pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(residu164581374pacity_type,type,
residu164581374pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(residu203630698pacity_type,type,
residu203630698pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(collec7649004at_nat_type,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(member701585322at_nat_type,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(c_type,type,
c: product_prod_nat_nat > capacity ).
thf(f_type,type,
f: product_prod_nat_nat > capacity ).
thf(p_type,type,
p: list_P559422087at_nat ).
thf(s_type,type,
s: nat ).
thf(t_type,type,
t: nat ).
thf(31,axiom,
! [A: capacity,B: capacity,C: capacity] :
( ( A = B )
=> ( ( ord_less_eq_capacity @ B @ C )
=> ( ord_less_eq_capacity @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_ord__eq__le__trans) ).
thf(365,plain,
! [A: capacity,B: capacity,C: capacity] :
( ( A = B )
=> ( ( ord_less_eq_capacity @ B @ C )
=> ( ord_less_eq_capacity @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,axiom,
ord_less_eq_capacity @ ( excess_capacity @ c @ f @ s ) @ zero_zero_capacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_excess__s__non__pos) ).
thf(479,plain,
ord_less_eq_capacity @ ( excess_capacity @ c @ f @ s ) @ zero_zero_capacity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(112,axiom,
! [A: capacity,B: capacity] :
( ( is_max2144541363pacity @ c @ s @ t @ A )
=> ( ( is_max2144541363pacity @ c @ s @ t @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_max__flow__val__unique) ).
thf(628,plain,
! [A: capacity,B: capacity] :
( ( is_max2144541363pacity @ c @ s @ t @ A )
=> ( ( is_max2144541363pacity @ c @ s @ t @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(60,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) )
= ( ? [E: set_nat] :
( ( nCut_capacity @ A @ B @ C @ E )
& ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_NFlow_Oford__fulkerson_I2_J) ).
thf(468,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) )
= ( ? [E: set_nat] :
( ( nCut_capacity @ A @ B @ C @ E )
& ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(90,axiom,
( isMinCut_capacity
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: set_nat] :
( ( nCut_capacity @ A @ B @ C @ D )
& ! [E: set_nat] :
( ( nCut_capacity @ A @ B @ C @ E )
=> ( ord_less_eq_capacity @ ( cap_capacity @ A @ D ) @ ( cap_capacity @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_isMinCut__def) ).
thf(555,plain,
( isMinCut_capacity
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: set_nat] :
( ( nCut_capacity @ A @ B @ C @ D )
& ! [E: set_nat] :
( ( nCut_capacity @ A @ B @ C @ E )
=> ( ord_less_eq_capacity @ ( cap_capacity @ A @ D ) @ ( cap_capacity @ A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(26,axiom,
! [A: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ c @ s @ t @ A )
= ( ( flow_capacity @ c @ s @ t @ A )
& ! [B: product_prod_nat_nat > capacity] :
( ( flow_capacity @ c @ s @ t @ B )
=> ( ord_less_eq_capacity @ ( val_capacity @ c @ s @ B ) @ ( val_capacity @ c @ s @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_isMaxFlow__def) ).
thf(352,plain,
! [A: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ c @ s @ t @ A )
= ( ( flow_capacity @ c @ s @ t @ A )
& ! [B: product_prod_nat_nat > capacity] :
( ( flow_capacity @ c @ s @ t @ B )
=> ( ord_less_eq_capacity @ ( val_capacity @ c @ s @ B ) @ ( val_capacity @ c @ s @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(118,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_order_Ostrict__implies__not__eq) ).
thf(645,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(204,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ C ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ C ) ) )
= bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Graph_OisSPath__nt__parallel__pf) ).
thf(892,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ C ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ C ) ) )
= bot_bo2130386637at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(159,axiom,
( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ? [A: set_nat] :
( ( nCut_capacity @ c @ s @ t @ A )
& ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_fofu__II__III) ).
thf(762,plain,
( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ? [A: set_nat] :
( ( nCut_capacity @ c @ s @ t @ A )
& ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(243,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B )
= ( inf_in586391887at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_inf_Oright__idem) ).
thf(1005,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B )
= ( inf_in586391887at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(201,axiom,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_inf__bot__right) ).
thf(878,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(255,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( inf_in586391887at_nat @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_inf_Oabsorb2) ).
thf(1041,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( inf_in586391887at_nat @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(267,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ~ ( ( ord_le841296385at_nat @ A @ B )
=> ~ ( ord_le841296385at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_inf_OboundedE) ).
thf(1078,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ~ ( ( ord_le841296385at_nat @ A @ B )
=> ~ ( ord_le841296385at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(36,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ( network_capacity @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_RGraph_Oaxioms_I1_J) ).
thf(384,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ( network_capacity @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(82,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat] :
( ( isShor1936442771pacity @ A @ B @ C @ D )
=> ( isSimp1359852763pacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Graph_OshortestPath__is__simple) ).
thf(533,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat] :
( ( isShor1936442771pacity @ A @ B @ C @ D )
=> ( isSimp1359852763pacity @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(169,axiom,
! [A: product_prod_nat_nat,B: product_prod_nat_nat > $o] :
( ( member701585322at_nat @ A @ ( collec7649004at_nat @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_mem__Collect__eq) ).
thf(797,plain,
! [A: product_prod_nat_nat,B: product_prod_nat_nat > $o] :
( ( member701585322at_nat @ A @ ( collec7649004at_nat @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(154,axiom,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ( ord_less_capacity @ zero_zero_capacity @ ( augmen68920357pacity @ c @ f @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_resCap__gzero) ).
thf(747,plain,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ( ord_less_capacity @ zero_zero_capacity @ ( augmen68920357pacity @ c @ f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(23,axiom,
! [A: nat,B: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( c @ ( product_Pair_nat_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_cap__non__negative) ).
thf(340,plain,
! [A: nat,B: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( c @ ( product_Pair_nat_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(85,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( residu164581374pacity @ A @ B @ C @ ( residu203630698pacity @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_NPreflow_Ois__RPreGraph) ).
thf(538,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( residu164581374pacity @ A @ B @ C @ ( residu203630698pacity @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(183,axiom,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat] :
( ! [C: nat,D: nat] : ( A @ ( product_Pair_nat_nat @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_prod__cases) ).
thf(829,plain,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat] :
( ! [C: nat,D: nat] : ( A @ ( product_Pair_nat_nat @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(206,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_cf_OisSPath__no__selfloop) ).
thf(898,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(165,axiom,
! [A: product_prod_nat_nat > capacity] :
( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ A )
=> ( flow_capacity @ c @ s @ t @ ( augmen887209518pacity @ c @ f @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_augment__flow__presv) ).
thf(782,plain,
! [A: product_prod_nat_nat > capacity] :
( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ A )
=> ( flow_capacity @ c @ s @ t @ ( augmen887209518pacity @ c @ f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(141,axiom,
! [A: product_prod_nat_nat > $o] :
~ ( ord_le1015898640_nat_o @ A @ bot_bo513358416_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_bot_Oextremum__strict) ).
thf(709,plain,
! [A: product_prod_nat_nat > $o] :
~ ( ord_le1015898640_nat_o @ A @ bot_bo513358416_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(188,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat,E: nat,F: nat,G: nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ C ) )
=> ( ( E != G )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ G @ F ) @ ( set_Pr2131844118at_nat @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_Graph_OisSPath__sg__incoming) ).
thf(841,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat,E: nat,F: nat,G: nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ C ) )
=> ( ( E != G )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ G @ F ) @ ( set_Pr2131844118at_nat @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(7,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_NFlow_Oford__fulkerson_I1_J) ).
thf(288,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(94,axiom,
! [A: capacity,B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_capacity @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_ord__le__eq__trans) ).
thf(565,plain,
! [A: capacity,B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_capacity @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(120,axiom,
( ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) )
= ( ? [A: set_nat] :
( ( nCut_capacity @ c @ s @ t @ A )
& ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_ford__fulkerson_I2_J) ).
thf(651,plain,
( ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) )
= ( ? [A: set_nat] :
( ( nCut_capacity @ c @ s @ t @ A )
& ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(95,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ( nFlow_capacity @ A @ B @ C @ D )
& ! [E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ E )
=> ( ord_less_eq_capacity @ ( val_capacity @ A @ B @ E ) @ ( val_capacity @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_Network_OisMaxFlow__alt) ).
thf(570,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ( nFlow_capacity @ A @ B @ C @ D )
& ! [E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ E )
=> ( ord_less_eq_capacity @ ( val_capacity @ A @ B @ E ) @ ( val_capacity @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(145,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( B @ C ) )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_order__subst1) ).
thf(719,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( B @ C ) )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(212,axiom,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ bot_bo2130386637at_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_bot_Oextremum) ).
thf(917,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ bot_bo2130386637at_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(25,axiom,
! [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity,D: capacity] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_capacity @ C @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_ord__eq__le__subst) ).
thf(344,plain,
! [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity,D: capacity] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_capacity @ C @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(28,axiom,
( nFlow_capacity
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
& ( flow_capacity @ A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_NFlow__def) ).
thf(357,plain,
( nFlow_capacity
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
& ( flow_capacity @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(261,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_inf__left__commute) ).
thf(1059,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(223,axiom,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_le__iff__inf) ).
thf(949,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(99,axiom,
! [A: capacity,B: capacity] :
( ( ord_less_capacity @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_dual__order_Ostrict__implies__not__eq) ).
thf(587,plain,
! [A: capacity,B: capacity] :
( ( ord_less_capacity @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(187,axiom,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_inf__idem) ).
thf(838,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(177,axiom,
( ( (=) @ set_Pr1986765409at_nat )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ B @ A )
& ( ord_le841296385at_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_dual__order_Oeq__iff) ).
thf(817,plain,
( ( (=) @ set_Pr1986765409at_nat )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ B @ A )
& ( ord_le841296385at_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(92,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( network_capacity @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_RPreGraph_Oaxioms_I1_J) ).
thf(559,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( network_capacity @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(270,axiom,
( ord_le116442893at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ A @ B ) )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_inf_Ostrict__order__iff) ).
thf(1087,plain,
( ord_le116442893at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ A @ B ) )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(202,axiom,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ A )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_inf__bot__left) ).
thf(881,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ A )
= bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(57,axiom,
! [A: capacity,B: capacity] :
( ( A = B )
=> ( ord_less_eq_capacity @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_eq__refl) ).
thf(448,plain,
! [A: capacity,B: capacity] :
( ( A = B )
=> ( ord_less_eq_capacity @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(70,axiom,
! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_f__non__negative) ).
thf(492,plain,
! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(100,axiom,
! [A: capacity,B: capacity] :
( ( ~ ( ord_less_capacity @ A @ B ) )
= ( ( ord_less_capacity @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_not__less__iff__gr__or__eq) ).
thf(591,plain,
! [A: capacity,B: capacity] :
( ( ~ ( ord_less_capacity @ A @ B ) )
= ( ( ord_less_capacity @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(55,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( preflow_capacity @ A @ B @ C @ D )
=> ( ( finite217307323pacity @ A )
=> ( finite1387368318pacity @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Finite__Preflow_Ointro) ).
thf(443,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( preflow_capacity @ A @ B @ C @ D )
=> ( ( finite217307323pacity @ A )
=> ( finite1387368318pacity @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(16,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ( residu164581374pacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_RGraph_Othis__loc__rpg) ).
thf(321,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ( residu164581374pacity @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(35,axiom,
! [A: capacity,B: capacity > capacity,C: capacity,D: capacity] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_capacity @ C @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ord__eq__le__subst) ).
thf(376,plain,
! [A: capacity,B: capacity > capacity,C: capacity,D: capacity] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_capacity @ C @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(110,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( residu800046103pacity @ A @ B @ C @ ( residu203630698pacity @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_NFlow_Ois__RGraph) ).
thf(623,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( residu800046103pacity @ A @ B @ C @ ( residu203630698pacity @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(67,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ ( augmen72931474pacity @ A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_NPreflow_OaugFlow__resFlow) ).
thf(485,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ ( augmen72931474pacity @ A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(219,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( converse_nat_nat @ ( inf_in586391887at_nat @ A @ B ) )
= ( inf_in586391887at_nat @ ( converse_nat_nat @ A ) @ ( converse_nat_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_converse__Int) ).
thf(937,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( converse_nat_nat @ ( inf_in586391887at_nat @ A @ B ) )
= ( inf_in586391887at_nat @ ( converse_nat_nat @ A ) @ ( converse_nat_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(96,axiom,
! [A: product_prod_nat_nat > capacity,B: set_nat] :
( ( isMaxFlow_capacity @ c @ s @ t @ A )
=> ( ( isMinCut_capacity @ c @ s @ t @ B )
=> ( ( val_capacity @ c @ s @ A )
= ( cap_capacity @ c @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_maxFlow__minCut) ).
thf(574,plain,
! [A: product_prod_nat_nat > capacity,B: set_nat] :
( ( isMaxFlow_capacity @ c @ s @ t @ A )
=> ( ( isMinCut_capacity @ c @ s @ t @ B )
=> ( ( val_capacity @ c @ s @ A )
= ( cap_capacity @ c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(179,axiom,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ? [B: list_P559422087at_nat] : ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ s @ B @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_augmenting__path__imp__shortest) ).
thf(821,plain,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ? [B: list_P559422087at_nat] : ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ s @ B @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(65,axiom,
! [A: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ c @ s @ t @ A )
= ( ( nFlow_capacity @ c @ s @ t @ A )
& ! [B: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ c @ s @ t @ B )
=> ( ord_less_eq_capacity @ ( val_capacity @ c @ s @ B ) @ ( val_capacity @ c @ s @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_isMaxFlow__alt) ).
thf(480,plain,
! [A: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ c @ s @ t @ A )
= ( ( nFlow_capacity @ c @ s @ t @ A )
& ! [B: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ c @ s @ t @ B )
=> ( ord_less_eq_capacity @ ( val_capacity @ c @ s @ B ) @ ( val_capacity @ c @ s @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(4,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( ord_less_eq_capacity @ zero_zero_capacity @ ( D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_RPreGraph_OresE__nonNegative) ).
thf(280,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( ord_less_eq_capacity @ zero_zero_capacity @ ( D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(150,axiom,
preflow_capacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Preflow__axioms) ).
thf(734,plain,
preflow_capacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(197,axiom,
( inf_in586391887at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_inf__sup__aci_I1_J) ).
thf(866,plain,
( inf_in586391887at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(265,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_less__infI2) ).
thf(1072,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(45,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( network_capacity @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_NPreflow_Oaxioms_I1_J) ).
thf(411,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( network_capacity @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(80,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ? [E: set_nat] :
( ( nCut_capacity @ A @ B @ C @ E )
& ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) )
=> ( isMaxFlow_capacity @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_NFlow_Ofofu__III__I) ).
thf(527,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ? [E: set_nat] :
( ( nCut_capacity @ A @ B @ C @ E )
& ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) )
=> ( isMaxFlow_capacity @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(235,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( A
= ( inf_in586391887at_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_inf_OorderE) ).
thf(981,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( A
= ( inf_in586391887at_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(160,axiom,
network_capacity @ c @ s @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Network__axioms) ).
thf(766,plain,
network_capacity @ c @ s @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(276,axiom,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_inf_Oabsorb__iff1) ).
thf(1104,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(191,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ C )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ ( converse_nat_nat @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_converse_Ointros) ).
thf(849,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ C )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ ( converse_nat_nat @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(13,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > capacity,D: capacity] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_ord__le__eq__subst) ).
thf(307,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > capacity,D: capacity] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,axiom,
! [A: capacity,B: capacity,C: capacity] :
( ( ( ord_less_eq_capacity @ A @ B )
=> ~ ( ord_less_eq_capacity @ B @ C ) )
=> ( ( ( ord_less_eq_capacity @ B @ A )
=> ~ ( ord_less_eq_capacity @ A @ C ) )
=> ( ( ( ord_less_eq_capacity @ A @ C )
=> ~ ( ord_less_eq_capacity @ C @ B ) )
=> ( ( ( ord_less_eq_capacity @ C @ B )
=> ~ ( ord_less_eq_capacity @ B @ A ) )
=> ( ( ( ord_less_eq_capacity @ B @ C )
=> ~ ( ord_less_eq_capacity @ C @ A ) )
=> ~ ( ( ord_less_eq_capacity @ C @ A )
=> ~ ( ord_less_eq_capacity @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_le__cases3) ).
thf(452,plain,
! [A: capacity,B: capacity,C: capacity] :
( ( ( ord_less_eq_capacity @ A @ B )
=> ~ ( ord_less_eq_capacity @ B @ C ) )
=> ( ( ( ord_less_eq_capacity @ B @ A )
=> ~ ( ord_less_eq_capacity @ A @ C ) )
=> ( ( ( ord_less_eq_capacity @ A @ C )
=> ~ ( ord_less_eq_capacity @ C @ B ) )
=> ( ( ( ord_less_eq_capacity @ C @ B )
=> ~ ( ord_less_eq_capacity @ B @ A ) )
=> ( ( ( ord_less_eq_capacity @ B @ C )
=> ~ ( ord_less_eq_capacity @ C @ A ) )
=> ~ ( ( ord_less_eq_capacity @ C @ A )
=> ~ ( ord_less_eq_capacity @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(131,axiom,
augmen1090971539pacity = augmen1090971539pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_NPreflow_OisAugmentingPath_Ocong) ).
thf(678,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(143,axiom,
! [A: product_prod_nat_nat] :
( ( product_swap_nat_nat @ ( product_swap_nat_nat @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_swap__swap) ).
thf(714,plain,
! [A: product_prod_nat_nat] :
( ( product_swap_nat_nat @ ( product_swap_nat_nat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(257,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_inf_Ostrict__coboundedI1) ).
thf(1047,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(76,axiom,
! [A: product_prod_nat_nat] :
( ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ A ) )
& ( ord_less_eq_capacity @ ( f @ A ) @ ( c @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_capacity__const) ).
thf(512,plain,
! [A: product_prod_nat_nat] :
( ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ A ) )
& ( ord_less_eq_capacity @ ( f @ A ) @ ( c @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(221,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat,F: nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( D != F )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ E ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_isSPath__sg__incoming) ).
thf(942,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat,F: nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( D != F )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ E ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(226,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_isSPath__no__selfloop) ).
thf(957,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(153,axiom,
isSimp1359852763pacity = isSimp1359852763pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Graph_OisSimplePath_Ocong) ).
thf(746,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(164,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
= ( isSimp1359852763pacity @ ( residu203630698pacity @ A @ D ) @ B @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_NPreflow_OisAugmentingPath__def) ).
thf(778,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
= ( isSimp1359852763pacity @ ( residu203630698pacity @ A @ D ) @ B @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(10,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( nPreflow_capacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_NFlow_Oaxioms_I1_J) ).
thf(302,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( nPreflow_capacity @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(196,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( converse_nat_nat @ B ) )
=> ~ ! [C: nat,D: nat] :
( ( A
= ( product_Pair_nat_nat @ D @ C ) )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_converseE) ).
thf(862,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( converse_nat_nat @ B ) )
=> ~ ! [C: nat,D: nat] :
( ( A
= ( product_Pair_nat_nat @ D @ C ) )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(102,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ? [F: list_P559422087at_nat] : ( isShor1936442771pacity @ ( residu203630698pacity @ A @ D ) @ B @ F @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_NFlow_Oaugmenting__path__imp__shortest) ).
thf(598,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ? [F: list_P559422087at_nat] : ( isShor1936442771pacity @ ( residu203630698pacity @ A @ D ) @ B @ F @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(50,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ( residu800046103pacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_RGraph_Othis__loc) ).
thf(424,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(136,axiom,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
=> ( A = bot_bo513358416_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_bot_Oextremum__uniqueI) ).
thf(693,plain,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
=> ( A = bot_bo513358416_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(52,axiom,
! [A: capacity,B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ C @ A )
=> ( ord_less_eq_capacity @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_dual__order_Otrans) ).
thf(429,plain,
! [A: capacity,B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ C @ A )
=> ( ord_less_eq_capacity @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(167,axiom,
( ( (=) @ set_Pr1986765409at_nat )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_order__class_Oorder_Oeq__iff) ).
thf(788,plain,
( ( (=) @ set_Pr1986765409at_nat )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(176,axiom,
( ( (=) @ set_Pr1986765409at_nat )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_eq__iff) ).
thf(815,plain,
( ( (=) @ set_Pr1986765409at_nat )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(190,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_converseD) ).
thf(847,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(252,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B )
= ( inf_in586391887at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_inf__right__idem) ).
thf(1032,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B )
= ( inf_in586391887at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(111,axiom,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat > $o] :
( ! [C: product_prod_nat_nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec7649004at_nat @ A )
= ( collec7649004at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Collect__cong) ).
thf(625,plain,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat > $o] :
( ! [C: product_prod_nat_nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec7649004at_nat @ A )
= ( collec7649004at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(126,axiom,
! [A: product_prod_nat_nat] :
? [B: nat,C: nat] :
( A
= ( product_Pair_nat_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_surj__pair) ).
thf(665,plain,
! [A: product_prod_nat_nat] :
? [B: nat,C: nat] :
( A
= ( product_Pair_nat_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(98,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ( C != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Network_Ot__not__s) ).
thf(583,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ( C != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(88,axiom,
is_max2144541363pacity = is_max2144541363pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Network_Ois__max__flow__val_Ocong) ).
thf(551,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(246,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ B @ C ) )
=> ( ( inf_in586391887at_nat @ D @ A )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_boolean__algebra__cancel_Oinf2) ).
thf(1012,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ B @ C ) )
=> ( ( inf_in586391887at_nat @ D @ A )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(6,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( isShor1936442771pacity @ ( residu203630698pacity @ A @ D ) @ B @ E @ C )
=> ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_NFlow_Oshortest__is__augmenting) ).
thf(285,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( isShor1936442771pacity @ ( residu203630698pacity @ A @ D ) @ B @ E @ C )
=> ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
=> ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_NFlow_Ofofu__I__II) ).
thf(324,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
=> ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(232,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_inf__sup__ord_I2_J) ).
thf(974,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(97,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( preflow_capacity @ A @ B @ C @ D )
=> ! [E: product_prod_nat_nat] :
( ( ord_less_eq_capacity @ zero_zero_capacity @ ( D @ E ) )
& ( ord_less_eq_capacity @ ( D @ E ) @ ( A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Preflow_Ocapacity__const) ).
thf(578,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( preflow_capacity @ A @ B @ C @ D )
=> ! [E: product_prod_nat_nat] :
( ( ord_less_eq_capacity @ zero_zero_capacity @ ( D @ E ) )
& ( ord_less_eq_capacity @ ( D @ E ) @ ( A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(271,axiom,
! [A: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
=> ( A = bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_bot_Oextremum__uniqueI) ).
thf(1089,plain,
! [A: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
=> ( A = bot_bo2130386637at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(247,axiom,
( inf_in586391887at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_inf__commute) ).
thf(1017,plain,
( inf_in586391887at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(107,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) )
= ( isMaxFlow_capacity @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_NFlow_OnoAugPath__iff__maxFlow) ).
thf(615,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) )
= ( isMaxFlow_capacity @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(147,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ! [C: nat,D: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ A )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ B ) )
=> ( ord_le841296385at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_subrelI) ).
thf(725,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ! [C: nat,D: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ A )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ D ) @ B ) )
=> ( ord_le841296385at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(42,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( preflow_capacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_NPreflow_Oaxioms_I2_J) ).
thf(403,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( preflow_capacity @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(273,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_inf_Ocobounded2) ).
thf(1096,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(238,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ B ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ B ) ) )
= bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_cf_OisSPath__nt__parallel__pf) ).
thf(989,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ B ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ B ) ) )
= bot_bo2130386637at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(194,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C )
= ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_inf__sup__aci_I2_J) ).
thf(857,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C )
= ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(61,axiom,
( ? [A: set_nat] :
( ( nCut_capacity @ c @ s @ t @ A )
& ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ A ) ) )
=> ( isMaxFlow_capacity @ c @ s @ t @ f ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_fofu__III__I) ).
thf(471,plain,
( ? [A: set_nat] :
( ( nCut_capacity @ c @ s @ t @ A )
& ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ A ) ) )
=> ( isMaxFlow_capacity @ c @ s @ t @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(203,axiom,
! [A: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ! [D: set_Pr1986765409at_nat,E: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( A @ D @ E ) @ D )
=> ( ! [D: set_Pr1986765409at_nat,E: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( A @ D @ E ) @ E )
=> ( ! [D: set_Pr1986765409at_nat,E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ D @ E )
=> ( ( ord_le841296385at_nat @ D @ F )
=> ( ord_le841296385at_nat @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_in586391887at_nat @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_inf__unique) ).
thf(884,plain,
! [A: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ! [D: set_Pr1986765409at_nat,E: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( A @ D @ E ) @ D )
=> ( ! [D: set_Pr1986765409at_nat,E: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( A @ D @ E ) @ E )
=> ( ! [D: set_Pr1986765409at_nat,E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ D @ E )
=> ( ( ord_le841296385at_nat @ D @ F )
=> ( ord_le841296385at_nat @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_in586391887at_nat @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(68,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: set_nat] :
( ( nCut_capacity @ A @ B @ C @ D )
=> ( network_capacity @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_NCut_Oaxioms_I1_J) ).
thf(488,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: set_nat] :
( ( nCut_capacity @ A @ B @ C @ D )
=> ( network_capacity @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(117,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ C @ A )
=> ( ord_le841296385at_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_dual__order_Otrans) ).
thf(642,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ C @ A )
=> ( ord_le841296385at_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(132,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ A )
=> ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ c @ f @ A @ ( product_Pair_nat_nat @ B @ C ) ) )
& ( ord_less_eq_capacity @ ( augmen887209518pacity @ c @ f @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ ( c @ ( product_Pair_nat_nat @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_augment__flow__presv__cap) ).
thf(679,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ A )
=> ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ c @ f @ A @ ( product_Pair_nat_nat @ B @ C ) ) )
& ( ord_less_eq_capacity @ ( augmen887209518pacity @ c @ f @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ ( c @ ( product_Pair_nat_nat @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(207,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ A @ C )
=> ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_inf__greatest) ).
thf(901,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ A @ C )
=> ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(266,axiom,
! [A: set_Pr1986765409at_nat] :
( ( A != bot_bo2130386637at_nat )
= ( ord_le116442893at_nat @ bot_bo2130386637at_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_bot_Onot__eq__extremum) ).
thf(1075,plain,
! [A: set_Pr1986765409at_nat] :
( ( A != bot_bo2130386637at_nat )
= ( ord_le116442893at_nat @ bot_bo2130386637at_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(63,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( preflow_capacity @ A @ B @ C @ D )
=> ( nPreflow_capacity @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_NPreflow_Ointro) ).
thf(476,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( preflow_capacity @ A @ B @ C @ D )
=> ( nPreflow_capacity @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(258,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_inf_OcoboundedI2) ).
thf(1050,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(236,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C )
= ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_inf_Oassoc) ).
thf(984,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C )
= ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(242,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C )
= ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_inf__assoc) ).
thf(1002,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ ( inf_in586391887at_nat @ A @ B ) @ C )
= ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(74,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ( nFlow_capacity @ A @ B @ C @ ( residu1549650759pacity @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_RGraph_Ois__NFlow) ).
thf(508,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ( nFlow_capacity @ A @ B @ C @ ( residu1549650759pacity @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(123,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isShor1936442771pacity @ c @ A @ B @ C )
=> ( isSimp1359852763pacity @ c @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_shortestPath__is__simple) ).
thf(657,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isShor1936442771pacity @ c @ A @ B @ C )
=> ( isSimp1359852763pacity @ c @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(81,axiom,
! [A: capacity,B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ C )
=> ( ord_less_eq_capacity @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_order_Otrans) ).
thf(530,plain,
! [A: capacity,B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ C )
=> ( ord_less_eq_capacity @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(125,axiom,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ bot_bo513358416_nat_o @ A )
= bot_bo513358416_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_inf__bot__left) ).
thf(662,plain,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ bot_bo513358416_nat_o @ A )
= bot_bo513358416_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(215,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_inf__le2) ).
thf(926,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(40,axiom,
augmen68920357pacity = augmen68920357pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_NPreflow_OresCap_Ocong) ).
thf(398,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(253,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat @ A )
= ( converse_nat_nat @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_converse__inject) ).
thf(1035,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat @ A )
= ( converse_nat_nat @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(229,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
= ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_converse__iff) ).
thf(965,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
= ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(108,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( finite1387368318pacity @ A @ B @ C @ D )
=> ( finite217307323pacity @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Finite__Preflow_Oaxioms_I2_J) ).
thf(618,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( finite1387368318pacity @ A @ B @ C @ D )
=> ( finite217307323pacity @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(51,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ( ( val_capacity @ ( residu203630698pacity @ A @ D ) @ B @ ( augmen72931474pacity @ A @ D @ E ) )
= ( augmen68920357pacity @ A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_NPreflow_OaugFlow__val) ).
thf(425,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: list_P559422087at_nat] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ( ( val_capacity @ ( residu203630698pacity @ A @ D ) @ B @ ( augmen72931474pacity @ A @ D @ E ) )
= ( augmen68920357pacity @ A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( product_swap_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
= ( product_Pair_nat_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_swap__simp) ).
thf(824,plain,
! [A: nat,B: nat] :
( ( product_swap_nat_nat @ ( product_Pair_nat_nat @ A @ B ) )
= ( product_Pair_nat_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(3,axiom,
excess_capacity = excess_capacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_Network_Oexcess_Ocong) ).
thf(279,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
cap_capacity = cap_capacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_NCut_Ocap_Ocong) ).
thf(375,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(103,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
=> ( flow_capacity @ A @ B @ C @ ( augmen887209518pacity @ A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_NFlow_Oaugment__flow__presv) ).
thf(601,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
=> ( flow_capacity @ A @ B @ C @ ( augmen887209518pacity @ A @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(178,axiom,
! [A: product_prod_nat_nat > $o] : ( ord_le1039616028_nat_o @ bot_bo513358416_nat_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_bot_Oextremum) ).
thf(819,plain,
! [A: product_prod_nat_nat > $o] : ( ord_le1039616028_nat_o @ bot_bo513358416_nat_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(49,axiom,
isMaxFlow_capacity = isMaxFlow_capacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Network_OisMaxFlow_Ocong) ).
thf(423,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(162,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_dual__order_Oantisym) ).
thf(772,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(152,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( product_Pair_nat_nat @ A @ B )
= ( product_Pair_nat_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_old_Oprod_Oinject) ).
thf(743,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( product_Pair_nat_nat @ A @ B )
= ( product_Pair_nat_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(200,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_inf_OcoboundedI1) ).
thf(875,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(8,axiom,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_antisym) ).
thf(291,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(93,axiom,
! [A: capacity] :
( ( is_max2144541363pacity @ c @ s @ t @ A )
= ( ? [B: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ c @ s @ t @ B )
& ( A
= ( val_capacity @ c @ s @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_is__max__flow__val__def) ).
thf(562,plain,
! [A: capacity] :
( ( is_max2144541363pacity @ c @ s @ t @ A )
= ( ? [B: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ c @ s @ t @ B )
& ( A
= ( val_capacity @ c @ s @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(208,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: product_prod_nat_nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ D @ ( set_Pr2131844118at_nat @ B ) )
=> ~ ( member701585322at_nat @ ( product_swap_nat_nat @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_isSPath__nt__parallel) ).
thf(904,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: product_prod_nat_nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ D @ ( set_Pr2131844118at_nat @ B ) )
=> ~ ( member701585322at_nat @ ( product_swap_nat_nat @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(38,axiom,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_antisym__conv) ).
thf(391,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(56,axiom,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_order__class_Oorder_Oantisym) ).
thf(445,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(106,axiom,
! [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity,D: capacity] :
( ( ord_le841296385at_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_capacity @ C @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_order__subst1) ).
thf(611,plain,
! [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity,D: capacity] :
( ( ord_le841296385at_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_capacity @ C @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(72,axiom,
! [A: capacity,B: set_Pr1986765409at_nat > capacity,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_ord__eq__le__subst) ).
thf(498,plain,
! [A: capacity,B: set_Pr1986765409at_nat > capacity,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(86,axiom,
! [A: capacity,B: capacity,C: capacity > capacity,D: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_ord__le__eq__subst) ).
thf(540,plain,
! [A: capacity,B: capacity,C: capacity > capacity,D: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(59,axiom,
( finite1387368318pacity
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( preflow_capacity @ A @ B @ C @ D )
& ( finite217307323pacity @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_Finite__Preflow__def) ).
thf(466,plain,
( finite1387368318pacity
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( preflow_capacity @ A @ B @ C @ D )
& ( finite217307323pacity @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(272,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ B ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ B ) ) )
= bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_isSPath__nt__parallel__pf) ).
thf(1092,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ B ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ B ) ) )
= bot_bo2130386637at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(213,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ ( converse_nat_nat @ A ) @ ( converse_nat_nat @ B ) )
= ( ord_le841296385at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_converse__mono) ).
thf(919,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ ( converse_nat_nat @ A ) @ ( converse_nat_nat @ B ) )
= ( ord_le841296385at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(173,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_ord__le__eq__subst) ).
thf(804,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(104,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ! [D: nat,E: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( A @ ( product_Pair_nat_nat @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Network_Ocap__non__negative) ).
thf(604,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ! [D: nat,E: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( A @ ( product_Pair_nat_nat @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(166,axiom,
! [A: product_prod_nat_nat] :
~ ! [B: nat,C: nat] :
( A
!= ( product_Pair_nat_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_old_Oprod_Oexhaust) ).
thf(784,plain,
! [A: product_prod_nat_nat] :
~ ! [B: nat,C: nat] :
( A
!= ( product_Pair_nat_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(48,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > capacity,D: capacity] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_less_eq_capacity @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_order__subst2) ).
thf(419,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > capacity,D: capacity] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_less_eq_capacity @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(240,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ A @ C )
=> ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_inf_OboundedI) ).
thf(996,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ A @ C )
=> ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(15,axiom,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_dual__order_Oantisym) ).
thf(318,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(119,axiom,
( ( isMaxFlow_capacity @ c @ s @ t @ f )
=> ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_fofu__I__II) ).
thf(649,plain,
( ( isMaxFlow_capacity @ c @ s @ t @ f )
=> ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(37,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ( B != C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Network_Os__not__t) ).
thf(387,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ( B != C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(71,axiom,
! [A: capacity,B: set_Pr1986765409at_nat > capacity,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_capacity @ A @ ( B @ C ) )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_order__subst1) ).
thf(494,plain,
! [A: capacity,B: set_Pr1986765409at_nat > capacity,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_capacity @ A @ ( B @ C ) )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(158,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ord_le841296385at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_eq__refl) ).
thf(758,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ord_le841296385at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(89,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( ( residu203630698pacity @ A @ ( residu1549650759pacity @ A @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_RPreGraph_Org__fo__inv) ).
thf(552,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( ( residu203630698pacity @ A @ ( residu1549650759pacity @ A @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(83,axiom,
augmen72931474pacity = augmen72931474pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_NPreflow_OaugmentingFlow_Ocong) ).
thf(535,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(17,axiom,
isShor1936442771pacity = isShor1936442771pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Graph_OisShortestPath_Ocong) ).
thf(323,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(101,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ? [E: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ E )
& ( D
= ( residu203630698pacity @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_RPreGraph_OEX__RPG) ).
thf(594,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ? [E: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ E )
& ( D
= ( residu203630698pacity @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(109,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( flow_capacity @ A @ B @ C @ D )
=> ( preflow_capacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_Flow_Oaxioms_I1_J) ).
thf(621,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( flow_capacity @ A @ B @ C @ D )
=> ( preflow_capacity @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(66,axiom,
! [A: capacity,B: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
=> ( ord_less_eq_capacity @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_le__cases) ).
thf(483,plain,
! [A: capacity,B: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
=> ( ord_less_eq_capacity @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(138,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( B = C )
=> ( ord_le841296385at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_ord__le__eq__trans) ).
thf(700,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( B = C )
=> ( ord_le841296385at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(251,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_le__inf__iff) ).
thf(1029,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(211,axiom,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_bot__empty__eq) ).
thf(915,plain,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(249,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_le__infI2) ).
thf(1022,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(127,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ C )
=> ( ord_le841296385at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__trans) ).
thf(668,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ C )
=> ( ord_le841296385at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(20,axiom,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_dual__order_Orefl) ).
thf(330,plain,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(41,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( is_max2144541363pacity @ A @ B @ C @ D )
= ( ? [E: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ A @ B @ C @ E )
& ( D
= ( val_capacity @ A @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Network_Ois__max__flow__val__def) ).
thf(399,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( is_max2144541363pacity @ A @ B @ C @ D )
= ( ? [E: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ A @ B @ C @ E )
& ( D
= ( val_capacity @ A @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(181,axiom,
finite1387368318pacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Finite__Preflow__axioms) ).
thf(827,plain,
finite1387368318pacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(198,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ A @ B ) )
=> ( ord_le841296385at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_inf_OorderI) ).
thf(868,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ A @ B ) )
=> ( ord_le841296385at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(192,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ C ) @ ( inf_in586391887at_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_inf__mono) ).
thf(851,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ C ) @ ( inf_in586391887at_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(54,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat > capacity,F: nat,G: nat] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
=> ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ F @ G ) ) )
& ( ord_less_eq_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ F @ G ) ) @ ( A @ ( product_Pair_nat_nat @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_NFlow_Oaugment__flow__presv__cap) ).
thf(438,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat > capacity,F: nat,G: nat] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
=> ( ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ F @ G ) ) )
& ( ord_less_eq_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ F @ G ) ) @ ( A @ ( product_Pair_nat_nat @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(121,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_order__class_Oorder_Oantisym) ).
thf(653,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(214,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat,E: nat,F: nat,G: nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ C ) )
=> ( ( F != G )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ G ) @ ( set_Pr2131844118at_nat @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_Graph_OisSPath__sg__outgoing) ).
thf(922,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat,E: nat,F: nat,G: nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ C ) )
=> ( ( F != G )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ G ) @ ( set_Pr2131844118at_nat @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(210,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_inf_Obounded__iff) ).
thf(912,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(78,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
( ( preflow_capacity @ A @ B @ C @ D )
=> ( ord_less_eq_capacity @ zero_zero_capacity @ ( D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Preflow_Of__non__negative) ).
thf(521,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
( ( preflow_capacity @ A @ B @ C @ D )
=> ( ord_less_eq_capacity @ zero_zero_capacity @ ( D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(115,axiom,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ( ( val_capacity @ ( residu203630698pacity @ c @ f ) @ s @ ( augmen72931474pacity @ c @ f @ A ) )
= ( augmen68920357pacity @ c @ f @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_augFlow__val) ).
thf(636,plain,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ( ( val_capacity @ ( residu203630698pacity @ c @ f ) @ s @ ( augmen72931474pacity @ c @ f @ A ) )
= ( augmen68920357pacity @ c @ f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(256,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat,E: product_prod_nat_nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ C ) )
=> ~ ( member701585322at_nat @ ( product_swap_nat_nat @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Graph_OisSPath__nt__parallel) ).
thf(1044,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat,E: product_prod_nat_nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ C ) )
=> ~ ( member701585322at_nat @ ( product_swap_nat_nat @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(39,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: set_nat] :
( ( network_capacity @ A @ B @ C )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
=> ( ( isMinCut_capacity @ A @ B @ C @ E )
=> ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_Network_OmaxFlow__minCut) ).
thf(394,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: set_nat] :
( ( network_capacity @ A @ B @ C )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
=> ( ( isMinCut_capacity @ A @ B @ C @ E )
=> ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(12,axiom,
augmen887209518pacity = augmen887209518pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_NFlow_Oaugment_Ocong) ).
thf(306,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(87,axiom,
! [A: capacity,B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ C )
=> ( ord_less_eq_capacity @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order__trans) ).
thf(548,plain,
! [A: capacity,B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ B @ C )
=> ( ord_less_eq_capacity @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(33,axiom,
val_capacity = val_capacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Flow_Oval_Ocong) ).
thf(374,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(174,axiom,
residu164581374pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_is__RPreGraph) ).
thf(812,plain,
residu164581374pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(24,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( nPreflow_capacity @ A @ B @ C @ ( residu1549650759pacity @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_RPreGraph_Ois__NPreflow) ).
thf(342,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( nPreflow_capacity @ A @ B @ C @ ( residu1549650759pacity @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(27,axiom,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
| ( ord_less_eq_capacity @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_linear) ).
thf(355,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
| ( ord_less_eq_capacity @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(230,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_inf_Oleft__commute) ).
thf(968,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(186,axiom,
( ( residu1549650759pacity @ c @ ( residu203630698pacity @ c @ f ) )
= f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_fo__rg__inv) ).
thf(836,plain,
( ( residu1549650759pacity @ c @ ( residu203630698pacity @ c @ f ) )
= f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(268,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( inf_in586391887at_nat @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_inf__absorb1) ).
thf(1081,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( inf_in586391887at_nat @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( product_Pair_nat_nat @ A @ B )
= ( product_Pair_nat_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_prod_Oinject) ).
thf(749,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( product_Pair_nat_nat @ A @ B )
= ( product_Pair_nat_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(250,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat,F: nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( E != F )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ F ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_isSPath__sg__outgoing) ).
thf(1025,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat,F: nat] :
( ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( E != F )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ F ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(139,axiom,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ ( augmen72931474pacity @ c @ f @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_augFlow__resFlow) ).
thf(705,plain,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
=> ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ ( augmen72931474pacity @ c @ f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(140,axiom,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_bot__fun__def) ).
thf(707,plain,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(225,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ~ ( ( ord_le116442893at_nat @ A @ B )
=> ~ ( ord_le116442893at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_inf_Ostrict__boundedE) ).
thf(954,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ~ ( ( ord_le116442893at_nat @ A @ B )
=> ~ ( ord_le116442893at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(44,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ ( residu1549650759pacity @ A @ D ) )
=> ( residu800046103pacity @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_RPreGraph_Omaxflow__imp__rgraph) ).
thf(409,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ ( residu1549650759pacity @ A @ D ) )
=> ( residu800046103pacity @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(274,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ A @ B ) )
= ( inf_in586391887at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_inf__sup__aci_I4_J) ).
thf(1098,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ A @ B ) )
= ( inf_in586391887at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(239,axiom,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_converse__converse) ).
thf(993,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(142,axiom,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_bot__apply) ).
thf(712,plain,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(91,axiom,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_order__refl) ).
thf(557,plain,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(46,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ? [E: set_nat] :
( ( nCut_capacity @ A @ B @ C @ E )
& ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_NFlow_Ofofu__II__III) ).
thf(414,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ? [E: set_nat] :
( ( nCut_capacity @ A @ B @ C @ E )
& ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(231,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( converse_nat_nat @ B ) )
= ( ord_le841296385at_nat @ ( converse_nat_nat @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_converse__subset__swap) ).
thf(971,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( converse_nat_nat @ B ) )
= ( ord_le841296385at_nat @ ( converse_nat_nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(259,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ A @ C )
=> ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_le__infI) ).
thf(1053,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ A @ C )
=> ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(129,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_antisym__conv) ).
thf(673,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(144,axiom,
( ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) )
= ( isMaxFlow_capacity @ c @ s @ t @ f ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_noAugPath__iff__maxFlow) ).
thf(717,plain,
( ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) )
= ( isMaxFlow_capacity @ c @ s @ t @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(224,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
= ( ? [D: nat,E: nat] :
( ( A = E )
& ( B = D )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_converse_Osimps) ).
thf(951,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
= ( ? [D: nat,E: nat] :
( ( A = E )
& ( B = D )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(29,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ? [E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ E )
& ( D
= ( residu203630698pacity @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_RGraph_OEX__RG) ).
thf(359,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu800046103pacity @ A @ B @ C @ D )
=> ? [E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ E )
& ( D
= ( residu203630698pacity @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(209,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ B @ C ) )
=> ( ( inf_in586391887at_nat @ A @ D )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_boolean__algebra__cancel_Oinf1) ).
thf(907,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ B @ C ) )
=> ( ( inf_in586391887at_nat @ A @ D )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(254,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ~ ( ( ord_le841296385at_nat @ A @ B )
=> ~ ( ord_le841296385at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_le__infE) ).
thf(1038,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ~ ( ( ord_le841296385at_nat @ A @ B )
=> ~ ( ord_le841296385at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(32,axiom,
! [A: capacity,B: capacity,C: capacity > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_le841296385at_nat @ ( C @ B ) @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_order__subst2) ).
thf(370,plain,
! [A: capacity,B: capacity,C: capacity > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_le841296385at_nat @ ( C @ B ) @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(22,axiom,
! [A: capacity,B: capacity,C: capacity > capacity,D: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ ( C @ B ) @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_order__subst2) ).
thf(336,plain,
! [A: capacity,B: capacity,C: capacity > capacity,D: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ord_less_eq_capacity @ ( C @ B ) @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(122,axiom,
nPreflow_capacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_NPreflow__axioms) ).
thf(656,plain,
nPreflow_capacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(234,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( inf_in586391887at_nat @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_inf_Oabsorb1) ).
thf(978,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( inf_in586391887at_nat @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(244,axiom,
augmen1090971539pacity @ c @ s @ t @ f @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1008,plain,
augmen1090971539pacity @ c @ s @ t @ f @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(189,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_converse_Ocases) ).
thf(845,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
=> ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(269,axiom,
! [A: set_Pr1986765409at_nat] :
~ ( ord_le116442893at_nat @ A @ bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_bot_Oextremum__strict) ).
thf(1084,plain,
! [A: set_Pr1986765409at_nat] :
~ ( ord_le116442893at_nat @ A @ bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(30,axiom,
( ( (=) @ capacity )
= ( ^ [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ B @ A )
& ( ord_less_eq_capacity @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_dual__order_Oeq__iff) ).
thf(363,plain,
( ( (=) @ capacity )
= ( ^ [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ B @ A )
& ( ord_less_eq_capacity @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(217,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat,F: nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( D != F )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ E ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_cf_OisSPath__sg__incoming) ).
thf(931,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat,F: nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( D != F )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ E ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(128,axiom,
! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ c @ f @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_resE__nonNegative) ).
thf(671,plain,
! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ c @ f @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(79,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ A @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_NPreflow_OresE__nonNegative) ).
thf(524,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ A @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(233,axiom,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_inf_Oabsorb__iff2) ).
thf(976,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(134,axiom,
! [A: product_prod_nat_nat > capacity] :
( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ A )
=> ( ( val_capacity @ c @ s @ ( augmen887209518pacity @ c @ f @ A ) )
= ( plus_plus_capacity @ ( val_capacity @ c @ s @ f ) @ ( val_capacity @ ( residu203630698pacity @ c @ f ) @ s @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_augment__flow__value) ).
thf(688,plain,
! [A: product_prod_nat_nat > capacity] :
( ( flow_capacity @ ( residu203630698pacity @ c @ f ) @ s @ t @ A )
=> ( ( val_capacity @ c @ s @ ( augmen887209518pacity @ c @ f @ A ) )
= ( plus_plus_capacity @ ( val_capacity @ c @ s @ f ) @ ( val_capacity @ ( residu203630698pacity @ c @ f ) @ s @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(175,axiom,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_order__refl) ).
thf(813,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(205,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_inf__le1) ).
thf(896,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(11,axiom,
( ( (=) @ capacity )
= ( ^ [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
& ( ord_less_eq_capacity @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_eq__iff) ).
thf(304,plain,
( ( (=) @ capacity )
= ( ^ [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
& ( ord_less_eq_capacity @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(262,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_inf_Ostrict__coboundedI2) ).
thf(1062,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(113,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ C )
=> ( ord_le841296385at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_order_Otrans) ).
thf(632,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ C )
=> ( ord_le841296385at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(228,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_inf__sup__ord_I1_J) ).
thf(963,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(77,axiom,
! [A: capacity,B: capacity] :
( ( ord_less_capacity @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_order_Ostrict__implies__not__eq) ).
thf(517,plain,
! [A: capacity,B: capacity] :
( ( ord_less_capacity @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(222,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_le__infI1) ).
thf(946,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(275,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_inf__sup__aci_I3_J) ).
thf(1101,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( inf_in586391887at_nat @ B @ ( inf_in586391887at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(149,axiom,
t != s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_t__not__s) ).
thf(731,plain,
t != s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(47,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( residu164581374pacity @ A @ B @ C @ D )
=> ( residu164581374pacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_RPreGraph_Othis__loc__rpg) ).
thf(418,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(75,axiom,
( ( (=) @ capacity )
= ( ^ [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
& ( ord_less_eq_capacity @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_order__class_Oorder_Oeq__iff) ).
thf(510,plain,
( ( (=) @ capacity )
= ( ^ [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
& ( ord_less_eq_capacity @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(84,axiom,
( nPreflow_capacity
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( network_capacity @ A @ B @ C )
& ( preflow_capacity @ A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_NPreflow__def) ).
thf(536,plain,
( nPreflow_capacity
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( network_capacity @ A @ B @ C )
& ( preflow_capacity @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(170,axiom,
finite217307323pacity @ ( residu203630698pacity @ c @ f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_cf_OFinite__Graph__axioms) ).
thf(800,plain,
finite217307323pacity @ ( residu203630698pacity @ c @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(184,axiom,
finite217307323pacity @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Finite__Graph__axioms) ).
thf(832,plain,
finite217307323pacity @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(133,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_dual__order_Ostrict__implies__not__eq) ).
thf(684,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(241,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: product_prod_nat_nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( ( member701585322at_nat @ D @ ( set_Pr2131844118at_nat @ B ) )
=> ~ ( member701585322at_nat @ ( product_swap_nat_nat @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_cf_OisSPath__nt__parallel) ).
thf(999,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: product_prod_nat_nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( ( member701585322at_nat @ D @ ( set_Pr2131844118at_nat @ B ) )
=> ~ ( member701585322at_nat @ ( product_swap_nat_nat @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(156,axiom,
! [A: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(752,plain,
! [A: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(14,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( residu1549650759pacity @ A @ ( residu203630698pacity @ A @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_NPreflow_Ofo__rg__inv) ).
thf(315,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( residu1549650759pacity @ A @ ( residu203630698pacity @ A @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(53,axiom,
! [A: capacity > capacity > $o,B: capacity,C: capacity] :
( ! [D: capacity,E: capacity] :
( ( ord_less_eq_capacity @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: capacity,E: capacity] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_linorder__wlog) ).
thf(432,plain,
! [A: capacity > capacity > $o,B: capacity,C: capacity] :
( ! [D: capacity,E: capacity] :
( ( ord_less_eq_capacity @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: capacity,E: capacity] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(185,axiom,
! [A: product_prod_nat_nat > $o] :
( ( A != bot_bo513358416_nat_o )
= ( ord_le1015898640_nat_o @ bot_bo513358416_nat_o @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_bot_Onot__eq__extremum) ).
thf(833,plain,
! [A: product_prod_nat_nat > $o] :
( ( A != bot_bo513358416_nat_o )
= ( ord_le1015898640_nat_o @ bot_bo513358416_nat_o @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(43,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
=> ( ( val_capacity @ A @ B @ ( augmen887209518pacity @ A @ D @ E ) )
= ( plus_plus_capacity @ ( val_capacity @ A @ B @ D ) @ ( val_capacity @ ( residu203630698pacity @ A @ D ) @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_NFlow_Oaugment__flow__value) ).
thf(405,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity,E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
=> ( ( val_capacity @ A @ B @ ( augmen887209518pacity @ A @ D @ E ) )
= ( plus_plus_capacity @ ( val_capacity @ A @ B @ D ) @ ( val_capacity @ ( residu203630698pacity @ A @ D ) @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(193,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( inf_in586391887at_nat @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_inf__absorb2) ).
thf(854,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( inf_in586391887at_nat @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(168,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( product_Pair_nat_nat @ A @ B )
= ( product_Pair_nat_nat @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Pair__inject) ).
thf(790,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( product_Pair_nat_nat @ A @ B )
= ( product_Pair_nat_nat @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(151,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_ord__eq__le__subst) ).
thf(735,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat > set_Pr1986765409at_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(19,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ( flow_capacity @ A @ B @ C @ D )
& ! [E: product_prod_nat_nat > capacity] :
( ( flow_capacity @ A @ B @ C @ E )
=> ( ord_less_eq_capacity @ ( val_capacity @ A @ B @ E ) @ ( val_capacity @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Network_OisMaxFlow__def) ).
thf(326,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ( flow_capacity @ A @ B @ C @ D )
& ! [E: product_prod_nat_nat > capacity] :
( ( flow_capacity @ A @ B @ C @ E )
=> ( ord_less_eq_capacity @ ( val_capacity @ A @ B @ E ) @ ( val_capacity @ A @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(73,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( finite1387368318pacity @ A @ B @ C @ D )
=> ( preflow_capacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Finite__Preflow_Oaxioms_I1_J) ).
thf(506,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( finite1387368318pacity @ A @ B @ C @ D )
=> ( preflow_capacity @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(260,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat,E: nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Graph_OisSPath__no__selfloop) ).
thf(1056,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat,D: nat,E: nat] :
( ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(182,axiom,
nFlow_capacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_NFlow__axioms) ).
thf(828,plain,
nFlow_capacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(263,axiom,
! [A: nat,B: nat,C: set_Pr1986765409at_nat,D: nat > nat > $o] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
=> ( ! [E: nat,F: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ C )
=> ( D @ F @ E ) )
=> ( D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_converse_Oinducts) ).
thf(1065,plain,
! [A: nat,B: nat,C: set_Pr1986765409at_nat,D: nat > nat > $o] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( converse_nat_nat @ C ) )
=> ( ! [E: nat,F: nat] :
( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ C )
=> ( D @ F @ E ) )
=> ( D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(137,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_order__subst2) ).
thf(696,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(5,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( flow_capacity @ A @ B @ C @ D )
=> ( nFlow_capacity @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_NFlow_Ointro) ).
thf(283,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ( ( flow_capacity @ A @ B @ C @ D )
=> ( nFlow_capacity @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(216,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_less__infI1) ).
thf(928,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ A @ B )
=> ( ord_le116442893at_nat @ ( inf_in586391887at_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(9,axiom,
! [A: capacity,B: capacity,C: capacity > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ord__le__eq__subst) ).
thf(294,plain,
! [A: capacity,B: capacity,C: capacity > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_capacity @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(171,axiom,
( ( isMaxFlow_capacity @ c @ s @ t @ f )
= ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_ford__fulkerson_I1_J) ).
thf(801,plain,
( ( isMaxFlow_capacity @ c @ s @ t @ f )
= ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(62,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( flow_capacity @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_NFlow_Oaxioms_I2_J) ).
thf(474,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ( flow_capacity @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(161,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ( ord_le841296385at_nat @ B @ C )
=> ( ord_le841296385at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_ord__eq__le__trans) ).
thf(767,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ( ord_le841296385at_nat @ B @ C )
=> ( ord_le841296385at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(227,axiom,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_inf_Oidem) ).
thf(960,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(114,axiom,
flow_capacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Flow__axioms) ).
thf(635,plain,
flow_capacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(148,axiom,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat] :
( ! [C: nat,D: nat] : ( A @ ( product_Pair_nat_nat @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_old_Oprod_Oinducts) ).
thf(728,plain,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat] :
( ! [C: nat,D: nat] : ( A @ ( product_Pair_nat_nat @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(237,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_inf_Ocobounded1) ).
thf(987,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(21,axiom,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: capacity,E: capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( is_max2144541363pacity @ A @ B @ C @ D )
=> ( ( is_max2144541363pacity @ A @ B @ C @ E )
=> ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Network_Omax__flow__val__unique) ).
thf(332,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: capacity,E: capacity] :
( ( network_capacity @ A @ B @ C )
=> ( ( is_max2144541363pacity @ A @ B @ C @ D )
=> ( ( is_max2144541363pacity @ A @ B @ C @ E )
=> ( D = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(195,axiom,
( inf_in586391887at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_inf_Ocommute) ).
thf(860,plain,
( inf_in586391887at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(248,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ A @ B ) )
= ( inf_in586391887at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_inf_Oleft__idem) ).
thf(1019,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ A @ B ) )
= ( inf_in586391887at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(146,axiom,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_dual__order_Orefl) ).
thf(723,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(199,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat,F: nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( E != F )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ F ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_cf_OisSPath__sg__outgoing) ).
thf(871,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat,F: nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( E != F )
=> ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ F ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(105,axiom,
! [A: capacity,B: capacity > capacity,C: capacity,D: capacity] :
( ( ord_less_eq_capacity @ A @ ( B @ C ) )
=> ( ( ord_less_eq_capacity @ C @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order__subst1) ).
thf(607,plain,
! [A: capacity,B: capacity > capacity,C: capacity,D: capacity] :
( ( ord_less_eq_capacity @ A @ ( B @ C ) )
=> ( ( ord_less_eq_capacity @ C @ D )
=> ( ! [E: capacity,F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1,conjecture,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bo2130386637at_nat ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(277,plain,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(135,axiom,
! [A: list_P559422087at_nat] :
( ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ s @ A @ t )
=> ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_shortest__is__augmenting) ).
thf(691,plain,
! [A: list_P559422087at_nat] :
( ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ s @ A @ t )
=> ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(172,axiom,
residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_is__RGraph) ).
thf(803,plain,
residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(220,axiom,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_inf_Oorder__iff) ).
thf(940,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(124,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_antisym) ).
thf(659,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(163,axiom,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
= ( A = bot_bo513358416_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_bot_Oextremum__unique) ).
thf(775,plain,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
= ( A = bot_bo513358416_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(116,axiom,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
= ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ A @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_isAugmentingPath__def) ).
thf(639,plain,
! [A: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ A )
= ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ A @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(69,axiom,
residu1549650759pacity = residu1549650759pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Network_Oflow__of__cf_Ocong) ).
thf(491,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(264,axiom,
! [A: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
= ( A = bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_bot_Oextremum__unique) ).
thf(1069,plain,
! [A: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
= ( A = bot_bo2130386637at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(218,axiom,
( ( converse_nat_nat @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_converse__empty) ).
thf(935,plain,
( ( converse_nat_nat @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(245,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ A @ B ) )
= ( inf_in586391887at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_inf__left__idem) ).
thf(1009,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ ( inf_in586391887at_nat @ A @ B ) )
= ( inf_in586391887at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(157,axiom,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ A @ bot_bo513358416_nat_o )
= bot_bo513358416_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_inf__bot__right) ).
thf(755,plain,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ A @ bot_bo513358416_nat_o )
= bot_bo513358416_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(130,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_cf_OshortestPath__is__simple) ).
thf(676,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isShor1936442771pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1159,plain,
$false,
inference(cvc4,[status(thm)],[365,479,628,468,555,352,645,892,762,1005,878,1041,1078,384,533,797,747,340,538,829,898,782,709,841,288,565,651,570,719,917,344,357,1059,949,587,838,817,559,1087,881,448,492,591,443,321,376,623,485,937,574,821,480,280,734,866,1072,411,527,981,766,1104,849,307,452,678,714,1047,512,942,957,746,778,302,862,598,424,693,429,788,815,847,1032,625,665,583,551,1012,285,324,974,578,1089,1017,615,725,403,1096,989,857,471,884,488,642,679,901,1075,476,1050,984,1002,508,657,530,662,926,398,1035,965,618,425,824,279,375,601,819,423,772,743,875,291,562,904,391,445,611,498,540,466,1092,919,804,604,784,419,996,318,649,387,494,758,552,535,323,594,621,483,700,1029,915,1022,668,330,399,827,868,851,438,653,922,912,521,636,1044,394,306,548,374,812,342,355,968,836,1081,749,1025,705,707,954,409,1098,993,712,557,414,971,1053,673,717,951,359,907,1038,370,336,656,978,1008,845,1084,363,931,671,524,976,688,813,896,304,1062,632,963,517,946,1101,731,418,510,536,800,832,684,999,752,315,432,833,405,854,790,735,326,506,1056,828,1065,696,283,928,294,801,474,767,960,635,728,987,332,860,1019,723,871,607,277,691,803,940,659,775,639,491,1069,935,1009,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP052^1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n027.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:50:08 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.03/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.17 % [INFO] Parsing done (250ms).
% 1.59/1.18 % [INFO] Running in sequential loop mode.
% 2.57/1.39 % [INFO] eprover registered as external prover.
% 2.57/1.39 % [INFO] cvc4 registered as external prover.
% 2.57/1.39 % [INFO] Scanning for conjecture ...
% 2.77/1.47 % [INFO] Found a conjecture and 279 axioms. Running axiom selection ...
% 2.97/1.57 % [INFO] Axiom selection finished. Selected 274 axioms (removed 5 axioms).
% 3.60/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 3.60/1.75 % [INFO] Type checking passed.
% 3.60/1.75 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 15.50/4.84 % External prover 'cvc4' found a proof!
% 15.50/4.84 % [INFO] Killing All external provers ...
% 15.50/4.84 % Time passed: 4312ms (effective reasoning time: 3661ms)
% 15.50/4.84 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 15.50/4.84 % Axioms used in derivation (274): fact_129_order__class_Oorder_Oeq__iff, fact_94_bot_Oextremum, fact_184_NFlow_Oaugment__flow__value, fact_255_prod__cases, fact_213_NPreflow_Ointro, fact_265_bot_Oextremum__strict, fact_269_inf_Ostrict__boundedE, fact_187_converse__mono, fact_4_max__flow__val__unique, fact_66_Graph_OisSimplePath_Ocong, fact_195_Flow_Oval_Ocong, fact_74_RGraph_Othis__loc__rpg, fact_13_converse__empty, fact_28_converse__inject, fact_254_Pair__inject, fact_243_old_Oprod_Oinject, fact_34_inf__commute, fact_162_inf_Oabsorb1, fact_45_augment__flow__presv, fact_127_antisym__conv, fact_101_order__subst1, fact_234_converse_Osimps, fact_259_NFlow_Oaugment__flow__presv__cap, fact_9_Preflow__axioms, fact_99_bot_Oextremum__uniqueI, fact_204_NFlow_Oaxioms_I1_J, fact_108_ord__eq__le__subst, fact_154_inf_Ocobounded1, fact_171_le__infE, fact_245_cap__non__negative, fact_181_ford__fulkerson_I2_J, fact_122_eq__refl, fact_166_inf_OorderE, fact_178_NPreflow_OaugFlow__val, fact_123_le__cases, fact_235_converse_Ointros, fact_64_Graph_OshortestPath__is__simple, fact_152_inf_Oabsorb__iff1, fact_23_inf__left__idem, fact_116_eq__iff, fact_139_order__trans, fact_61_shortestPath__is__simple, fact_215_NFlow_Ofofu__I__II, fact_100_order__subst1, fact_57_Graph_OisSPath__nt__parallel__pf, fact_107_order__subst2, fact_199_NFlow_Ofofu__II__III, fact_173_inf__le1, fact_248_resE__nonNegative, fact_55_shortest__is__augmenting, fact_247_swap__swap, fact_271_inf_Ostrict__coboundedI1, fact_98_bot_Oextremum__uniqueI, fact_237_Graph_OisSPath__sg__outgoing, fact_29_augFlow__resFlow, fact_63_Graph_OisShortestPath_Ocong, fact_56_augmenting__path__imp__shortest, fact_136_order__class_Oorder_Oantisym, fact_125_order_Otrans, fact_90_order__refl, fact_7_fofu__I__II, fact_223_cf_OisSPath__no__selfloop, fact_148_dual__order_Oantisym, fact_253_old_Oprod_Oexhaust, fact_132_ord__eq__le__trans, fact_18_is__RPreGraph, fact_39_boolean__algebra__cancel_Oinf1, fact_203_NPreflow_Oaxioms_I1_J, fact_150_inf_OcoboundedI1, fact_76_RPreGraph_OEX__RPG, fact_168_le__infI1, fact_50_Collect__cong, fact_216_NFlow_OnoAugPath__iff__maxFlow, fact_97_bot_Oextremum__unique, fact_228_isSPath__no__selfloop, fact_31_bot__empty__eq, fact_246_capacity__const, fact_71_Network_Oflow__of__cf_Ocong, fact_37_inf_Oassoc, fact_11_Flow__axioms, fact_141_dual__order_Orefl, fact_88_bot__apply, fact_232_converseE, fact_21_inf__right__idem, fact_212_NFlow__def, fact_262_Network_Oexcess_Ocong, fact_273_dual__order_Ostrict__implies__not__eq, fact_233_converse_Ocases, fact_104_order__subst2, fact_16_inf__bot__right, fact_250_Preflow_Ocapacity__const, fact_194_Network_Os__not__t, fact_251_Preflow_Of__non__negative, fact_163_le__iff__inf, fact_219_NFlow_Oaugment__flow__presv, fact_211_NFlow_Ointro, fact_179_bot__fun__def, fact_2_isSPath__nt__parallel__pf, fact_32_inf__left__commute, fact_147_dual__order_Oantisym, fact_183_fofu__II__III, fact_252_old_Oprod_Oinducts, fact_60_Finite__Graph__axioms, fact_106_order__subst2, fact_239_Graph_OisSPath__no__selfloop, fact_270_inf_Ostrict__order__iff, fact_192_isMinCut__def, fact_180_NPreflow_OisAugmentingPath__def, fact_240_augment__flow__presv__cap, fact_83_augFlow__val, fact_59_isSPath__nt__parallel, fact_14_inf__bot__left, fact_20_fo__rg__inv, fact_142_linorder__wlog, fact_174_inf__sup__ord_I1_J, fact_169_inf__mono, fact_69_NFlow_Oaugmenting__path__imp__shortest, fact_197_NFlow_Oaugment_Ocong, fact_73_RGraph_Oaxioms_I1_J, fact_140_dual__order_Orefl, fact_6_Finite__Preflow__axioms, fact_257_Network_Ocap__non__negative, fact_24_inf_Oleft__idem, fact_5_isAugmentingPath__def, fact_264_bot_Onot__eq__extremum, fact_170_le__infI, fact_221_Network_Ois__max__flow__val__def, fact_230_subrelI, fact_109_ord__eq__le__subst, fact_236_converse_Oinducts, fact_131_ord__eq__le__trans, fact_105_order__subst2, fact_85_isMaxFlow__alt, fact_1_cf_OisSPath__nt__parallel__pf, fact_86_isMaxFlow__def, fact_121_eq__refl, fact_27_converse__converse, fact_42_inf__sup__aci_I3_J, fact_41_inf__sup__aci_I2_J, fact_196_Network_OisMaxFlow_Ocong, fact_241_swap__simp, fact_249_RPreGraph_OresE__nonNegative, fact_172_inf__le2, fact_193_Network_Ot__not__s, fact_149_inf_OcoboundedI2, fact_95_bot_Oextremum, fact_274_dual__order_Ostrict__implies__not__eq, fact_260_excess__s__non__pos, fact_185_Network_OmaxFlow__minCut, fact_160_inf__absorb1, fact_115_ord__le__eq__subst, fact_133_ord__le__eq__trans, fact_220_NFlow_Oford__fulkerson_I1_J, fact_8_noAugPath__iff__maxFlow, fact_191_converse__subset__swap, fact_53_cf_OFinite__Graph__axioms, fact_52_is__max__flow__val__def, fact_224_cf_OisSPath__sg__incoming, fact_164_inf__unique, fact_186_Network_OisMaxFlow__alt, fact_84_augment__flow__value, fact_114_ord__le__eq__subst, fact_119_antisym, fact_198_NCut_Ocap_Ocong, fact_12_NPreflow__axioms, fact_67_RPreGraph_Othis__loc__rpg, fact_65_Graph_OisSPath__nt__parallel, fact_182_fofu__III__I, fact_117_eq__iff, fact_267_less__infI1, fact_110_ord__eq__le__subst, fact_54_ford__fulkerson_I1_J, fact_225_cf_OisSPath__sg__outgoing, fact_231_converseD, fact_207_Flow_Oaxioms_I1_J, fact_229_converse__iff, fact_277_not__less__iff__gr__or__eq, fact_268_less__infI2, fact_77_NFlow_Ois__RGraph, fact_206_NPreflow_Oaxioms_I2_J, fact_210_Finite__Preflow_Oaxioms_I1_J, fact_120_linear, fact_92_inf_Obounded__iff, fact_44_converse__Int, fact_208_Network_Omax__flow__val__unique, fact_103_order__subst1, fact_35_inf_Ocommute, fact_146_dual__order_Oeq__iff, fact_161_inf_Oabsorb2, fact_165_inf_OorderI, fact_3_NFlow__axioms, fact_158_inf_OboundedE, fact_72_RPreGraph_Oaxioms_I1_J, fact_87_NPreflow_OaugFlow__resFlow, fact_49_Collect__mem__eq, fact_113_ord__le__eq__subst, fact_26_inf_Oidem, fact_266_bot_Oextremum__strict, fact_102_order__subst1, fact_157_inf_OboundedI, fact_10_is__RGraph, fact_258_NPreflow_OresE__nonNegative, fact_40_inf__sup__aci_I1_J, fact_276_order_Ostrict__implies__not__eq, fact_153_inf_Ocobounded2, fact_62_cf_OshortestPath__is__simple, fact_36_inf__assoc, fact_15_inf__bot__left, fact_226_isSPath__sg__outgoing, fact_202_NFlow_Oford__fulkerson_I2_J, fact_261_resCap__gzero, fact_155_inf_Oorder__iff, fact_68_NFlow_Oshortest__is__augmenting, fact_0_t__not__s, fact_51_cf_OisSPath__nt__parallel, fact_242_f__non__negative, fact_80_RPreGraph_Org__fo__inv, fact_96_bot_Oextremum__unique, fact_159_inf__absorb2, fact_214_NPreflow__def, fact_82_RGraph_Ois__NFlow, fact_70_RGraph_Othis__loc, fact_138_order__trans, fact_144_dual__order_Otrans, fact_176_NPreflow_OisAugmentingPath_Ocong, fact_22_inf_Oright__idem, fact_19_Network__axioms, fact_200_NFlow_Ofofu__III__I, fact_33_inf_Oleft__commute, fact_81_RPreGraph_Ois__NPreflow, fact_238_Graph_OisSPath__sg__incoming, fact_143_dual__order_Otrans, fact_112_ord__le__eq__subst, fact_256_surj__pair, fact_128_antisym__conv, fact_209_Finite__Preflow_Oaxioms_I2_J, fact_47_mem__Collect__eq, fact_111_ord__eq__le__subst, fact_126_le__cases3, fact_188_NCut_Oaxioms_I1_J, fact_93_le__inf__iff, fact_244_prod_Oinject, fact_124_order_Otrans, fact_177_NPreflow_OaugmentingFlow_Ocong, fact_118_antisym, fact_263_bot_Onot__eq__extremum, fact_145_dual__order_Oeq__iff, fact_275_order_Ostrict__implies__not__eq, fact_151_inf_Oabsorb__iff2, fact_58_RPreGraph_Omaxflow__imp__rgraph, fact_130_order__class_Oorder_Oeq__iff, fact_79_NPreflow_Ofo__rg__inv, fact_135_order__class_Oorder_Oantisym, conj_0, fact_17_inf__bot__right, fact_156_inf__greatest, fact_201_Network_Ois__max__flow__val_Ocong, fact_43_inf__sup__aci_I4_J, fact_91_order__refl, fact_38_boolean__algebra__cancel_Oinf2, fact_75_NPreflow_Ois__RPreGraph, fact_218_Finite__Preflow__def, fact_222_Network_OisMaxFlow__def, fact_89_maxFlow__minCut, fact_272_inf_Ostrict__coboundedI2, fact_137_NPreflow_OresCap_Ocong, fact_78_RGraph_OEX__RG, fact_217_Finite__Preflow_Ointro, fact_205_NFlow_Oaxioms_I2_J, fact_167_le__infI2, fact_134_ord__le__eq__trans, fact_175_inf__sup__ord_I2_J, fact_227_isSPath__sg__incoming, fact_25_inf__idem
% 15.50/4.84 % No. of inferences in proof: 552
% 15.50/4.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4312 ms resp. 3661 ms w/o parsing
% 16.26/5.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.26/5.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------