%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP050^1 : 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 : n001.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 178.54s 139.10s
% Output : Refutation 179.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 284
% Syntax : Number of formulae : 605 ( 211 unt; 0 typ; 4 def)
% Number of atoms : 2069 ( 526 equ; 26 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 7171 ( 184 ~; 50 |; 111 &;5927 @)
% ( 0 <=>; 899 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 228 ( 228 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 8 con; 0-4 aty)
% Number of variables : 1783 ( 214 ^;1538 !; 27 ?;1783 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(set_se1612935105at_nat_type,type,
set_se1612935105at_nat: $tType ).
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_set_nat_type,type,
set_set_nat: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(edmond1517640972ysis_a_decl,type,
edmond1517640972ysis_a: ( product_prod_nat_nat > a ) > $o ).
thf(edmond475474835dges_a_decl,type,
edmond475474835dges_a: ( product_prod_nat_nat > a ) > nat > nat > set_Pr1986765409at_nat ).
thf(edmond771116670s_uE_a_decl,type,
edmond771116670s_uE_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(finite_card_nat_decl,type,
finite_card_nat: set_nat > nat ).
thf(finite447719721at_nat_decl,type,
finite447719721at_nat: set_Pr1986765409at_nat > nat ).
thf(finite_finite_nat_decl,type,
finite_finite_nat: set_nat > $o ).
thf(finite772653738at_nat_decl,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(finite1457549322at_nat_decl,type,
finite1457549322at_nat: set_se1612935105at_nat > $o ).
thf(finite_Graph_a_decl,type,
finite_Graph_a: ( product_prod_nat_nat > a ) > $o ).
thf(e_a_decl,type,
e_a: ( product_prod_nat_nat > a ) > set_Pr1986765409at_nat ).
thf(v_a_decl,type,
v_a: ( product_prod_nat_nat > a ) > set_nat ).
thf(adjacent_nodes_a_decl,type,
adjacent_nodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(incoming_a_decl,type,
incoming_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(incoming_a2_decl,type,
incoming_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(isPath_a_decl,type,
isPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(isShortestPath_a_decl,type,
isShortestPath_a: ( product_prod_nat_nat > a ) > nat > list_P559422087at_nat > nat > $o ).
thf(outgoing_a_decl,type,
outgoing_a: ( product_prod_nat_nat > a ) > nat > set_Pr1986765409at_nat ).
thf(outgoing_a2_decl,type,
outgoing_a2: ( product_prod_nat_nat > a ) > set_nat > set_Pr1986765409at_nat ).
thf(pathVertices_decl,type,
pathVertices: nat > list_P559422087at_nat > list_nat ).
thf(reachableNodes_a_decl,type,
reachableNodes_a: ( product_prod_nat_nat > a ) > nat > set_nat ).
thf(inf_in586391887at_nat_decl,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(cons_nat_decl,type,
cons_nat: nat > list_nat > list_nat ).
thf(cons_P66992567at_nat_decl,type,
cons_P66992567at_nat: product_prod_nat_nat > list_P559422087at_nat > list_P559422087at_nat ).
thf(nil_Pr1308055047at_nat_decl,type,
nil_Pr1308055047at_nat: list_P559422087at_nat ).
thf(set_nat2_decl,type,
set_nat2: list_nat > set_nat ).
thf(set_Pr2131844118at_nat_decl,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(size_s1990949619at_nat_decl,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_set_nat_decl,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(ord_le841296385at_nat_decl,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(product_Pair_nat_nat_decl,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(collec7649004at_nat_decl,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(member_nat_decl,type,
member_nat: nat > set_nat > $o ).
thf(member701585322at_nat_decl,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(member298845450at_nat_decl,type,
member298845450at_nat: set_Pr1986765409at_nat > set_se1612935105at_nat > $o ).
thf(c_decl,type,
c: product_prod_nat_nat > a ).
thf(edges_decl,type,
edges: set_Pr1986765409at_nat ).
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: ( nat > $o ) > ( nat > $o ) > nat ).
thf(sk92_decl,type,
sk92: $o > nat > list_P559422087at_nat > nat > nat ).
thf(sk93_decl,type,
sk93: $o > nat > list_P559422087at_nat > nat > nat ).
thf(sk94_decl,type,
sk94: $o > nat > list_P559422087at_nat > nat > list_P559422087at_nat ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: nat > $o,B: nat > $o] :
@+[C: nat] :
~ ( ( B @ C )
=> ( A @ C ) ) ) ) ).
thf(sk92_def,definition,
( sk92
= ( ^ [A: $o,B: nat,C: list_P559422087at_nat,D: nat] :
@+[E: nat] :
~ ! [F: nat,G: list_P559422087at_nat] :
( ( C
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ E @ F ) @ G ) )
=> ( A
= ( ~ ( ( D = E )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( e_a @ c ) )
& ( isPath_a @ c @ F @ G @ B ) ) ) ) ) ) ) ).
thf(sk93_def,definition,
( sk93
= ( ^ [A: $o,B: nat,C: list_P559422087at_nat,D: nat] :
@+[E: nat] :
~ ! [F: list_P559422087at_nat] :
( ( C
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ ( sk92 @ A @ B @ C @ D ) @ E ) @ F ) )
=> ( A
= ( ~ ( ( D
= ( sk92 @ A @ B @ C @ D ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ A @ B @ C @ D ) @ E ) @ ( e_a @ c ) )
& ( isPath_a @ c @ E @ F @ B ) ) ) ) ) ) ) ).
thf(sk94_def,definition,
( sk94
= ( ^ [A: $o,B: nat,C: list_P559422087at_nat,D: nat] :
@+[E: list_P559422087at_nat] :
~ ( ( C
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ ( sk92 @ A @ B @ C @ D ) @ ( sk93 @ A @ B @ C @ D ) ) @ E ) )
=> ( A
= ( ~ ( ( D
= ( sk92 @ A @ B @ C @ D ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ A @ B @ C @ D ) @ ( sk93 @ A @ B @ C @ D ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ A @ B @ C @ D ) @ E @ B ) ) ) ) ) ) ) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat] :
( ( member_nat @ A @ ( reachableNodes_a @ c @ B ) )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ ( e_a @ c ) )
=> ( member_nat @ C @ ( reachableNodes_a @ c @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_reachableNodes__append__edge) ).
thf(892,plain,
! [A: nat,B: nat,C: nat] :
( ( member_nat @ A @ ( reachableNodes_a @ c @ B ) )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ C ) @ ( e_a @ c ) )
=> ( member_nat @ C @ ( reachableNodes_a @ c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(148,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_272_inf__absorb1) ).
thf(809,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)],[148]) ).
thf(224,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_74_ord__le__eq__subst) ).
thf(1105,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)],[224]) ).
thf(157,axiom,
! [A: nat] : ( ord_le841296385at_nat @ ( incoming_a @ c @ A ) @ ( e_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_incoming__edges) ).
thf(846,plain,
! [A: nat] : ( ord_le841296385at_nat @ ( incoming_a @ c @ A ) @ ( e_a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(188,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ord_le841296385at_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_equalityD2) ).
thf(962,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ord_le841296385at_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(75,axiom,
! [A: product_prod_nat_nat > a,B: nat,C: list_P559422087at_nat,D: nat,E: nat,F: nat] :
( ( isPath_a @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ C ) )
=> ( ( F != D )
=> ? [G: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ G ) @ ( set_Pr2131844118at_nat @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_Graph_OisPath__ex__edge2) ).
thf(555,plain,
! [A: product_prod_nat_nat > a,B: nat,C: list_P559422087at_nat,D: nat,E: nat,F: nat] :
( ( isPath_a @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ C ) )
=> ( ( F != D )
=> ? [G: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ G ) @ ( set_Pr2131844118at_nat @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(101,axiom,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_subset__eq) ).
thf(666,plain,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(55,axiom,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_equalityD1) ).
thf(481,plain,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(245,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( E != C )
=> ? [F: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_isPath__ex__edge2) ).
thf(1168,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( E != C )
=> ? [F: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(131,axiom,
e_a = e_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_Graph_OE_Ocong) ).
thf(760,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(35,axiom,
edmond1517640972ysis_a = finite_Graph_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ek__analysis__def) ).
thf(407,plain,
edmond1517640972ysis_a = finite_Graph_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(408,plain,
finite_Graph_a = edmond1517640972ysis_a,
inference(lifteq,[status(thm)],[407]) ).
thf(9,axiom,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_eq__refl) ).
thf(308,plain,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(218,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > set_nat,D: set_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ord__le__eq__subst) ).
thf(1073,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > set_nat,D: set_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(237,axiom,
! [A: set_Pr1986765409at_nat,B: nat] :
( ~ ( finite772653738at_nat @ A )
=> ? [C: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ C )
& ( ( finite447719721at_nat @ C )
= B )
& ( ord_le841296385at_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_infinite__arbitrarily__large) ).
thf(1142,plain,
! [A: set_Pr1986765409at_nat,B: nat] :
( ~ ( finite772653738at_nat @ A )
=> ? [C: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ C )
& ( ( finite447719721at_nat @ C )
= B )
& ( ord_le841296385at_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(96,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_104_Collect__mem__eq) ).
thf(655,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)],[96]) ).
thf(198,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: $o] :
( ( ( isPath_a @ c @ A @ B @ C )
= D )
=> ( ( ( B = nil_Pr1308055047at_nat )
=> ( D
= ( A != C ) ) )
=> ~ ! [E: nat,F: nat,G: list_P559422087at_nat] :
( ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ E @ F ) @ G ) )
=> ( D
= ( ~ ( ( A = E )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( e_a @ c ) )
& ( isPath_a @ c @ F @ G @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_isPath_Oelims_I1_J) ).
thf(996,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: $o] :
( ( ( isPath_a @ c @ A @ B @ C )
= D )
=> ( ( ( B = nil_Pr1308055047at_nat )
=> ( D
= ( A != C ) ) )
=> ~ ! [E: nat,F: nat,G: list_P559422087at_nat] :
( ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ E @ F ) @ G ) )
=> ( D
= ( ~ ( ( A = E )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( e_a @ c ) )
& ( isPath_a @ c @ F @ G @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(997,plain,
! [D: $o,C: nat,B: list_P559422087at_nat,A: nat] :
( ( ( ( isPath_a @ c @ A @ B @ C )
!= D )
| ( B = nil_Pr1308055047at_nat )
| ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ ( sk92 @ D @ C @ B @ A ) @ ( sk93 @ D @ C @ B @ A ) ) @ ( sk94 @ D @ C @ B @ A ) ) ) )
& ( ( ( isPath_a @ c @ A @ B @ C )
!= D )
| ( B = nil_Pr1308055047at_nat )
| ( D
!= ( ~ ( ( A
= ( sk92 @ D @ C @ B @ A ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ D @ C @ B @ A ) @ ( sk93 @ D @ C @ B @ A ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ D @ C @ B @ A ) @ ( sk94 @ D @ C @ B @ A ) @ C ) ) ) ) )
& ( ( ( isPath_a @ c @ A @ B @ C )
!= D )
| ( D
!= ( A != C ) )
| ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ ( sk92 @ D @ C @ B @ A ) @ ( sk93 @ D @ C @ B @ A ) ) @ ( sk94 @ D @ C @ B @ A ) ) ) )
& ( ( ( isPath_a @ c @ A @ B @ C )
!= D )
| ( D
!= ( A != C ) )
| ( D
!= ( ~ ( ( A
= ( sk92 @ D @ C @ B @ A ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ D @ C @ B @ A ) @ ( sk93 @ D @ C @ B @ A ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ D @ C @ B @ A ) @ ( sk94 @ D @ C @ B @ A ) @ C ) ) ) ) ) ),
inference(cnf,[status(esa)],[996]) ).
thf(1001,plain,
! [D: $o,C: nat,B: list_P559422087at_nat,A: nat] :
( ( ( isPath_a @ c @ A @ B @ C )
!= D )
| ( D
!= ( A != C ) )
| ( D
!= ( ~ ( ( A
= ( sk92 @ D @ C @ B @ A ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ D @ C @ B @ A ) @ ( sk93 @ D @ C @ B @ A ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ D @ C @ B @ A ) @ ( sk94 @ D @ C @ B @ A ) @ C ) ) ) ) ),
inference(cnfConj,[status(thm)],[997]) ).
thf(1008,plain,
! [D: $o,C: nat,B: list_P559422087at_nat,A: nat] :
( ( ( isPath_a @ c @ A @ B @ C )
!= D )
| ( D
!= ( A != C ) )
| ( ( ~ ( ( A
= ( sk92 @ D @ C @ B @ A ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ D @ C @ B @ A ) @ ( sk93 @ D @ C @ B @ A ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ D @ C @ B @ A ) @ ( sk94 @ D @ C @ B @ A ) @ C ) ) )
!= D ) ),
inference(lifteq,[status(thm)],[1001]) ).
thf(1009,plain,
! [C: nat,B: list_P559422087at_nat,A: nat] :
( ( ( isPath_a @ c @ A @ B @ C )
!= ( A != C ) )
| ( ( ~ ( ( A
= ( sk92 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ ( sk93 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ ( sk94 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ C ) ) )
!= ( isPath_a @ c @ A @ B @ C ) ) ),
inference(simp,[status(thm)],[1008]) ).
thf(1433,plain,
! [C: nat,B: list_P559422087at_nat,A: nat] :
( ( ( isPath_a @ c @ A @ B @ C )
!= ( A != C ) )
| ( ( ~ ( ( A
= ( sk92 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ ( sk93 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ ( sk94 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ C ) ) )
!= ( A != C ) )
| ( ( isPath_a @ c @ A @ B @ C )
!= ( isPath_a @ c @ A @ B @ C ) ) ),
inference(eqfactor_ordered,[status(thm)],[1009]) ).
thf(1437,plain,
! [C: nat,B: list_P559422087at_nat,A: nat] :
( ( ( isPath_a @ c @ A @ B @ C )
!= ( A != C ) )
| ( ( ( A
= ( sk92 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ ( sk93 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ ( sk94 @ ( isPath_a @ c @ A @ B @ C ) @ C @ B @ A ) @ C ) )
!= ( A = C ) ) ),
inference(simp,[status(thm)],[1433]) ).
thf(207,axiom,
! [A: nat,B: set_Pr1986765409at_nat > 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_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_ord__eq__le__subst) ).
thf(1041,plain,
! [A: nat,B: set_Pr1986765409at_nat > 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_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(163,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ B ) @ ( finite447719721at_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_card__mono) ).
thf(861,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ B ) @ ( finite447719721at_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(279,axiom,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( ord_less_eq_nat @ A @ ( finite447719721at_nat @ B ) )
=> ~ ! [C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ C @ B )
=> ( ( ( finite447719721at_nat @ C )
= A )
=> ~ ( finite772653738at_nat @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_obtain__subset__with__card__n) ).
thf(1310,plain,
! [A: nat,B: set_Pr1986765409at_nat] :
( ( ord_less_eq_nat @ A @ ( finite447719721at_nat @ B ) )
=> ~ ! [C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ C @ B )
=> ( ( ( finite447719721at_nat @ C )
= A )
=> ~ ( finite772653738at_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(54,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ord__le__eq__subst) ).
thf(472,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(264,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_173_Int__lower2) ).
thf(1260,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)],[264]) ).
thf(103,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_102_mem__Collect__eq) ).
thf(670,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)],[103]) ).
thf(214,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_41_order__trans) ).
thf(1063,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)],[214]) ).
thf(19,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_dual__order_Oantisym) ).
thf(340,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(34,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( ( member701585322at_nat @ A @ B )
& ( member701585322at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Int__iff) ).
thf(404,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
= ( ( member701585322at_nat @ A @ B )
& ( member701585322at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(175,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( finite772653738at_nat @ B )
=> ( finite772653738at_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_finite__subset) ).
thf(898,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( finite772653738at_nat @ B )
=> ( finite772653738at_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(258,axiom,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_subset__iff) ).
thf(1243,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(171,axiom,
! [A: nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( outgoing_a @ c @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_finite__outgoing) ).
thf(885,plain,
! [A: nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( outgoing_a @ c @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(187,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_281_le__iff__inf) ).
thf(960,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)],[187]) ).
thf(961,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ A @ B )
= A ) ) ),
inference(lifteq,[status(thm)],[960]) ).
thf(150,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_245_inf_Oabsorb__iff2) ).
thf(817,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)],[150]) ).
thf(818,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( inf_in586391887at_nat @ B @ A )
= A ) ) ),
inference(lifteq,[status(thm)],[817]) ).
thf(1386,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(rewrite,[status(thm)],[961,818]) ).
thf(7,axiom,
! [A: product_prod_nat_nat > a] :
( ( finite_Graph_a @ A )
=> ( finite_finite_nat @ ( v_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Finite__Graph_Ofinite__V) ).
thf(301,plain,
! [A: product_prod_nat_nat > a] :
( ( finite_Graph_a @ A )
=> ( finite_finite_nat @ ( v_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(262,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_260_inf__greatest) ).
thf(1254,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)],[262]) ).
thf(31,axiom,
! [A: nat,B: list_nat] :
( ( member_nat @ A @ ( set_nat2 @ B ) )
=> ( ! [C: list_nat] :
( B
!= ( cons_nat @ A @ C ) )
=> ~ ! [C: nat,D: list_nat] :
( ( B
= ( cons_nat @ C @ D ) )
=> ~ ( member_nat @ A @ ( set_nat2 @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_list_Oset__cases) ).
thf(389,plain,
! [A: nat,B: list_nat] :
( ( member_nat @ A @ ( set_nat2 @ B ) )
=> ( ! [C: list_nat] :
( B
!= ( cons_nat @ A @ C ) )
=> ~ ! [C: nat,D: list_nat] :
( ( B
= ( cons_nat @ C @ D ) )
=> ~ ( member_nat @ A @ ( set_nat2 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(211,axiom,
! [A: nat,B: product_prod_nat_nat > a,C: nat,D: nat] :
( ( member_nat @ A @ ( reachableNodes_a @ B @ C ) )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ D ) @ ( e_a @ B ) )
=> ( member_nat @ D @ ( reachableNodes_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Graph_OreachableNodes__append__edge) ).
thf(1055,plain,
! [A: nat,B: product_prod_nat_nat > a,C: nat,D: nat] :
( ( member_nat @ A @ ( reachableNodes_a @ B @ C ) )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ D ) @ ( e_a @ B ) )
=> ( member_nat @ D @ ( reachableNodes_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(78,axiom,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_order__subst1) ).
thf(570,plain,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(60,axiom,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ B @ A )
& ( ord_less_eq_set_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_dual__order_Oeq__iff) ).
thf(504,plain,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ B @ A )
& ( ord_less_eq_set_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(266,axiom,
! [A: set_Pr1986765409at_nat,B: nat] :
( ! [C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ C @ A )
=> ( ( finite772653738at_nat @ C )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ C ) @ B ) ) )
=> ( ( finite772653738at_nat @ A )
& ( ord_less_eq_nat @ ( finite447719721at_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_finite__if__finite__subsets__card__bdd) ).
thf(1264,plain,
! [A: set_Pr1986765409at_nat,B: nat] :
( ! [C: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ C @ A )
=> ( ( finite772653738at_nat @ C )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ C ) @ B ) ) )
=> ( ( finite772653738at_nat @ A )
& ( ord_less_eq_nat @ ( finite447719721at_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(82,axiom,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__has__minimal2) ).
thf(587,plain,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(113,axiom,
! [A: list_P559422087at_nat] : ( finite772653738at_nat @ ( set_Pr2131844118at_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_List_Ofinite__set) ).
thf(702,plain,
! [A: list_P559422087at_nat] : ( finite772653738at_nat @ ( set_Pr2131844118at_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(145,axiom,
finite772653738at_nat @ ( edmond771116670s_uE_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_finite__uE) ).
thf(802,plain,
finite772653738at_nat @ ( edmond771116670s_uE_a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(270,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > set_nat,D: set_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_order__subst2) ).
thf(1279,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > set_nat,D: set_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_antisym__conv) ).
thf(559,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(160,axiom,
ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_card__spEdges__le) ).
thf(853,plain,
ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ c @ s @ t ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(40,axiom,
outgoing_a = outgoing_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Graph_Ooutgoing_Ocong) ).
thf(421,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(190,axiom,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ ( collec7649004at_nat @ A ) @ ( collec7649004at_nat @ B ) )
= ( ! [C: product_prod_nat_nat] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Collect__mono__iff) ).
thf(969,plain,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ ( collec7649004at_nat @ A ) @ ( collec7649004at_nat @ B ) )
= ( ! [C: product_prod_nat_nat] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(200,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_208_inf_Obounded__iff) ).
thf(1013,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)],[200]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_dual__order_Oantisym) ).
thf(325,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_finite__subset) ).
thf(316,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(177,axiom,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat > $o] :
( ! [C: product_prod_nat_nat] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le841296385at_nat @ ( collec7649004at_nat @ A ) @ ( collec7649004at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Collect__mono) ).
thf(902,plain,
! [A: product_prod_nat_nat > $o,B: product_prod_nat_nat > $o] :
( ! [C: product_prod_nat_nat] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le841296385at_nat @ ( collec7649004at_nat @ A ) @ ( collec7649004at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(129,axiom,
! [A: list_nat] : ( finite_finite_nat @ ( set_nat2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_List_Ofinite__set) ).
thf(756,plain,
! [A: list_nat] : ( finite_finite_nat @ ( set_nat2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(28,axiom,
! [A: set_nat,B: nat] :
( ~ ( finite_finite_nat @ A )
=> ? [C: set_nat] :
( ( finite_finite_nat @ C )
& ( ( finite_card_nat @ C )
= B )
& ( ord_less_eq_set_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_infinite__arbitrarily__large) ).
thf(376,plain,
! [A: set_nat,B: nat] :
( ~ ( finite_finite_nat @ A )
=> ? [C: set_nat] :
( ( finite_finite_nat @ C )
& ( ( finite_card_nat @ C )
= B )
& ( ord_less_eq_set_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(90,axiom,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_subsetD) ).
thf(623,plain,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(93,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_dual__order_Oeq__iff) ).
thf(646,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(239,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_275_inf_Oabsorb2) ).
thf(1151,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)],[239]) ).
thf(147,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_287_inf_OorderI) ).
thf(806,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)],[147]) ).
thf(189,axiom,
! [A: list_P559422087at_nat,B: product_prod_nat_nat > a,C: nat,D: nat] :
( ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ A ) @ ( e_a @ c ) ) @ ( e_a @ B ) )
=> ( ( isPath_a @ c @ C @ A @ D )
=> ( isPath_a @ B @ C @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_transfer__path) ).
thf(966,plain,
! [A: list_P559422087at_nat,B: product_prod_nat_nat > a,C: nat,D: nat] :
( ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ A ) @ ( e_a @ c ) ) @ ( e_a @ B ) )
=> ( ( isPath_a @ c @ C @ A @ D )
=> ( isPath_a @ B @ C @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(247,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > nat,D: nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_ord__le__eq__subst) ).
thf(1183,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > nat,D: nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(56,axiom,
! [A: nat,B: set_nat] :
( ( ord_less_eq_nat @ A @ ( finite_card_nat @ B ) )
=> ~ ! [C: set_nat] :
( ( ord_less_eq_set_nat @ C @ B )
=> ( ( ( finite_card_nat @ C )
= A )
=> ~ ( finite_finite_nat @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_obtain__subset__with__card__n) ).
thf(485,plain,
! [A: nat,B: set_nat] :
( ( ord_less_eq_nat @ A @ ( finite_card_nat @ B ) )
=> ~ ! [C: set_nat] :
( ( ord_less_eq_set_nat @ C @ B )
=> ( ( ( finite_card_nat @ C )
= A )
=> ~ ( finite_finite_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(234,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_subsetD) ).
thf(1136,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(203,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ~ ( ( ord_le841296385at_nat @ A @ B )
=> ~ ( ord_le841296385at_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_equalityE) ).
thf(1020,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ~ ( ( ord_le841296385at_nat @ A @ B )
=> ~ ( ord_le841296385at_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(21,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_subset__antisym) ).
thf(348,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(108,axiom,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_order__subst1) ).
thf(687,plain,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(124,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_order__class_Oorder_Oeq__iff) ).
thf(734,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(165,axiom,
! [A: product_prod_nat_nat > a,B: nat,C: list_P559422087at_nat,D: nat,E: product_prod_nat_nat] :
( ( isPath_a @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ C ) )
=> ( member701585322at_nat @ E @ ( e_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Graph_OisPath__edgeset) ).
thf(866,plain,
! [A: product_prod_nat_nat > a,B: nat,C: list_P559422087at_nat,D: nat,E: product_prod_nat_nat] :
( ( isPath_a @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ E @ ( set_Pr2131844118at_nat @ C ) )
=> ( member701585322at_nat @ E @ ( e_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(217,axiom,
finite_finite_nat @ ( v_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_finite__V) ).
thf(1072,plain,
finite_finite_nat @ ( v_a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat > set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_order__subst2) ).
thf(396,plain,
! [A: nat,B: nat,C: nat > set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_set__eq__subset) ).
thf(312,plain,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(169,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_92_order__subst2) ).
thf(877,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)],[169]) ).
thf(109,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_order__class_Oorder_Oantisym) ).
thf(692,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(227,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( member_nat @ A @ ( v_a @ c ) )
=> ( ( isPath_a @ c @ A @ B @ C )
=> ( ord_less_eq_set_nat @ ( set_nat2 @ ( pathVertices @ A @ B ) ) @ ( v_a @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_pathVertices__edgeset) ).
thf(1119,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( member_nat @ A @ ( v_a @ c ) )
=> ( ( isPath_a @ c @ A @ B @ C )
=> ( ord_less_eq_set_nat @ ( set_nat2 @ ( pathVertices @ A @ B ) ) @ ( v_a @ c ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(137,axiom,
! [A: nat,B: set_Pr1986765409at_nat > nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_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_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_order__subst1) ).
thf(774,plain,
! [A: nat,B: set_Pr1986765409at_nat > nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_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_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(43,axiom,
! [A: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ? [B: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_finite__list) ).
thf(428,plain,
! [A: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ? [B: list_P559422087at_nat] :
( ( set_Pr2131844118at_nat @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(249,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: product_prod_nat_nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ D @ ( set_Pr2131844118at_nat @ B ) )
=> ( member701585322at_nat @ D @ ( e_a @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_isPath__edgeset) ).
thf(1201,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: product_prod_nat_nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ D @ ( set_Pr2131844118at_nat @ B ) )
=> ( member701585322at_nat @ D @ ( e_a @ c ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(47,axiom,
! [A: product_prod_nat_nat > a,B: nat,C: nat] :
( ( edmond1517640972ysis_a @ A )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_ek__analysis_Ofinite__spEdges) ).
thf(452,plain,
! [A: product_prod_nat_nat > a,B: nat,C: nat] :
( ( edmond1517640972ysis_a @ A )
=> ( finite772653738at_nat @ ( edmond475474835dges_a @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(65,axiom,
! [A: product_prod_nat_nat > a,B: set_nat] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( outgoing_a2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Graph_Ofinite__outgoing_H) ).
thf(529,plain,
! [A: product_prod_nat_nat > a,B: set_nat] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( outgoing_a2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(98,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ( member701585322at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_IntD1) ).
thf(661,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ( member701585322at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(72,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ A )
=> ( ord_less_eq_set_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_dual__order_Otrans) ).
thf(546,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ A )
=> ( ord_less_eq_set_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(277,axiom,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_Graph_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Finite__Graph__EI) ).
thf(1306,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_Graph_a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(132,axiom,
! [A: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ c @ A ) @ ( v_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_adjacent__nodes__ss__V) ).
thf(761,plain,
! [A: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ c @ A ) @ ( v_a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(67,axiom,
! [A: product_prod_nat_nat > a,B: nat] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( incoming_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Graph_Ofinite__incoming) ).
thf(534,plain,
! [A: product_prod_nat_nat > a,B: nat] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( incoming_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(117,axiom,
! [A: product_prod_nat_nat > a,B: nat,C: list_P559422087at_nat,D: nat,E: nat,F: nat] :
( ( isPath_a @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ C ) )
=> ( ( E != B )
=> ? [G: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ G @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_Graph_OisPath__ex__edge1) ).
thf(714,plain,
! [A: product_prod_nat_nat > a,B: nat,C: list_P559422087at_nat,D: nat,E: nat,F: nat] :
( ( isPath_a @ A @ B @ C @ D )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ E @ F ) @ ( set_Pr2131844118at_nat @ C ) )
=> ( ( E != B )
=> ? [G: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ G @ E ) @ ( set_Pr2131844118at_nat @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(268,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_34_dual__order_Otrans) ).
thf(1274,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)],[268]) ).
thf(17,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_order_Otrans) ).
thf(334,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( isPath_a @ c @ A @ nil_Pr1308055047at_nat @ B )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_isPath_Osimps_I1_J) ).
thf(957,plain,
! [A: nat,B: nat] :
( ( isPath_a @ c @ A @ nil_Pr1308055047at_nat @ B )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(42,axiom,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_equalityD2) ).
thf(424,plain,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(122,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ~ ( ( member701585322at_nat @ A @ B )
=> ~ ( member701585322at_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_IntE) ).
thf(729,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ~ ( ( member701585322at_nat @ A @ B )
=> ~ ( member701585322at_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(100,axiom,
isPath_a = isPath_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_Graph_OisPath_Ocong) ).
thf(665,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(153,axiom,
! [A: set_nat,B: set_nat,C: set_nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_order__subst2) ).
thf(830,plain,
! [A: set_nat,B: set_nat,C: set_nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(51,axiom,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_card__mono) ).
thf(461,plain,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( ord_less_eq_nat @ ( finite_card_nat @ B ) @ ( finite_card_nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(106,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ( member701585322at_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_IntD2) ).
thf(682,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) )
=> ( member701585322at_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(74,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ A )
| ( finite772653738at_nat @ B ) )
=> ( finite772653738at_nat @ ( inf_in586391887at_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_finite__Int) ).
thf(551,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ( finite772653738at_nat @ A )
| ( finite772653738at_nat @ B ) )
=> ( finite772653738at_nat @ ( inf_in586391887at_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(274,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_302_le__infI) ).
thf(1291,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)],[274]) ).
thf(49,axiom,
outgoing_a2 = outgoing_a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Graph_Ooutgoing_H_Ocong) ).
thf(456,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Collect__mono) ).
thf(283,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(284,plain,
! [B: nat > $o,A: nat > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
| ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) )
& ( ~ ( B @ ( sk1 @ B @ A ) )
| ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ) ),
inference(cnf,[status(esa)],[283]) ).
thf(285,plain,
! [B: nat > $o,A: nat > $o] :
( ( A @ ( sk1 @ B @ A ) )
| ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
inference(cnfConj,[status(thm)],[284]) ).
thf(58,axiom,
! [A: set_nat,B: set_nat,C: set_nat > nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ord__le__eq__subst) ).
thf(493,plain,
! [A: set_nat,B: set_nat,C: set_nat > nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(252,axiom,
! [A: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( incoming_a2 @ c @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_finite__incoming_H) ).
thf(1210,plain,
! [A: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( incoming_a2 @ c @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(81,axiom,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ord__eq__le__subst) ).
thf(578,plain,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(168,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_239_inf_OcoboundedI2) ).
thf(874,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)],[168]) ).
thf(183,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_308_inf__le2) ).
thf(948,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)],[183]) ).
thf(1,conjecture,
ord_le841296385at_nat @ edges @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(282,plain,
~ ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1324,plain,
! [B: nat > $o,A: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
| ~ $true
| ( ( A @ ( sk1 @ B @ A ) )
!= ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[285,282]) ).
thf(1325,plain,
! [B: nat > $o,A: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ) ) ),
inference(simp,[status(thm)],[1324]) ).
thf(1357,plain,
! [A: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ) )
@ ( collect_nat @ A ) ),
inference(pre_uni,[status(thm)],[1325:[bind(A,$thf( ^ [C: nat] : ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ) )),bind(B,$thf( B ))]]) ).
thf(1371,plain,
! [A: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_le841296385at_nat @ edges @ ( e_a @ c ) ) )
@ ( collect_nat @ A ) ),
inference(simp,[status(thm)],[1357]) ).
thf(1534,plain,
! [A: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [B: nat] : $false )
@ ( collect_nat @ A ) ),
inference(rewrite,[status(thm)],[1371,282]) ).
thf(88,axiom,
! [A: product_prod_nat_nat > a,B: nat,C: nat] :
( ( edmond1517640972ysis_a @ A )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ A @ B @ C ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ek__analysis_Ocard__spEdges__le) ).
thf(615,plain,
! [A: product_prod_nat_nat > a,B: nat,C: nat] :
( ( edmond1517640972ysis_a @ A )
=> ( ord_less_eq_nat @ ( finite447719721at_nat @ ( edmond475474835dges_a @ A @ B @ C ) ) @ ( finite447719721at_nat @ ( edmond771116670s_uE_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(193,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_60_order_Otrans) ).
thf(980,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)],[193]) ).
thf(166,axiom,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_dual__order_Orefl) ).
thf(869,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(87,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ord__le__eq__trans) ).
thf(610,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(196,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_266_inf_OboundedE) ).
thf(989,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)],[196]) ).
thf(111,axiom,
! [A: product_prod_nat_nat > a,B: nat] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( outgoing_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Graph_Ofinite__outgoing) ).
thf(697,plain,
! [A: product_prod_nat_nat > a,B: nat] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( outgoing_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(220,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_47_ord__le__eq__trans) ).
thf(1089,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)],[220]) ).
thf(15,axiom,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( ( ( finite_card_nat @ B )
= ( finite_card_nat @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_card__subset__eq) ).
thf(328,plain,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( ( ( finite_card_nat @ B )
= ( finite_card_nat @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(243,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > nat,D: nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_order__subst2) ).
thf(1160,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat > nat,D: nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1986765409at_nat,F: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_order__trans) ).
thf(537,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(64,axiom,
! [A: set_nat] :
( ( finite_finite_nat @ A )
=> ? [B: list_nat] :
( ( set_nat2 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_finite__list) ).
thf(526,plain,
! [A: set_nat] :
( ( finite_finite_nat @ A )
=> ? [B: list_nat] :
( ( set_nat2 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(206,axiom,
! [A: nat] :
( ( member_nat @ A @ ( v_a @ c ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ A ) @ ( v_a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_reachable__ss__V) ).
thf(1039,plain,
! [A: nat] :
( ( member_nat @ A @ ( v_a @ c ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ c @ A ) @ ( v_a @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(204,axiom,
! [A: set_nat,B: set_Pr1986765409at_nat > set_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_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_ord__eq__le__subst) ).
thf(1028,plain,
! [A: set_nat,B: set_Pr1986765409at_nat > set_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_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(219,axiom,
! [A: set_se1612935105at_nat,B: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A )
=> ( ( member298845450at_nat @ B @ A )
=> ? [C: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ C @ A )
& ( ord_le841296385at_nat @ B @ C )
& ! [D: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ D @ A )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite__has__maximal2) ).
thf(1082,plain,
! [A: set_se1612935105at_nat,B: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A )
=> ( ( member298845450at_nat @ B @ A )
=> ? [C: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ C @ A )
& ( ord_le841296385at_nat @ B @ C )
& ! [D: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ D @ A )
=> ( ( ord_le841296385at_nat @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(201,axiom,
! [A: set_nat] : ( ord_le841296385at_nat @ ( incoming_a2 @ c @ A ) @ ( e_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_incoming_H__edges) ).
thf(1016,plain,
! [A: set_nat] : ( ord_le841296385at_nat @ ( incoming_a2 @ c @ A ) @ ( e_a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(251,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_263_inf_OboundedI) ).
thf(1207,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)],[251]) ).
thf(155,axiom,
! [A: product_prod_nat_nat > a] :
( ( finite_Graph_a @ A )
=> ( finite772653738at_nat @ ( e_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_Finite__Graph_Ofinite__E) ).
thf(837,plain,
! [A: product_prod_nat_nat > a] :
( ( finite_Graph_a @ A )
=> ( finite772653738at_nat @ ( e_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(225,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_248_inf_Oabsorb__iff1) ).
thf(1114,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)],[225]) ).
thf(647,plain,
( ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) )
= ( (=) @ nat ) ),
inference(lifteq,[status(thm)],[646]) ).
thf(261,axiom,
! [A: nat,B: nat,C: nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_order__subst2) ).
thf(1249,plain,
! [A: nat,B: nat,C: nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_le841296385at_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(256,axiom,
! [A: set_Pr1986765409at_nat,B: nat > set_Pr1986765409at_nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_ord__eq__le__subst) ).
thf(1231,plain,
! [A: set_Pr1986765409at_nat,B: nat > set_Pr1986765409at_nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(232,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_171_Int__lower1) ).
thf(1131,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)],[232]) ).
thf(248,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_83_ord__eq__le__subst) ).
thf(1192,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)],[248]) ).
thf(260,axiom,
! [A: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( outgoing_a2 @ c @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_finite__outgoing_H) ).
thf(1246,plain,
! [A: set_nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( outgoing_a2 @ c @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(138,axiom,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_subset__refl) ).
thf(779,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_order_Otrans) ).
thf(605,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(208,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isShortestPath_a @ c @ A @ B @ C )
=> ( isPath_a @ c @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_shortestPath__is__path) ).
thf(1050,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isShortestPath_a @ c @ A @ B @ C )
=> ( isPath_a @ c @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(50,axiom,
! [A: set_nat,B: set_nat] :
( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) )
=> ( ord_less_eq_set_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_subsetI) ).
thf(457,plain,
! [A: set_nat,B: set_nat] :
( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) )
=> ( ord_less_eq_set_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(23,axiom,
! [A: product_prod_nat_nat > a,B: nat] :
( ( finite_Graph_a @ A )
=> ( finite_finite_nat @ ( adjacent_nodes_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_Finite__Graph_Oadjacent__nodes__finite) ).
thf(360,plain,
! [A: product_prod_nat_nat > a,B: nat] :
( ( finite_Graph_a @ A )
=> ( finite_finite_nat @ ( adjacent_nodes_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(62,axiom,
! [A: set_nat,B: set_nat,C: set_nat > set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_ord__le__eq__subst) ).
thf(508,plain,
! [A: set_nat,B: set_nat,C: set_nat > set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(286,plain,
! [B: nat > $o,A: nat > $o] :
( ~ ( B @ ( sk1 @ B @ A ) )
| ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
inference(cnfConj,[status(thm)],[284]) ).
thf(1545,plain,
! [C: nat > $o,B: nat > $o,A: nat > $o] :
( ~ $true
| ( ord_less_eq_set_nat @ ( collect_nat @ B ) @ ( collect_nat @ C ) )
| ( ( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [D: nat] : $false )
@ ( collect_nat @ A ) )
!= ( C @ ( sk1 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1534,286]) ).
thf(1546,plain,
! [C: nat > $o,B: nat > $o,A: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ B ) @ ( collect_nat @ C ) )
| ( ( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [D: nat] : $false )
@ ( collect_nat @ A ) )
!= ( C @ ( sk1 @ C @ B ) ) ) ),
inference(simp,[status(thm)],[1545]) ).
thf(1587,plain,
! [B: nat > nat > $o,A: nat > $o] :
( ord_less_eq_set_nat @ ( collect_nat @ A )
@ ( collect_nat
@ ^ [C: nat] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [D: nat] : $false )
@ ( collect_nat @ ( B @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[1546:[bind(A,$thf( F @ ( sk1 @ ^ [E: nat] : ( ord_less_eq_set_nat @ ( collect_nat @ ^ [F: nat] : $false ) @ ( collect_nat @ ( F @ E ) ) ) @ B ) )),bind(B,$thf( B )),bind(C,$thf( ^ [E: nat] : ( ord_less_eq_set_nat @ ( collect_nat @ ^ [F: nat] : $false ) @ ( collect_nat @ ( F @ E ) ) ) ))]]) ).
thf(1617,plain,
! [B: nat > nat > $o,A: nat > $o] :
( ord_less_eq_set_nat @ ( collect_nat @ A )
@ ( collect_nat
@ ^ [C: nat] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [D: nat] : $false )
@ ( collect_nat @ ( B @ C ) ) ) ) ),
inference(simp,[status(thm)],[1587]) ).
thf(1695,plain,
! [A: nat > $o] :
( ord_less_eq_set_nat @ ( collect_nat @ A )
@ ( collect_nat
@ ^ [B: nat] : $true ) ),
inference(rewrite,[status(thm)],[1617,1534]) ).
thf(70,axiom,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ B )
=> ( ( member701585322at_nat @ A @ C )
=> ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_IntI) ).
thf(541,plain,
! [A: product_prod_nat_nat,B: set_Pr1986765409at_nat,C: set_Pr1986765409at_nat] :
( ( member701585322at_nat @ A @ B )
=> ( ( member701585322at_nat @ A @ C )
=> ( member701585322at_nat @ A @ ( inf_in586391887at_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(210,axiom,
ord_le841296385at_nat @ ( e_a @ c ) @ ( edmond771116670s_uE_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_E__ss__uE) ).
thf(1054,plain,
ord_le841296385at_nat @ ( e_a @ c ) @ ( edmond771116670s_uE_a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(272,axiom,
! [A: nat] : ( ord_le841296385at_nat @ ( outgoing_a @ c @ A ) @ ( e_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_outgoing__edges) ).
thf(1286,plain,
! [A: nat] : ( ord_le841296385at_nat @ ( outgoing_a @ c @ A ) @ ( e_a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(216,axiom,
finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_finite__spEdges) ).
thf(1071,plain,
finite772653738at_nat @ ( edmond475474835dges_a @ c @ s @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(136,axiom,
edmond1517640972ysis_a @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_ek__analysis__axioms) ).
thf(773,plain,
edmond1517640972ysis_a @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(20,axiom,
! [A: set_nat,B: set_nat,C: set_nat > set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_order__subst2) ).
thf(343,plain,
! [A: set_nat,B: set_nat,C: set_nat > set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(281,axiom,
isShortestPath_a @ c @ s @ p @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_SP) ).
thf(1318,plain,
isShortestPath_a @ c @ s @ p @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(118,axiom,
! [A: product_prod_nat_nat > a,B: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ A @ B ) @ ( v_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_Graph_Oadjacent__nodes__ss__V) ).
thf(718,plain,
! [A: product_prod_nat_nat > a,B: nat] : ( ord_less_eq_set_nat @ ( adjacent_nodes_a @ A @ B ) @ ( v_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(172,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite447719721at_nat @ A ) @ ( finite447719721at_nat @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_card__seteq) ).
thf(888,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite447719721at_nat @ A ) @ ( finite447719721at_nat @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(178,axiom,
! [A: set_Pr1986765409at_nat,B: set_nat > set_Pr1986765409at_nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_ord__eq__le__subst) ).
thf(906,plain,
! [A: set_Pr1986765409at_nat,B: set_nat > set_Pr1986765409at_nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_dual__order_Otrans) ).
thf(298,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,axiom,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( finite_finite_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_rev__finite__subset) ).
thf(412,plain,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( finite_finite_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(127,axiom,
! [A: set_nat,B: set_nat,C: set_nat > nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_order__subst2) ).
thf(750,plain,
! [A: set_nat,B: set_nat,C: set_nat > nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(89,axiom,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_order__subst1) ).
thf(618,plain,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(162,axiom,
! [A: set_Pr1986765409at_nat,B: set_nat > set_Pr1986765409at_nat,C: set_nat,D: set_nat] :
( ( ord_le841296385at_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_order__subst1) ).
thf(856,plain,
! [A: set_Pr1986765409at_nat,B: set_nat > set_Pr1986765409at_nat,C: set_nat,D: set_nat] :
( ( ord_le841296385at_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(126,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( A = B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ord__eq__le__trans) ).
thf(745,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( A = B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(123,axiom,
incoming_a2 = incoming_a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_Graph_Oincoming_H_Ocong) ).
thf(733,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(240,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_53_order__class_Oorder_Oeq__iff) ).
thf(1154,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)],[240]) ).
thf(151,axiom,
! [A: set_nat,B: set_nat,C: set_nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_ord__le__eq__subst) ).
thf(819,plain,
! [A: set_nat,B: set_nat,C: set_nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(115,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_eq__iff) ).
thf(711,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(229,axiom,
! [A: product_prod_nat_nat > a,B: nat] : ( ord_le841296385at_nat @ ( incoming_a @ A @ B ) @ ( e_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Graph_Oincoming__edges) ).
thf(1124,plain,
! [A: product_prod_nat_nat > a,B: nat] : ( ord_le841296385at_nat @ ( incoming_a @ A @ B ) @ ( e_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(77,axiom,
! [A: set_nat,B: nat] :
( ! [C: set_nat] :
( ( ord_less_eq_set_nat @ C @ A )
=> ( ( finite_finite_nat @ C )
=> ( ord_less_eq_nat @ ( finite_card_nat @ C ) @ B ) ) )
=> ( ( finite_finite_nat @ A )
& ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_finite__if__finite__subsets__card__bdd) ).
thf(562,plain,
! [A: set_nat,B: nat] :
( ! [C: set_nat] :
( ( ord_less_eq_set_nat @ C @ A )
=> ( ( finite_finite_nat @ C )
=> ( ord_less_eq_nat @ ( finite_card_nat @ C ) @ B ) ) )
=> ( ( finite_finite_nat @ A )
& ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(192,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_105_order__subst1) ).
thf(975,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)],[192]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_ord__le__eq__trans) ).
thf(641,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(235,axiom,
! [A: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ A )
=> ( ord_le841296385at_nat @ ( e_a @ A ) @ ( edmond771116670s_uE_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_ek__analysis_OE__ss__uE) ).
thf(1139,plain,
! [A: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ A )
=> ( ord_le841296385at_nat @ ( e_a @ A ) @ ( edmond771116670s_uE_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(313,plain,
( ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) )
= ( (=) @ set_nat ) ),
inference(lifteq,[status(thm)],[312]) ).
thf(141,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_28_dual__order_Oantisym) ).
thf(787,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)],[141]) ).
thf(116,axiom,
incoming_a = incoming_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_Graph_Oincoming_Ocong) ).
thf(713,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(212,axiom,
! [A: nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( incoming_a @ c @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_finite__incoming) ).
thf(1058,plain,
! [A: nat] :
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( incoming_a @ c @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(180,axiom,
! [A: nat,B: nat,C: nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ord__le__eq__subst) ).
thf(919,plain,
! [A: nat,B: nat,C: nat > set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le841296385at_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(114,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_linorder__wlog) ).
thf(704,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(69,axiom,
v_a = v_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Graph_OV_Ocong) ).
thf(540,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(176,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_314_inf__sup__ord_I1_J) ).
thf(900,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)],[176]) ).
thf(140,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_Int__mono) ).
thf(784,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)],[140]) ).
thf(39,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_subset__refl) ).
thf(419,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1476,plain,
! [E: nat,D: list_P559422087at_nat,C: nat,B: nat > $o,A: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
| ( ( isPath_a @ c @ C @ D @ E )
!= ( C != E ) )
| ( ( $true
& ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) @ ( sk93 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) @ ( sk94 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) @ E ) )
!= ( C = E ) )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( C
= ( sk92 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[285,1437]) ).
thf(1477,plain,
! [E: nat,D: list_P559422087at_nat,C: nat,B: nat > $o,A: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
| ( ( isPath_a @ c @ C @ D @ E )
!= ( C != E ) )
| ( ( ( member701585322at_nat @ ( product_Pair_nat_nat @ ( sk92 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) @ ( sk93 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) ) @ ( e_a @ c ) )
& ( isPath_a @ c @ ( sk93 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) @ ( sk94 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) @ E ) )
!= ( C = E ) )
| ( ( A @ ( sk1 @ B @ A ) )
!= ( C
= ( sk92 @ ( isPath_a @ c @ C @ D @ E ) @ E @ D @ C ) ) ) ),
inference(simp,[status(thm)],[1476]) ).
thf(1492,plain,
! [H: nat > nat,G: nat > list_P559422087at_nat,F: nat > nat,E: nat > nat,D: nat > list_P559422087at_nat,C: nat > nat,B: nat > nat,A: nat > $o] :
( ( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) )
@ ( collect_nat @ A ) )
| ( ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
!= ( ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) )
| ( ( ( member701585322at_nat
@ ( product_Pair_nat_nat
@ ( sk92
@ ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( sk93
@ ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) )
@ ( e_a @ c ) )
& ( isPath_a @ c
@ ( sk93
@ ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( sk94
@ ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) )
!= ( ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
= ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) )
| ( ( E
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
| ( ( H
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
| ( ( G
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
| ( ( F
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1477:[bind(A,$thf( ^ [M: nat] : ( ( F @ M ) = ( sk92 @ ( isPath_a @ c @ ( M @ M ) @ ( N @ M ) @ ( O @ M ) ) @ ( I @ M ) @ ( J @ M ) @ ( K @ M ) ) ) )),bind(B,$thf( B )),bind(C,$thf( F @ ( sk1 @ B @ ^ [M: nat] : ( ( F @ M ) = ( sk92 @ ( isPath_a @ c @ ( M @ M ) @ ( N @ M ) @ ( O @ M ) ) @ ( I @ M ) @ ( J @ M ) @ ( K @ M ) ) ) ) )),bind(D,$thf( J @ ( sk1 @ B @ ^ [M: nat] : ( ( F @ M ) = ( sk92 @ ( isPath_a @ c @ ( M @ M ) @ ( N @ M ) @ ( O @ M ) ) @ ( I @ M ) @ ( J @ M ) @ ( K @ M ) ) ) ) )),bind(E,$thf( I @ ( sk1 @ B @ ^ [M: nat] : ( ( F @ M ) = ( sk92 @ ( isPath_a @ c @ ( M @ M ) @ ( N @ M ) @ ( O @ M ) ) @ ( I @ M ) @ ( J @ M ) @ ( K @ M ) ) ) ) ))]]) ).
thf(1524,plain,
! [H: nat > nat,G: nat > list_P559422087at_nat,F: nat > nat,E: nat > nat,D: nat > list_P559422087at_nat,C: nat > nat,B: nat > nat,A: nat > $o] :
( ( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) )
@ ( collect_nat @ A ) )
| ( ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
!= ( ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) )
| ( ( ( member701585322at_nat
@ ( product_Pair_nat_nat
@ ( sk92
@ ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( sk93
@ ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) )
@ ( e_a @ c ) )
& ( isPath_a @ c
@ ( sk93
@ ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( sk94
@ ( isPath_a @ c
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
@ ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
@ ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) )
!= ( ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
= ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) )
| ( ( E
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
| ( ( H
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( C
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
| ( ( G
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( D
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) )
| ( ( F
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) )
!= ( B
@ ( sk1 @ A
@ ^ [I: nat] :
( ( B @ I )
= ( sk92 @ ( isPath_a @ c @ ( F @ I ) @ ( G @ I ) @ ( H @ I ) ) @ ( C @ I ) @ ( D @ I ) @ ( E @ I ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1492]) ).
thf(125,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_ord__eq__le__subst) ).
thf(736,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(13,axiom,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ B @ C )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_finite__has__maximal2) ).
thf(318,plain,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ B @ C )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_eq__refl) ).
thf(434,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(8,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_order__subst1) ).
thf(303,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(228,axiom,
! [A: product_prod_nat_nat > a,B: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a2 @ A @ B ) @ ( e_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Graph_Ooutgoing_H__edges) ).
thf(1122,plain,
! [A: product_prod_nat_nat > a,B: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a2 @ A @ B ) @ ( e_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(130,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_31_dual__order_Oeq__iff) ).
thf(758,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)],[130]) ).
thf(83,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_order__refl) ).
thf(594,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(174,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_290_inf_OorderE) ).
thf(895,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)],[174]) ).
thf(238,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_set__eq__subset) ).
thf(1149,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)],[238]) ).
thf(135,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( ( ( finite447719721at_nat @ B )
= ( finite447719721at_nat @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_card__subset__eq) ).
thf(769,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( ( ( finite447719721at_nat @ B )
= ( finite447719721at_nat @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(102,axiom,
! [A: product_prod_nat_nat > a] :
( ( finite_Graph_a @ A )
=> ( edmond1517640972ysis_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_ek__analysis_Ointro) ).
thf(668,plain,
! [A: product_prod_nat_nat > a] :
( ( finite_Graph_a @ A )
=> ( edmond1517640972ysis_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(213,axiom,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_finite_nat @ ( v_a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_Efin__imp__Vfin) ).
thf(1061,plain,
( ( finite772653738at_nat @ ( e_a @ c ) )
=> ( finite_finite_nat @ ( v_a @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(144,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_44_order__class_Oorder_Oantisym) ).
thf(799,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)],[144]) ).
thf(121,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_antisym__conv) ).
thf(726,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(158,axiom,
! [A: product_prod_nat_nat > a,B: nat,C: nat] :
( ( edmond1517640972ysis_a @ A )
=> ( ord_le841296385at_nat @ ( edmond475474835dges_a @ A @ B @ C ) @ ( e_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_ek__analysis_OspEdges__ss__E) ).
thf(848,plain,
! [A: product_prod_nat_nat > a,B: nat,C: nat] :
( ( edmond1517640972ysis_a @ A )
=> ( ord_le841296385at_nat @ ( edmond475474835dges_a @ A @ B @ C ) @ ( e_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(112,axiom,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_order__class_Oorder_Oeq__iff) ).
thf(700,plain,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(91,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_le__cases3) ).
thf(626,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(179,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ord_le841296385at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_eq__refl) ).
thf(915,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ord_le841296385at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(194,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_305_le__infE) ).
thf(983,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)],[194]) ).
thf(215,axiom,
! [A: set_nat,B: set_Pr1986765409at_nat > set_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_set_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_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_order__subst1) ).
thf(1066,plain,
! [A: set_nat,B: set_Pr1986765409at_nat > set_nat,C: set_Pr1986765409at_nat,D: set_Pr1986765409at_nat] :
( ( ord_less_eq_set_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_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(48,axiom,
adjacent_nodes_a = adjacent_nodes_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_Graph_Oadjacent__nodes_Ocong) ).
thf(455,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_le__cases) ).
thf(608,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_antisym) ).
thf(431,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(95,axiom,
! [A: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite_Graph_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Finite__Graph_Ointro) ).
thf(653,plain,
! [A: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite_Graph_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(97,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_order__trans) ).
thf(658,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(253,axiom,
! [A: nat,B: nat,C: nat,D: list_P559422087at_nat,E: nat] :
( ( isPath_a @ c @ A @ ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ B @ C ) @ D ) @ E )
= ( ( A = B )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( e_a @ c ) )
& ( isPath_a @ c @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_isPath_Osimps_I2_J) ).
thf(1213,plain,
! [A: nat,B: nat,C: nat,D: list_P559422087at_nat,E: nat] :
( ( isPath_a @ c @ A @ ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ B @ C ) @ D ) @ E )
= ( ( A = B )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( e_a @ c ) )
& ( isPath_a @ c @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(134,axiom,
finite772653738at_nat @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_finite__E) ).
thf(768,plain,
finite772653738at_nat @ ( e_a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_linear) ).
thf(695,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(259,axiom,
ord_le841296385at_nat @ ( edmond475474835dges_a @ c @ s @ t ) @ ( e_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_spEdges__ss__E) ).
thf(1245,plain,
ord_le841296385at_nat @ ( edmond475474835dges_a @ c @ s @ t ) @ ( e_a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(159,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_311_inf__le1) ).
thf(851,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)],[159]) ).
thf(223,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_118_subset__trans) ).
thf(1102,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)],[223]) ).
thf(505,plain,
( ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ B @ A )
& ( ord_less_eq_set_nat @ A @ B ) ) )
= ( (=) @ set_nat ) ),
inference(lifteq,[status(thm)],[504]) ).
thf(46,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_bounded__Max__nat) ).
thf(438,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(105,axiom,
! [A: product_prod_nat_nat,B: list_P559422087at_nat] :
( ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ B ) )
=> ( ! [C: list_P559422087at_nat] :
( B
!= ( cons_P66992567at_nat @ A @ C ) )
=> ~ ! [C: product_prod_nat_nat,D: list_P559422087at_nat] :
( ( B
= ( cons_P66992567at_nat @ C @ D ) )
=> ~ ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_list_Oset__cases) ).
thf(675,plain,
! [A: product_prod_nat_nat,B: list_P559422087at_nat] :
( ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ B ) )
=> ( ! [C: list_P559422087at_nat] :
( B
!= ( cons_P66992567at_nat @ A @ C ) )
=> ~ ! [C: product_prod_nat_nat,D: list_P559422087at_nat] :
( ( B
= ( cons_P66992567at_nat @ C @ D ) )
=> ~ ( member701585322at_nat @ A @ ( set_Pr2131844118at_nat @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(27,axiom,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_eq__iff) ).
thf(374,plain,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(269,axiom,
! [A: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ A ) )
=> ( finite_Graph_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_Graph_OFinite__Graph__EI) ).
thf(1277,plain,
! [A: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ A ) )
=> ( finite_Graph_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_ord__eq__le__trans) ).
thf(648,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(149,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_50_ord__eq__le__trans) ).
thf(812,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)],[149]) ).
thf(202,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_71_eq__iff) ).
thf(1018,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)],[202]) ).
thf(712,plain,
( ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) )
= ( (=) @ nat ) ),
inference(lifteq,[status(thm)],[711]) ).
thf(185,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_in__mono) ).
thf(954,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(222,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) )
=> ( ord_le841296385at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_subsetI) ).
thf(1098,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) )
=> ( ord_le841296385at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(197,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_179_Int__greatest) ).
thf(993,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)],[197]) ).
thf(241,axiom,
finite_Graph_a @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Finite__Graph__axioms) ).
thf(1156,plain,
finite_Graph_a @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(36,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_order__class_Oorder_Oantisym) ).
thf(409,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(255,axiom,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_SP__EDGES) ).
thf(1230,plain,
ord_le841296385at_nat @ edges @ ( set_Pr2131844118at_nat @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(104,axiom,
! [A: product_prod_nat_nat > a,B: nat,C: list_P559422087at_nat,D: nat] :
( ( isShortestPath_a @ A @ B @ C @ D )
=> ( isPath_a @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Graph_OshortestPath__is__path) ).
thf(673,plain,
! [A: product_prod_nat_nat > a,B: nat,C: list_P559422087at_nat,D: nat] :
( ( isShortestPath_a @ A @ B @ C @ D )
=> ( isPath_a @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(59,axiom,
( finite_finite_nat
= ( ^ [A: set_nat] :
? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_finite__nat__set__iff__bounded__le) ).
thf(502,plain,
( finite_finite_nat
= ( ^ [A: set_nat] :
? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(265,axiom,
! [A: product_prod_nat_nat > a,B: nat] : ( ord_le841296385at_nat @ ( outgoing_a @ A @ B ) @ ( e_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Graph_Ooutgoing__edges) ).
thf(1262,plain,
! [A: product_prod_nat_nat > a,B: nat] : ( ord_le841296385at_nat @ ( outgoing_a @ A @ B ) @ ( e_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(80,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_order__refl) ).
thf(576,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(71,axiom,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_subset__iff) ).
thf(544,plain,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(263,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_242_inf_OcoboundedI1) ).
thf(1257,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)],[263]) ).
thf(236,axiom,
member_nat @ s @ ( v_a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_SV) ).
thf(1141,plain,
member_nat @ s @ ( v_a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(271,axiom,
! [A: product_prod_nat_nat > a,B: set_nat] : ( ord_le841296385at_nat @ ( incoming_a2 @ A @ B ) @ ( e_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Graph_Oincoming_H__edges) ).
thf(1284,plain,
! [A: product_prod_nat_nat > a,B: set_nat] : ( ord_le841296385at_nat @ ( incoming_a2 @ A @ B ) @ ( e_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(209,axiom,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_subset__eq) ).
thf(1052,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ A )
=> ( member701585322at_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(164,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_254_inf_Ocobounded1) ).
thf(864,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)],[164]) ).
thf(11,axiom,
! [A: nat,B: product_prod_nat_nat > a] :
( ( member_nat @ A @ ( v_a @ B ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ B @ A ) @ ( v_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_Graph_Oreachable__ss__V) ).
thf(314,plain,
! [A: nat,B: product_prod_nat_nat > a] :
( ( member_nat @ A @ ( v_a @ B ) )
=> ( ord_less_eq_set_nat @ ( reachableNodes_a @ B @ A ) @ ( v_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(267,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_251_inf_Ocobounded2) ).
thf(1272,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)],[267]) ).
thf(257,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_269_inf__absorb2) ).
thf(1240,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)],[257]) ).
thf(221,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( D != A )
=> ? [F: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_isPath__ex__edge1) ).
thf(1094,plain,
! [A: nat,B: list_P559422087at_nat,C: nat,D: nat,E: nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( set_Pr2131844118at_nat @ B ) )
=> ( ( D != A )
=> ? [F: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ F @ D ) @ ( set_Pr2131844118at_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(30,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_antisym) ).
thf(386,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(280,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_317_inf__sup__ord_I2_J) ).
thf(1316,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)],[280]) ).
thf(24,axiom,
edmond771116670s_uE_a = edmond771116670s_uE_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_ek__analysis__defs_OuE_Ocong) ).
thf(363,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(242,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( finite772653738at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_rev__finite__subset) ).
thf(1157,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( finite772653738at_nat @ A )
=> ( ( ord_le841296385at_nat @ B @ A )
=> ( finite772653738at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(254,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( ( B = nil_Pr1308055047at_nat )
=> ( C != A ) )
=> ~ ! [D: list_P559422087at_nat,E: nat] :
( ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ A @ E ) @ D ) )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ E ) @ ( e_a @ c ) )
=> ~ ( isPath_a @ c @ E @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_isPath__fwd__cases) ).
thf(1216,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( ( B = nil_Pr1308055047at_nat )
=> ( C != A ) )
=> ~ ! [D: list_P559422087at_nat,E: nat] :
( ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ A @ E ) @ D ) )
=> ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ E ) @ ( e_a @ c ) )
=> ~ ( isPath_a @ c @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(230,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_278_inf_Oabsorb1) ).
thf(1126,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)],[230]) ).
thf(199,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_11_subset__antisym) ).
thf(1010,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)],[199]) ).
thf(231,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_257_inf_Oorder__iff) ).
thf(1129,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)],[231]) ).
thf(1130,plain,
( ord_le841296385at_nat
= ( ^ [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( A
= ( inf_in586391887at_nat @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[1129]) ).
thf(1390,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 ) ) ) ),
inference(rewrite,[status(thm)],[1130,818]) ).
thf(63,axiom,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_ord__eq__le__subst) ).
thf(517,plain,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(182,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ~ ( finite772653738at_nat @ A )
=> ~ ( finite772653738at_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_infinite__super) ).
thf(946,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ~ ( finite772653738at_nat @ A )
=> ~ ( finite772653738at_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(22,axiom,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_ord__eq__le__subst) ).
thf(351,plain,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(33,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_mem__Collect__eq) ).
thf(401,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(139,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_154_Int__subset__iff) ).
thf(781,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)],[139]) ).
thf(5,axiom,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_nat @ A @ B )
=> ~ ( ord_less_eq_set_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_equalityE) ).
thf(290,plain,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_nat @ A @ B )
=> ~ ( ord_less_eq_set_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(275,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_284_inf__unique) ).
thf(1294,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)],[275]) ).
thf(278,axiom,
! [A: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a2 @ c @ A ) @ ( e_a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_outgoing_H__edges) ).
thf(1308,plain,
! [A: set_nat] : ( ord_le841296385at_nat @ ( outgoing_a2 @ c @ A ) @ ( e_a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(133,axiom,
! [A: set_Pr1986765409at_nat,B: nat > set_Pr1986765409at_nat,C: nat,D: nat] :
( ( ord_le841296385at_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_order__subst1) ).
thf(763,plain,
! [A: set_Pr1986765409at_nat,B: nat > set_Pr1986765409at_nat,C: nat,D: nat] :
( ( ord_le841296385at_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le841296385at_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le841296385at_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(29,axiom,
! [A: product_prod_nat_nat,B: list_P559422087at_nat,C: product_prod_nat_nat,D: list_P559422087at_nat] :
( ( ( cons_P66992567at_nat @ A @ B )
= ( cons_P66992567at_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_list_Oinject) ).
thf(383,plain,
! [A: product_prod_nat_nat,B: list_P559422087at_nat,C: product_prod_nat_nat,D: list_P559422087at_nat] :
( ( ( cons_P66992567at_nat @ A @ B )
= ( cons_P66992567at_nat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(107,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_subset__trans) ).
thf(684,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(73,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ~ ( finite_finite_nat @ A )
=> ~ ( finite_finite_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_infinite__super) ).
thf(549,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ~ ( finite_finite_nat @ A )
=> ~ ( finite_finite_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(4,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
= ( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Collect__mono__iff) ).
thf(287,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
= ( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(226,axiom,
! [A: list_P559422087at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ ( set_Pr2131844118at_nat @ A ) @ B )
= ( ! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ ( set_Pr2131844118at_nat @ A ) )
=> ( member701585322at_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_subset__code_I1_J) ).
thf(1116,plain,
! [A: list_P559422087at_nat,B: set_Pr1986765409at_nat] :
( ( ord_le841296385at_nat @ ( set_Pr2131844118at_nat @ A ) @ B )
= ( ! [C: product_prod_nat_nat] :
( ( member701585322at_nat @ C @ ( set_Pr2131844118at_nat @ A ) )
=> ( member701585322at_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(233,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_299_inf__mono) ).
thf(1133,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)],[233]) ).
thf(26,axiom,
! [A: list_P559422087at_nat,B: list_P559422087at_nat,C: product_prod_nat_nat] :
( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ A ) @ ( size_s1990949619at_nat @ B ) )
=> ( A
!= ( cons_P66992567at_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_impossible__Cons) ).
thf(369,plain,
! [A: list_P559422087at_nat,B: list_P559422087at_nat,C: product_prod_nat_nat] :
( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ A ) @ ( size_s1990949619at_nat @ B ) )
=> ( A
!= ( cons_P66992567at_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(370,plain,
! [A: list_P559422087at_nat,B: list_P559422087at_nat] :
( ( ord_less_eq_nat @ ( size_s1990949619at_nat @ A ) @ ( size_s1990949619at_nat @ B ) )
=> ~ ? [C: product_prod_nat_nat] :
( A
= ( cons_P66992567at_nat @ C @ B ) ) ),
inference(miniscope,[status(thm)],[369]) ).
thf(371,plain,
! [C: product_prod_nat_nat,B: list_P559422087at_nat,A: list_P559422087at_nat] :
( ~ ( ord_less_eq_nat @ ( size_s1990949619at_nat @ A ) @ ( size_s1990949619at_nat @ B ) )
| ( A
!= ( cons_P66992567at_nat @ C @ B ) ) ),
inference(cnf,[status(esa)],[370]) ).
thf(372,plain,
! [C: product_prod_nat_nat,B: list_P559422087at_nat,A: list_P559422087at_nat] :
( ( A
!= ( cons_P66992567at_nat @ C @ B ) )
| ~ ( ord_less_eq_nat @ ( size_s1990949619at_nat @ A ) @ ( size_s1990949619at_nat @ B ) ) ),
inference(lifteq,[status(thm)],[371]) ).
thf(373,plain,
! [B: product_prod_nat_nat,A: list_P559422087at_nat] :
~ ( ord_less_eq_nat @ ( size_s1990949619at_nat @ ( cons_P66992567at_nat @ B @ A ) ) @ ( size_s1990949619at_nat @ A ) ),
inference(simp,[status(thm)],[372]) ).
thf(184,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ord_le841296385at_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_equalityD1) ).
thf(950,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat] :
( ( A = B )
=> ( ord_le841296385at_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(154,axiom,
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( e_a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_Vfin__imp__Efin) ).
thf(835,plain,
( ( finite_finite_nat @ ( v_a @ c ) )
=> ( finite772653738at_nat @ ( e_a @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(161,axiom,
! [A: nat] : ( finite_finite_nat @ ( adjacent_nodes_a @ c @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_adjacent__nodes__finite) ).
thf(854,plain,
! [A: nat] : ( finite_finite_nat @ ( adjacent_nodes_a @ c @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(276,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_293_le__infI2) ).
thf(1303,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)],[276]) ).
thf(41,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_dual__order_Orefl) ).
thf(422,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(142,axiom,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat > $o,D: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ! [E: product_prod_nat_nat] :
( ( member701585322at_nat @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ ( collec7649004at_nat @ C ) ) @ ( inf_in586391887at_nat @ B @ ( collec7649004at_nat @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Int__Collect__mono) ).
thf(790,plain,
! [A: set_Pr1986765409at_nat,B: set_Pr1986765409at_nat,C: product_prod_nat_nat > $o,D: product_prod_nat_nat > $o] :
( ( ord_le841296385at_nat @ A @ B )
=> ( ! [E: product_prod_nat_nat] :
( ( member701585322at_nat @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ A @ ( collec7649004at_nat @ C ) ) @ ( inf_in586391887at_nat @ B @ ( collec7649004at_nat @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(61,axiom,
! [A: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ A )
=> ( finite_Graph_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_ek__analysis_Oaxioms) ).
thf(506,plain,
! [A: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ A )
=> ( finite_Graph_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(246,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ~ ( isPath_a @ c @ A @ B @ C )
=> ( ( ( B = nil_Pr1308055047at_nat )
=> ( A = C ) )
=> ~ ! [D: nat,E: nat,F: list_P559422087at_nat] :
( ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ D @ E ) @ F ) )
=> ( ( A = D )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( e_a @ c ) )
& ( isPath_a @ c @ E @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_isPath_Oelims_I3_J) ).
thf(1172,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ~ ( isPath_a @ c @ A @ B @ C )
=> ( ( ( B = nil_Pr1308055047at_nat )
=> ( A = C ) )
=> ~ ! [D: nat,E: nat,F: list_P559422087at_nat] :
( ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ D @ E ) @ F ) )
=> ( ( A = D )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( e_a @ c ) )
& ( isPath_a @ c @ E @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(99,axiom,
isShortestPath_a = isShortestPath_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Graph_OisShortestPath_Ocong) ).
thf(664,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(273,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_175_Int__absorb1) ).
thf(1288,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)],[273]) ).
thf(152,axiom,
! [A: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( e_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_Graph_OVfin__imp__Efin) ).
thf(828,plain,
! [A: product_prod_nat_nat > a] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( e_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(66,axiom,
( finite_Graph_a
= ( ^ [A: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Finite__Graph__def) ).
thf(532,plain,
( finite_Graph_a
= ( ^ [A: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(119,axiom,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_in__mono) ).
thf(720,plain,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(244,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_177_Int__absorb2) ).
thf(1165,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)],[244]) ).
thf(143,axiom,
! [A: list_P559422087at_nat,B: product_prod_nat_nat > a,C: product_prod_nat_nat > a,D: nat,E: nat] :
( ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ A ) @ ( e_a @ B ) ) @ ( e_a @ C ) )
=> ( ( isPath_a @ B @ D @ A @ E )
=> ( isPath_a @ C @ D @ A @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_Graph_Otransfer__path) ).
thf(796,plain,
! [A: list_P559422087at_nat,B: product_prod_nat_nat > a,C: product_prod_nat_nat > a,D: nat,E: nat] :
( ( ord_le841296385at_nat @ ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ A ) @ ( e_a @ B ) ) @ ( e_a @ C ) )
=> ( ( isPath_a @ B @ D @ A @ E )
=> ( isPath_a @ C @ D @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(181,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( ( B = nil_Pr1308055047at_nat )
=> ( A != C ) )
=> ~ ! [D: nat,E: nat,F: list_P559422087at_nat] :
( ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ D @ E ) @ F ) )
=> ~ ( ( A = D )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( e_a @ c ) )
& ( isPath_a @ c @ E @ F @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_isPath_Oelims_I2_J) ).
thf(928,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isPath_a @ c @ A @ B @ C )
=> ( ( ( B = nil_Pr1308055047at_nat )
=> ( A != C ) )
=> ~ ! [D: nat,E: nat,F: list_P559422087at_nat] :
( ( B
= ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ D @ E ) @ F ) )
=> ~ ( ( A = D )
& ( member701585322at_nat @ ( product_Pair_nat_nat @ D @ E ) @ ( e_a @ c ) )
& ( isPath_a @ c @ E @ F @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(38,axiom,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ ( finite_card_nat @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_card__seteq) ).
thf(415,plain,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ ( finite_card_nat @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(156,axiom,
! [A: set_se1612935105at_nat,B: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A )
=> ( ( member298845450at_nat @ B @ A )
=> ? [C: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ C @ A )
& ( ord_le841296385at_nat @ C @ B )
& ! [D: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ D @ A )
=> ( ( ord_le841296385at_nat @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_finite__has__minimal2) ).
thf(839,plain,
! [A: set_se1612935105at_nat,B: set_Pr1986765409at_nat] :
( ( finite1457549322at_nat @ A )
=> ( ( member298845450at_nat @ B @ A )
=> ? [C: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ C @ A )
& ( ord_le841296385at_nat @ C @ B )
& ! [D: set_Pr1986765409at_nat] :
( ( member298845450at_nat @ D @ A )
=> ( ( ord_le841296385at_nat @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(195,axiom,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_order__refl) ).
thf(987,plain,
! [A: set_Pr1986765409at_nat] : ( ord_le841296385at_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_order__subst2) ).
thf(464,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(79,axiom,
reachableNodes_a = reachableNodes_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Graph_OreachableNodes_Ocong) ).
thf(575,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat > set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_ord__le__eq__subst) ).
thf(596,plain,
! [A: nat,B: nat,C: nat > set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(120,axiom,
! [A: list_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ ( set_nat2 @ A ) @ B )
= ( ! [C: nat] :
( ( member_nat @ C @ ( set_nat2 @ A ) )
=> ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_subset__code_I1_J) ).
thf(723,plain,
! [A: list_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ ( set_nat2 @ A ) @ B )
= ( ! [C: nat] :
( ( member_nat @ C @ ( set_nat2 @ A ) )
=> ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(167,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_56_antisym__conv) ).
thf(871,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)],[167]) ).
thf(16,axiom,
! [A: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ A )
=> ( finite772653738at_nat @ ( edmond771116670s_uE_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_ek__analysis_Ofinite__uE) ).
thf(332,plain,
! [A: product_prod_nat_nat > a] :
( ( edmond1517640972ysis_a @ A )
=> ( finite772653738at_nat @ ( edmond771116670s_uE_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(146,axiom,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isShortestPath_a @ c @ A @ B @ C )
= ( ( isPath_a @ c @ A @ B @ C )
& ! [D: list_P559422087at_nat] :
( ( isPath_a @ c @ A @ D @ C )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ B ) @ ( size_s1990949619at_nat @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_isShortestPath__def) ).
thf(803,plain,
! [A: nat,B: list_P559422087at_nat,C: nat] :
( ( isShortestPath_a @ c @ A @ B @ C )
= ( ( isPath_a @ c @ A @ B @ C )
& ! [D: list_P559422087at_nat] :
( ( isPath_a @ c @ A @ D @ C )
=> ( ord_less_eq_nat @ ( size_s1990949619at_nat @ B ) @ ( size_s1990949619at_nat @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(533,plain,
( finite_Graph_a
= ( ^ [A: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ A ) ) ) ),
inference(lifteq,[status(thm)],[532]) ).
thf(1320,plain,
( ( ^ [A: product_prod_nat_nat > a] : ( finite_finite_nat @ ( v_a @ A ) ) )
= edmond1517640972ysis_a ),
inference(rewrite,[status(thm)],[533,408]) ).
thf(18,axiom,
! [A: product_prod_nat_nat > a,B: set_nat] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( incoming_a2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Graph_Ofinite__incoming_H) ).
thf(337,plain,
! [A: product_prod_nat_nat > a,B: set_nat] :
( ( finite_finite_nat @ ( v_a @ A ) )
=> ( finite772653738at_nat @ ( incoming_a2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(53,axiom,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Collect__mem__eq) ).
thf(469,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(205,axiom,
! [A: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ A ) )
=> ( finite_finite_nat @ ( v_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Graph_OEfin__imp__Vfin) ).
thf(1037,plain,
! [A: product_prod_nat_nat > a] :
( ( finite772653738at_nat @ ( e_a @ A ) )
=> ( finite_finite_nat @ ( v_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(128,axiom,
edmond475474835dges_a = edmond475474835dges_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_ek__analysis__defs_OspEdges_Ocong) ).
thf(755,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(57,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_dual__order_Orefl) ).
thf(491,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(250,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_205_le__inf__iff) ).
thf(1204,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)],[250]) ).
thf(25,axiom,
! [A: nat > list_P559422087at_nat > nat > $o,B: nat,C: list_P559422087at_nat,D: nat] :
( ! [E: nat,F: nat] : ( A @ E @ nil_Pr1308055047at_nat @ F )
=> ( ! [E: nat,F: nat,G: nat,H: list_P559422087at_nat,I: nat] :
( ( A @ G @ H @ I )
=> ( A @ E @ ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ F @ G ) @ H ) @ I ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_Graph_OisPath_Oinduct) ).
thf(364,plain,
! [A: nat > list_P559422087at_nat > nat > $o,B: nat,C: list_P559422087at_nat,D: nat] :
( ! [E: nat,F: nat] : ( A @ E @ nil_Pr1308055047at_nat @ F )
=> ( ! [E: nat,F: nat,G: nat,H: list_P559422087at_nat,I: nat] :
( ( A @ G @ H @ I )
=> ( A @ E @ ( cons_P66992567at_nat @ ( product_Pair_nat_nat @ F @ G ) @ H ) @ I ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(170,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_296_le__infI1) ).
thf(882,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)],[170]) ).
thf(191,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_68_antisym) ).
thf(972,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)],[191]) ).
thf(1836,plain,
$false,
inference(e,[status(thm)],[892,809,1105,846,962,555,666,481,1168,760,408,308,1073,1142,655,1437,1041,861,1310,472,1260,670,1063,340,404,898,1243,885,1386,301,1254,389,1055,570,504,1264,587,702,802,1279,559,853,421,969,1013,325,316,817,902,756,376,623,646,1151,806,966,1183,485,1136,1020,348,687,734,866,1072,396,312,877,692,1119,774,428,1201,452,529,661,546,1306,761,534,714,1274,334,957,424,407,729,665,830,461,682,551,1291,456,285,493,1210,578,874,948,1534,615,980,869,610,989,697,1089,328,1160,537,526,1039,1028,1082,1016,1207,837,1114,647,1249,1231,1131,1192,1246,779,605,1050,457,360,508,1695,541,1054,1286,1071,773,343,1318,718,888,906,298,412,750,618,856,745,733,1154,819,286,711,1124,562,975,641,1139,313,787,713,1058,919,704,540,900,784,419,1524,736,996,318,434,303,1122,758,594,895,1149,769,668,1061,799,726,848,700,626,915,983,1066,455,608,431,653,658,1213,768,695,1245,851,1102,505,438,675,374,1277,648,812,1018,712,954,1098,993,282,1156,409,1230,673,502,1262,576,544,1257,1141,1284,1052,864,314,1272,1240,1094,386,1316,363,1157,1216,1126,1010,1390,517,946,351,401,781,290,1294,1308,763,383,684,549,287,1116,1133,818,373,950,835,854,1303,422,790,506,1172,664,1288,828,960,532,720,1165,796,283,928,415,839,987,464,575,596,723,871,369,332,1129,803,1320,337,469,1009,1037,755,491,1204,364,882,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP050^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n001.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:49:20 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.14/1.20 % [INFO] Parsing done (412ms).
% 2.47/1.21 % [INFO] Running in sequential loop mode.
% 3.22/1.59 % [INFO] eprover registered as external prover.
% 3.22/1.59 % [INFO] Scanning for conjecture ...
% 3.65/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 353 axioms. Running axiom selection ...
% 3.84/1.87 % [INFO] Axiom selection finished. Selected 279 axioms (removed 74 axioms).
% 4.52/2.13 % [INFO] Problem is higher-order (TPTP THF).
% 4.84/2.16 % [INFO] Type checking passed.
% 4.84/2.16 % [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 ...
% 178.54/139.09 % External prover 'e' found a proof!
% 178.54/139.09 % [INFO] Killing All external provers ...
% 178.54/139.09 % Time passed: 138745ms (effective reasoning time: 137875ms)
% 178.54/139.09 % 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)>
% 178.54/139.09 % Axioms used in derivation (279): fact_218_Vfin__imp__Efin, fact_91_ord__eq__le__subst, fact_332_card__subset__eq, fact_204_List_Ofinite__set, fact_61_order_Otrans, fact_89_ord__eq__le__subst, fact_60_order_Otrans, fact_216_finite__V, fact_81_ord__le__eq__subst, fact_228_Graph_OVfin__imp__Efin, fact_111_order__subst1, fact_116_set__eq__subset, fact_166_Graph_OreachableNodes_Ocong, fact_221_finite__incoming_H, fact_214_card__seteq, fact_146_Graph_OisPath__edgeset, fact_145_Graph_Ooutgoing__edges, fact_308_inf__le2, fact_327_finite__list, fact_191_Graph_OE_Ocong, fact_112_order__subst1, fact_238_finite__has__maximal2, fact_153_reachableNodes__append__edge, fact_22_ek__analysis_Ointro, fact_266_inf_OboundedE, fact_346_finite__nat__set__iff__bounded__le, fact_199_Graph_Oincoming_H_Ocong, fact_235_finite__has__minimal2, fact_1_SP__EDGES, fact_18_isPath__edgeset, fact_107_order__subst1, fact_76_ord__le__eq__subst, fact_302_le__infI, fact_119_subset__trans, fact_164_IntD2, fact_55_order__class_Oorder_Oeq__iff, fact_13_order__refl, fact_139_transfer__path, fact_138_reachable__ss__V, fact_6_incoming__edges, fact_350_isPath__fwd__cases, fact_85_ord__eq__le__subst, fact_102_mem__Collect__eq, fact_162_IntD1, fact_347_isPath_Oelims_I3_J, fact_59_le__cases3, fact_229_Graph_Ofinite__outgoing, fact_92_order__subst2, fact_168_Graph_Oreachable__ss__V, fact_212_card__mono, fact_106_order__subst1, fact_129_equalityD1, fact_124_subset__iff, fact_232_Graph_Ofinite__incoming_H, fact_21_ek__analysis__def, fact_342_impossible__Cons, fact_9_subsetI, fact_220_finite__outgoing, fact_135_subsetD, fact_51_ord__eq__le__trans, fact_27_ek__analysis_OE__ss__uE, fact_26_ek__analysis_OspEdges__ss__E, fact_208_inf_Obounded__iff, fact_43_order__trans, fact_177_Int__absorb2, fact_336_pathVertices__edgeset, fact_201_finite__Int, fact_31_dual__order_Oeq__iff, fact_95_order__subst2, fact_211_card__mono, fact_46_order__class_Oorder_Oantisym, fact_284_inf__unique, fact_103_Collect__mem__eq, fact_130_subset__eq, fact_343_list_Oset__cases, fact_222_finite__outgoing_H, fact_104_Collect__mem__eq, fact_109_order__subst1, fact_101_mem__Collect__eq, fact_200_Graph_OshortestPath__is__path, fact_29_dual__order_Oantisym, fact_32_dual__order_Oeq__iff, fact_340_isShortestPath__def, fact_196_Graph_Ooutgoing_Ocong, fact_156_finite__E, fact_217_adjacent__nodes__finite, fact_58_antisym__conv, fact_45_order__class_Oorder_Oantisym, fact_165_Graph_OreachableNodes__append__edge, fact_0_SP, fact_38_dual__order_Orefl, fact_37_linorder__wlog, fact_94_order__subst2, fact_181_Int__Collect__mono, fact_128_equalityD1, fact_333_card__subset__eq, fact_7_outgoing__edges, fact_90_ord__eq__le__subst, fact_19_shortestPath__is__path, fact_320_rev__finite__subset, fact_341_list_Oinject, fact_12_subset__antisym, fact_93_order__subst2, fact_338_obtain__subset__with__card__n, fact_331_infinite__arbitrarily__large, fact_314_inf__sup__ord_I1_J, fact_231_Graph_Ofinite__outgoing_H, fact_193_Graph_OV_Ocong, fact_69_antisym, fact_67_linear, fact_349_isPath_Osimps_I1_J, fact_344_list_Oset__cases, fact_281_le__iff__inf, fact_36_dual__order_Otrans, fact_184_Graph_OisPath__ex__edge2, fact_125_subset__iff, fact_2_ek__analysis__axioms, fact_5_E__ss__uE, fact_263_inf_OboundedI, fact_34_dual__order_Otrans, fact_223_Finite__Graph__def, fact_121_Collect__mono, fact_83_ord__eq__le__subst, fact_100_order__subst2, fact_236_finite__has__maximal2, fact_49_ord__le__eq__trans, fact_98_order__subst2, fact_175_Int__absorb1, fact_25_ek__analysis__defs_OuE_Ocong, fact_239_inf_OcoboundedI2, fact_152_isPath__ex__edge1, fact_194_ek__analysis_Ocard__spEdges__le, fact_185_Graph_OisPath__ex__edge1, fact_299_inf__mono, fact_99_order__subst2, fact_96_order__subst2, fact_115_Collect__mono__iff, fact_325_finite__subset, fact_149_IntI, fact_190_Graph_Otransfer__path, fact_230_Graph_Ofinite__incoming, fact_72_eq__iff, fact_296_le__infI1, fact_117_set__eq__subset, fact_225_Finite__Graph_Ofinite__V, fact_348_isPath_Oelims_I2_J, fact_186_Graph_OFinite__Graph__EI, fact_144_Graph_Oincoming__edges, fact_351_isPath_Oelims_I1_J, fact_11_subset__antisym, fact_337_obtain__subset__with__card__n, fact_97_order__subst2, fact_154_Int__subset__iff, fact_330_infinite__arbitrarily__large, fact_169_Int__mono, fact_74_ord__le__eq__subst, fact_213_card__seteq, fact_14_order__refl, fact_118_subset__trans, fact_269_inf__absorb2, fact_160_IntE, fact_23_ek__analysis_Oaxioms, fact_251_inf_Ocobounded2, fact_189_ek__analysis_Ofinite__uE, fact_105_order__subst1, fact_287_inf_OorderI, fact_73_eq__iff, fact_233_finite__has__minimal2, fact_167_Graph_Oadjacent__nodes_Ocong, fact_334_finite__if__finite__subsets__card__bdd, fact_4_outgoing_H__edges, fact_158_finite__spEdges, fact_197_Graph_Oincoming_Ocong, fact_33_dual__order_Oeq__iff, fact_41_order__trans, fact_57_antisym__conv, fact_134_subsetD, fact_326_finite__list, fact_122_subset__refl, fact_183_Graph_Oadjacent__nodes__ss__V, fact_260_inf__greatest, fact_254_inf_Ocobounded1, fact_339_isPath_Osimps_I2_J, fact_171_Int__lower1, fact_224_Finite__Graph_Ointro, fact_75_ord__le__eq__subst, fact_278_inf_Oabsorb1, fact_88_ord__eq__le__subst, fact_335_finite__if__finite__subsets__card__bdd, fact_203_List_Ofinite__set, fact_80_ord__le__eq__subst, fact_3_incoming_H__edges, fact_324_finite__subset, fact_195_Graph_OisShortestPath_Ocong, fact_20_adjacent__nodes__ss__V, fact_329_subset__code_I1_J, fact_328_subset__code_I1_J, fact_257_inf_Oorder__iff, fact_226_Finite__Graph_Oadjacent__nodes__finite, fact_219_finite__incoming, fact_179_Int__greatest, fact_40_dual__order_Orefl, fact_120_Collect__mono, fact_78_ord__le__eq__subst, fact_16_SV, fact_71_eq__iff, fact_137_in__mono, fact_311_inf__le1, fact_15_order__refl, fact_293_le__infI2, fact_133_equalityE, fact_132_equalityE, fact_198_Graph_Ooutgoing_H_Ocong, fact_39_dual__order_Orefl, fact_322_infinite__super, fact_352_Graph_OisPath_Oinduct, fact_173_Int__lower2, fact_317_inf__sup__ord_I2_J, fact_77_ord__le__eq__subst, fact_242_inf_OcoboundedI1, fact_84_ord__eq__le__subst, fact_63_le__cases, fact_68_antisym, fact_108_order__subst1, fact_82_ord__le__eq__subst, fact_272_inf__absorb1, fact_50_ord__eq__le__trans, fact_28_dual__order_Oantisym, fact_30_dual__order_Oantisym, fact_140_card__spEdges__le, fact_248_inf_Oabsorb__iff1, fact_127_equalityD2, fact_123_subset__refl, fact_62_order_Otrans, fact_53_order__class_Oorder_Oeq__iff, fact_87_ord__eq__le__subst, fact_64_eq__refl, fact_142_Graph_Oincoming_H__edges, fact_188_ek__analysis_Ofinite__spEdges, fact_215_Efin__imp__Vfin, fact_24_ek__analysis__defs_OspEdges_Ocong, fact_275_inf_Oabsorb2, fact_245_inf_Oabsorb__iff2, fact_126_equalityD2, fact_290_inf_OorderE, fact_47_ord__le__eq__trans, fact_323_infinite__super, fact_79_ord__le__eq__subst, fact_143_Graph_Ooutgoing_H__edges, fact_131_subset__eq, fact_54_order__class_Oorder_Oeq__iff, fact_113_order__subst1, fact_345_bounded__Max__nat, fact_114_Collect__mono__iff, fact_70_antisym, fact_192_Graph_OisPath_Ocong, fact_157_finite__uE, fact_66_eq__refl, fact_35_dual__order_Otrans, fact_187_Finite__Graph_Ofinite__E, fact_17_spEdges__ss__E, fact_321_rev__finite__subset, fact_147_isPath__ex__edge2, fact_42_order__trans, fact_8_Finite__Graph__axioms, fact_136_in__mono, fact_151_Int__iff, fact_56_antisym__conv, fact_48_ord__le__eq__trans, fact_44_order__class_Oorder_Oantisym, fact_10_subsetI, fact_305_le__infE, fact_86_ord__eq__le__subst, fact_227_Graph_OEfin__imp__Vfin, fact_52_ord__eq__le__trans, fact_205_le__inf__iff, fact_141_Finite__Graph__EI, fact_110_order__subst1, fact_65_eq__refl
% 178.54/139.10 % No. of inferences in proof: 601
% 178.54/139.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 138745 ms resp. 137875 ms w/o parsing
% 179.50/139.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 179.50/139.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------