%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP052^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:33 AM UTC 2026
% Result : Theorem 187.40s 107.45s
% Output : Refutation 189.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 301
% Syntax : Number of formulae : 1055 ( 465 unt; 0 typ; 26 def)
% Number of atoms : 2971 ( 924 equ; 16 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 10457 ( 707 ~; 410 |; 107 &;8565 @)
% ( 0 <=>; 668 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 569 ( 569 >; 0 *; 0 +; 0 <<)
% Number of symbols : 87 ( 83 usr; 23 con; 0-5 aty)
% Number of variables : 2916 ( 640 ^;2171 !; 79 ?;2916 :)
% ( 0 !>; 0 ?*; 0 @-; 26 @+)
% 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_decl,type,
augmen887209518pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(augmen72931474pacity_decl,type,
augmen72931474pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > product_prod_nat_nat > capacity ).
thf(augmen1090971539pacity_decl,type,
augmen1090971539pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > $o ).
thf(augmen68920357pacity_decl,type,
augmen68920357pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > capacity ).
thf(finite217307323pacity_decl,type,
finite217307323pacity: ( product_prod_nat_nat > capacity ) > $o ).
thf(isShor1936442771pacity_decl,type,
isShor1936442771pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(isSimp1359852763pacity_decl,type,
isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(plus_plus_capacity_decl,type,
plus_plus_capacity: capacity > capacity > capacity ).
thf(zero_zero_capacity_decl,type,
zero_zero_capacity: capacity ).
thf(inf_in2138576462_nat_o_decl,type,
inf_in2138576462_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(inf_in586391887at_nat_decl,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(set_Pr2131844118at_nat_decl,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(finite1387368318pacity_decl,type,
finite1387368318pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(flow_capacity_decl,type,
flow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(val_capacity_decl,type,
val_capacity: ( product_prod_nat_nat > capacity ) > nat > ( product_prod_nat_nat > capacity ) > capacity ).
thf(nCut_capacity_decl,type,
nCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
thf(cap_capacity_decl,type,
cap_capacity: ( product_prod_nat_nat > capacity ) > set_nat > capacity ).
thf(nFlow_capacity_decl,type,
nFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(nPreflow_capacity_decl,type,
nPreflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(network_capacity_decl,type,
network_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > $o ).
thf(excess_capacity_decl,type,
excess_capacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > nat > capacity ).
thf(isMaxFlow_capacity_decl,type,
isMaxFlow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(is_max2144541363pacity_decl,type,
is_max2144541363pacity: ( product_prod_nat_nat > capacity ) > nat > nat > capacity > $o ).
thf(preflow_capacity_decl,type,
preflow_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(isMinCut_capacity_decl,type,
isMinCut_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > set_nat > $o ).
thf(bot_bo513358416_nat_o_decl,type,
bot_bo513358416_nat_o: product_prod_nat_nat > $o ).
thf(bot_bot_o_decl,type,
bot_bot_o: $o ).
thf(bot_bo2130386637at_nat_decl,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(ord_le1015898640_nat_o_decl,type,
ord_le1015898640_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(ord_le116442893at_nat_decl,type,
ord_le116442893at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(ord_less_capacity_decl,type,
ord_less_capacity: capacity > capacity > $o ).
thf(ord_le1039616028_nat_o_decl,type,
ord_le1039616028_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(ord_le841296385at_nat_decl,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(ord_less_eq_capacity_decl,type,
ord_less_eq_capacity: capacity > capacity > $o ).
thf(product_Pair_nat_nat_decl,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(product_swap_nat_nat_decl,type,
product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).
thf(converse_nat_nat_decl,type,
converse_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(residu1549650759pacity_decl,type,
residu1549650759pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(residu800046103pacity_decl,type,
residu800046103pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(residu164581374pacity_decl,type,
residu164581374pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > $o ).
thf(residu203630698pacity_decl,type,
residu203630698pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(collec7649004at_nat_decl,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(member701585322at_nat_decl,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(c_decl,type,
c: product_prod_nat_nat > capacity ).
thf(f_decl,type,
f: product_prod_nat_nat > capacity ).
thf(p_decl,type,
p: list_P559422087at_nat ).
thf(s_decl,type,
s: nat ).
thf(t_decl,type,
t: nat ).
thf(sk1_decl,type,
sk1: set_Pr1986765409at_nat > ( capacity > set_Pr1986765409at_nat ) > capacity > capacity > capacity ).
thf(sk2_decl,type,
sk2: set_Pr1986765409at_nat > ( capacity > set_Pr1986765409at_nat ) > capacity > capacity > capacity ).
thf(sk3_decl,type,
sk3: capacity > ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(sk4_decl,type,
sk4: capacity > ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(sk5_decl,type,
sk5: capacity > ( capacity > capacity ) > capacity > capacity > capacity ).
thf(sk6_decl,type,
sk6: capacity > ( capacity > capacity ) > capacity > capacity > capacity ).
thf(sk7_decl,type,
sk7: capacity > capacity > ( capacity > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > capacity ).
thf(sk8_decl,type,
sk8: capacity > capacity > ( capacity > set_Pr1986765409at_nat ) > set_Pr1986765409at_nat > capacity ).
thf(sk9_decl,type,
sk9: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(sk10_decl,type,
sk10: set_Pr1986765409at_nat > ( capacity > set_Pr1986765409at_nat ) > capacity > capacity > capacity ).
thf(sk11_decl,type,
sk11: set_Pr1986765409at_nat > ( capacity > set_Pr1986765409at_nat ) > capacity > capacity > capacity ).
thf(sk12_decl,type,
sk12: capacity > capacity > ( capacity > capacity ) > capacity > capacity ).
thf(sk13_decl,type,
sk13: capacity > capacity > ( capacity > capacity ) > capacity > capacity ).
thf(sk14_decl,type,
sk14: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat ).
thf(sk15_decl,type,
sk15: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > set_nat ).
thf(sk16_decl,type,
sk16: capacity > ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(sk17_decl,type,
sk17: capacity > ( set_Pr1986765409at_nat > capacity ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(sk18_decl,type,
sk18: ( capacity > capacity > $o ) > capacity ).
thf(sk19_decl,type,
sk19: ( capacity > capacity > $o ) > capacity ).
thf(sk20_decl,type,
sk20: ( capacity > capacity > $o ) > capacity ).
thf(sk21_decl,type,
sk21: ( capacity > capacity > $o ) > capacity ).
thf(sk51_decl,type,
sk51: list_P559422087at_nat ).
thf(sk52_decl,type,
sk52: set_nat ).
thf(sk80_decl,type,
sk80: list_P559422087at_nat ).
thf(sk81_decl,type,
sk81: list_P559422087at_nat ).
thf(sk82_decl,type,
sk82: product_prod_nat_nat ).
thf(sk83_decl,type,
sk83: list_P559422087at_nat ).
thf(sk88_decl,type,
sk88: product_prod_nat_nat ).
thf(sk89_decl,type,
sk89: product_prod_nat_nat ).
thf(sk93_decl,type,
sk93: product_prod_nat_nat ).
thf(sk95_decl,type,
sk95: product_prod_nat_nat ).
thf(sk103_decl,type,
sk103: product_prod_nat_nat ).
thf(sk107_decl,type,
sk107: product_prod_nat_nat ).
thf(sk108_decl,type,
sk108: product_prod_nat_nat ).
thf(sk112_decl,type,
sk112: product_prod_nat_nat ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity,D: capacity] :
@+[E: capacity] :
~ ! [F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity,D: capacity] :
@+[E: capacity] :
~ ( ( ord_less_eq_capacity @ ( sk1 @ A @ B @ C @ D ) @ E )
=> ( ord_le841296385at_nat @ ( B @ ( sk1 @ A @ B @ C @ D ) ) @ ( B @ E ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: capacity,B: set_Pr1986765409at_nat > capacity,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
@+[E: set_Pr1986765409at_nat] :
~ ! [F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: capacity,B: set_Pr1986765409at_nat > capacity,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
@+[E: set_Pr1986765409at_nat] :
~ ( ( ord_le841296385at_nat @ ( sk3 @ A @ B @ C @ D ) @ E )
=> ( ord_less_eq_capacity @ ( B @ ( sk3 @ A @ B @ C @ D ) ) @ ( B @ E ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: capacity,B: capacity > capacity,C: capacity,D: capacity] :
@+[E: capacity] :
~ ! [F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: capacity,B: capacity > capacity,C: capacity,D: capacity] :
@+[E: capacity] :
~ ( ( ord_less_eq_capacity @ ( sk5 @ A @ B @ C @ D ) @ E )
=> ( ord_less_eq_capacity @ ( B @ ( sk5 @ A @ B @ C @ D ) ) @ ( B @ E ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: capacity,B: capacity,C: capacity > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
@+[E: capacity] :
~ ! [F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: capacity,B: capacity,C: capacity > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
@+[E: capacity] :
~ ( ( ord_less_eq_capacity @ ( sk7 @ A @ B @ C @ D ) @ E )
=> ( ord_le841296385at_nat @ ( C @ ( sk7 @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
@+[E: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ D @ C @ B @ E )
& ( A
= ( residu203630698pacity @ D @ E ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity,D: capacity] :
@+[E: capacity] :
~ ! [F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity,D: capacity] :
@+[E: capacity] :
~ ( ( ord_less_eq_capacity @ ( sk10 @ A @ B @ C @ D ) @ E )
=> ( ord_le841296385at_nat @ ( B @ ( sk10 @ A @ B @ C @ D ) ) @ ( B @ E ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: capacity,B: capacity,C: capacity > capacity,D: capacity] :
@+[E: capacity] :
~ ! [F: capacity] :
( ( ord_less_eq_capacity @ E @ F )
=> ( ord_less_eq_capacity @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: capacity,B: capacity,C: capacity > capacity,D: capacity] :
@+[E: capacity] :
~ ( ( ord_less_eq_capacity @ ( sk12 @ A @ B @ C @ D ) @ E )
=> ( ord_less_eq_capacity @ ( C @ ( sk12 @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
@+[E: list_P559422087at_nat] : ( augmen1090971539pacity @ D @ C @ B @ A @ E ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
@+[E: set_nat] :
( ( nCut_capacity @ D @ C @ B @ E )
& ( ( val_capacity @ D @ C @ A )
= ( cap_capacity @ D @ E ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: capacity,B: set_Pr1986765409at_nat > capacity,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
@+[E: set_Pr1986765409at_nat] :
~ ! [F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_capacity @ ( B @ E ) @ ( B @ F ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: capacity,B: set_Pr1986765409at_nat > capacity,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
@+[E: set_Pr1986765409at_nat] :
~ ( ( ord_le841296385at_nat @ ( sk16 @ A @ B @ C @ D ) @ E )
=> ( ord_less_eq_capacity @ ( B @ ( sk16 @ A @ B @ C @ D ) ) @ ( B @ E ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: capacity > capacity > $o] :
@+[B: capacity] :
~ ! [C: capacity] :
( ( ord_less_eq_capacity @ B @ C )
=> ( A @ B @ C ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: capacity > capacity > $o] :
@+[B: capacity] :
~ ( ( ord_less_eq_capacity @ ( sk18 @ A ) @ B )
=> ( A @ ( sk18 @ A ) @ B ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: capacity > capacity > $o] :
@+[B: capacity] :
~ ! [C: capacity] :
( ( A @ C @ B )
=> ( A @ B @ C ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: capacity > capacity > $o] :
@+[B: capacity] :
~ ( ( A @ B @ ( sk20 @ A ) )
=> ( A @ ( sk20 @ A ) @ B ) ) ) ) ).
thf(sk51_def,definition,
( sk51
= ( @+[A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ) ).
thf(sk52_def,definition,
( sk52
= ( @+[A: set_nat] :
( ( nCut_capacity @ c @ s @ t @ A )
& ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ A ) ) ) ) ) ).
thf(sk80_def,definition,
( sk80
= ( @+[A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ) ).
thf(sk81_def,definition,
( sk81
= ( @+[A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ) ).
thf(sk83_def,definition,
( sk83
= ( @+[A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ) ).
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(645,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(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(1036,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(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(1024,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(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(363,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(364,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ~ ( residu800046103pacity @ A @ B @ C @ D )
| ( nFlow_capacity @ A @ B @ C @ ( sk9 @ D @ C @ B @ A ) ) )
& ( ~ ( residu800046103pacity @ A @ B @ C @ D )
| ( D
= ( residu203630698pacity @ A @ ( sk9 @ D @ C @ B @ A ) ) ) ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( residu800046103pacity @ A @ B @ C @ D )
| ( nFlow_capacity @ A @ B @ C @ ( sk9 @ D @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(150,axiom,
preflow_capacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Preflow__axioms) ).
thf(760,plain,
preflow_capacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
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(779,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(780,plain,
! [A: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[779]) ).
thf(781,plain,
! [A: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[780]) ).
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(1030,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1031,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
= A ),
inference(cnf,[status(esa)],[1030]) ).
thf(1032,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
= A ),
inference(lifteq,[status(thm)],[1031]) ).
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(278,plain,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bo2130386637at_nat ),
inference(lifteq,[status(thm)],[277]) ).
thf(2059,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ A )
!= bot_bo2130386637at_nat )
| ( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(paramod_ordered,[status(thm)],[1032,278]) ).
thf(2078,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ A )
!= bot_bo2130386637at_nat )
| ( ( converse_nat_nat @ A )
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(simp,[status(thm)],[2059]) ).
thf(2099,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ A ) )
!= bot_bo2130386637at_nat )
| ( ( converse_nat_nat @ B )
!= ( set_Pr2131844118at_nat @ p ) )
| ( A
!= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[781,2078]) ).
thf(2100,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ A ) ) )
!= bot_bo2130386637at_nat )
| ( ( converse_nat_nat @ A )
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(pattern_uni,[status(thm)],[2099:[bind(A,$thf( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ D )),bind(B,$thf( D ))]]) ).
thf(2109,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ A ) ) )
!= bot_bo2130386637at_nat )
| ( ( converse_nat_nat @ A )
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(simp,[status(thm)],[2100]) ).
thf(218,axiom,
( ( converse_nat_nat @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_converse__empty) ).
thf(971,plain,
( ( converse_nat_nat @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(972,plain,
( ( converse_nat_nat @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
inference(lifteq,[status(thm)],[971]) ).
thf(2062,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ A ) ) )
= B )
| ( A
!= ( converse_nat_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[781,1032]) ).
thf(2063,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[2062:[bind(A,$thf( converse_nat_nat @ C )),bind(B,$thf( C ))]]) ).
thf(2083,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
= A ),
inference(simp,[status(thm)],[2063]) ).
thf(201,axiom,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_inf__bot__right) ).
thf(913,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(914,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
inference(cnf,[status(esa)],[913]) ).
thf(915,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
= bot_bo2130386637at_nat ),
inference(lifteq,[status(thm)],[914]) ).
thf(2566,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ) )
= bot_bo2130386637at_nat )
| ( A
!= ( inf_in586391887at_nat @ B @ bot_bo2130386637at_nat ) ) ),
inference(paramod_ordered,[status(thm)],[2083,915]) ).
thf(2567,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(pattern_uni,[status(thm)],[2566:[bind(A,$thf( inf_in586391887at_nat @ C @ bot_bo2130386637at_nat )),bind(B,$thf( C ))]]) ).
thf(2680,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(simp,[status(thm)],[2567]) ).
thf(2757,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[2680,915]) ).
thf(2552,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ A ) ) )
= B )
| ( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
!= ( converse_nat_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1032,2083]) ).
thf(2553,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) ) )
= ( converse_nat_nat @ A ) ),
inference(pattern_uni,[status(thm)],[2552:[bind(A,$thf( C )),bind(B,$thf( converse_nat_nat @ C ))]]) ).
thf(2725,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) ) )
= ( converse_nat_nat @ A ) ),
inference(simp,[status(thm)],[2553]) ).
thf(5248,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) ) )
= bot_bo2130386637at_nat )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) )
!= ( converse_nat_nat @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2757,2725]) ).
thf(5249,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(pattern_uni,[status(thm)],[5248:[bind(A,$thf( collec7649004at_nat @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ))]]) ).
thf(5721,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[5249,972]) ).
thf(2546,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat @ A )
= B )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2083,1032]) ).
thf(2547,plain,
! [A: set_Pr1986765409at_nat] :
( ( converse_nat_nat @ A )
= ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2546:[bind(A,$thf( A )),bind(B,$thf( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ))]]) ).
thf(5749,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) )
= bot_bo2130386637at_nat )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5721,2547]) ).
thf(5750,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(pattern_uni,[status(thm)],[5749:[bind(A,$thf( collec7649004at_nat @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ))]]) ).
thf(5733,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) )
= A )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5721,2083]) ).
thf(5734,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) )
= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ) ),
inference(pattern_uni,[status(thm)],[5733:[bind(A,$thf( collec7649004at_nat @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ))]]) ).
thf(4530,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) )
= bot_bo2130386637at_nat )
| ( ( converse_nat_nat @ bot_bo2130386637at_nat )
!= ( converse_nat_nat @ A ) ) ),
inference(paramod_ordered,[status(thm)],[972,2547]) ).
thf(4531,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) )
= bot_bo2130386637at_nat ),
inference(pattern_uni,[status(thm)],[4530:[bind(A,$thf( bot_bo2130386637at_nat ))]]) ).
thf(4696,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[4531,972]) ).
thf(6187,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
= ( converse_nat_nat @ bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[5734,4696]) ).
thf(6551,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[5750,6187]) ).
thf(6633,plain,
( ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
= bot_bo2130386637at_nat )
| ( ( converse_nat_nat @ bot_bo2130386637at_nat )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ),
inference(paramod_ordered,[status(thm)],[972,6551]) ).
thf(6634,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(pattern_uni,[status(thm)],[6633:[]]) ).
thf(6566,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat @ bot_bo2130386637at_nat )
= A )
| ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6551,2083]) ).
thf(6567,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) )
= ( converse_nat_nat @ bot_bo2130386637at_nat ) ),
inference(pattern_uni,[status(thm)],[6566:[bind(A,$thf( collec7649004at_nat @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ))]]) ).
thf(6658,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[6567,972]) ).
thf(6982,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[6634,6658]) ).
thf(2509,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ B ) ) )
!= bot_bo2130386637at_nat )
| ( A
!= ( set_Pr2131844118at_nat @ p ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2083,2109]) ).
thf(2510,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ) ) ) )
!= bot_bo2130386637at_nat )
| ( A
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(pattern_uni,[status(thm)],[2509:[bind(A,$thf( A )),bind(B,$thf( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ))]]) ).
thf(2694,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= bot_bo2130386637at_nat ),
inference(simp,[status(thm)],[2510]) ).
thf(10057,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6982,2694]) ).
thf(10058,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(simp,[status(thm)],[10057]) ).
thf(10083,plain,
( ( ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(simp,[status(thm)],[10058]) ).
thf(18304,plain,
( ( ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(rewrite,[status(thm)],[10083,972]) ).
thf(18305,plain,
( ( ( ^ [A: product_prod_nat_nat] : A )
!= ( ^ [A: product_prod_nat_nat] : A ) )
| ( ( ^ [A: product_prod_nat_nat] :
( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[18304]) ).
thf(18365,plain,
( ( ^ [A: product_prod_nat_nat] :
( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[18305]) ).
thf(2529,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ A ) ) )
= B )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2083,2083]) ).
thf(2530,plain,
! [A: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) )
= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2529:[bind(A,$thf( A )),bind(B,$thf( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ))]]) ).
thf(18504,plain,
( ( ^ [A: product_prod_nat_nat] :
( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[18365,2530]) ).
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(478,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(479,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(lifteq,[status(thm)],[478]) ).
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(347,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(20,axiom,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_dual__order_Orefl) ).
thf(332,plain,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(333,plain,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
inference(cnf,[status(esa)],[332]) ).
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(962,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(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(555,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(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(1108,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(1109,plain,
! [A: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
= ( A = bot_bo2130386637at_nat ) ),
inference(cnf,[status(esa)],[1108]) ).
thf(1110,plain,
! [A: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ bot_bo2130386637at_nat )
= ( A = bot_bo2130386637at_nat ) ),
inference(lifteq,[status(thm)],[1109]) ).
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(976,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(977,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[976]) ).
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(985,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(986,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ),
inference(lifteq,[status(thm)],[985]) ).
thf(1158,plain,
( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ),
inference(rewrite,[status(thm)],[986,977]) ).
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(1005,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(2595,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ B )
!= bot_bo2130386637at_nat )
| ( A
!= ( set_Pr2131844118at_nat @ p ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2083,2078]) ).
thf(2596,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
!= bot_bo2130386637at_nat )
| ( A
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(pattern_uni,[status(thm)],[2595:[bind(A,$thf( A )),bind(B,$thf( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ))]]) ).
thf(2684,plain,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= bot_bo2130386637at_nat ),
inference(simp,[status(thm)],[2596]) ).
thf(18514,plain,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[2684,2530]) ).
thf(1494,plain,
! [A: set_Pr1986765409at_nat] :
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
!= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[915,278]) ).
thf(1495,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
!= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(simp,[status(thm)],[1494]) ).
thf(1503,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( set_Pr2131844118at_nat @ p ) )
| ( ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[1495]) ).
thf(1513,plain,
( ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) )
!= bot_bo2130386637at_nat ),
inference(simp,[status(thm)],[1503]) ).
thf(2613,plain,
! [A: set_Pr1986765409at_nat] :
( ( A != bot_bo2130386637at_nat )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(paramod_ordered,[status(thm)],[2083,1513]) ).
thf(2657,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(simp,[status(thm)],[2613]) ).
thf(2737,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(rewrite,[status(thm)],[2657,972]) ).
thf(2745,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
!= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1032,2737]) ).
thf(2752,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) )
!= ( converse_nat_nat @ ( converse_nat_nat @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(simp,[status(thm)],[2745]) ).
thf(2762,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) )
= A )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) )
!= ( converse_nat_nat @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2757,2083]) ).
thf(2763,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) )
= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ) ),
inference(pattern_uni,[status(thm)],[2762:[bind(A,$thf( collec7649004at_nat @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ))]]) ).
thf(202,axiom,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ A )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_inf__bot__left) ).
thf(916,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ A )
= bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(917,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ A )
= bot_bo2130386637at_nat ),
inference(cnf,[status(esa)],[916]) ).
thf(918,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ A )
= bot_bo2130386637at_nat ),
inference(lifteq,[status(thm)],[917]) ).
thf(1792,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ A ) )
= bot_bo2130386637at_nat )
| ( A
!= ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[781,918]) ).
thf(1793,plain,
! [A: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ A ) ) )
= bot_bo2130386637at_nat ),
inference(pattern_uni,[status(thm)],[1792:[bind(A,$thf( inf_in586391887at_nat @ bot_bo2130386637at_nat @ D )),bind(B,$thf( D ))]]) ).
thf(1823,plain,
! [A: set_Pr1986765409at_nat] :
( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( inf_in586391887at_nat @ bot_bo2130386637at_nat @ A ) ) )
= bot_bo2130386637at_nat ),
inference(simp,[status(thm)],[1793]) ).
thf(1850,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[1823,918]) ).
thf(2876,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
= ( converse_nat_nat @ bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[2763,1850,972]) ).
thf(3119,plain,
( ( converse_nat_nat @ ( converse_nat_nat @ bot_bo2130386637at_nat ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(rewrite,[status(thm)],[2752,1032,2876]) ).
thf(3122,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat @ A )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ),
inference(paramod_ordered,[status(thm)],[2083,3119]) ).
thf(3138,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( set_Pr2131844118at_nat @ p ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[3122]) ).
thf(3150,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[3138]) ).
thf(3356,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[3150,972]) ).
thf(3367,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2757,3356]) ).
thf(3368,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ),
inference(simp,[status(thm)],[3367]) ).
thf(3387,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(simp,[status(thm)],[3368]) ).
thf(3736,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(rewrite,[status(thm)],[3387,972]) ).
thf(3737,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[3736]) ).
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(951,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(952,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
= bot_bo513358416_nat_o ),
inference(lifteq,[status(thm)],[951]) ).
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(729,plain,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(730,plain,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(lifteq,[status(thm)],[729]) ).
thf(1152,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[952,730]) ).
thf(1153,plain,
! [A: product_prod_nat_nat] :
( ( member701585322at_nat @ A @ bot_bo2130386637at_nat )
= bot_bot_o ),
inference(func_ext,[status(esa)],[1152]) ).
thf(3762,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[3737,1153]) ).
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(994,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(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(308,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(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(741,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(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(375,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(376,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ! [C: capacity > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( 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(miniscope,[status(thm)],[375]) ).
thf(377,plain,
! [D: set_Pr1986765409at_nat,C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_le841296385at_nat @ ( C @ B ) @ D )
| ( ord_less_eq_capacity @ ( sk10 @ D @ C @ B @ A ) @ ( sk11 @ D @ C @ B @ A ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) )
& ( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_le841296385at_nat @ ( C @ B ) @ D )
| ~ ( ord_le841296385at_nat @ ( C @ ( sk10 @ D @ C @ B @ A ) ) @ ( C @ ( sk11 @ D @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[376]) ).
thf(379,plain,
! [D: set_Pr1986765409at_nat,C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_le841296385at_nat @ ( C @ B ) @ D )
| ~ ( ord_le841296385at_nat @ ( C @ ( sk10 @ D @ C @ B @ A ) ) @ ( C @ ( sk11 @ D @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[377]) ).
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(677,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(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(861,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(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(438,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(439,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ! [C: capacity] :
( ( ord_less_eq_capacity @ C @ A )
=> ( ord_less_eq_capacity @ C @ B ) ) ),
inference(miniscope,[status(thm)],[438]) ).
thf(440,plain,
! [C: capacity,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_less_eq_capacity @ C @ A )
| ( ord_less_eq_capacity @ C @ B ) ),
inference(cnf,[status(esa)],[439]) ).
thf(114,axiom,
flow_capacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Flow__axioms) ).
thf(655,plain,
flow_capacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
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(511,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(83,axiom,
augmen72931474pacity = augmen72931474pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_NPreflow_OaugmentingFlow_Ocong) ).
thf(550,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(2741,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2083,2737]) ).
thf(2755,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[2741]) ).
thf(3671,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[2755,1032,2876]) ).
thf(4412,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat @ A )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) )
| ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) )
!= ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2547,3671]) ).
thf(4570,plain,
! [A: set_Pr1986765409at_nat] :
( ( A != bot_bo2130386637at_nat )
| ( ( ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) )
!= ( ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(simp,[status(thm)],[4412]) ).
thf(4616,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(simp,[status(thm)],[4570]) ).
thf(4780,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(rewrite,[status(thm)],[4616,972]) ).
thf(4782,plain,
( ( member701585322at_nat @ sk93 @ ( set_Pr2131844118at_nat @ p ) )
!= ( member701585322at_nat @ sk93 @ bot_bo2130386637at_nat ) ),
inference(func_ext,[status(esa)],[4780]) ).
thf(4884,plain,
( ( member701585322at_nat @ sk93 @ ( set_Pr2131844118at_nat @ p ) )
!= bot_bot_o ),
inference(rewrite,[status(thm)],[4782,1153]) ).
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(500,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(3121,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[2083,3119]) ).
thf(3149,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[3121]) ).
thf(3347,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[3149,1032,972]) ).
thf(3348,plain,
( ( ( converse_nat_nat @ bot_bo2130386637at_nat )
!= bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[2876,3347]) ).
thf(3355,plain,
( ( ( converse_nat_nat @ bot_bo2130386637at_nat )
!= bot_bo2130386637at_nat )
| ( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ) ),
inference(simp,[status(thm)],[3348]) ).
thf(3392,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ) ),
inference(rewrite,[status(thm)],[3355,1153,972]) ).
thf(3393,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(simp,[status(thm)],[3392]) ).
thf(3394,plain,
( ( member701585322at_nat @ sk88 @ ( set_Pr2131844118at_nat @ p ) )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[3393]) ).
thf(3446,plain,
( ( member701585322at_nat @ sk88 @ ( set_Pr2131844118at_nat @ p ) )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[3394]) ).
thf(3080,plain,
! [A: set_Pr1986765409at_nat] :
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
!= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[915,2684]) ).
thf(3081,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ bot_bo2130386637at_nat )
!= ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ),
inference(simp,[status(thm)],[3080]) ).
thf(3096,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( set_Pr2131844118at_nat @ p ) )
| ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[3081]) ).
thf(3100,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= bot_bo2130386637at_nat ),
inference(simp,[status(thm)],[3096]) ).
thf(6629,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6551,3100]) ).
thf(6630,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(simp,[status(thm)],[6629]) ).
thf(6648,plain,
( ( ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(simp,[status(thm)],[6630]) ).
thf(8791,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(rewrite,[status(thm)],[6648,6982]) ).
thf(8793,plain,
( ( member701585322at_nat @ sk107 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( member701585322at_nat @ sk107 @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ),
inference(func_ext,[status(esa)],[8791]) ).
thf(8838,plain,
( ( member701585322at_nat @ sk107 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( member701585322at_nat @ sk107 @ bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[8793,972]) ).
thf(6631,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6551,3347]) ).
thf(6632,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(simp,[status(thm)],[6631]) ).
thf(6643,plain,
( ( ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(simp,[status(thm)],[6632]) ).
thf(8161,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(rewrite,[status(thm)],[6643,6982]) ).
thf(8163,plain,
( ( member701585322at_nat @ sk103 @ ( converse_nat_nat @ bot_bo2130386637at_nat ) )
!= ( member701585322at_nat @ sk103 @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(func_ext,[status(esa)],[8161]) ).
thf(8204,plain,
( ( member701585322at_nat @ sk103 @ ( set_Pr2131844118at_nat @ p ) )
!= ( member701585322at_nat @ sk103 @ bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[8163,972]) ).
thf(7039,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6982,3100]) ).
thf(7040,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(simp,[status(thm)],[7039]) ).
thf(7049,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(simp,[status(thm)],[7040]) ).
thf(7098,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(rewrite,[status(thm)],[7049,972]) ).
thf(7100,plain,
( ( member701585322at_nat @ sk95 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( member701585322at_nat @ sk95 @ bot_bo2130386637at_nat ) ),
inference(func_ext,[status(esa)],[7098]) ).
thf(7146,plain,
( ( member701585322at_nat @ sk95 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bot_o ),
inference(rewrite,[status(thm)],[7100,1153]) ).
thf(7147,plain,
( ~ ( member701585322at_nat @ sk95 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[7146]) ).
thf(131,axiom,
augmen1090971539pacity = augmen1090971539pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_NPreflow_OisAugmentingPath_Ocong) ).
thf(698,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
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(746,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(747,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
inference(cnf,[status(esa)],[746]) ).
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(401,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(402,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ! [D: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ A @ B @ C @ D )
=> ! [E: set_nat] :
( ( isMinCut_capacity @ A @ B @ C @ E )
=> ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) ) ) ) ),
inference(miniscope,[status(thm)],[401]) ).
thf(403,plain,
! [E: set_nat,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( 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(cnf,[status(esa)],[402]) ).
thf(404,plain,
! [E: set_nat,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ E ) )
| ~ ( network_capacity @ A @ B @ C )
| ~ ( isMaxFlow_capacity @ A @ B @ C @ D )
| ~ ( isMinCut_capacity @ A @ B @ C @ E ) ),
inference(lifteq,[status(thm)],[403]) ).
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(1127,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(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(782,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(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(709,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(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(416,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(417,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( residu164581374pacity @ A @ B @ C @ D )
| ~ ( isMaxFlow_capacity @ A @ B @ C @ ( residu1549650759pacity @ A @ D ) )
| ( residu800046103pacity @ A @ B @ C @ D ) ),
inference(cnf,[status(esa)],[416]) ).
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(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(320,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(172,axiom,
residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_is__RGraph) ).
thf(834,plain,
residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(4961,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ $true
| ( nFlow_capacity @ A @ B @ C @ ( sk9 @ D @ C @ B @ A ) )
| ( ( residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ) )
!= ( residu800046103pacity @ A @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[834,365]) ).
thf(4962,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ ( sk9 @ D @ C @ B @ A ) )
| ( ( residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ) )
!= ( residu800046103pacity @ A @ B @ C @ D ) ) ),
inference(simp,[status(thm)],[4961]) ).
thf(4963,plain,
nFlow_capacity @ c @ s @ t @ ( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ),
inference(pattern_uni,[status(thm)],[4962:[bind(A,$thf( c )),bind(B,$thf( s )),bind(C,$thf( t )),bind(D,$thf( residu203630698pacity @ c @ f ))]]) ).
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(973,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(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(885,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(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(1046,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(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(785,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(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(504,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(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(619,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(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(934,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(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(542,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(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(343,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(344,plain,
! [B: nat,A: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( c @ ( product_Pair_nat_nat @ A @ B ) ) ),
inference(cnf,[status(esa)],[343]) ).
thf(3746,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) )
| ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
!= ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[781,3736]) ).
thf(3747,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(pattern_uni,[status(thm)],[3746:[bind(A,$thf( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ))]]) ).
thf(3776,plain,
( ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[3747,2876]) ).
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(1059,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(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(1132,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(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(816,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(817,plain,
( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
& ( ord_le841296385at_nat @ B @ A ) ) )
= ( (=) @ set_Pr1986765409at_nat ) ),
inference(lifteq,[status(thm)],[816]) ).
thf(17,axiom,
isShor1936442771pacity = isShor1936442771pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Graph_OisShortestPath_Ocong) ).
thf(325,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
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(448,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(309,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ! [C: set_Pr1986765409at_nat > capacity,D: 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(miniscope,[status(thm)],[308]) ).
thf(310,plain,
! [D: capacity,C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ A @ B )
| ( ( C @ B )
!= D )
| ( ord_le841296385at_nat @ ( sk3 @ D @ C @ B @ A ) @ ( sk4 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) )
& ( ~ ( ord_le841296385at_nat @ A @ B )
| ( ( C @ B )
!= D )
| ~ ( ord_less_eq_capacity @ ( C @ ( sk3 @ D @ C @ B @ A ) ) @ ( C @ ( sk4 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[309]) ).
thf(312,plain,
! [D: capacity,C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ A @ B )
| ( ( C @ B )
!= D )
| ~ ( ord_less_eq_capacity @ ( C @ ( sk3 @ D @ C @ B @ A ) ) @ ( C @ ( sk4 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[310]) ).
thf(315,plain,
! [D: capacity,C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( C @ B )
!= D )
| ~ ( ord_le841296385at_nat @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ ( sk3 @ D @ C @ B @ A ) ) @ ( C @ ( sk4 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ),
inference(lifteq,[status(thm)],[312]) ).
thf(316,plain,
! [C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ ( sk3 @ ( C @ B ) @ C @ B @ A ) ) @ ( C @ ( sk4 @ ( C @ B ) @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ ( C @ B ) ) ),
inference(simp,[status(thm)],[315]) ).
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(638,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(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(853,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(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(421,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(186,axiom,
( ( residu1549650759pacity @ c @ ( residu203630698pacity @ c @ f ) )
= f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_fo__rg__inv) ).
thf(870,plain,
( ( residu1549650759pacity @ c @ ( residu203630698pacity @ c @ f ) )
= f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
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(1013,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(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(284,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nPreflow_capacity @ A @ B @ C @ D )
| ~ ( flow_capacity @ A @ B @ C @ D )
| ( nFlow_capacity @ A @ B @ C @ D ) ),
inference(cnf,[status(esa)],[283]) ).
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(770,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(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(881,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(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(1100,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(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(492,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(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(789,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(8206,plain,
( ~ ( member701585322at_nat @ sk103 @ ( set_Pr2131844118at_nat @ p ) )
| ~ ( member701585322at_nat @ sk103 @ bot_bo2130386637at_nat ) ),
inference(bool_ext,[status(thm)],[8204]) ).
thf(8229,plain,
( ~ ( member701585322at_nat @ sk103 @ ( set_Pr2131844118at_nat @ p ) )
| ~ bot_bot_o ),
inference(rewrite,[status(thm)],[8206,1153]) ).
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(937,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(348,plain,
! [A: set_Pr1986765409at_nat,B: capacity > set_Pr1986765409at_nat,C: capacity] :
( ( A
= ( B @ C ) )
=> ! [D: capacity] :
( ( 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(miniscope,[status(thm)],[347]) ).
thf(349,plain,
! [D: capacity,C: capacity,B: capacity > set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ( ord_less_eq_capacity @ ( sk7 @ D @ C @ B @ A ) @ ( sk8 @ D @ C @ B @ A ) )
| ( ord_le841296385at_nat @ A @ ( B @ D ) ) )
& ( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ~ ( ord_le841296385at_nat @ ( B @ ( sk7 @ D @ C @ B @ A ) ) @ ( B @ ( sk8 @ D @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [D: capacity,C: capacity,B: capacity > set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ( ord_less_eq_capacity @ ( sk7 @ D @ C @ B @ A ) @ ( sk8 @ D @ C @ B @ A ) )
| ( ord_le841296385at_nat @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[349]) ).
thf(352,plain,
! [D: capacity,C: capacity,B: capacity > set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ( ord_less_eq_capacity @ ( sk7 @ D @ C @ B @ A ) @ ( sk8 @ D @ C @ B @ A ) )
| ( ord_le841296385at_nat @ A @ ( B @ D ) ) ),
inference(lifteq,[status(thm)],[350]) ).
thf(353,plain,
! [C: capacity,B: capacity,A: capacity > set_Pr1986765409at_nat] :
( ~ ( ord_less_eq_capacity @ B @ C )
| ( ord_less_eq_capacity @ ( sk7 @ C @ B @ A @ ( A @ B ) ) @ ( sk8 @ C @ B @ A @ ( A @ B ) ) )
| ( ord_le841296385at_nat @ ( A @ B ) @ ( A @ C ) ) ),
inference(simp,[status(thm)],[352]) ).
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(480,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(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(1136,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(8207,plain,
( ( member701585322at_nat @ sk103 @ ( set_Pr2131844118at_nat @ p ) )
| ( member701585322at_nat @ sk103 @ bot_bo2130386637at_nat ) ),
inference(bool_ext,[status(thm)],[8204]) ).
thf(8246,plain,
( ( member701585322at_nat @ sk103 @ ( set_Pr2131844118at_nat @ p ) )
| bot_bot_o ),
inference(rewrite,[status(thm)],[8207,1153]) ).
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(806,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(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(394,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(395,plain,
! [C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( network_capacity @ A @ B @ C )
| ( B != C ) ),
inference(cnf,[status(esa)],[394]) ).
thf(396,plain,
! [C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( B != C )
| ~ ( network_capacity @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[395]) ).
thf(397,plain,
! [B: nat,A: product_prod_nat_nat > capacity] :
~ ( network_capacity @ A @ B @ B ),
inference(simp,[status(thm)],[396]) ).
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(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(691,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(692,plain,
! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( residu203630698pacity @ c @ f @ A ) ),
inference(cnf,[status(esa)],[691]) ).
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(734,plain,
( bot_bo513358416_nat_o
= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
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(292,plain,
! [B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_less_eq_capacity @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[291]) ).
thf(293,plain,
! [B: capacity,A: capacity] :
( ( A = B )
| ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_less_eq_capacity @ B @ A ) ),
inference(lifteq,[status(thm)],[292]) ).
thf(184,axiom,
finite217307323pacity @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Finite__Graph__axioms) ).
thf(866,plain,
finite217307323pacity @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
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(774,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(10075,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[6658,2694]) ).
thf(10076,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[10075]) ).
thf(10086,plain,
( ( ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[10076]) ).
thf(10906,plain,
( ( ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[10086,1153]) ).
thf(10907,plain,
( ( member701585322at_nat @ sk112
@ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p )
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[10906]) ).
thf(10964,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( member701585322at_nat @ sk112 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ A ) ) )
!= bot_bot_o )
| ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) )
!= ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2547,10907]) ).
thf(10965,plain,
( ( member701585322at_nat @ sk112 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= bot_bot_o ),
inference(pattern_uni,[status(thm)],[10964:[bind(A,$thf( set_Pr2131844118at_nat @ p ))]]) ).
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(410,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(411,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nPreflow_capacity @ A @ B @ C @ D )
| ( preflow_capacity @ A @ B @ C @ D ) ),
inference(cnf,[status(esa)],[410]) ).
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(849,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(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(1072,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(449,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ! [E: product_prod_nat_nat > capacity] :
( ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
=> ( ! [F: nat,G: nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ F @ G ) ) )
& ! [F: nat,G: nat] : ( ord_less_eq_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ F @ G ) ) @ ( A @ ( product_Pair_nat_nat @ F @ G ) ) ) ) ) ),
inference(miniscope,[status(thm)],[448]) ).
thf(450,plain,
! [I: nat,H: nat,G: nat,F: nat,E: product_prod_nat_nat > capacity,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ~ ( 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 ) ) ) )
& ( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ~ ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
| ( ord_less_eq_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ H @ I ) ) @ ( A @ ( product_Pair_nat_nat @ H @ I ) ) ) ) ),
inference(cnf,[status(esa)],[449]) ).
thf(452,plain,
! [G: nat,F: nat,E: product_prod_nat_nat > capacity,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ~ ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
| ( ord_less_eq_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ F @ G ) ) @ ( A @ ( product_Pair_nat_nat @ F @ G ) ) ) ),
inference(cnfConj,[status(thm)],[450]) ).
thf(453,plain,
! [G: nat,F: nat,E: product_prod_nat_nat > capacity,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ~ ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E )
| ( ord_less_eq_capacity @ ( augmen887209518pacity @ A @ D @ E @ ( product_Pair_nat_nat @ F @ G ) ) @ ( A @ ( product_Pair_nat_nat @ F @ G ) ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(7148,plain,
( ( member701585322at_nat @ sk95 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[7146]) ).
thf(33,axiom,
val_capacity = val_capacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Flow_Oval_Ocong) ).
thf(380,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
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(940,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(941,plain,
! [A: nat,B: list_P559422087at_nat] :
( ? [C: nat] : ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ ( set_Pr2131844118at_nat @ B ) )
=> ~ ( member701585322at_nat @ ( product_swap_nat_nat @ C ) @ ( set_Pr2131844118at_nat @ B ) ) ) ),
inference(miniscope,[status(thm)],[940]) ).
thf(942,plain,
! [D: product_prod_nat_nat,C: nat,B: list_P559422087at_nat,A: 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(cnf,[status(esa)],[941]) ).
thf(182,axiom,
nFlow_capacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_NFlow__axioms) ).
thf(860,plain,
nFlow_capacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(289,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: 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(cnf,[status(esa)],[288]) ).
thf(290,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) )
| ~ ( nFlow_capacity @ A @ B @ C @ D ) ),
inference(lifteq,[status(thm)],[289]) ).
thf(1291,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) )
| ~ $true
| ( ( nFlow_capacity @ c @ s @ t @ f )
!= ( nFlow_capacity @ A @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[860,290]) ).
thf(1292,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( isMaxFlow_capacity @ A @ B @ C @ D )
= ( ~ ? [E: list_P559422087at_nat] : ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) )
| ( ( nFlow_capacity @ c @ s @ t @ f )
!= ( nFlow_capacity @ A @ B @ C @ D ) ) ),
inference(simp,[status(thm)],[1291]) ).
thf(1293,plain,
( ( isMaxFlow_capacity @ c @ s @ t @ f )
= ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ),
inference(pattern_uni,[status(thm)],[1292:[bind(A,$thf( c )),bind(B,$thf( s )),bind(C,$thf( t )),bind(D,$thf( f ))]]) ).
thf(244,axiom,
augmen1090971539pacity @ c @ s @ t @ f @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1045,plain,
augmen1090971539pacity @ c @ s @ t @ f @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
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(669,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(670,plain,
! [A: list_P559422087at_nat] :
( ~ ( isMaxFlow_capacity @ c @ s @ t @ f )
| ~ ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ),
inference(cnf,[status(esa)],[669]) ).
thf(1341,plain,
! [A: list_P559422087at_nat] :
( ~ ( isMaxFlow_capacity @ c @ s @ t @ f )
| ~ $true
| ( ( augmen1090971539pacity @ c @ s @ t @ f @ p )
!= ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1045,670]) ).
thf(1342,plain,
! [A: list_P559422087at_nat] :
( ~ ( isMaxFlow_capacity @ c @ s @ t @ f )
| ( ( augmen1090971539pacity @ c @ s @ t @ f @ p )
!= ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ),
inference(simp,[status(thm)],[1341]) ).
thf(1343,plain,
~ ( isMaxFlow_capacity @ c @ s @ t @ f ),
inference(pattern_uni,[status(thm)],[1342:[bind(A,$thf( p ))]]) ).
thf(2471,plain,
~ ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ),
inference(rewrite,[status(thm)],[1293,1343]) ).
thf(2472,plain,
? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ),
inference(simp,[status(thm)],[2471]) ).
thf(2473,plain,
augmen1090971539pacity @ c @ s @ t @ f @ sk83,
inference(cnf,[status(esa)],[2472]) ).
thf(790,plain,
( ( ( augmen1090971539pacity @ c @ s @ t @ f @ sk51 )
| ( nCut_capacity @ c @ s @ t @ sk52 ) )
& ( ( augmen1090971539pacity @ c @ s @ t @ f @ sk51 )
| ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ sk52 ) ) ) ),
inference(cnf,[status(esa)],[789]) ).
thf(792,plain,
( ( augmen1090971539pacity @ c @ s @ t @ f @ sk51 )
| ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ sk52 ) ) ),
inference(cnfConj,[status(thm)],[790]) ).
thf(793,plain,
( ( ( val_capacity @ c @ s @ f )
= ( cap_capacity @ c @ sk52 ) )
| ( augmen1090971539pacity @ c @ s @ t @ f @ sk51 ) ),
inference(lifteq,[status(thm)],[792]) ).
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(810,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(34,axiom,
cap_capacity = cap_capacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_NCut_Ocap_Ocong) ).
thf(381,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
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(714,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(12,axiom,
augmen887209518pacity = augmen887209518pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_NFlow_Oaugment_Ocong) ).
thf(307,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2234,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ B ) ) )
!= bot_bo2130386637at_nat )
| ( A
!= ( set_Pr2131844118at_nat @ p ) )
| ( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
!= ( converse_nat_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1032,2109]) ).
thf(2235,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ A ) ) ) )
!= bot_bo2130386637at_nat )
| ( A
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(pattern_uni,[status(thm)],[2234:[bind(A,$thf( C )),bind(B,$thf( converse_nat_nat @ C ))]]) ).
thf(2256,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= bot_bo2130386637at_nat ),
inference(simp,[status(thm)],[2235]) ).
thf(7016,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6982,2256]) ).
thf(7017,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(simp,[status(thm)],[7016]) ).
thf(7059,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ),
inference(simp,[status(thm)],[7017]) ).
thf(8975,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(rewrite,[status(thm)],[7059,972]) ).
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(761,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(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(334,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(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(803,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(804,plain,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
= ( A = bot_bo513358416_nat_o ) ),
inference(cnf,[status(esa)],[803]) ).
thf(805,plain,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1039616028_nat_o @ A @ bot_bo513358416_nat_o )
= ( A = bot_bo513358416_nat_o ) ),
inference(lifteq,[status(thm)],[804]) ).
thf(1146,plain,
! [A: product_prod_nat_nat] :
( ( bot_bo513358416_nat_o @ A )
= bot_bot_o ),
inference(func_ext,[status(esa)],[730]) ).
thf(2409,plain,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1039616028_nat_o @ A
@ ^ [B: product_prod_nat_nat] : bot_bot_o )
= ( A
= ( ^ [B: product_prod_nat_nat] : bot_bot_o ) ) ),
inference(rewrite,[status(thm)],[805,1146]) ).
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(910,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(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(894,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(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(1021,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(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(1042,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(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(295,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ! [C: capacity > set_Pr1986765409at_nat,D: set_Pr1986765409at_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(miniscope,[status(thm)],[294]) ).
thf(296,plain,
! [D: set_Pr1986765409at_nat,C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ( ~ ( ord_less_eq_capacity @ A @ B )
| ( ( C @ B )
!= D )
| ( ord_less_eq_capacity @ ( sk1 @ D @ C @ B @ A ) @ ( sk2 @ D @ C @ B @ A ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) )
& ( ~ ( ord_less_eq_capacity @ A @ B )
| ( ( C @ B )
!= D )
| ~ ( ord_le841296385at_nat @ ( C @ ( sk1 @ D @ C @ B @ A ) ) @ ( C @ ( sk2 @ D @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[295]) ).
thf(298,plain,
! [D: set_Pr1986765409at_nat,C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ( ( C @ B )
!= D )
| ~ ( ord_le841296385at_nat @ ( C @ ( sk1 @ D @ C @ B @ A ) ) @ ( C @ ( sk2 @ D @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[296]) ).
thf(301,plain,
! [D: set_Pr1986765409at_nat,C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ( ( C @ B )
!= D )
| ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_le841296385at_nat @ ( C @ ( sk1 @ D @ C @ B @ A ) ) @ ( C @ ( sk2 @ D @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) ),
inference(lifteq,[status(thm)],[298]) ).
thf(302,plain,
! [C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_le841296385at_nat @ ( C @ ( sk1 @ ( C @ B ) @ C @ B @ A ) ) @ ( C @ ( sk2 @ ( C @ B ) @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ ( C @ B ) ) ),
inference(simp,[status(thm)],[301]) ).
thf(4781,plain,
( ( ( ^ [A: product_prod_nat_nat] : A )
!= ( ^ [A: product_prod_nat_nat] : A ) )
| ( ( ^ [A: product_prod_nat_nat] : ( set_Pr2131844118at_nat @ p ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[4780]) ).
thf(4785,plain,
( ( ^ [A: product_prod_nat_nat] : ( set_Pr2131844118at_nat @ p ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[4781]) ).
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(867,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(868,plain,
! [A: product_prod_nat_nat > $o] :
( ( A != bot_bo513358416_nat_o )
= ( ord_le1015898640_nat_o @ bot_bo513358416_nat_o @ A ) ),
inference(cnf,[status(esa)],[867]) ).
thf(869,plain,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1015898640_nat_o @ bot_bo513358416_nat_o @ A )
= ( A != bot_bo513358416_nat_o ) ),
inference(lifteq,[status(thm)],[868]) ).
thf(10102,plain,
! [A: product_prod_nat_nat > $o] :
( ( ord_le1015898640_nat_o
@ ^ [B: product_prod_nat_nat] : bot_bot_o
@ A )
= ( A
!= ( ^ [B: product_prod_nat_nat] : bot_bot_o ) ) ),
inference(rewrite,[status(thm)],[869,1146]) ).
thf(995,plain,
! [A: nat,B: list_P559422087at_nat] :
( ? [C: nat] : ( isSimp1359852763pacity @ c @ A @ B @ C )
=> ~ ? [C: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ C ) @ ( set_Pr2131844118at_nat @ B ) ) ),
inference(miniscope,[status(thm)],[994]) ).
thf(996,plain,
! [D: nat,C: nat,B: list_P559422087at_nat,A: nat] :
( ~ ( isSimp1359852763pacity @ c @ A @ B @ C )
| ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ),
inference(cnf,[status(esa)],[995]) ).
thf(1578,plain,
! [E: nat,D: nat,C: list_P559422087at_nat,B: nat,A: product_prod_nat_nat] :
( ~ ( isSimp1359852763pacity @ c @ B @ C @ D )
| ~ bot_bot_o
| ( ( member701585322at_nat @ A @ bot_bo2130386637at_nat )
!= ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1153,996]) ).
thf(1583,plain,
! [E: nat,D: nat,C: list_P559422087at_nat,B: nat,A: product_prod_nat_nat] :
( ~ ( isSimp1359852763pacity @ c @ B @ C @ D )
| ~ bot_bot_o
| ( A
!= ( product_Pair_nat_nat @ E @ E ) )
| ( ( set_Pr2131844118at_nat @ C )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[1578]) ).
thf(1588,plain,
! [C: nat,B: list_P559422087at_nat,A: nat] :
( ~ ( isSimp1359852763pacity @ c @ A @ B @ C )
| ~ bot_bot_o
| ( ( set_Pr2131844118at_nat @ B )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[1583]) ).
thf(1770,plain,
! [D: nat,C: list_P559422087at_nat,B: nat,A: set_Pr1986765409at_nat] :
( ~ ( isSimp1359852763pacity @ c @ B @ C @ D )
| ~ bot_bot_o
| ( ( collec7649004at_nat
@ ^ [E: product_prod_nat_nat] : ( member701585322at_nat @ E @ A ) )
!= bot_bo2130386637at_nat )
| ( A
!= ( set_Pr2131844118at_nat @ C ) ) ),
inference(paramod_ordered,[status(thm)],[781,1588]) ).
thf(1771,plain,
! [C: list_P559422087at_nat,B: nat,A: nat] :
( ~ ( isSimp1359852763pacity @ c @ A @ C @ B )
| ~ bot_bot_o
| ( ( collec7649004at_nat
@ ^ [D: product_prod_nat_nat] : ( member701585322at_nat @ D @ ( set_Pr2131844118at_nat @ C ) ) )
!= bot_bo2130386637at_nat ) ),
inference(pattern_uni,[status(thm)],[1770:[bind(A,$thf( set_Pr2131844118at_nat @ E )),bind(B,$thf( B )),bind(C,$thf( E ))]]) ).
thf(1845,plain,
! [C: list_P559422087at_nat,B: nat,A: nat] :
( ~ ( isSimp1359852763pacity @ c @ A @ C @ B )
| ~ bot_bot_o
| ( ( collec7649004at_nat
@ ^ [D: product_prod_nat_nat] : ( member701585322at_nat @ D @ ( set_Pr2131844118at_nat @ C ) ) )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[1771]) ).
thf(1876,plain,
! [D: list_P559422087at_nat,C: nat,B: nat,A: set_Pr1986765409at_nat] :
( ~ ( isSimp1359852763pacity @ c @ B @ D @ C )
| ~ bot_bot_o
| ( A != bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [E: product_prod_nat_nat] : ( member701585322at_nat @ E @ A ) )
!= ( collec7649004at_nat
@ ^ [E: product_prod_nat_nat] : ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[781,1845]) ).
thf(1877,plain,
! [C: list_P559422087at_nat,B: nat,A: nat] :
( ~ ( isSimp1359852763pacity @ c @ A @ C @ B )
| ~ bot_bot_o
| ( ( set_Pr2131844118at_nat @ C )
!= bot_bo2130386637at_nat ) ),
inference(pattern_uni,[status(thm)],[1876:[bind(A,$thf( set_Pr2131844118at_nat @ E )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(1883,plain,
! [C: list_P559422087at_nat,B: nat,A: nat] :
( ~ ( isSimp1359852763pacity @ c @ A @ C @ B )
| ~ bot_bot_o
| ( ( set_Pr2131844118at_nat @ C )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[1877]) ).
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(1091,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(693,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(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(630,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(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(847,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(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(361,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(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(625,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(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(879,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(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(665,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(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(522,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(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(1079,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(149,axiom,
t != s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_t__not__s) ).
thf(757,plain,
t != s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
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(682,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(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(456,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(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(323,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(324,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( residu800046103pacity @ A @ B @ C @ D )
| ( residu164581374pacity @ A @ B @ C @ D ) ),
inference(cnf,[status(esa)],[323]) ).
thf(3445,plain,
( ~ ( member701585322at_nat @ sk88 @ ( set_Pr2131844118at_nat @ p ) )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[3394]) ).
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(3763,plain,
( ( member701585322at_nat @ sk89 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[3762]) ).
thf(3778,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(paramod_ordered,[status(thm)],[2083,3776]) ).
thf(3788,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(simp,[status(thm)],[3778]) ).
thf(4082,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(rewrite,[status(thm)],[3788,1032]) ).
thf(4090,plain,
! [A: set_Pr1986765409at_nat] :
( ( A
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
!= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1032,4082]) ).
thf(4102,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
!= ( converse_nat_nat @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(simp,[status(thm)],[4090]) ).
thf(4104,plain,
( ( converse_nat_nat @ bot_bo2130386637at_nat )
!= ( set_Pr2131844118at_nat @ p ) ),
inference(rewrite,[status(thm)],[4102,1032,2876]) ).
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(551,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(1128,plain,
( ord_le116442893at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A
= ( inf_in586391887at_nat @ A @ B ) )
& ( A != B ) ) ) ),
inference(lifteq,[status(thm)],[1127]) ).
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(578,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(187,axiom,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_inf__idem) ).
thf(872,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(873,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
inference(cnf,[status(esa)],[872]) ).
thf(874,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
inference(lifteq,[status(thm)],[873]) ).
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(317,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(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(948,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(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(1121,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(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(1111,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(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(1094,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(1095,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: list_P559422087at_nat] :
( ? [D: nat] : ( isSimp1359852763pacity @ A @ B @ C @ D )
=> ~ ? [D: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ D ) @ ( set_Pr2131844118at_nat @ C ) ) ),
inference(miniscope,[status(thm)],[1094]) ).
thf(1096,plain,
! [E: nat,D: nat,C: list_P559422087at_nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( isSimp1359852763pacity @ A @ B @ C @ D )
| ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ),
inference(cnf,[status(esa)],[1095]) ).
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(382,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(383,plain,
! [A: capacity,B: capacity > capacity,C: capacity] :
( ( A
= ( B @ C ) )
=> ! [D: capacity] :
( ( 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(miniscope,[status(thm)],[382]) ).
thf(384,plain,
! [D: capacity,C: capacity,B: capacity > capacity,A: capacity] :
( ( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ( ord_less_eq_capacity @ ( sk12 @ D @ C @ B @ A ) @ ( sk13 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ A @ ( B @ D ) ) )
& ( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ~ ( ord_less_eq_capacity @ ( B @ ( sk12 @ D @ C @ B @ A ) ) @ ( B @ ( sk13 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[383]) ).
thf(385,plain,
! [D: capacity,C: capacity,B: capacity > capacity,A: capacity] :
( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ( ord_less_eq_capacity @ ( sk12 @ D @ C @ B @ A ) @ ( sk13 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[384]) ).
thf(387,plain,
! [D: capacity,C: capacity,B: capacity > capacity,A: capacity] :
( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ( ord_less_eq_capacity @ ( sk12 @ D @ C @ B @ A ) @ ( sk13 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ A @ ( B @ D ) ) ),
inference(lifteq,[status(thm)],[385]) ).
thf(388,plain,
! [C: capacity,B: capacity,A: capacity > capacity] :
( ~ ( ord_less_eq_capacity @ B @ C )
| ( ord_less_eq_capacity @ ( sk12 @ C @ B @ A @ ( A @ B ) ) @ ( sk13 @ C @ B @ A @ ( A @ B ) ) )
| ( ord_less_eq_capacity @ ( A @ B ) @ ( A @ C ) ) ),
inference(simp,[status(thm)],[387]) ).
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(418,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(419,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(miniscope,[status(thm)],[418]) ).
thf(420,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nPreflow_capacity @ A @ B @ C @ D )
| ( network_capacity @ A @ B @ C ) ),
inference(cnf,[status(esa)],[419]) ).
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(1138,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(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(356,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(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(328,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(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(1082,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(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(488,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(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(932,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(933,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ A ),
inference(cnf,[status(esa)],[932]) ).
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(526,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(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(901,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(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(1075,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(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(590,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(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(679,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(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(1039,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(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(622,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(227,axiom,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_inf_Oidem) ).
thf(997,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(895,plain,
( inf_in586391887at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B @ A ) ) ),
inference(lifteq,[status(thm)],[894]) ).
thf(1150,plain,
! [A: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A )
= ( ^ [B: set_Pr1986765409at_nat] : ( inf_in586391887at_nat @ B @ A ) ) ),
inference(func_ext,[status(esa)],[895]) ).
thf(8841,plain,
( ( member701585322at_nat @ sk107 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ( member701585322at_nat @ sk107 @ bot_bo2130386637at_nat ) ),
inference(bool_ext,[status(thm)],[8838]) ).
thf(8896,plain,
( ( member701585322at_nat @ sk107 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| bot_bot_o ),
inference(rewrite,[status(thm)],[8841,1153]) ).
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(1002,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(783,plain,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ A @ bot_bo513358416_nat_o )
= bot_bo513358416_nat_o ),
inference(cnf,[status(esa)],[782]) ).
thf(784,plain,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ A @ bot_bo513358416_nat_o )
= bot_bo513358416_nat_o ),
inference(lifteq,[status(thm)],[783]) ).
thf(1428,plain,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ A
@ ^ [B: product_prod_nat_nat] : bot_bot_o )
= ( ^ [B: product_prod_nat_nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[784,1146]) ).
thf(1429,plain,
! [B: product_prod_nat_nat,A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ A
@ ^ [C: product_prod_nat_nat] : bot_bot_o
@ B )
= bot_bot_o ),
inference(func_ext,[status(esa)],[1428]) ).
thf(7104,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
!= ( ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) )
| ( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(paramod_ordered,[status(thm)],[1032,7098]) ).
thf(7114,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] : B )
!= ( ^ [B: product_prod_nat_nat] : B ) )
| ( ( ^ [B: product_prod_nat_nat] : A )
!= ( ^ [B: product_prod_nat_nat] : bot_bo2130386637at_nat ) )
| ( ( converse_nat_nat @ A )
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(simp,[status(thm)],[7104]) ).
thf(7123,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] : A )
!= ( ^ [B: product_prod_nat_nat] : bot_bo2130386637at_nat ) )
| ( ( converse_nat_nat @ A )
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(simp,[status(thm)],[7114]) ).
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(391,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(392,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(miniscope,[status(thm)],[391]) ).
thf(393,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( residu800046103pacity @ A @ B @ C @ D )
| ( network_capacity @ A @ B @ C ) ),
inference(cnf,[status(esa)],[392]) ).
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(1114,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(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(736,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(737,plain,
! [A: product_prod_nat_nat] :
( ( product_swap_nat_nat @ ( product_swap_nat_nat @ A ) )
= A ),
inference(cnf,[status(esa)],[736]) ).
thf(738,plain,
! [A: product_prod_nat_nat] :
( ( product_swap_nat_nat @ ( product_swap_nat_nat @ A ) )
= A ),
inference(lifteq,[status(thm)],[737]) ).
thf(2263,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1850,2256]) ).
thf(2264,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[2263]) ).
thf(2277,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[2264]) ).
thf(2287,plain,
( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[2277,1153]) ).
thf(2288,plain,
( ( member701585322at_nat @ sk82 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[2287]) ).
thf(2304,plain,
( ( member701585322at_nat @ sk82 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[2288]) ).
thf(5751,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) )
= ( converse_nat_nat @ A ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5721,2547]) ).
thf(5752,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(pattern_uni,[status(thm)],[5751:[bind(A,$thf( collec7649004at_nat @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ))]]) ).
thf(7174,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[5752,6658]) ).
thf(69,axiom,
residu1549650759pacity = residu1549650759pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Network_Oflow__of__cf_Ocong) ).
thf(503,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
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(359,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(360,plain,
! [B: capacity,A: capacity] :
( ( ord_less_eq_capacity @ A @ B )
| ( ord_less_eq_capacity @ B @ A ) ),
inference(cnf,[status(esa)],[359]) ).
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(1054,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(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(398,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(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(1026,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(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(953,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ bot_bo2130386637at_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(153,axiom,
isSimp1359852763pacity = isSimp1359852763pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Graph_OisSimplePath_Ocong) ).
thf(773,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(160,axiom,
network_capacity @ c @ s @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Network__axioms) ).
thf(794,plain,
network_capacity @ c @ s @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
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(586,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(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(662,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(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(888,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(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(906,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(8977,plain,
( ( member701585322at_nat @ sk108 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( member701585322at_nat @ sk108 @ bot_bo2130386637at_nat ) ),
inference(func_ext,[status(esa)],[8975]) ).
thf(10860,plain,
( ( member701585322at_nat @ sk108 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= bot_bot_o ),
inference(rewrite,[status(thm)],[8977,1153]) ).
thf(10862,plain,
( ( member701585322at_nat @ sk108 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[10860]) ).
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(412,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(422,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ( augmen1090971539pacity @ A @ B @ C @ D @ ( sk14 @ D @ C @ B @ A ) )
| ( nCut_capacity @ A @ B @ C @ ( sk15 @ D @ C @ B @ A ) ) )
& ( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ( augmen1090971539pacity @ A @ B @ C @ D @ ( sk14 @ D @ C @ B @ A ) )
| ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ ( sk15 @ D @ C @ B @ A ) ) ) ) ),
inference(cnf,[status(esa)],[421]) ).
thf(424,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ( augmen1090971539pacity @ A @ B @ C @ D @ ( sk14 @ D @ C @ B @ A ) )
| ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ ( sk15 @ D @ C @ B @ A ) ) ) ),
inference(cnfConj,[status(thm)],[422]) ).
thf(425,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( val_capacity @ A @ B @ D )
= ( cap_capacity @ A @ ( sk15 @ D @ C @ B @ A ) ) )
| ~ ( nFlow_capacity @ A @ B @ C @ D )
| ( augmen1090971539pacity @ A @ B @ C @ D @ ( sk14 @ D @ C @ B @ A ) ) ),
inference(lifteq,[status(thm)],[424]) ).
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(1103,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(7099,plain,
( ( ( ^ [A: product_prod_nat_nat] : A )
!= ( ^ [A: product_prod_nat_nat] : A ) )
| ( ( ^ [A: product_prod_nat_nat] : ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[7098]) ).
thf(7128,plain,
( ( ^ [A: product_prod_nat_nat] : ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[7099]) ).
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(856,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(91,axiom,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_order__refl) ).
thf(573,plain,
! [A: capacity] : ( ord_less_eq_capacity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
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(441,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(442,plain,
! [A: capacity > capacity > $o] :
( ! [B: capacity,C: capacity] :
( ( ord_less_eq_capacity @ B @ C )
=> ( A @ B @ C ) )
=> ( ! [B: capacity,C: capacity] :
( ( A @ C @ B )
=> ( A @ B @ C ) )
=> ! [B: capacity,C: capacity] : ( A @ B @ C ) ) ),
inference(miniscope,[status(thm)],[441]) ).
thf(443,plain,
! [C: capacity,B: capacity,A: capacity > capacity > $o] :
( ( ( ord_less_eq_capacity @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ ( sk21 @ A ) @ ( sk20 @ A ) )
| ( A @ B @ C ) )
& ( ( ord_less_eq_capacity @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ~ ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ( A @ B @ C ) )
& ( ~ ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ ( sk21 @ A ) @ ( sk20 @ A ) )
| ( A @ B @ C ) )
& ( ~ ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ~ ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ( A @ B @ C ) ) ),
inference(cnf,[status(esa)],[442]) ).
thf(444,plain,
! [C: capacity,B: capacity,A: capacity > capacity > $o] :
( ( ord_less_eq_capacity @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ ( sk21 @ A ) @ ( sk20 @ A ) )
| ( A @ B @ C ) ),
inference(cnfConj,[status(thm)],[443]) ).
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(427,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(428,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ! [C: set_Pr1986765409at_nat > capacity,D: capacity] :
( ( 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(miniscope,[status(thm)],[427]) ).
thf(429,plain,
! [D: capacity,C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ~ ( ord_le841296385at_nat @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ B ) @ D )
| ( ord_le841296385at_nat @ ( sk16 @ D @ C @ B @ A ) @ ( sk17 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) )
& ( ~ ( ord_le841296385at_nat @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ B ) @ D )
| ~ ( ord_less_eq_capacity @ ( C @ ( sk16 @ D @ C @ B @ A ) ) @ ( C @ ( sk17 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[428]) ).
thf(430,plain,
! [D: capacity,C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ B ) @ D )
| ( ord_le841296385at_nat @ ( sk16 @ D @ C @ B @ A ) @ ( sk17 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[429]) ).
thf(423,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ( augmen1090971539pacity @ A @ B @ C @ D @ ( sk14 @ D @ C @ B @ A ) )
| ( nCut_capacity @ A @ B @ C @ ( sk15 @ D @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[422]) ).
thf(8976,plain,
( ( ( ^ [A: product_prod_nat_nat] : A )
!= ( ^ [A: product_prod_nat_nat] : A ) )
| ( ( ^ [A: product_prod_nat_nat] : ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[8975]) ).
thf(9025,plain,
( ( ^ [A: product_prod_nat_nat] : ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[8976]) ).
thf(12164,plain,
( ( ord_less_eq_capacity
@ ( sk18
@ ^ [A: capacity,B: capacity] : $false )
@ ( sk19
@ ^ [A: capacity,B: capacity] : $false ) )
| $false
| $false ),
inference(prim_subst,[status(thm)],[444:[bind(A,$thf( ^ [D: capacity] : ^ [E: capacity] : $false ))]]) ).
thf(12868,plain,
( ord_less_eq_capacity
@ ( sk18
@ ^ [A: capacity,B: capacity] : $false )
@ ( sk19
@ ^ [A: capacity,B: capacity] : $false ) ),
inference(simp,[status(thm)],[12164]) ).
thf(399,plain,
! [B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ( ( ord_less_eq_capacity @ B @ A )
= ( B = A ) ) ),
inference(cnf,[status(esa)],[398]) ).
thf(400,plain,
! [B: capacity,A: capacity] :
( ( ( ord_less_eq_capacity @ B @ A )
= ( B = A ) )
| ~ ( ord_less_eq_capacity @ A @ B ) ),
inference(lifteq,[status(thm)],[399]) ).
thf(13031,plain,
! [B: capacity,A: capacity] :
( ( ( ord_less_eq_capacity @ B @ A )
= ( B = A ) )
| ~ $true
| ( ( ord_less_eq_capacity
@ ( sk18
@ ^ [C: capacity,D: capacity] : $false )
@ ( sk19
@ ^ [C: capacity,D: capacity] : $false ) )
!= ( ord_less_eq_capacity @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12868,400]) ).
thf(13032,plain,
! [B: capacity,A: capacity] :
( ( ( ord_less_eq_capacity @ B @ A )
= ( B = A ) )
| ( ( ord_less_eq_capacity
@ ( sk18
@ ^ [C: capacity,D: capacity] : $false )
@ ( sk19
@ ^ [C: capacity,D: capacity] : $false ) )
!= ( ord_less_eq_capacity @ A @ B ) ) ),
inference(simp,[status(thm)],[13031]) ).
thf(13033,plain,
( ( ord_less_eq_capacity
@ ( sk19
@ ^ [A: capacity,B: capacity] : $false )
@ ( sk18
@ ^ [A: capacity,B: capacity] : $false ) )
= ( ( sk19
@ ^ [A: capacity,B: capacity] : $false )
= ( sk18
@ ^ [A: capacity,B: capacity] : $false ) ) ),
inference(pattern_uni,[status(thm)],[13032:[bind(A,$thf( sk18 @ ^ [C: capacity] : ^ [D: capacity] : $false )),bind(B,$thf( sk19 @ ^ [C: capacity] : ^ [D: capacity] : $false ))]]) ).
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(875,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(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(958,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(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(1124,plain,
! [A: set_Pr1986765409at_nat] :
~ ( ord_le116442893at_nat @ A @ bot_bo2130386637at_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
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(545,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(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(641,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(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(571,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(572,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(lifteq,[status(thm)],[571]) ).
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(611,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(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(919,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(8167,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) )
!= ( ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( set_Pr2131844118at_nat @ p ) ) ) )
| ( ( converse_nat_nat @ ( converse_nat_nat @ A ) )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ),
inference(paramod_ordered,[status(thm)],[1032,8161]) ).
thf(8191,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] : B )
!= ( ^ [B: product_prod_nat_nat] : B ) )
| ( ( ^ [B: product_prod_nat_nat] : A )
!= ( ^ [B: product_prod_nat_nat] : ( set_Pr2131844118at_nat @ p ) ) )
| ( ( converse_nat_nat @ A )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[8167]) ).
thf(8202,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] : A )
!= ( ^ [B: product_prod_nat_nat] : ( set_Pr2131844118at_nat @ p ) ) )
| ( ( converse_nat_nat @ A )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[8191]) ).
thf(445,plain,
! [C: capacity,B: capacity,A: capacity > capacity > $o] :
( ( ord_less_eq_capacity @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ~ ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ( A @ B @ C ) ),
inference(cnfConj,[status(thm)],[443]) ).
thf(935,plain,
! [A: nat,B: list_P559422087at_nat] :
( ? [C: nat] : ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
=> ~ ? [C: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ C @ C ) @ ( set_Pr2131844118at_nat @ B ) ) ),
inference(miniscope,[status(thm)],[934]) ).
thf(936,plain,
! [D: nat,C: nat,B: list_P559422087at_nat,A: nat] :
( ~ ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
| ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ),
inference(cnf,[status(esa)],[935]) ).
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(604,plain,
! [A: capacity,B: capacity] :
( ( ord_less_capacity @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(447,plain,
! [C: capacity,B: capacity,A: capacity > capacity > $o] :
( ~ ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ~ ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ( A @ B @ C ) ),
inference(cnfConj,[status(thm)],[443]) ).
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(731,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(732,plain,
~ ? [A: product_prod_nat_nat > $o] : ( ord_le1015898640_nat_o @ A @ bot_bo513358416_nat_o ),
inference(miniscope,[status(thm)],[731]) ).
thf(733,plain,
! [A: product_prod_nat_nat > $o] :
~ ( ord_le1015898640_nat_o @ A @ bot_bo513358416_nat_o ),
inference(cnf,[status(esa)],[732]) ).
thf(1149,plain,
! [A: product_prod_nat_nat > $o] :
~ ( ord_le1015898640_nat_o @ A
@ ^ [B: product_prod_nat_nat] : bot_bot_o ),
inference(rewrite,[status(thm)],[733,730]) ).
thf(16880,plain,
! [D: product_prod_nat_nat > $o,C: capacity,B: capacity,A: capacity > capacity > $o] :
( ~ ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ~ ( A @ ( sk20 @ A ) @ ( sk21 @ A ) )
| ~ ( ord_le1015898640_nat_o @ D
@ ^ [E: product_prod_nat_nat] : $true )
| ( ( A @ B @ C )
!= bot_bot_o ) ),
inference(paramod_ordered,[status(thm)],[447,1149]) ).
thf(17402,plain,
! [A: product_prod_nat_nat > $o] :
( ~ bot_bot_o
| ~ bot_bot_o
| ~ ( ord_le1015898640_nat_o @ A
@ ^ [B: product_prod_nat_nat] : $true ) ),
inference(pre_uni,[status(thm)],[16880:[bind(A,$thf( ^ [E: capacity] : ^ [F: capacity] : bot_bot_o ))]]) ).
thf(18067,plain,
! [A: product_prod_nat_nat > $o] :
( ~ bot_bot_o
| ~ ( ord_le1015898640_nat_o @ A
@ ^ [B: product_prod_nat_nat] : $true ) ),
inference(simp,[status(thm)],[17402]) ).
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(406,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(170,axiom,
finite217307323pacity @ ( residu203630698pacity @ c @ f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_cf_OFinite__Graph__axioms) ).
thf(831,plain,
finite217307323pacity @ ( residu203630698pacity @ c @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
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(1117,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(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(1011,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(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(1144,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(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(739,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(740,plain,
( ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) )
= ( isMaxFlow_capacity @ c @ s @ t @ f ) ),
inference(lifteq,[status(thm)],[739]) ).
thf(2114,plain,
~ ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ),
inference(rewrite,[status(thm)],[740,1343]) ).
thf(2115,plain,
? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ),
inference(simp,[status(thm)],[2114]) ).
thf(2116,plain,
augmen1090971539pacity @ c @ s @ t @ f @ sk80,
inference(cnf,[status(esa)],[2115]) ).
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(434,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(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(990,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(362,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(lifteq,[status(thm)],[361]) ).
thf(451,plain,
! [G: nat,F: nat,E: product_prod_nat_nat > capacity,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( 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 ) ) ) ),
inference(cnfConj,[status(thm)],[450]) ).
thf(88,axiom,
is_max2144541363pacity = is_max2144541363pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Network_Ois__max__flow__val_Ocong) ).
thf(567,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
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(616,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(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(303,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(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(532,plain,
! [A: capacity,B: capacity] :
( ( ord_less_capacity @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(533,plain,
! [B: capacity,A: capacity] :
( ~ ( ord_less_capacity @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[532]) ).
thf(534,plain,
! [B: capacity,A: capacity] :
( ( A != B )
| ~ ( ord_less_capacity @ A @ B ) ),
inference(lifteq,[status(thm)],[533]) ).
thf(535,plain,
! [A: capacity] :
~ ( ord_less_capacity @ A @ A ),
inference(simp,[status(thm)],[534]) ).
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(594,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(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(483,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(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(520,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(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(943,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(666,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ~ ( ord_le116442893at_nat @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[665]) ).
thf(667,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( A != B )
| ~ ( ord_le116442893at_nat @ A @ B ) ),
inference(lifteq,[status(thm)],[666]) ).
thf(668,plain,
! [A: set_Pr1986765409at_nat] :
~ ( ord_le116442893at_nat @ A @ A ),
inference(simp,[status(thm)],[667]) ).
thf(8840,plain,
( ~ ( member701585322at_nat @ sk107 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ~ ( member701585322at_nat @ sk107 @ bot_bo2130386637at_nat ) ),
inference(bool_ext,[status(thm)],[8838]) ).
thf(10467,plain,
( ~ ( member701585322at_nat @ sk107 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ~ bot_bot_o ),
inference(rewrite,[status(thm)],[8840,1153]) ).
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(345,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(366,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( residu800046103pacity @ A @ B @ C @ D )
| ( D
= ( residu203630698pacity @ A @ ( sk9 @ D @ C @ B @ A ) ) ) ),
inference(cnfConj,[status(thm)],[364]) ).
thf(367,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( D
= ( residu203630698pacity @ A @ ( sk9 @ D @ C @ B @ A ) ) )
| ~ ( residu800046103pacity @ A @ B @ C @ D ) ),
inference(lifteq,[status(thm)],[366]) ).
thf(552,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(lifteq,[status(thm)],[551]) ).
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(964,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(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(685,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(5055,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( D
= ( residu203630698pacity @ A @ ( sk9 @ D @ C @ B @ A ) ) )
| ~ $true
| ( ( residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ) )
!= ( residu800046103pacity @ A @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[834,367]) ).
thf(5056,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( D
= ( residu203630698pacity @ A @ ( sk9 @ D @ C @ B @ A ) ) )
| ( ( residu800046103pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ) )
!= ( residu800046103pacity @ A @ B @ C @ D ) ) ),
inference(simp,[status(thm)],[5055]) ).
thf(5057,plain,
( ( residu203630698pacity @ c @ ( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ) )
= ( residu203630698pacity @ c @ f ) ),
inference(pattern_uni,[status(thm)],[5056:[bind(A,$thf( c )),bind(B,$thf( s )),bind(C,$thf( t )),bind(D,$thf( residu203630698pacity @ c @ f ))]]) ).
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(883,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(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(1015,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(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(608,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(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(1000,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(2303,plain,
( ~ ( member701585322at_nat @ sk82 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[2288]) ).
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(851,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(431,plain,
! [D: capacity,C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ B ) @ D )
| ~ ( ord_less_eq_capacity @ ( C @ ( sk16 @ D @ C @ B @ A ) ) @ ( C @ ( sk17 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[429]) ).
thf(3148,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( converse_nat_nat @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) )
!= ( converse_nat_nat @ ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ),
inference(simp,[status(thm)],[3121]) ).
thf(4982,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) )
!= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[3148,1032]) ).
thf(5781,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5721,4982]) ).
thf(5782,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ) ),
inference(simp,[status(thm)],[5781]) ).
thf(5820,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(simp,[status(thm)],[5782]) ).
thf(8131,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ p ) ) )
!= ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) ),
inference(rewrite,[status(thm)],[5820,6658]) ).
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(1066,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(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(305,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(306,plain,
( ( ^ [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
& ( ord_less_eq_capacity @ B @ A ) ) )
= ( (=) @ capacity ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(505,plain,
! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ A ) ),
inference(cnf,[status(esa)],[504]) ).
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(722,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(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(426,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(527,plain,
( ! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ A ) )
& ! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ ( f @ A ) @ ( c @ A ) ) ),
inference(miniscope,[status(thm)],[526]) ).
thf(528,plain,
! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
( ( ord_less_eq_capacity @ zero_zero_capacity @ ( f @ A ) )
& ( ord_less_eq_capacity @ ( f @ B ) @ ( c @ B ) ) ),
inference(cnf,[status(esa)],[527]) ).
thf(530,plain,
! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ ( f @ A ) @ ( c @ A ) ),
inference(cnfConj,[status(thm)],[528]) ).
thf(531,plain,
! [A: product_prod_nat_nat] : ( ord_less_eq_capacity @ ( f @ A ) @ ( c @ A ) ),
inference(simp,[status(thm)],[530]) ).
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(795,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(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(548,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(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(491,plain,
ord_less_eq_capacity @ ( excess_capacity @ c @ f @ s ) @ zero_zero_capacity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(7537,plain,
! [B: capacity,A: capacity] :
( ( ( ord_less_eq_capacity @ B @ A )
= ( B = A ) )
| ~ $true
| ( ( ord_less_eq_capacity @ ( excess_capacity @ c @ f @ s ) @ zero_zero_capacity )
!= ( ord_less_eq_capacity @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[491,400]) ).
thf(7538,plain,
! [B: capacity,A: capacity] :
( ( ( ord_less_eq_capacity @ B @ A )
= ( B = A ) )
| ( ( ord_less_eq_capacity @ ( excess_capacity @ c @ f @ s ) @ zero_zero_capacity )
!= ( ord_less_eq_capacity @ A @ B ) ) ),
inference(simp,[status(thm)],[7537]) ).
thf(7539,plain,
( ( ord_less_eq_capacity @ zero_zero_capacity @ ( excess_capacity @ c @ f @ s ) )
= ( zero_zero_capacity
= ( excess_capacity @ c @ f @ s ) ) ),
inference(pattern_uni,[status(thm)],[7538:[bind(A,$thf( excess_capacity @ c @ f @ s )),bind(B,$thf( zero_zero_capacity ))]]) ).
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(648,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(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(812,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(871,plain,
( ( residu1549650759pacity @ c @ ( residu203630698pacity @ c @ f ) )
= f ),
inference(lifteq,[status(thm)],[870]) ).
thf(1340,plain,
! [A: product_prod_nat_nat] :
( ( residu1549650759pacity @ c @ ( residu203630698pacity @ c @ f ) @ A )
= ( f @ A ) ),
inference(func_ext,[status(esa)],[871]) ).
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(338,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(339,plain,
! [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ A @ B )
=> ! [C: capacity > capacity,D: capacity] :
( ( 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(miniscope,[status(thm)],[338]) ).
thf(340,plain,
! [D: capacity,C: capacity > capacity,B: capacity,A: capacity] :
( ( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ B ) @ D )
| ( ord_less_eq_capacity @ ( sk5 @ D @ C @ B @ A ) @ ( sk6 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) )
& ( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ B ) @ D )
| ~ ( ord_less_eq_capacity @ ( C @ ( sk5 @ D @ C @ B @ A ) ) @ ( C @ ( sk6 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[339]) ).
thf(342,plain,
! [D: capacity,C: capacity > capacity,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ B ) @ D )
| ~ ( ord_less_eq_capacity @ ( C @ ( sk5 @ D @ C @ B @ A ) ) @ ( C @ ( sk6 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[340]) ).
thf(351,plain,
! [D: capacity,C: capacity,B: capacity > set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ~ ( ord_le841296385at_nat @ ( B @ ( sk7 @ D @ C @ B @ A ) ) @ ( B @ ( sk8 @ D @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[349]) ).
thf(354,plain,
! [D: capacity,C: capacity,B: capacity > set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ~ ( ord_le841296385at_nat @ ( B @ ( sk7 @ D @ C @ B @ A ) ) @ ( B @ ( sk8 @ D @ C @ B @ A ) ) )
| ( ord_le841296385at_nat @ A @ ( B @ D ) ) ),
inference(lifteq,[status(thm)],[351]) ).
thf(355,plain,
! [C: capacity,B: capacity,A: capacity > set_Pr1986765409at_nat] :
( ~ ( ord_less_eq_capacity @ B @ C )
| ~ ( ord_le841296385at_nat @ ( A @ ( sk7 @ C @ B @ A @ ( A @ B ) ) ) @ ( A @ ( sk8 @ C @ B @ A @ ( A @ B ) ) ) )
| ( ord_le841296385at_nat @ ( A @ B ) @ ( A @ C ) ) ),
inference(simp,[status(thm)],[354]) ).
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(553,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(1014,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) ) ),
inference(lifteq,[status(thm)],[1013]) ).
thf(1161,plain,
( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) ) ),
inference(rewrite,[status(thm)],[1014,977]) ).
thf(1166,plain,
( ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) ) )
| ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) )
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1161,1158]) ).
thf(1178,plain,
( ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) ) )
| ( inf_in586391887at_nat
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : A ) )
| ( inf_in586391887at_nat
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : A ) ) ),
inference(simp,[status(thm)],[1166]) ).
thf(1181,plain,
( ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) ) )
| ( inf_in586391887at_nat
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : A ) ) ),
inference(simp,[status(thm)],[1178]) ).
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(1049,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(4886,plain,
( ( member701585322at_nat @ sk93 @ ( set_Pr2131844118at_nat @ p ) )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[4884]) ).
thf(304,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ( nPreflow_capacity @ A @ B @ C @ D ) ),
inference(cnf,[status(esa)],[303]) ).
thf(5023,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ $true
| ( nPreflow_capacity @ A @ B @ C @ D )
| ( ( nFlow_capacity @ c @ s @ t @ ( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ) )
!= ( nFlow_capacity @ A @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[4963,304]) ).
thf(5024,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
| ( ( nFlow_capacity @ c @ s @ t @ ( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ) )
!= ( nFlow_capacity @ A @ B @ C @ D ) ) ),
inference(simp,[status(thm)],[5023]) ).
thf(5025,plain,
nPreflow_capacity @ c @ s @ t @ ( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ),
inference(pattern_uni,[status(thm)],[5024:[bind(A,$thf( c )),bind(B,$thf( s )),bind(C,$thf( t )),bind(D,$thf( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ))]]) ).
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(1018,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(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(776,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(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(712,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(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(326,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(327,plain,
! [E: list_P559422087at_nat,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ~ ( isMaxFlow_capacity @ A @ B @ C @ D )
| ~ ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ),
inference(cnf,[status(esa)],[326]) ).
thf(954,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ bot_bo2130386637at_nat @ A ),
inference(cnf,[status(esa)],[953]) ).
thf(852,plain,
! [A: product_prod_nat_nat > $o] : ( ord_le1039616028_nat_o @ bot_bo513358416_nat_o @ A ),
inference(cnf,[status(esa)],[851]) ).
thf(1267,plain,
! [A: product_prod_nat_nat > $o] :
( ord_le1039616028_nat_o
@ ^ [B: product_prod_nat_nat] : bot_bot_o
@ A ),
inference(rewrite,[status(thm)],[852,730]) ).
thf(407,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ! [D: capacity] :
( ( 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(miniscope,[status(thm)],[406]) ).
thf(408,plain,
! [D: capacity,C: nat,B: nat,A: product_prod_nat_nat > 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(cnf,[status(esa)],[407]) ).
thf(409,plain,
! [D: capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( is_max2144541363pacity @ A @ B @ C @ D )
= ( ? [E: product_prod_nat_nat > capacity] :
( ( isMaxFlow_capacity @ A @ B @ C @ E )
& ( D
= ( val_capacity @ A @ B @ E ) ) ) ) )
| ~ ( network_capacity @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[408]) ).
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(705,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(281,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] : ( ord_less_eq_capacity @ zero_zero_capacity @ ( D @ E ) ) ),
inference(miniscope,[status(thm)],[280]) ).
thf(282,plain,
! [E: product_prod_nat_nat,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( residu164581374pacity @ A @ B @ C @ D )
| ( ord_less_eq_capacity @ zero_zero_capacity @ ( D @ E ) ) ),
inference(cnf,[status(esa)],[281]) ).
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(673,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(791,plain,
( ( augmen1090971539pacity @ c @ s @ t @ f @ sk51 )
| ( nCut_capacity @ c @ s @ t @ sk52 ) ),
inference(cnfConj,[status(thm)],[790]) ).
thf(329,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ! [D: product_prod_nat_nat > capacity] :
( ( 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(miniscope,[status(thm)],[328]) ).
thf(330,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: 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(cnf,[status(esa)],[329]) ).
thf(331,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( 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 ) ) ) ) )
| ~ ( network_capacity @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[330]) ).
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(370,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(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(717,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(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(463,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(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(1085,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(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(643,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(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(1141,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(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(656,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(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(600,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(1154,plain,
( ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ bot_bo2130386637at_nat )
!= bot_bo2130386637at_nat )
| ( ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) )
!= ( converse_nat_nat @ bot_bo2130386637at_nat ) ) ),
inference(paramod_ordered,[status(thm)],[972,278]) ).
thf(1155,plain,
( ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ bot_bo2130386637at_nat )
!= bot_bo2130386637at_nat )
| ( ( set_Pr2131844118at_nat @ p )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[1154]) ).
thf(1484,plain,
( ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( set_Pr2131844118at_nat @ p )
!= bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[1155,915]) ).
thf(1485,plain,
( ( set_Pr2131844118at_nat @ p )
!= bot_bo2130386637at_nat ),
inference(simp,[status(thm)],[1484]) ).
thf(683,plain,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ bot_bo513358416_nat_o @ A )
= bot_bo513358416_nat_o ),
inference(cnf,[status(esa)],[682]) ).
thf(684,plain,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o @ bot_bo513358416_nat_o @ A )
= bot_bo513358416_nat_o ),
inference(lifteq,[status(thm)],[683]) ).
thf(1426,plain,
! [A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o
@ ^ [B: product_prod_nat_nat] : bot_bot_o
@ A )
= ( ^ [B: product_prod_nat_nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[684,1146]) ).
thf(1427,plain,
! [B: product_prod_nat_nat,A: product_prod_nat_nat > $o] :
( ( inf_in2138576462_nat_o
@ ^ [C: product_prod_nat_nat] : bot_bot_o
@ A
@ B )
= bot_bot_o ),
inference(func_ext,[status(esa)],[1426]) ).
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(727,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(8732,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ $true
| ( preflow_capacity @ A @ B @ C @ D )
| ( ( nPreflow_capacity @ c @ s @ t @ ( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ) )
!= ( nPreflow_capacity @ A @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[5025,411]) ).
thf(8733,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( preflow_capacity @ A @ B @ C @ D )
| ( ( nPreflow_capacity @ c @ s @ t @ ( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ) )
!= ( nPreflow_capacity @ A @ B @ C @ D ) ) ),
inference(simp,[status(thm)],[8732]) ).
thf(8734,plain,
preflow_capacity @ c @ s @ t @ ( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ),
inference(pattern_uni,[status(thm)],[8733:[bind(A,$thf( c )),bind(B,$thf( s )),bind(C,$thf( t )),bind(D,$thf( sk9 @ ( residu203630698pacity @ c @ f ) @ t @ s @ c ))]]) ).
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(1008,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(311,plain,
! [D: capacity,C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ A @ B )
| ( ( C @ B )
!= D )
| ( ord_le841296385at_nat @ ( sk3 @ D @ C @ B @ A ) @ ( sk4 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[310]) ).
thf(313,plain,
! [D: capacity,C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( C @ B )
!= D )
| ~ ( ord_le841296385at_nat @ A @ B )
| ( ord_le841296385at_nat @ ( sk3 @ D @ C @ B @ A ) @ ( sk4 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ),
inference(lifteq,[status(thm)],[311]) ).
thf(314,plain,
! [C: set_Pr1986765409at_nat > capacity,B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ~ ( ord_le841296385at_nat @ A @ B )
| ( ord_le841296385at_nat @ ( sk3 @ ( C @ B ) @ C @ B @ A ) @ ( sk4 @ ( C @ B ) @ C @ B @ A ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ ( C @ B ) ) ),
inference(simp,[status(thm)],[313]) ).
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(497,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(181,axiom,
finite1387368318pacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Finite__Preflow__axioms) ).
thf(859,plain,
finite1387368318pacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1577,plain,
! [E: nat,D: nat,C: list_P559422087at_nat,B: nat,A: product_prod_nat_nat] :
( ~ ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ B @ C @ D )
| ~ bot_bot_o
| ( ( member701585322at_nat @ A @ bot_bo2130386637at_nat )
!= ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[1153,936]) ).
thf(1580,plain,
! [E: nat,D: nat,C: list_P559422087at_nat,B: nat,A: product_prod_nat_nat] :
( ~ ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ B @ C @ D )
| ~ bot_bot_o
| ( A
!= ( product_Pair_nat_nat @ E @ E ) )
| ( ( set_Pr2131844118at_nat @ C )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[1577]) ).
thf(1585,plain,
! [C: nat,B: list_P559422087at_nat,A: nat] :
( ~ ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ A @ B @ C )
| ~ bot_bot_o
| ( ( set_Pr2131844118at_nat @ B )
!= bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[1580]) ).
thf(11351,plain,
( ( member701585322at_nat @ sk112 @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[10965]) ).
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(978,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(446,plain,
! [C: capacity,B: capacity,A: capacity > capacity > $o] :
( ~ ( A @ ( sk18 @ A ) @ ( sk19 @ A ) )
| ( A @ ( sk21 @ A ) @ ( sk20 @ A ) )
| ( A @ B @ C ) ),
inference(cnfConj,[status(thm)],[443]) ).
thf(175,axiom,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_order__refl) ).
thf(845,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
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(539,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(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(671,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(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(495,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(758,plain,
t != s,
inference(polarity_switch,[status(thm)],[757]) ).
thf(759,plain,
t != s,
inference(lifteq,[status(thm)],[758]) ).
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(891,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(1125,plain,
~ ? [A: set_Pr1986765409at_nat] : ( ord_le116442893at_nat @ A @ bot_bo2130386637at_nat ),
inference(miniscope,[status(thm)],[1124]) ).
thf(1126,plain,
! [A: set_Pr1986765409at_nat] :
~ ( ord_le116442893at_nat @ A @ bot_bo2130386637at_nat ),
inference(cnf,[status(esa)],[1125]) ).
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(688,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(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(903,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(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(524,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(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(581,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(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(368,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(174,axiom,
residu164581374pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_is__RPreGraph) ).
thf(844,plain,
residu164581374pacity @ c @ s @ t @ ( residu203630698pacity @ c @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
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(699,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(963,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ B ) @ B ),
inference(cnf,[status(esa)],[962]) ).
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(1062,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(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(652,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(386,plain,
! [D: capacity,C: capacity,B: capacity > capacity,A: capacity] :
( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ~ ( ord_less_eq_capacity @ ( B @ ( sk12 @ D @ C @ B @ A ) ) @ ( B @ ( sk13 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[384]) ).
thf(389,plain,
! [D: capacity,C: capacity,B: capacity > capacity,A: capacity] :
( ( A
!= ( B @ C ) )
| ~ ( ord_less_eq_capacity @ C @ D )
| ~ ( ord_less_eq_capacity @ ( B @ ( sk12 @ D @ C @ B @ A ) ) @ ( B @ ( sk13 @ D @ C @ B @ A ) ) )
| ( ord_less_eq_capacity @ A @ ( B @ D ) ) ),
inference(lifteq,[status(thm)],[386]) ).
thf(390,plain,
! [C: capacity,B: capacity,A: capacity > capacity] :
( ~ ( ord_less_eq_capacity @ B @ C )
| ~ ( ord_less_eq_capacity @ ( A @ ( sk12 @ C @ B @ A @ ( A @ B ) ) ) @ ( A @ ( sk13 @ C @ B @ A @ ( A @ B ) ) ) )
| ( ord_less_eq_capacity @ ( A @ B ) @ ( A @ C ) ) ),
inference(simp,[status(thm)],[389]) ).
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(832,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(833,plain,
( ( isMaxFlow_capacity @ c @ s @ t @ f )
= ( ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ) ) ),
inference(lifteq,[status(thm)],[832]) ).
thf(2260,plain,
~ ~ ? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ),
inference(rewrite,[status(thm)],[833,1343]) ).
thf(2261,plain,
? [A: list_P559422087at_nat] : ( augmen1090971539pacity @ c @ s @ t @ f @ A ),
inference(simp,[status(thm)],[2260]) ).
thf(2262,plain,
augmen1090971539pacity @ c @ s @ t @ f @ sk81,
inference(cnf,[status(esa)],[2261]) ).
thf(318,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nPreflow_capacity @ A @ B @ C @ D )
| ( ( residu1549650759pacity @ A @ ( residu203630698pacity @ A @ D ) )
= D ) ),
inference(cnf,[status(esa)],[317]) ).
thf(319,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( residu1549650759pacity @ A @ ( residu203630698pacity @ A @ D ) )
= D )
| ~ ( nPreflow_capacity @ A @ B @ C @ D ) ),
inference(lifteq,[status(thm)],[318]) ).
thf(5768,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ A ) ) )
= bot_bo2130386637at_nat )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5721,2725]) ).
thf(5769,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(pattern_uni,[status(thm)],[5768:[bind(A,$thf( collec7649004at_nat @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ))]]) ).
thf(7653,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
= bot_bo2130386637at_nat ),
inference(rewrite,[status(thm)],[5769,6658]) ).
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(896,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(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(748,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(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(568,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(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(433,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(346,plain,
! [D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( residu164581374pacity @ A @ B @ C @ D )
| ( nPreflow_capacity @ A @ B @ C @ ( residu1549650759pacity @ A @ D ) ) ),
inference(cnf,[status(esa)],[345]) ).
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(536,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(378,plain,
! [D: set_Pr1986765409at_nat,C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_le841296385at_nat @ ( C @ B ) @ D )
| ( ord_less_eq_capacity @ ( sk10 @ D @ C @ B @ A ) @ ( sk11 @ D @ C @ B @ A ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[377]) ).
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(800,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(286,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] :
( ( isShor1936442771pacity @ ( residu203630698pacity @ A @ D ) @ B @ E @ C )
=> ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ) ),
inference(miniscope,[status(thm)],[285]) ).
thf(287,plain,
! [E: list_P559422087at_nat,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( nFlow_capacity @ A @ B @ C @ D )
| ~ ( isShor1936442771pacity @ ( residu203630698pacity @ A @ D ) @ B @ E @ C )
| ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ),
inference(cnf,[status(esa)],[286]) ).
thf(1115,plain,
! [A: set_Pr1986765409at_nat] :
( ( A != bot_bo2130386637at_nat )
= ( ord_le116442893at_nat @ bot_bo2130386637at_nat @ A ) ),
inference(cnf,[status(esa)],[1114]) ).
thf(1116,plain,
! [A: set_Pr1986765409at_nat] :
( ( ord_le116442893at_nat @ bot_bo2130386637at_nat @ A )
= ( A != bot_bo2130386637at_nat ) ),
inference(lifteq,[status(thm)],[1115]) ).
thf(297,plain,
! [D: set_Pr1986765409at_nat,C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ( ( C @ B )
!= D )
| ( ord_less_eq_capacity @ ( sk1 @ D @ C @ B @ A ) @ ( sk2 @ D @ C @ B @ A ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[296]) ).
thf(299,plain,
! [D: set_Pr1986765409at_nat,C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ( ( C @ B )
!= D )
| ~ ( ord_less_eq_capacity @ A @ B )
| ( ord_less_eq_capacity @ ( sk1 @ D @ C @ B @ A ) @ ( sk2 @ D @ C @ B @ A ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ D ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(300,plain,
! [C: capacity > set_Pr1986765409at_nat,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ( ord_less_eq_capacity @ ( sk1 @ ( C @ B ) @ C @ B @ A ) @ ( sk2 @ ( C @ B ) @ C @ B @ A ) )
| ( ord_le841296385at_nat @ ( C @ A ) @ ( C @ B ) ) ),
inference(simp,[status(thm)],[299]) ).
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(752,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(49,axiom,
isMaxFlow_capacity = isMaxFlow_capacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Network_OisMaxFlow_Ocong) ).
thf(432,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(40,axiom,
augmen68920357pacity = augmen68920357pacity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_NPreflow_OresCap_Ocong) ).
thf(405,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(4885,plain,
( ~ ( member701585322at_nat @ sk93 @ ( set_Pr2131844118at_nat @ p ) )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[4884]) ).
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(967,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(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(1097,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(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(835,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(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(818,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(10134,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] : A )
!= ( ^ [B: product_prod_nat_nat] : ( set_Pr2131844118at_nat @ p ) ) )
| ( bot_bo2130386637at_nat != bot_bo2130386637at_nat )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7653,8202]) ).
thf(10135,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] : A )
!= ( ^ [B: product_prod_nat_nat] : ( set_Pr2131844118at_nat @ p ) ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ A ) ) ),
inference(simp,[status(thm)],[10134]) ).
thf(10136,plain,
( ( ^ [A: product_prod_nat_nat] :
( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] :
( member701585322at_nat @ B
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( set_Pr2131844118at_nat @ p ) ) ),
inference(pattern_uni,[status(thm)],[10135:[bind(A,$thf( collec7649004at_nat @ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ bot_bo2130386637at_nat ) ) ) ))]]) ).
thf(10453,plain,
( ( ^ [A: product_prod_nat_nat] :
( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) )
!= ( ^ [A: product_prod_nat_nat] : ( set_Pr2131844118at_nat @ p ) ) ),
inference(rewrite,[status(thm)],[10136,6658]) ).
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(564,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(341,plain,
! [D: capacity,C: capacity > capacity,B: capacity,A: capacity] :
( ~ ( ord_less_eq_capacity @ A @ B )
| ~ ( ord_less_eq_capacity @ ( C @ B ) @ D )
| ( ord_less_eq_capacity @ ( sk5 @ D @ C @ B @ A ) @ ( sk6 @ D @ C @ B @ A ) )
| ( ord_less_eq_capacity @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[340]) ).
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(506,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(435,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nPreflow_capacity @ A @ B @ C @ D )
=> ! [E: list_P559422087at_nat] :
( ( augmen1090971539pacity @ A @ B @ C @ D @ E )
=> ( ( val_capacity @ ( residu203630698pacity @ A @ D ) @ B @ ( augmen72931474pacity @ A @ D @ E ) )
= ( augmen68920357pacity @ A @ D @ E ) ) ) ),
inference(miniscope,[status(thm)],[434]) ).
thf(436,plain,
! [E: list_P559422087at_nat,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( 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(cnf,[status(esa)],[435]) ).
thf(437,plain,
! [E: list_P559422087at_nat,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( val_capacity @ ( residu203630698pacity @ A @ D ) @ B @ ( augmen72931474pacity @ A @ D @ E ) )
= ( augmen68920357pacity @ A @ D @ E ) )
| ~ ( nPreflow_capacity @ A @ B @ C @ D )
| ~ ( augmen1090971539pacity @ A @ B @ C @ D @ E ) ),
inference(lifteq,[status(thm)],[436]) ).
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(1056,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(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(828,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(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(635,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(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(696,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(1164,plain,
( ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) )
| ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) )
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1161,1158]) ).
thf(1165,plain,
( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ),
inference(pattern_uni,[status(thm)],[1164:[]]) ).
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(955,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(3805,plain,
( ( member701585322at_nat @ sk89 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[3763]) ).
thf(357,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(cnf,[status(esa)],[356]) ).
thf(358,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(lifteq,[status(thm)],[357]) ).
thf(3804,plain,
( ~ ( member701585322at_nat @ sk89 @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[3763]) ).
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(1033,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(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(928,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(413,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat,D: product_prod_nat_nat > capacity] :
( ( nFlow_capacity @ A @ B @ C @ D )
=> ! [E: product_prod_nat_nat > capacity] :
( ( 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(miniscope,[status(thm)],[412]) ).
thf(414,plain,
! [E: product_prod_nat_nat > capacity,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: 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(cnf,[status(esa)],[413]) ).
thf(415,plain,
! [E: product_prod_nat_nat > capacity,D: product_prod_nat_nat > capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( ( val_capacity @ A @ B @ ( augmen887209518pacity @ A @ D @ E ) )
= ( plus_plus_capacity @ ( val_capacity @ A @ B @ D ) @ ( val_capacity @ ( residu203630698pacity @ A @ D ) @ B @ E ) ) )
| ~ ( nFlow_capacity @ A @ B @ C @ D )
| ~ ( flow_capacity @ ( residu203630698pacity @ A @ D ) @ B @ C @ E ) ),
inference(lifteq,[status(thm)],[414]) ).
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(987,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(1237,plain,
( ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) ) )
| ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) )
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1158,1165]) ).
thf(1253,plain,
( ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) ) )
| ( inf_in586391887at_nat
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : A ) )
| ( inf_in586391887at_nat
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : A ) ) ),
inference(simp,[status(thm)],[1237]) ).
thf(1261,plain,
( ( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) )
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) ) )
| ( inf_in586391887at_nat
!= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] : A ) ) ),
inference(simp,[status(thm)],[1253]) ).
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(575,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(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(459,plain,
! [A: capacity,B: capacity] :
( ( A = B )
=> ( ord_less_eq_capacity @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(850,plain,
( ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ B @ A )
& ( ord_le841296385at_nat @ A @ B ) ) )
= ( (=) @ set_Pr1986765409at_nat ) ),
inference(lifteq,[status(thm)],[849]) ).
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(982,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(369,plain,
( ( ^ [A: capacity,B: capacity] :
( ( ord_less_eq_capacity @ B @ A )
& ( ord_less_eq_capacity @ A @ B ) ) )
= ( (=) @ capacity ) ),
inference(lifteq,[status(thm)],[368]) ).
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(1129,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(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(486,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(335,plain,
! [A: product_prod_nat_nat > capacity,B: nat,C: nat] :
( ( network_capacity @ A @ B @ C )
=> ! [D: capacity] :
( ( is_max2144541363pacity @ A @ B @ C @ D )
=> ! [E: capacity] :
( ( is_max2144541363pacity @ A @ B @ C @ E )
=> ( D = E ) ) ) ),
inference(miniscope,[status(thm)],[334]) ).
thf(336,plain,
! [E: capacity,D: capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ~ ( network_capacity @ A @ B @ C )
| ~ ( is_max2144541363pacity @ A @ B @ C @ D )
| ~ ( is_max2144541363pacity @ A @ B @ C @ E )
| ( D = E ) ),
inference(cnf,[status(esa)],[335]) ).
thf(337,plain,
! [E: capacity,D: capacity,C: nat,B: nat,A: product_prod_nat_nat > capacity] :
( ( D = E )
| ~ ( network_capacity @ A @ B @ C )
| ~ ( is_max2144541363pacity @ A @ B @ C @ D )
| ~ ( is_max2144541363pacity @ A @ B @ C @ E ) ),
inference(lifteq,[status(thm)],[336]) ).
thf(7704,plain,
( ( ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
!= ( ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ),
inference(paramod_ordered,[status(thm)],[7653,7098]) ).
thf(7705,plain,
( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) )
!= ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ),
inference(simp,[status(thm)],[7704]) ).
thf(7759,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] :
( member701585322at_nat @ A
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ bot_bo2130386637at_nat ) ) ) )
!= ( set_Pr2131844118at_nat @ p ) ),
inference(simp,[status(thm)],[7705]) ).
thf(8023,plain,
( ( collec7649004at_nat
@ ^ [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ bot_bo2130386637at_nat ) )
!= ( set_Pr2131844118at_nat @ p ) ),
inference(rewrite,[status(thm)],[7759,6658]) ).
thf(8046,plain,
! [B: set_Pr1986765409at_nat,A: set_Pr1986765409at_nat] :
( ( ( ^ [C: product_prod_nat_nat] : B )
!= ( ^ [C: product_prod_nat_nat] : bot_bo2130386637at_nat ) )
| ( A
!= ( set_Pr2131844118at_nat @ p ) )
| ( ( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ) )
!= ( converse_nat_nat @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2083,7123]) ).
thf(8047,plain,
! [A: set_Pr1986765409at_nat] :
( ( ( ^ [B: product_prod_nat_nat] :
( collec7649004at_nat
@ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ) )
!= ( ^ [B: product_prod_nat_nat] : bot_bo2130386637at_nat ) )
| ( A
!= ( set_Pr2131844118at_nat @ p ) ) ),
inference(pattern_uni,[status(thm)],[8046:[bind(A,$thf( A )),bind(B,$thf( collec7649004at_nat @ ^ [C: product_prod_nat_nat] : ( member701585322at_nat @ C @ ( converse_nat_nat @ A ) ) ))]]) ).
thf(8072,plain,
( ( ^ [A: product_prod_nat_nat] :
( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ),
inference(simp,[status(thm)],[8047]) ).
thf(18510,plain,
( ( ^ [A: product_prod_nat_nat] :
( converse_nat_nat
@ ( collec7649004at_nat
@ ^ [B: product_prod_nat_nat] : ( member701585322at_nat @ B @ ( set_Pr2131844118at_nat @ p ) ) ) ) )
!= ( ^ [A: product_prod_nat_nat] : bot_bo2130386637at_nat ) ),
inference(rewrite,[status(thm)],[8072,2530]) ).
thf(12183,plain,
( ( ord_less_eq_capacity
@ ( sk18
@ ^ [A: capacity,B: capacity] : bot_bot_o )
@ ( sk19
@ ^ [A: capacity,B: capacity] : bot_bot_o ) )
| bot_bot_o
| bot_bot_o ),
inference(prim_subst,[status(thm)],[444:[bind(A,$thf( ^ [D: capacity] : ^ [E: capacity] : bot_bot_o ))]]) ).
thf(12887,plain,
( ( ord_less_eq_capacity
@ ( sk18
@ ^ [A: capacity,B: capacity] : bot_bot_o )
@ ( sk19
@ ^ [A: capacity,B: capacity] : bot_bot_o ) )
| bot_bot_o ),
inference(simp,[status(thm)],[12183]) ).
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(659,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(122,axiom,
nPreflow_capacity @ c @ s @ t @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_NPreflow__axioms) ).
thf(676,plain,
nPreflow_capacity @ c @ s @ t @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
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(1088,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(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(454,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(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(1069,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(19575,plain,
$false,
inference(e,[status(thm)],[645,1036,1024,365,760,2109,18504,479,347,333,962,555,1110,977,1158,1005,18514,3762,994,308,741,379,677,861,440,655,511,550,4884,500,3446,8838,8204,7147,698,747,913,404,1127,782,709,417,288,320,4963,973,885,1046,785,504,619,934,542,344,3776,1059,1132,817,325,448,316,638,853,421,870,1013,284,770,881,416,1100,8161,492,789,8229,3393,8791,937,353,480,1136,834,8246,806,397,280,692,734,293,866,774,10965,411,849,1072,2530,453,7148,380,942,2473,793,810,381,714,307,8975,1153,761,334,2409,910,894,1343,1021,1042,302,4785,10102,729,1883,746,1091,693,630,916,847,1032,361,625,879,665,522,1079,757,682,456,324,3445,285,3763,4104,551,1128,578,874,317,948,1121,1111,1096,388,3119,420,1138,356,328,1082,488,933,669,526,901,1075,590,3671,679,1039,622,997,1150,8896,1002,1429,7123,779,393,1114,1588,985,738,2304,7174,503,343,360,1054,398,1026,953,773,794,586,662,888,906,10862,412,425,1103,7128,856,279,573,444,375,1146,430,423,9025,13033,875,291,958,1124,545,641,391,382,572,611,919,8202,445,936,604,18067,406,831,1117,1011,736,1144,2116,434,990,996,362,451,567,616,303,535,816,323,594,483,520,7098,895,915,943,668,932,10467,345,367,552,1149,964,685,5057,883,1015,608,1000,2303,851,431,8131,2725,1066,278,394,306,2288,505,438,722,426,531,795,548,7539,648,812,1340,342,355,553,1181,1049,4886,5025,1018,2256,1845,776,712,872,971,327,954,739,1267,409,705,282,673,791,331,441,370,717,463,338,1085,951,4982,359,643,1141,656,12868,600,1485,10860,1427,727,8734,1008,314,497,859,1585,11351,1094,978,446,571,845,7146,363,539,671,2078,495,4780,759,891,1126,1108,976,688,903,524,581,368,844,699,963,304,1062,652,390,401,781,2262,319,7653,896,748,731,418,1030,568,433,478,1513,832,346,536,1045,290,378,1161,800,287,1116,300,2287,752,447,432,405,867,4885,410,967,1097,835,818,10453,564,305,326,341,3347,506,437,1056,828,635,532,696,1165,955,3805,283,294,918,358,3804,1033,400,928,415,987,1261,575,427,860,459,850,982,6658,369,332,1129,277,3394,691,486,803,337,940,8023,18510,12887,659,676,972,491,1088,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP052^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n003.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 19:45:28 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.93/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.88/1.05 % [INFO] Parsing done (347ms).
% 1.88/1.07 % [INFO] Running in sequential loop mode.
% 3.07/1.45 % [INFO] eprover registered as external prover.
% 3.07/1.46 % [INFO] Scanning for conjecture ...
% 3.41/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 279 axioms. Running axiom selection ...
% 3.89/1.74 % [INFO] Axiom selection finished. Selected 274 axioms (removed 5 axioms).
% 4.50/1.99 % [INFO] Problem is higher-order (TPTP THF).
% 4.50/2.02 % [INFO] Type checking passed.
% 4.50/2.02 % [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 ...
% 187.40/107.44 % External prover 'e' found a proof!
% 187.40/107.44 % [INFO] Killing All external provers ...
% 187.40/107.44 % Time passed: 107132ms (effective reasoning time: 106367ms)
% 187.40/107.44 % 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)>
% 187.40/107.45 % 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
% 187.40/107.45 % No. of inferences in proof: 1029
% 187.40/107.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 107132 ms resp. 106367 ms w/o parsing
% 189.18/107.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 189.18/107.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------