%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW470^2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.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 08:40:13 AM UTC 2026
% Result : Theorem 70.56s 16.11s
% Output : Refutation 64.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 632
% Syntax : Number of formulae : 1310 ( 576 unt; 0 typ; 0 def)
% Number of atoms : 6251 (1579 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 10718 ( 494 ~; 91 |; 267 &;8570 @)
% ( 0 <=>;1296 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 2277 (2277 >; 0 *; 0 +; 0 <<)
% Number of symbols : 103 ( 100 usr; 5 con; 0-4 aty)
% Number of variables : 3678 ( 280 ^;3308 !; 90 ?;3678 :)
% Comments :
%------------------------------------------------------------------------------
thf(x_a_type,type,
x_a: $tType ).
thf(com_type,type,
com: $tType ).
thf(glb_type,type,
glb: $tType ).
thf(loc_type,type,
loc: $tType ).
thf(state_type,type,
state: $tType ).
thf(vname_type,type,
vname: $tType ).
thf(hoare_1775062406iple_a_type,type,
hoare_1775062406iple_a: $tType ).
thf(hoare_1167836817_state_type,type,
hoare_1167836817_state: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(big_la43341705in_nat_decl,type,
big_la43341705in_nat: ( nat > $o ) > nat ).
thf(ass_decl,type,
ass: vname > ( state > nat ) > com ).
thf(local_decl,type,
local: loc > ( state > nat ) > com > com ).
thf(skip_decl,type,
skip: com ).
thf(semi_decl,type,
semi: com > com > com ).
thf(glb_1_decl,type,
glb_1: glb > vname ).
thf(loc_1_decl,type,
loc_1: loc > vname ).
thf(finite2064891473iple_a_decl,type,
finite2064891473iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > $o ).
thf(finite2120172977le_a_o_decl,type,
finite2120172977le_a_o: ( hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ) > $o ).
thf(finite856902323tate_o_decl,type,
finite856902323tate_o: ( hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > $o ).
thf(finite389864113_nat_o_decl,type,
finite389864113_nat_o: ( nat > ( nat > $o ) > nat > $o ) > $o ).
thf(finite_finite_nat_o_decl,type,
finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
thf(finite2063573081iple_a_decl,type,
finite2063573081iple_a: ( hoare_1775062406iple_a > $o ) > $o ).
thf(finite1084549118_state_decl,type,
finite1084549118_state: ( hoare_1167836817_state > $o ) > $o ).
thf(finite_finite_nat_decl,type,
finite_finite_nat: ( nat > $o ) > $o ).
thf(finite1946188886iple_a_decl,type,
finite1946188886iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(finite309220289_state_decl,type,
finite309220289_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(finite_fold1Set_nat_decl,type,
finite_fold1Set_nat: ( nat > nat > nat ) > ( nat > $o ) > nat > $o ).
thf(finite1790765286iple_a_decl,type,
finite1790765286iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ).
thf(finite1646097201_state_decl,type,
finite1646097201_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(finite_fold1_nat_decl,type,
finite_fold1_nat: ( nat > nat > nat ) > ( nat > $o ) > nat ).
thf(finite1544171829le_a_o_decl,type,
finite1544171829le_a_o: ( hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(finite1842721992iple_a_decl,type,
finite1842721992iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ).
thf(finite291020855tate_o_decl,type,
finite291020855tate_o: ( hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(finite1731015960_state_decl,type,
finite1731015960_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(finite326637109_nat_o_decl,type,
finite326637109_nat_o: ( nat > ( nat > $o ) > nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(finite_fold_nat_nat_decl,type,
finite_fold_nat_nat: ( nat > nat > nat ) > nat > ( nat > $o ) > nat ).
thf(finite727644230iple_a_decl,type,
finite727644230iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(finite2078349315iple_a_decl,type,
finite2078349315iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > ( ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ) > $o ).
thf(finite1074406356_state_decl,type,
finite1074406356_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
thf(finite988810631ne_nat_decl,type,
finite988810631ne_nat: ( nat > nat > nat ) > ( ( nat > $o ) > nat ) > $o ).
thf(finite1358382848iple_a_decl,type,
finite1358382848iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a ) > ( ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ) > $o ).
thf(minus_1944206118le_a_o_decl,type,
minus_1944206118le_a_o: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(minus_2107060239tate_o_decl,type,
minus_2107060239tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(minus_minus_nat_o_decl,type,
minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(the_Ho1155011127iple_a_decl,type,
the_Ho1155011127iple_a: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ).
thf(the_Ho310147232_state_decl,type,
the_Ho310147232_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(the_nat_decl,type,
the_nat: ( nat > $o ) > nat ).
thf(hoare_1508237396rivs_a_decl,type,
hoare_1508237396rivs_a: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > $o ).
thf(hoare_123228589_state_decl,type,
hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(hoare_1766022166iple_a_decl,type,
hoare_1766022166iple_a: ( x_a > state > $o ) > com > ( x_a > state > $o ) > hoare_1775062406iple_a ).
thf(hoare_908217195_state_decl,type,
hoare_908217195_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1167836817_state ).
thf(hoare_1462269968alid_a_decl,type,
hoare_1462269968alid_a: nat > hoare_1775062406iple_a > $o ).
thf(semila966743401le_a_o_decl,type,
semila966743401le_a_o: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(semila179895820tate_o_decl,type,
semila179895820tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(semila1947288293_nat_o_decl,type,
semila1947288293_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(semila854092349_inf_o_decl,type,
semila854092349_inf_o: $o > $o > $o ).
thf(semila13410563le_a_o_decl,type,
semila13410563le_a_o: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(semila1172322802tate_o_decl,type,
semila1172322802tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(semila848761471_nat_o_decl,type,
semila848761471_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(semila10642723_sup_o_decl,type,
semila10642723_sup_o: $o > $o > $o ).
thf(semila972727038up_nat_decl,type,
semila972727038up_nat: nat > nat > nat ).
thf(evalc_decl,type,
evalc: com > state > state > $o ).
thf(evaln_decl,type,
evaln: com > state > nat > state > $o ).
thf(getlocs_decl,type,
getlocs: state > loc > nat ).
thf(update_decl,type,
update: state > vname > nat > state ).
thf(bot_bot_nat_o_o_decl,type,
bot_bot_nat_o_o: ( nat > $o ) > $o ).
thf(bot_bo751897185le_a_o_decl,type,
bot_bo751897185le_a_o: hoare_1775062406iple_a > $o ).
thf(bot_bo70021908tate_o_decl,type,
bot_bo70021908tate_o: hoare_1167836817_state > $o ).
thf(bot_bot_nat_o_decl,type,
bot_bot_nat_o: nat > $o ).
thf(bot_bot_o_decl,type,
bot_bot_o: $o ).
thf(ord_le1143225901le_a_o_decl,type,
ord_le1143225901le_a_o: ( hoare_1775062406iple_a > $o ) > ( hoare_1775062406iple_a > $o ) > $o ).
thf(ord_le827224136tate_o_decl,type,
ord_le827224136tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(ord_less_eq_nat_o_decl,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(ord_less_eq_o_decl,type,
ord_less_eq_o: $o > $o > $o ).
thf(partia126998524iple_a_decl,type,
partia126998524iple_a: hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ).
thf(partia715677851_state_decl,type,
partia715677851_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(partial_flat_lub_nat_decl,type,
partial_flat_lub_nat: nat > ( nat > $o ) > nat ).
thf(collect_nat_o_decl,type,
collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(collec676402587iple_a_decl,type,
collec676402587iple_a: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(collec1027672124_state_decl,type,
collec1027672124_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(image_1170193413iple_a_decl,type,
image_1170193413iple_a: ( hoare_1775062406iple_a > hoare_1775062406iple_a ) > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(image_1021683026_state_decl,type,
image_1021683026_state: ( hoare_1775062406iple_a > hoare_1167836817_state ) > ( hoare_1775062406iple_a > $o ) > hoare_1167836817_state > $o ).
thf(image_1806517641_a_nat_decl,type,
image_1806517641_a_nat: ( hoare_1775062406iple_a > nat ) > ( hoare_1775062406iple_a > $o ) > nat > $o ).
thf(image_1802845250iple_a_decl,type,
image_1802845250iple_a: ( hoare_1167836817_state > hoare_1775062406iple_a ) > ( hoare_1167836817_state > $o ) > hoare_1775062406iple_a > $o ).
thf(image_31595733_state_decl,type,
image_31595733_state: ( hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(image_1476618182te_nat_decl,type,
image_1476618182te_nat: ( hoare_1167836817_state > nat ) > ( hoare_1167836817_state > $o ) > nat > $o ).
thf(image_43014529iple_a_decl,type,
image_43014529iple_a: ( nat > hoare_1775062406iple_a ) > ( nat > $o ) > hoare_1775062406iple_a > $o ).
thf(image_2121260246_state_decl,type,
image_2121260246_state: ( nat > hoare_1167836817_state ) > ( nat > $o ) > hoare_1167836817_state > $o ).
thf(image_nat_nat_decl,type,
image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
thf(insert_nat_o_decl,type,
insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
thf(insert1281456128iple_a_decl,type,
insert1281456128iple_a: hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a > $o ).
thf(insert2134838167_state_decl,type,
insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(insert_nat_decl,type,
insert_nat: nat > ( nat > $o ) > nat > $o ).
thf(the_el1844711461iple_a_decl,type,
the_el1844711461iple_a: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a ).
thf(the_el323660082_state_decl,type,
the_el323660082_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(the_elem_nat_decl,type,
the_elem_nat: ( nat > $o ) > nat ).
thf(fequal_nat_o_decl,type,
fequal_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(fequal1288209029iple_a_decl,type,
fequal1288209029iple_a: hoare_1775062406iple_a > hoare_1775062406iple_a > $o ).
thf(fequal1831255762_state_decl,type,
fequal1831255762_state: hoare_1167836817_state > hoare_1167836817_state > $o ).
thf(fequal_nat_decl,type,
fequal_nat: nat > nat > $o ).
thf(member2122167641iple_a_decl,type,
member2122167641iple_a: hoare_1775062406iple_a > ( hoare_1775062406iple_a > $o ) > $o ).
thf(member2058392318_state_decl,type,
member2058392318_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > $o ).
thf(member_nat_decl,type,
member_nat: nat > ( nat > $o ) > $o ).
thf(g_decl,type,
g: hoare_1775062406iple_a > $o ).
thf(p_decl,type,
p: x_a > state > $o ).
thf(b_decl,type,
b: state > $o ).
thf(c_decl,type,
c: com ).
thf(415,axiom,
! [A: nat,B: nat] :
( ( member_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_singleton__iff) ).
thf(2163,plain,
! [A: nat,B: nat] :
( ( member_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(292,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ! [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ B )
=> ( member2122167641iple_a @ C @ A ) )
=> ( ord_le1143225901le_a_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_subsetI) ).
thf(1665,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ! [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ B )
=> ( member2122167641iple_a @ C @ A ) )
=> ( ord_le1143225901le_a_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(548,axiom,
! [A: nat,B: hoare_1775062406iple_a > $o] :
( ( ( B = bot_bo751897185le_a_o )
=> ( ( image_1806517641_a_nat
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= bot_bot_nat_o ) )
& ( ( B != bot_bo751897185le_a_o )
=> ( ( image_1806517641_a_nat
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_image__constant__conv) ).
thf(2630,plain,
! [A: nat,B: hoare_1775062406iple_a > $o] :
( ( ( B = bot_bo751897185le_a_o )
=> ( ( image_1806517641_a_nat
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= bot_bot_nat_o ) )
& ( ( B != bot_bo751897185le_a_o )
=> ( ( image_1806517641_a_nat
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(228,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_insert__commute) ).
thf(1411,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(407,axiom,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_com_Osimps_I13_J) ).
thf(2131,plain,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(588,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
=> ~ ! [C: hoare_1775062406iple_a > $o] :
( ( B
= ( insert1281456128iple_a @ A @ C ) )
=> ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Set_Oset__insert) ).
thf(2778,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
=> ~ ! [C: hoare_1775062406iple_a > $o] :
( ( B
= ( insert1281456128iple_a @ A @ C ) )
=> ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(446,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( finite1790765286iple_a @ A @ B )
= ( the_Ho1155011127iple_a @ ( finite1946188886iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_fold1__def) ).
thf(2263,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( finite1790765286iple_a @ A @ B )
= ( the_Ho1155011127iple_a @ ( finite1946188886iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(269,axiom,
! [A: com,B: state,C: loc,D: state > nat,E: nat,F: state] :
( ( evaln @ A @ ( update @ B @ ( loc_1 @ C ) @ ( D @ B ) ) @ E @ F )
=> ( evaln @ ( local @ C @ D @ A ) @ B @ E @ ( update @ F @ ( loc_1 @ C ) @ ( getlocs @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_evaln_OLocal) ).
thf(1559,plain,
! [A: com,B: state,C: loc,D: state > nat,E: nat,F: state] :
( ( evaln @ A @ ( update @ B @ ( loc_1 @ C ) @ ( D @ B ) ) @ E @ F )
=> ( evaln @ ( local @ C @ D @ A ) @ B @ E @ ( update @ F @ ( loc_1 @ C ) @ ( getlocs @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(93,axiom,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( A @ B )
=> ( ! [C: nat,D: nat > $o] :
( ( finite_finite_nat @ D )
=> ( ( member_nat @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_minus_nat_o @ D @ ( insert_nat @ C @ bot_bot_nat_o ) ) ) ) ) )
=> ( A @ bot_bot_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_finite__empty__induct) ).
thf(909,plain,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( A @ B )
=> ( ! [C: nat,D: nat > $o] :
( ( finite_finite_nat @ D )
=> ( ( member_nat @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_minus_nat_o @ D @ ( insert_nat @ C @ bot_bot_nat_o ) ) ) ) ) )
=> ( A @ bot_bot_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(345,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( minus_1944206118le_a_o @ B @ C ) )
= ( ( member2122167641iple_a @ A @ B )
& ~ ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_Diff__iff) ).
thf(1899,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( minus_1944206118le_a_o @ B @ C ) )
= ( ( member2122167641iple_a @ A @ B )
& ~ ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(99,axiom,
! [A: nat > $o] :
( ( semila1947288293_nat_o @ bot_bot_nat_o @ A )
= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_inf__bot__left) ).
thf(941,plain,
! [A: nat > $o] :
( ( semila1947288293_nat_o @ bot_bot_nat_o @ A )
= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(468,axiom,
! [A: hoare_1167836817_state,B: hoare_1775062406iple_a > $o] :
( ( ( B = bot_bo751897185le_a_o )
=> ( ( image_1021683026_state
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= bot_bo70021908tate_o ) )
& ( ( B != bot_bo751897185le_a_o )
=> ( ( image_1021683026_state
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_image__constant__conv) ).
thf(2331,plain,
! [A: hoare_1167836817_state,B: hoare_1775062406iple_a > $o] :
( ( ( B = bot_bo751897185le_a_o )
=> ( ( image_1021683026_state
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= bot_bo70021908tate_o ) )
& ( ( B != bot_bo751897185le_a_o )
=> ( ( image_1021683026_state
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(580,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ( member2122167641iple_a @ B @ C )
=> ( ( minus_1944206118le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( minus_1944206118le_a_o @ A @ C ) ) )
& ( ~ ( member2122167641iple_a @ B @ C )
=> ( ( minus_1944206118le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( insert1281456128iple_a @ B @ ( minus_1944206118le_a_o @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_insert__Diff__if) ).
thf(2744,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ( member2122167641iple_a @ B @ C )
=> ( ( minus_1944206118le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( minus_1944206118le_a_o @ A @ C ) ) )
& ( ~ ( member2122167641iple_a @ B @ C )
=> ( ( minus_1944206118le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( insert1281456128iple_a @ B @ ( minus_1944206118le_a_o @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(164,axiom,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ E ) @ bot_bo70021908tate_o ) )
=> ( ! [F: state,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ D @ E ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_conseq1) ).
thf(1190,plain,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ E ) @ bot_bo70021908tate_o ) )
=> ( ! [F: state,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ D @ E ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(156,axiom,
! [A: nat > $o] :
( ( minus_minus_nat_o @ A @ bot_bot_nat_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_Diff__empty) ).
thf(1168,plain,
! [A: nat > $o] :
( ( minus_minus_nat_o @ A @ bot_bot_nat_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(45,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_nat_o @ ( insert_nat @ A @ B ) @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_insert__mono) ).
thf(760,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_nat_o @ ( insert_nat @ A @ B ) @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(202,axiom,
! [A: ( nat > $o ) > $o] :
( ( bot_bot_nat_o_o
= ( collect_nat_o @ A ) )
= ( ! [B: nat > $o] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_empty__Collect__eq) ).
thf(1315,plain,
! [A: ( nat > $o ) > $o] :
( ( bot_bot_nat_o_o
= ( collect_nat_o @ A ) )
= ( ! [B: nat > $o] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(538,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C = A )
| ( member2122167641iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_insert__compr__raw) ).
thf(2595,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C = A )
| ( member2122167641iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(333,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ ( collect_nat @ C ) ) )
= ( ( member_nat @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_Int__Collect) ).
thf(1850,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ ( collect_nat @ C ) ) )
= ( ( member_nat @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(496,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
=> ( ( insert1281456128iple_a @ A @ ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_insert__Diff) ).
thf(2427,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
=> ( ( insert1281456128iple_a @ A @ ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(366,axiom,
! [A: $o] :
( ( semila10642723_sup_o @ bot_bot_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_sup__bot__left) ).
thf(1978,plain,
! [A: $o] :
( ( semila10642723_sup_o @ bot_bot_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1981,plain,
( ( semila10642723_sup_o @ bot_bot_o @ $false )
= $false ),
inference(instance,[status(thm)],[1978]) ).
thf(1982,plain,
~ ( semila10642723_sup_o @ bot_bot_o @ $false ),
inference(simp,[status(thm)],[1981]) ).
thf(14,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ ( insert2134838167_state @ A @ B ) )
= ( finite1084549118_state @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_finite__insert) ).
thf(666,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ ( insert2134838167_state @ A @ B ) )
= ( finite1084549118_state @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(196,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1775062406iple_a,C: hoare_1167836817_state > hoare_1775062406iple_a,D: hoare_1167836817_state] :
( ( B
= ( C @ D ) )
=> ( ( member2058392318_state @ D @ A )
=> ( member2122167641iple_a @ B @ ( image_1802845250iple_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_image__eqI) ).
thf(1295,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1775062406iple_a,C: hoare_1167836817_state > hoare_1775062406iple_a,D: hoare_1167836817_state] :
( ( B
= ( C @ D ) )
=> ( ( member2058392318_state @ D @ A )
=> ( member2122167641iple_a @ B @ ( image_1802845250iple_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(171,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( finite_finite_nat @ A )
=> ( finite_finite_nat @ ( semila848761471_nat_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_finite__UnI) ).
thf(1211,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( finite_finite_nat @ A )
=> ( finite_finite_nat @ ( semila848761471_nat_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(46,axiom,
! [A: glb,B: glb] :
( ( ( glb_1 @ A )
= ( glb_1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_vname_Osimps_I1_J) ).
thf(762,plain,
! [A: glb,B: glb] :
( ( ( glb_1 @ A )
= ( glb_1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(598,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ord_le1143225901le_a_o @ B @ ( insert1281456128iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_subset__insertI2) ).
thf(2808,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ord_le1143225901le_a_o @ B @ ( insert1281456128iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(515,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( ( partia126998524iple_a @ B @ A )
= B ) )
& ( ~ ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( ( partia126998524iple_a @ B @ A )
= ( the_Ho1155011127iple_a
@ ^ [C: hoare_1775062406iple_a] : ( member2122167641iple_a @ C @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_flat__lub__def) ).
thf(2495,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( ( partia126998524iple_a @ B @ A )
= B ) )
& ( ~ ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( ( partia126998524iple_a @ B @ A )
= ( the_Ho1155011127iple_a
@ ^ [C: hoare_1775062406iple_a] : ( member2122167641iple_a @ C @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(237,axiom,
! [A: nat > $o] :
( ( ? [B: nat] : ( member_nat @ B @ A ) )
= ( A != bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_ex__in__conv) ).
thf(1443,plain,
! [A: nat > $o] :
( ( ? [B: nat] : ( member_nat @ B @ A ) )
= ( A != bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(280,axiom,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_bot__fun__def) ).
thf(1618,plain,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(536,axiom,
( bot_bo751897185le_a_o
= ( collec676402587iple_a
@ ^ [A: hoare_1775062406iple_a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_empty__def) ).
thf(2590,plain,
( bot_bo751897185le_a_o
= ( collec676402587iple_a
@ ^ [A: hoare_1775062406iple_a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(230,axiom,
! [A: nat > $o] :
( ( collect_nat_o
@ ^ [B: nat > $o] : ( B = A ) )
= ( insert_nat_o @ A @ bot_bot_nat_o_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_singleton__conv) ).
thf(1422,plain,
! [A: nat > $o] :
( ( collect_nat_o
@ ^ [B: nat > $o] : ( B = A ) )
= ( insert_nat_o @ A @ bot_bot_nat_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(306,axiom,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Collect__conv__if) ).
thf(1728,plain,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(235,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
!= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_insert__not__empty) ).
thf(1437,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
!= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(252,axiom,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_bot__apply) ).
thf(1486,plain,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(436,axiom,
! [A: nat,B: nat > $o] :
( ~ ( member_nat @ A @ B )
=> ( ( minus_minus_nat_o @ ( insert_nat @ A @ B ) @ ( insert_nat @ A @ bot_bot_nat_o ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_Diff__insert__absorb) ).
thf(2231,plain,
! [A: nat,B: nat > $o] :
( ~ ( member_nat @ A @ B )
=> ( ( minus_minus_nat_o @ ( insert_nat @ A @ B ) @ ( insert_nat @ A @ bot_bot_nat_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(545,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a] : ( finite727644230iple_a @ A @ B @ bot_bo751897185le_a_o @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_fold__graph_OemptyI) ).
thf(2622,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a] : ( finite727644230iple_a @ A @ B @ bot_bo751897185le_a_o @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(486,axiom,
! [A: hoare_1775062406iple_a > $o,B: x_a > state > $o] : ( hoare_1508237396rivs_a @ A @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ B @ skip @ B ) @ bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_hoare__derivs_OSkip) ).
thf(2395,plain,
! [A: hoare_1775062406iple_a > $o,B: x_a > state > $o] : ( hoare_1508237396rivs_a @ A @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ B @ skip @ B ) @ bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(389,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( collect_nat @ B ) )
= ( collect_nat
@ ^ [C: nat] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_insert__Collect) ).
thf(2062,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( collect_nat @ B ) )
= ( collect_nat
@ ^ [C: nat] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(557,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ bot_bo751897185le_a_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_sup__bot__left) ).
thf(2671,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ bot_bo751897185le_a_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(376,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( member2122167641iple_a @ B @ A )
=> ( member2122167641iple_a @ B @ ( semila966743401le_a_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_IntI) ).
thf(2014,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( member2122167641iple_a @ B @ A )
=> ( member2122167641iple_a @ B @ ( semila966743401le_a_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(81,axiom,
! [A: state > state > $o,B: com,C: state > state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( ( hoare_908217195_state @ A @ B @ C )
= ( hoare_908217195_state @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_triple_Oinject) ).
thf(873,plain,
! [A: state > state > $o,B: com,C: state > state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( ( hoare_908217195_state @ A @ B @ C )
= ( hoare_908217195_state @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(169,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ( A = bot_bo70021908tate_o )
& ( B = bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_Un__empty) ).
thf(1205,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ( A = bot_bo70021908tate_o )
& ( B = bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(603,axiom,
! [A: hoare_1775062406iple_a > $o] : ( ord_le1143225901le_a_o @ bot_bo751897185le_a_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_empty__subsetI) ).
thf(2837,plain,
! [A: hoare_1775062406iple_a > $o] : ( ord_le1143225901le_a_o @ bot_bo751897185le_a_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(188,axiom,
! [A: com,B: state,C: com,D: state,E: nat,F: state] :
( ( evaln @ C @ D @ E @ F )
=> ( ( evaln @ A @ F @ E @ B )
=> ( evaln @ ( semi @ C @ A ) @ D @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_evaln_OSemi) ).
thf(1269,plain,
! [A: com,B: state,C: com,D: state,E: nat,F: state] :
( ( evaln @ C @ D @ E @ F )
=> ( ( evaln @ A @ F @ E @ B )
=> ( evaln @ ( semi @ C @ A ) @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(83,axiom,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: com,D: state > state > $o,E: $o] :
( ( E
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ C @ D ) @ bot_bo70021908tate_o ) ) )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [F: state,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_constant) ).
thf(878,plain,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: com,D: state > state > $o,E: $o] :
( ( E
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ C @ D ) @ bot_bo70021908tate_o ) ) )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [F: state,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(482,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( insert1281456128iple_a @ B @ ( semila966743401le_a_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_Int__insert__left__if1) ).
thf(2380,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( insert1281456128iple_a @ B @ ( semila966743401le_a_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(425,axiom,
! [A: vname,B: state > nat,C: state,D: nat] : ( evaln @ ( ass @ A @ B ) @ C @ D @ ( update @ C @ A @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_evaln_OAssign) ).
thf(2195,plain,
! [A: vname,B: state > nat,C: state,D: nat] : ( evaln @ ( ass @ A @ B ) @ C @ D @ ( update @ C @ A @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(33,axiom,
! [A: nat > $o,B: nat > $o,C: nat] :
( ( semila848761471_nat_o
@ ^ [D: nat] : ( member_nat @ D @ A )
@ ^ [D: nat] : ( member_nat @ D @ B )
@ C )
= ( member_nat @ C @ ( semila848761471_nat_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_sup__Un__eq) ).
thf(715,plain,
! [A: nat > $o,B: nat > $o,C: nat] :
( ( semila848761471_nat_o
@ ^ [D: nat] : ( member_nat @ D @ A )
@ ^ [D: nat] : ( member_nat @ D @ B )
@ C )
= ( member_nat @ C @ ( semila848761471_nat_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(191,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( semila13410563le_a_o
@ ^ [D: hoare_1775062406iple_a] : ( member2122167641iple_a @ D @ A )
@ ^ [D: hoare_1775062406iple_a] : ( member2122167641iple_a @ D @ B )
@ C )
= ( member2122167641iple_a @ C @ ( semila13410563le_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_sup__Un__eq) ).
thf(1275,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( semila13410563le_a_o
@ ^ [D: hoare_1775062406iple_a] : ( member2122167641iple_a @ D @ A )
@ ^ [D: hoare_1775062406iple_a] : ( member2122167641iple_a @ D @ B )
@ C )
= ( member2122167641iple_a @ C @ ( semila13410563le_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(177,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( minus_minus_nat_o @ B @ C ) )
= ( ( member_nat @ A @ B )
& ~ ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_Diff__iff) ).
thf(1233,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( minus_minus_nat_o @ B @ C ) )
= ( ( member_nat @ A @ B )
& ~ ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(547,axiom,
! [A: nat > hoare_1775062406iple_a,B: nat > $o] :
( ( bot_bo751897185le_a_o
= ( image_43014529iple_a @ A @ B ) )
= ( B = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_empty__is__image) ).
thf(2627,plain,
! [A: nat > hoare_1775062406iple_a,B: nat > $o] :
( ( bot_bo751897185le_a_o
= ( image_43014529iple_a @ A @ B ) )
= ( B = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(506,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) ) )
= ( finite2063573081iple_a @ ( minus_1944206118le_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_finite__Diff__insert) ).
thf(2459,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) ) )
= ( finite2063573081iple_a @ ( minus_1944206118le_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(315,axiom,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ! [C: nat] : ( A @ ( insert_nat @ C @ bot_bot_nat_o ) )
=> ( ! [C: nat,D: nat > $o] :
( ( finite_finite_nat @ D )
=> ( ( D != bot_bot_nat_o )
=> ( ~ ( member_nat @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_nat @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_finite__ne__induct) ).
thf(1761,plain,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ! [C: nat] : ( A @ ( insert_nat @ C @ bot_bot_nat_o ) )
=> ( ! [C: nat,D: nat > $o] :
( ( finite_finite_nat @ D )
=> ( ( D != bot_bot_nat_o )
=> ( ~ ( member_nat @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_nat @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(287,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ B @ ( semila13410563le_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_UnI2) ).
thf(1640,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ B @ ( semila13410563le_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(619,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( minus_1944206118le_a_o @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_Diff__insert2) ).
thf(2901,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( minus_1944206118le_a_o @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(384,axiom,
! [A: hoare_1167836817_state] :
( ( collec1027672124_state
@ ^ [B: hoare_1167836817_state] : ( B = A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_singleton__conv) ).
thf(2042,plain,
! [A: hoare_1167836817_state] :
( ( collec1027672124_state
@ ^ [B: hoare_1167836817_state] : ( B = A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(410,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ A )
& ~ ( member2122167641iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_set__diff__eq) ).
thf(2146,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ A )
& ~ ( member2122167641iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(242,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ C )
=> ? [D: hoare_1775062406iple_a] : ( finite727644230iple_a @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_finite__imp__fold__graph) ).
thf(1458,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ C )
=> ? [D: hoare_1775062406iple_a] : ( finite727644230iple_a @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(531,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( insert1281456128iple_a @ B @ ( semila13410563le_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_Un__insert__right) ).
thf(2575,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( insert1281456128iple_a @ B @ ( semila13410563le_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(339,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ( collec1027672124_state @ A )
= bot_bo70021908tate_o )
= ( ! [B: hoare_1167836817_state] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__empty__eq) ).
thf(1867,plain,
! [A: hoare_1167836817_state > $o] :
( ( ( collec1027672124_state @ A )
= bot_bo70021908tate_o )
= ( ! [B: hoare_1167836817_state] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(422,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( member2122167641iple_a @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_folding__one__idem_Oin__idem) ).
thf(2184,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( member2122167641iple_a @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(371,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( minus_minus_nat_o @ A @ ( insert_nat @ B @ C ) )
= ( minus_minus_nat_o @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_Diff__insert2) ).
thf(1999,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( minus_minus_nat_o @ A @ ( insert_nat @ B @ C ) )
= ( minus_minus_nat_o @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(58,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > hoare_1167836817_state,C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( member2058392318_state @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2058392318_state @ A @ ( image_31595733_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_rev__image__eqI) ).
thf(797,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > hoare_1167836817_state,C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( member2058392318_state @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2058392318_state @ A @ ( image_31595733_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(463,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ B @ C ) )
=> ( ( A != B )
=> ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_insertE) ).
thf(2316,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ B @ C ) )
=> ( ( A != B )
=> ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(358,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( insert_nat @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_insert__absorb) ).
thf(1954,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( insert_nat @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(605,axiom,
( bot_bo70021908tate_o
= ( collec1027672124_state
@ ^ [A: hoare_1167836817_state] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_empty__def) ).
thf(2843,plain,
( bot_bo70021908tate_o
= ( collec1027672124_state
@ ^ [A: hoare_1167836817_state] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(2844,plain,
( ( collec1027672124_state
@ ^ [A: hoare_1167836817_state] : $false )
= bot_bo70021908tate_o ),
inference(lifteq,[status(thm)],[2843]) ).
thf(258,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_set__mp) ).
thf(1507,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(174,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ( A = bot_bo70021908tate_o )
& ( B = bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_sup__eq__bot__iff) ).
thf(1222,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ( A = bot_bo70021908tate_o )
& ( B = bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(166,axiom,
! [A: nat > $o] :
( ( semila848761471_nat_o @ bot_bot_nat_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_Un__empty__left) ).
thf(1196,plain,
! [A: nat > $o] :
( ( semila848761471_nat_o @ bot_bot_nat_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(431,axiom,
finite856902323tate_o @ insert2134838167_state,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_comp__fun__idem__insert) ).
thf(2216,plain,
finite856902323tate_o @ insert2134838167_state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(110,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( semila848761471_nat_o @ A @ B )
= bot_bot_nat_o )
= ( ( A = bot_bot_nat_o )
& ( B = bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_Un__empty) ).
thf(1001,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( semila848761471_nat_o @ A @ B )
= bot_bot_nat_o )
= ( ( A = bot_bot_nat_o )
& ( B = bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(31,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( semila848761471_nat_o @ B @ A ) )
= ( semila972727038up_nat @ ( big_la43341705in_nat @ B ) @ ( big_la43341705in_nat @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_Sup__fin_Ounion__idem) ).
thf(709,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( semila848761471_nat_o @ B @ A ) )
= ( semila972727038up_nat @ ( big_la43341705in_nat @ B ) @ ( big_la43341705in_nat @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(214,axiom,
! [A: nat] :
( ( big_la43341705in_nat @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_Sup__fin_Osingleton) ).
thf(1359,plain,
! [A: nat] :
( ( big_la43341705in_nat @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(276,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A @ C ) @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_Diff__insert) ).
thf(1601,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A @ C ) @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(488,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
!= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insert__not__empty) ).
thf(2400,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
!= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(184,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( image_1170193413iple_a @ B @ C ) )
= ( ? [D: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_image__iff) ).
thf(1254,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( image_1170193413iple_a @ B @ C ) )
= ( ? [D: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(68,axiom,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_empty__subsetI) ).
thf(829,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(133,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] : ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_subset__insertI) ).
thf(1095,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] : ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(144,axiom,
! [A: com,B: state,C: state] :
( ( evalc @ A @ B @ C )
= ( ? [D: nat] : ( evaln @ A @ B @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_eval__eq) ).
thf(1127,plain,
! [A: com,B: state,C: state] :
( ( evalc @ A @ B @ C )
= ( ? [D: nat] : ( evaln @ A @ B @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(583,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ~ ( member2122167641iple_a @ A @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_folding__one_Oinsert) ).
thf(2763,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ~ ( member2122167641iple_a @ A @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(53,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_Sup__fin_Oinsert) ).
thf(782,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(236,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_subsetD) ).
thf(1441,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(85,axiom,
! [A: nat,B: nat > $o,C: nat > nat > nat,D: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ C @ D )
=> ( ( finite_finite_nat @ B )
=> ( ( member_nat @ A @ B )
=> ( ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= bot_bot_nat_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
!= bot_bot_nat_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_folding__one_Oremove) ).
thf(885,plain,
! [A: nat,B: nat > $o,C: nat > nat > nat,D: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ C @ D )
=> ( ( finite_finite_nat @ B )
=> ( ( member_nat @ A @ B )
=> ( ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= bot_bot_nat_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
!= bot_bot_nat_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(123,axiom,
! [A: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ bot_bo70021908tate_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_Diff__empty) ).
thf(1046,plain,
! [A: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ bot_bo70021908tate_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(283,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ? [B: hoare_1167836817_state] : ( member2058392318_state @ B @ A ) )
= ( A != bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_ex__in__conv) ).
thf(1628,plain,
! [A: hoare_1167836817_state > $o] :
( ( ? [B: hoare_1167836817_state] : ( member2058392318_state @ B @ A ) )
= ( A != bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(126,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ bot_bo70021908tate_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_sup__bot__left) ).
thf(1055,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ bot_bo70021908tate_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(301,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila13410563le_a_o @ B @ C ) )
=> ( ~ ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_UnE) ).
thf(1709,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila13410563le_a_o @ B @ C ) )
=> ( ~ ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(467,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ bot_bo751897185le_a_o )
= ( A = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_bot__unique) ).
thf(2328,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ bot_bo751897185le_a_o )
= ( A = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(319,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ C ) )
= ( ( A = B )
| ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_insert__iff) ).
thf(1792,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ C ) )
= ( ( A = B )
| ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(54,axiom,
! [A: nat > $o] :
( ( minus_minus_nat_o @ bot_bot_nat_o @ A )
= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_empty__Diff) ).
thf(785,plain,
! [A: nat > $o] :
( ( minus_minus_nat_o @ bot_bot_nat_o @ A )
= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(432,axiom,
! [A: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ A )
= ( ( A = bot_bo70021908tate_o )
| ? [B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( A
= ( insert2134838167_state @ C @ B ) )
& ( finite1084549118_state @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_finite_Osimps) ).
thf(2217,plain,
! [A: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ A )
= ( ( A = bot_bo70021908tate_o )
| ? [B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( A
= ( insert2134838167_state @ C @ B ) )
& ( finite1084549118_state @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(561,axiom,
! [A: nat > hoare_1775062406iple_a] :
( ( image_43014529iple_a @ A @ bot_bot_nat_o )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_image__empty) ).
thf(2682,plain,
! [A: nat > hoare_1775062406iple_a] :
( ( image_43014529iple_a @ A @ bot_bot_nat_o )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(201,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ ( A @ B ) @ ( image_1170193413iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_imageI) ).
thf(1313,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ ( A @ B ) @ ( image_1170193413iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(527,axiom,
! [A: hoare_1775062406iple_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( image_43014529iple_a
@ ^ [D: nat] : A
@ C )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_image__constant) ).
thf(2562,plain,
! [A: hoare_1775062406iple_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( image_43014529iple_a
@ ^ [D: nat] : A
@ C )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(146,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ C ) )
= ( insert2134838167_state @ A @ ( semila179895820tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_insert__inter__insert) ).
thf(1132,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ C ) )
= ( insert2134838167_state @ A @ ( semila179895820tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(474,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_folding__one__idem_Oinsert__idem) ).
thf(2356,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(450,axiom,
! [A: nat,B: nat > $o,C: nat > nat > nat,D: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ C @ D )
=> ( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( D @ ( insert_nat @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_folding__one_Oinsert) ).
thf(2274,plain,
! [A: nat,B: nat > $o,C: nat > nat > nat,D: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ C @ D )
=> ( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( D @ ( insert_nat @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(28,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( hoare_123228589_state @ A @ B )
=> ( hoare_123228589_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_cut) ).
thf(702,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( hoare_123228589_state @ A @ B )
=> ( hoare_123228589_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(274,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_in__mono) ).
thf(1577,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(241,axiom,
! [A: nat > $o,B: nat > $o] :
( ( semila1947288293_nat_o @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_Int__def) ).
thf(1455,plain,
! [A: nat > $o,B: nat > $o] :
( ( semila1947288293_nat_o @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(4,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( semila848761471_nat_o @ B @ A )
= ( finite326637109_nat_o @ insert_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_union__fold__insert) ).
thf(638,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( semila848761471_nat_o @ B @ A )
= ( finite326637109_nat_o @ insert_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(151,axiom,
! [A: com,B: state,C: com,D: state,E: state] :
( ( evalc @ C @ D @ E )
=> ( ( evalc @ A @ E @ B )
=> ( evalc @ ( semi @ C @ A ) @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_evalc_OSemi) ).
thf(1147,plain,
! [A: com,B: state,C: com,D: state,E: state] :
( ( evalc @ C @ D @ E )
=> ( ( evalc @ A @ E @ B )
=> ( evalc @ ( semi @ C @ A ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(182,axiom,
! [A: nat,B: nat > nat > nat,C: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ B @ C )
=> ( ( C @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_folding__one_Osingleton) ).
thf(1247,plain,
! [A: nat,B: nat > nat > nat,C: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ B @ C )
=> ( ( C @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(80,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ C ) ) )
= ( finite1084549118_state @ ( minus_2107060239tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_finite__Diff__insert) ).
thf(870,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ C ) ) )
= ( finite1084549118_state @ ( minus_2107060239tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(249,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
=> ( ( hoare_123228589_state @ B @ A )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_hoare__derivs_Oinsert) ).
thf(1479,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
=> ( ( hoare_123228589_state @ B @ A )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(139,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_nat_o @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_subset__insertI2) ).
thf(1115,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ord_less_eq_nat_o @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(135,axiom,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
= ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_bot__unique) ).
thf(1100,plain,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
= ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(351,axiom,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_empty__iff) ).
thf(1922,plain,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(90,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ C ) )
=> ( member_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_IntD2) ).
thf(902,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ C ) )
=> ( member_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(479,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( insert1281456128iple_a @ B @ ( semila966743401le_a_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_Int__insert__right__if1) ).
thf(2373,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( insert1281456128iple_a @ B @ ( semila966743401le_a_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(273,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ? [C: hoare_1167836817_state > $o] :
( ( B
= ( insert2134838167_state @ A @ C ) )
& ~ ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_mk__disjoint__insert) ).
thf(1572,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ? [C: hoare_1167836817_state > $o] :
( ( B
= ( insert2134838167_state @ A @ C ) )
& ~ ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(522,axiom,
! [A: hoare_1775062406iple_a,B: nat > $o] :
( ( ( B = bot_bot_nat_o )
=> ( ( image_43014529iple_a
@ ^ [C: nat] : A
@ B )
= bot_bo751897185le_a_o ) )
& ( ( B != bot_bot_nat_o )
=> ( ( image_43014529iple_a
@ ^ [C: nat] : A
@ B )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_image__constant__conv) ).
thf(2520,plain,
! [A: hoare_1775062406iple_a,B: nat > $o] :
( ( ( B = bot_bot_nat_o )
=> ( ( image_43014529iple_a
@ ^ [C: nat] : A
@ B )
= bot_bo751897185le_a_o ) )
& ( ( B != bot_bot_nat_o )
=> ( ( image_43014529iple_a
@ ^ [C: nat] : A
@ B )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(577,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( ( ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= bot_bo751897185le_a_o )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= A ) )
& ( ( ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
!= bot_bo751897185le_a_o )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( C @ A @ ( D @ ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_folding__one_Oinsert__remove) ).
thf(2730,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( ( ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= bot_bo751897185le_a_o )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= A ) )
& ( ( ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
!= bot_bo751897185le_a_o )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( C @ A @ ( D @ ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(300,axiom,
! [A: $o,B: $o] :
( ( ( semila10642723_sup_o @ A @ B )
= bot_bot_o )
= ( ( A = bot_bot_o )
& ( B = bot_bot_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_sup__eq__bot__iff) ).
thf(1696,plain,
! [A: $o,B: $o] :
( ( ( semila10642723_sup_o @ A @ B )
= bot_bot_o )
= ( ( A = bot_bot_o )
& ( B = bot_bot_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(1701,plain,
( ( ( semila10642723_sup_o @ $false @ $true )
= bot_bot_o )
= ( ( $false = bot_bot_o )
& ( $true = bot_bot_o ) ) ),
inference(instance,[status(thm)],[1696]) ).
thf(1702,plain,
( ( semila10642723_sup_o @ $false @ $true )
!= bot_bot_o ),
inference(simp,[status(thm)],[1701]) ).
thf(1707,plain,
( ( semila10642723_sup_o @ $false @ $true )
!= bot_bot_o ),
inference(lifteq,[status(thm)],[1702]) ).
thf(2989,plain,
( ~ ( semila10642723_sup_o @ $false @ $true )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[1707]) ).
thf(215,axiom,
! [A: nat,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( image_1806517641_a_nat
@ ^ [D: hoare_1775062406iple_a] : A
@ C )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_image__constant) ).
thf(1362,plain,
! [A: nat,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( image_1806517641_a_nat
@ ^ [D: hoare_1775062406iple_a] : A
@ C )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(361,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
=> ( ( A != B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_insertE) ).
thf(1963,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
=> ( ( A != B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(505,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( semila966743401le_a_o @ A @ B )
= bot_bo751897185le_a_o )
=> ( ( minus_1944206118le_a_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_Diff__triv) ).
thf(2456,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( semila966743401le_a_o @ A @ B )
= bot_bo751897185le_a_o )
=> ( ( minus_1944206118le_a_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(543,axiom,
! [A: nat > hoare_1775062406iple_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( insert1281456128iple_a @ ( A @ B ) @ ( image_43014529iple_a @ A @ C ) )
= ( image_43014529iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_insert__image) ).
thf(2616,plain,
! [A: nat > hoare_1775062406iple_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( insert1281456128iple_a @ ( A @ B ) @ ( image_43014529iple_a @ A @ C ) )
= ( image_43014529iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(303,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( collec676402587iple_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Collect__def) ).
thf(1714,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( collec676402587iple_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(403,axiom,
! [A: hoare_1775062406iple_a > hoare_1167836817_state,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2058392318_state @ ( A @ B ) @ ( image_1021683026_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_imageI) ).
thf(2105,plain,
! [A: hoare_1775062406iple_a > hoare_1167836817_state,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2058392318_state @ ( A @ B ) @ ( image_1021683026_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(398,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_com_Osimps_I3_J) ).
thf(2090,plain,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(338,axiom,
! [A: nat,B: nat] :
( ( ( insert_nat @ A @ bot_bot_nat_o )
= ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_singleton__inject) ).
thf(1864,plain,
! [A: nat,B: nat] :
( ( ( insert_nat @ A @ bot_bot_nat_o )
= ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(116,axiom,
! [A: nat > $o] :
( ( semila1947288293_nat_o @ A @ bot_bot_nat_o )
= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_inf__bot__right) ).
thf(1020,plain,
! [A: nat > $o] :
( ( semila1947288293_nat_o @ A @ bot_bot_nat_o )
= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(360,axiom,
! [A: hoare_1167836817_state > $o] :
( ( A != bot_bo70021908tate_o )
= ( ? [B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( A
= ( insert2134838167_state @ B @ C ) )
& ~ ( member2058392318_state @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_nonempty__iff) ).
thf(1960,plain,
! [A: hoare_1167836817_state > $o] :
( ( A != bot_bo70021908tate_o )
= ( ? [B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( A
= ( insert2134838167_state @ B @ C ) )
& ~ ( member2058392318_state @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(66,axiom,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: com,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ? [G: state > state > $o,H: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ G @ C @ H ) @ bot_bo70021908tate_o ) )
& ! [I: state] :
( ! [J: state] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ C @ A ) @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_conseq) ).
thf(821,plain,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: com,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ? [G: state > state > $o,H: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ G @ C @ H ) @ bot_bo70021908tate_o ) )
& ! [I: state] :
( ! [J: state] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ C @ A ) @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(253,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,C: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ B @ C )
=> ( ( finite2063573081iple_a @ A )
=> ( ( C @ A )
= ( finite1790765286iple_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_folding__one_Oeq__fold) ).
thf(1489,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,C: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ B @ C )
=> ( ( finite2063573081iple_a @ A )
=> ( ( C @ A )
= ( finite1790765286iple_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(438,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ B @ C )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ! [D: hoare_1167836817_state,E: hoare_1167836817_state] : ( member2058392318_state @ ( B @ D @ E ) @ ( insert2134838167_state @ D @ ( insert2134838167_state @ E @ bot_bo70021908tate_o ) ) )
=> ( member2058392318_state @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_folding__one_Oclosed) ).
thf(2237,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ B @ C )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ! [D: hoare_1167836817_state,E: hoare_1167836817_state] : ( member2058392318_state @ ( B @ D @ E ) @ ( insert2134838167_state @ D @ ( insert2134838167_state @ E @ bot_bo70021908tate_o ) ) )
=> ( member2058392318_state @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(198,axiom,
! [A: vname,B: state > nat] :
( skip
!= ( ass @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_com_Osimps_I8_J) ).
thf(1302,plain,
! [A: vname,B: state > nat] :
( skip
!= ( ass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(593,axiom,
! [A: hoare_1775062406iple_a] :
( ( bot_bo751897185le_a_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_bot__apply) ).
thf(2794,plain,
! [A: hoare_1775062406iple_a] :
( ( bot_bo751897185le_a_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(122,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= A ) )
& ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
!= bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_folding__one_Oinsert__remove) ).
thf(1040,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= A ) )
& ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
!= bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(138,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( member2058392318_state @ A @ B )
=> ( ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= bot_bo70021908tate_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
!= bot_bo70021908tate_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_folding__one_Oremove) ).
thf(1109,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( member2058392318_state @ A @ B )
=> ( ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= bot_bo70021908tate_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
!= bot_bo70021908tate_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(161,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_insert__mono) ).
thf(1183,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(194,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( ( B = bot_bo70021908tate_o )
=> ( ( image_31595733_state
@ ^ [C: hoare_1167836817_state] : A
@ B )
= bot_bo70021908tate_o ) )
& ( ( B != bot_bo70021908tate_o )
=> ( ( image_31595733_state
@ ^ [C: hoare_1167836817_state] : A
@ B )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_image__constant__conv) ).
thf(1283,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( ( B = bot_bo70021908tate_o )
=> ( ( image_31595733_state
@ ^ [C: hoare_1167836817_state] : A
@ B )
= bot_bo70021908tate_o ) )
& ( ( B != bot_bo70021908tate_o )
=> ( ( image_31595733_state
@ ^ [C: hoare_1167836817_state] : A
@ B )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(518,axiom,
! [A: hoare_1775062406iple_a] :
( ( bot_bo751897185le_a_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_bot__fun__def) ).
thf(2508,plain,
! [A: hoare_1775062406iple_a] :
( ( bot_bo751897185le_a_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(331,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( minus_minus_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( minus_minus_nat_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_insert__Diff1) ).
thf(1843,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( minus_minus_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( minus_minus_nat_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(219,axiom,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_com_Osimps_I12_J) ).
thf(1377,plain,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1,conjecture,
( hoare_1508237396rivs_a @ g
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hoare_1508237396rivs_a @ g
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo751897185le_a_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(634,plain,
~ ( hoare_1508237396rivs_a @ g
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( finite309220289_state @ A @ B @ C )
=> ( B != bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_fold1Set__nonempty) ).
thf(956,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( finite309220289_state @ A @ B @ C )
=> ( B != bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(586,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( image_1170193413iple_a
@ ^ [D: hoare_1775062406iple_a] : A
@ C )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_image__constant) ).
thf(2772,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( image_1170193413iple_a
@ ^ [D: hoare_1775062406iple_a] : A
@ C )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(372,axiom,
! [A: $o] : ( ord_less_eq_o @ bot_bot_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_bot__least) ).
thf(2002,plain,
! [A: $o] : ( ord_less_eq_o @ bot_bot_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(75,axiom,
! [A: nat > $o,B: nat] :
( ( ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( ( partial_flat_lub_nat @ B @ A )
= B ) )
& ( ~ ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( ( partial_flat_lub_nat @ B @ A )
= ( the_nat
@ ^ [C: nat] : ( member_nat @ C @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_flat__lub__def) ).
thf(849,plain,
! [A: nat > $o,B: nat] :
( ( ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( ( partial_flat_lub_nat @ B @ A )
= B ) )
& ( ~ ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( ( partial_flat_lub_nat @ B @ A )
= ( the_nat
@ ^ [C: nat] : ( member_nat @ C @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(477,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ ( insert1281456128iple_a @ A @ B ) @ C )
= ( ( member2122167641iple_a @ A @ C )
& ( ord_le1143225901le_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_insert__subset) ).
thf(2367,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ ( insert1281456128iple_a @ A @ B ) @ C )
= ( ( member2122167641iple_a @ A @ C )
& ( ord_le1143225901le_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(353,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( semila179895820tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_Int__insert__right) ).
thf(1928,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( semila179895820tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(344,axiom,
! [A: nat] :
( ( collect_nat
@ ^ [B: nat] : ( B = A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_singleton__conv) ).
thf(1896,plain,
! [A: nat] :
( ( collect_nat
@ ^ [B: nat] : ( B = A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(424,axiom,
! [A: $o] :
( ( semila10642723_sup_o @ A @ bot_bot_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_sup__bot__right) ).
thf(2190,plain,
! [A: $o] :
( ( semila10642723_sup_o @ A @ bot_bot_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(454,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( finite2063573081iple_a @ ( collec676402587iple_a @ B ) )
| ( finite2063573081iple_a @ ( collec676402587iple_a @ A ) ) )
=> ( finite2063573081iple_a
@ ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_finite__Collect__conjI) ).
thf(2286,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( finite2063573081iple_a @ ( collec676402587iple_a @ B ) )
| ( finite2063573081iple_a @ ( collec676402587iple_a @ A ) ) )
=> ( finite2063573081iple_a
@ ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(549,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ A @ bot_bo751897185le_a_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_sup__bot__right) ).
thf(2639,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ A @ bot_bo751897185le_a_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(365,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ C ) )
=> ( ( A != B )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_insertE) ).
thf(1975,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ C ) )
=> ( ( A != B )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(271,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( semila179895820tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_Int__insert__left__if0) ).
thf(1564,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( semila179895820tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(277,axiom,
! [A: nat > $o,B: nat > $o] :
( ( semila848761471_nat_o @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
| ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_Un__def) ).
thf(1604,plain,
! [A: nat > $o,B: nat > $o] :
( ( semila848761471_nat_o @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
| ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(375,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( semila1172322802tate_o
@ ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] : ( C = A ) )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_insert__def) ).
thf(2011,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( semila1172322802tate_o
@ ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] : ( C = A ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(428,axiom,
! [A: $o] :
( ( semila854092349_inf_o @ bot_bot_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_inf__bot__left) ).
thf(2204,plain,
! [A: $o] :
( ( semila854092349_inf_o @ bot_bot_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(18,axiom,
! [A: nat > $o,B: nat > $o] :
( ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila848761471_nat_o @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_Collect__disj__eq) ).
thf(678,plain,
! [A: nat > $o,B: nat > $o] :
( ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila848761471_nat_o @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(298,axiom,
! [A: com,B: state > state > $o,C: hoare_1167836817_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ E @ F ) @ bot_bo70021908tate_o ) )
=> ( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ F @ A @ B ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ ( semi @ E @ A ) @ B ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_Comp) ).
thf(1691,plain,
! [A: com,B: state > state > $o,C: hoare_1167836817_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ E @ F ) @ bot_bo70021908tate_o ) )
=> ( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ F @ A @ B ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ ( semi @ E @ A ) @ B ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(12,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ B @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_subset__insertI2) ).
thf(661,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ B @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(551,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( insert1281456128iple_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_insert__code) ).
thf(2646,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( insert1281456128iple_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(199,axiom,
! [A: nat > $o] :
( ( ! [B: nat] :
~ ( member_nat @ B @ A ) )
= ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_all__not__in__conv) ).
thf(1306,plain,
! [A: nat > $o] :
( ( ! [B: nat] :
~ ( member_nat @ B @ A ) )
= ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(167,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ~ ( member_nat @ B @ C )
=> ( member_nat @ B @ A ) )
=> ( member_nat @ B @ ( semila848761471_nat_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_UnCI) ).
thf(1199,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ~ ( member_nat @ B @ C )
=> ( member_nat @ B @ A ) )
=> ( member_nat @ B @ ( semila848761471_nat_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(153,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_nat_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_rev__image__eqI) ).
thf(1153,plain,
! [A: nat,B: nat > nat,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_nat_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(62,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ? [C: hoare_1167836817_state] : ( finite309220289_state @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_finite__nonempty__imp__fold1Set) ).
thf(810,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ? [C: hoare_1167836817_state] : ( finite309220289_state @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(386,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( insert_nat @ A @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_insert__Diff) ).
thf(2047,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( insert_nat @ A @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(316,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_singleton__iff) ).
thf(1783,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(246,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( semila966743401le_a_o
@ ^ [D: hoare_1775062406iple_a] : ( member2122167641iple_a @ D @ A )
@ ^ [D: hoare_1775062406iple_a] : ( member2122167641iple_a @ D @ B )
@ C )
= ( member2122167641iple_a @ C @ ( semila966743401le_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_inf__Int__eq) ).
thf(1470,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( semila966743401le_a_o
@ ^ [D: hoare_1775062406iple_a] : ( member2122167641iple_a @ D @ A )
@ ^ [D: hoare_1775062406iple_a] : ( member2122167641iple_a @ D @ B )
@ C )
= ( member2122167641iple_a @ C @ ( semila966743401le_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(399,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ~ ( member2122167641iple_a @ B @ A )
=> ( member2122167641iple_a @ B @ ( minus_1944206118le_a_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_DiffI) ).
thf(2093,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ~ ( member2122167641iple_a @ B @ A )
=> ( member2122167641iple_a @ B @ ( minus_1944206118le_a_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(395,axiom,
! [A: hoare_1167836817_state > nat,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_1476618182te_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_imageI) ).
thf(2083,plain,
! [A: hoare_1167836817_state > nat,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_1476618182te_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(130,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_Sup__fin_Oinsert__idem) ).
thf(1067,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(307,axiom,
! [A: vname,B: state > nat,C: vname,D: state > nat] :
( ( ( ass @ A @ B )
= ( ass @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_com_Osimps_I1_J) ).
thf(1736,plain,
! [A: vname,B: state > nat,C: vname,D: state > nat] :
( ( ( ass @ A @ B )
= ( ass @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(222,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( insert2134838167_state @ A @ B ) @ C )
= ( ( member2058392318_state @ A @ C )
& ( ord_le827224136tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_insert__subset) ).
thf(1387,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( insert2134838167_state @ A @ B ) @ C )
= ( ( member2058392318_state @ A @ C )
& ( ord_le827224136tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(87,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( semila848761471_nat_o @ ( insert_nat @ A @ B ) @ C )
= ( insert_nat @ A @ ( semila848761471_nat_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_Un__insert__left) ).
thf(894,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( semila848761471_nat_o @ ( insert_nat @ A @ B ) @ C )
= ( insert_nat @ A @ ( semila848761471_nat_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(209,axiom,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_bot__fun__def) ).
thf(1343,plain,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(442,axiom,
! [A: nat > hoare_1167836817_state,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member2058392318_state @ ( A @ B ) @ ( image_2121260246_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_imageI) ).
thf(2249,plain,
! [A: nat > hoare_1167836817_state,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member2058392318_state @ ( A @ B ) @ ( image_2121260246_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(451,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] : ( member2058392318_state @ A @ ( insert2134838167_state @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_insertI1) ).
thf(2277,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] : ( member2058392318_state @ A @ ( insert2134838167_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(142,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
= ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_bot__unique) ).
thf(1123,plain,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
= ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(64,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( image_31595733_state @ B @ C ) )
= ( ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_image__iff) ).
thf(815,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( image_31595733_state @ B @ C ) )
= ( ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(569,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ~ ( member2122167641iple_a @ B @ C )
=> ( B = A ) )
=> ( member2122167641iple_a @ B @ ( insert1281456128iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_insertCI) ).
thf(2705,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ~ ( member2122167641iple_a @ B @ C )
=> ( B = A ) )
=> ( member2122167641iple_a @ B @ ( insert1281456128iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(491,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( insert1281456128iple_a @ B @ ( semila966743401le_a_o @ C @ A ) ) ) )
& ( ~ ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( semila966743401le_a_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_Int__insert__right) ).
thf(2409,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( insert1281456128iple_a @ B @ ( semila966743401le_a_o @ C @ A ) ) ) )
& ( ~ ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( semila966743401le_a_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(256,axiom,
! [A: $o] :
( ( semila854092349_inf_o @ A @ bot_bot_o )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_inf__bot__right) ).
thf(1499,plain,
! [A: $o] :
( ( semila854092349_inf_o @ A @ bot_bot_o )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1500,plain,
( ( semila854092349_inf_o @ $true @ bot_bot_o )
= bot_bot_o ),
inference(instance,[status(thm)],[1499]) ).
thf(1502,plain,
( ( semila854092349_inf_o @ $true @ bot_bot_o )
= bot_bot_o ),
inference(lifteq,[status(thm)],[1500]) ).
thf(312,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = A )
| ( member2058392318_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_insert__compr) ).
thf(1751,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = A )
| ( member2058392318_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(327,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ? [C: hoare_1775062406iple_a] :
( ( B @ C )
& ! [D: hoare_1775062406iple_a] :
( ( B @ D )
=> ( D = C ) ) )
=> ( ( B @ A )
=> ( ( the_Ho1155011127iple_a @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_the1__equality) ).
thf(1824,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ? [C: hoare_1775062406iple_a] :
( ( B @ C )
& ! [D: hoare_1775062406iple_a] :
( ( B @ D )
=> ( D = C ) ) )
=> ( ( B @ A )
=> ( ( the_Ho1155011127iple_a @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(55,axiom,
! [A: nat > $o,B: nat > nat > nat,C: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ B @ C )
=> ( ( finite_finite_nat @ A )
=> ( ( C @ A )
= ( finite_fold1_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_folding__one_Oeq__fold) ).
thf(788,plain,
! [A: nat > $o,B: nat > nat > nat,C: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ B @ C )
=> ( ( finite_finite_nat @ A )
=> ( ( C @ A )
= ( finite_fold1_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(120,axiom,
! [A: nat,B: nat > $o,C: nat > nat > nat,D: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ C @ D )
=> ( ( finite_finite_nat @ B )
=> ( ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= bot_bot_nat_o )
=> ( ( D @ ( insert_nat @ A @ B ) )
= A ) )
& ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
!= bot_bot_nat_o )
=> ( ( D @ ( insert_nat @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_folding__one_Oinsert__remove) ).
thf(1032,plain,
! [A: nat,B: nat > $o,C: nat > nat > nat,D: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ C @ D )
=> ( ( finite_finite_nat @ B )
=> ( ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= bot_bot_nat_o )
=> ( ( D @ ( insert_nat @ A @ B ) )
= A ) )
& ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
!= bot_bot_nat_o )
=> ( ( D @ ( insert_nat @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(216,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_insertI2) ).
thf(1365,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(528,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ ( insert1281456128iple_a @ A @ B ) @ C )
= ( insert1281456128iple_a @ A @ ( semila13410563le_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_Un__insert__left) ).
thf(2565,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ ( insert1281456128iple_a @ A @ B ) @ C )
= ( insert1281456128iple_a @ A @ ( semila13410563le_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(268,axiom,
! [A: nat > $o,B: hoare_1775062406iple_a,C: nat > hoare_1775062406iple_a,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member2122167641iple_a @ B @ ( image_43014529iple_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_image__eqI) ).
thf(1555,plain,
! [A: nat > $o,B: hoare_1775062406iple_a,C: nat > hoare_1775062406iple_a,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member2122167641iple_a @ B @ ( image_43014529iple_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(420,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( semila1172322802tate_o @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_insert__is__Un) ).
thf(2179,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( semila1172322802tate_o @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(329,axiom,
! [A: nat > $o] :
( ( the_elem_nat @ A )
= ( the_nat
@ ^ [B: nat] :
( A
= ( insert_nat @ B @ bot_bot_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_the__elem__def) ).
thf(1836,plain,
! [A: nat > $o] :
( ( the_elem_nat @ A )
= ( the_nat
@ ^ [B: nat] :
( A
= ( insert_nat @ B @ bot_bot_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(44,axiom,
! [A: nat > nat > nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ? [C: nat] : ( finite_fold1Set_nat @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_finite__nonempty__imp__fold1Set) ).
thf(757,plain,
! [A: nat > nat > nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ? [C: nat] : ( finite_fold1Set_nat @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(585,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ ( insert1281456128iple_a @ A @ B ) )
= ( finite2063573081iple_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_finite__insert) ).
thf(2769,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ ( insert1281456128iple_a @ A @ B ) )
= ( finite2063573081iple_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(498,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
~ ( finite1946188886iple_a @ A @ bot_bo751897185le_a_o @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_empty__fold1SetE) ).
thf(2433,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
~ ( finite1946188886iple_a @ A @ bot_bo751897185le_a_o @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(510,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ C @ bot_bo751897185le_a_o ) )
=> ( ( hoare_1508237396rivs_a @ B @ A )
=> ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_hoare__derivs_Oinsert) ).
thf(2477,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ C @ bot_bo751897185le_a_o ) )
=> ( ( hoare_1508237396rivs_a @ B @ A )
=> ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(391,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
= ( ( A = B )
| ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_insert__iff) ).
thf(2068,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ A @ ( insert_nat @ B @ C ) )
= ( ( A = B )
| ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(282,axiom,
! [A: vname] :
( ! [B: glb] :
( A
!= ( glb_1 @ B ) )
=> ~ ! [B: loc] :
( A
!= ( loc_1 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_vname_Oexhaust) ).
thf(1624,plain,
! [A: vname] :
( ! [B: glb] :
( A
!= ( glb_1 @ B ) )
=> ~ ! [B: loc] :
( A
!= ( loc_1 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(427,axiom,
! [A: hoare_1167836817_state,B: nat > hoare_1167836817_state,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2058392318_state @ A @ ( image_2121260246_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_rev__image__eqI) ).
thf(2200,plain,
! [A: hoare_1167836817_state,B: nat > hoare_1167836817_state,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2058392318_state @ A @ ( image_2121260246_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(830,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
inference(cnf,[status(esa)],[829]) ).
thf(20,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ B )
| ( finite_finite_nat @ A ) )
=> ( finite_finite_nat @ ( semila1947288293_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_finite__Int) ).
thf(682,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ B )
| ( finite_finite_nat @ A ) )
=> ( finite_finite_nat @ ( semila1947288293_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(227,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( B = bot_bo70021908tate_o )
=> ~ ( member2058392318_state @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_equals0D) ).
thf(1407,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( B = bot_bo70021908tate_o )
=> ~ ( member2058392318_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(285,axiom,
! [A: nat > $o] :
( ( A != bot_bot_nat_o )
= ( ? [B: nat,C: nat > $o] :
( ( A
= ( insert_nat @ B @ C ) )
& ~ ( member_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_nonempty__iff) ).
thf(1634,plain,
! [A: nat > $o] :
( ( A != bot_bot_nat_o )
= ( ? [B: nat,C: nat > $o] :
( ( A
= ( insert_nat @ B @ C ) )
& ~ ( member_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(435,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_insert__absorb2) ).
thf(2228,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(347,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state] :
( ( finite1646097201_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_fold1__singleton) ).
thf(1910,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state] :
( ( finite1646097201_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(73,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ ( insert_nat @ A @ B ) )
= ( finite_finite_nat @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_finite__insert) ).
thf(842,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ ( insert_nat @ A @ B ) )
= ( finite_finite_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(553,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( ( B = bot_bo751897185le_a_o )
=> ( ( image_1170193413iple_a
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= bot_bo751897185le_a_o ) )
& ( ( B != bot_bo751897185le_a_o )
=> ( ( image_1170193413iple_a
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_image__constant__conv) ).
thf(2653,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( ( B = bot_bo751897185le_a_o )
=> ( ( image_1170193413iple_a
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= bot_bo751897185le_a_o ) )
& ( ( B != bot_bo751897185le_a_o )
=> ( ( image_1170193413iple_a
@ ^ [C: hoare_1775062406iple_a] : A
@ B )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(137,axiom,
! [A: nat,B: nat > nat,C: nat > $o] :
( ( member_nat @ A @ ( image_nat_nat @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_image__iff) ).
thf(1106,plain,
! [A: nat,B: nat > nat,C: nat > $o] :
( ( member_nat @ A @ ( image_nat_nat @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(354,axiom,
! [A: loc,B: state > nat,C: com,D: state,E: state] :
( ( evalc @ ( local @ A @ B @ C ) @ D @ E )
=> ~ ! [F: state] :
( ( E
= ( update @ F @ ( loc_1 @ A ) @ ( getlocs @ D @ A ) ) )
=> ~ ( evalc @ C @ ( update @ D @ ( loc_1 @ A ) @ ( B @ D ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_evalc__elim__cases_I3_J) ).
thf(1936,plain,
! [A: loc,B: state > nat,C: com,D: state,E: state] :
( ( evalc @ ( local @ A @ B @ C ) @ D @ E )
=> ~ ! [F: state] :
( ( E
= ( update @ F @ ( loc_1 @ A ) @ ( getlocs @ D @ A ) ) )
=> ~ ( evalc @ C @ ( update @ D @ ( loc_1 @ A ) @ ( B @ D ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(25,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_set__mp) ).
thf(697,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(367,axiom,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_emptyE) ).
thf(1983,plain,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(186,axiom,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( ( A @ B )
=> ( ( collect_nat_o
@ ^ [C: nat > $o] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_nat_o @ B @ bot_bot_nat_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat_o
@ ^ [C: nat > $o] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_nat_o_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Collect__conv__if) ).
thf(1259,plain,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( ( A @ B )
=> ( ( collect_nat_o
@ ^ [C: nat > $o] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_nat_o @ B @ bot_bot_nat_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat_o
@ ^ [C: nat > $o] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_nat_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(8,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( finite_fold_nat_nat @ semila972727038up_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_Sup__fin_Oeq__fold_H) ).
thf(650,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( finite_fold_nat_nat @ semila972727038up_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(322,axiom,
! [A: ( nat > $o ) > $o] :
( ( ( collect_nat_o @ A )
= bot_bot_nat_o_o )
= ( ! [B: nat > $o] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Collect__empty__eq) ).
thf(1804,plain,
! [A: ( nat > $o ) > $o] :
( ( ( collect_nat_o @ A )
= bot_bot_nat_o_o )
= ( ! [B: nat > $o] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(617,axiom,
! [A: hoare_1167836817_state > hoare_1775062406iple_a] :
( ( image_1802845250iple_a @ A @ bot_bo70021908tate_o )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_image__empty) ).
thf(2895,plain,
! [A: hoare_1167836817_state > hoare_1775062406iple_a] :
( ( image_1802845250iple_a @ A @ bot_bo70021908tate_o )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(475,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( member2122167641iple_a @ A @ B )
=> ( ( ( ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= bot_bo751897185le_a_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
!= bot_bo751897185le_a_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_folding__one_Oremove) ).
thf(2359,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( member2122167641iple_a @ A @ B )
=> ( ( ( ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= bot_bo751897185le_a_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
!= bot_bo751897185le_a_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(129,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ C ) )
= ( ( ( member_nat @ B @ A )
=> ( ord_less_eq_nat_o @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) ) @ C ) )
& ( ~ ( member_nat @ B @ A )
=> ( ord_less_eq_nat_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_subset__insert__iff) ).
thf(1064,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ C ) )
= ( ( ( member_nat @ B @ A )
=> ( ord_less_eq_nat_o @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) ) @ C ) )
& ( ~ ( member_nat @ B @ A )
=> ( ord_less_eq_nat_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(176,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( member_nat @ A @ B )
=> ( ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ B )
= A ) )
& ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
!= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ B )
= ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_Sup__fin_Oremove) ).
thf(1227,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( member_nat @ A @ B )
=> ( ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ B )
= A ) )
& ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
!= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ B )
= ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(335,axiom,
! [A: hoare_1167836817_state] :
( ( collec1027672124_state @ ( fequal1831255762_state @ A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_singleton__conv2) ).
thf(1856,plain,
! [A: hoare_1167836817_state] :
( ( collec1027672124_state @ ( fequal1831255762_state @ A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(231,axiom,
! [A: hoare_1775062406iple_a] :
( ( the_Ho1155011127iple_a
@ ^ [B: hoare_1775062406iple_a] : ( B = A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_the__eq__trivial) ).
thf(1425,plain,
! [A: hoare_1775062406iple_a] :
( ( the_Ho1155011127iple_a
@ ^ [B: hoare_1775062406iple_a] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(294,axiom,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_nat_o )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__empty__eq) ).
thf(1672,plain,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_nat_o )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(265,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ A )
& ( member2122167641iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_Int__def) ).
thf(1540,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ A )
& ( member2122167641iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(575,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ A @ bot_bo751897185le_a_o )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_inf__bot__right) ).
thf(2724,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ A @ bot_bo751897185le_a_o )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(448,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( collec1027672124_state @ B ) )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_insert__Collect) ).
thf(2268,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( collec1027672124_state @ B ) )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(76,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila848761471_nat_o @ B @ C ) )
= ( ( member_nat @ A @ B )
| ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_Un__iff) ).
thf(857,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila848761471_nat_o @ B @ C ) )
= ( ( member_nat @ A @ B )
| ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(115,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_inf__bot__left) ).
thf(1017,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(562,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] : ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_insertI1) ).
thf(2685,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] : ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(272,axiom,
! [A: loc,B: state > nat,C: com,D: state,E: nat,F: state] :
( ( evaln @ ( local @ A @ B @ C ) @ D @ E @ F )
=> ~ ! [G: state] :
( ( F
= ( update @ G @ ( loc_1 @ A ) @ ( getlocs @ D @ A ) ) )
=> ~ ( evaln @ C @ ( update @ D @ ( loc_1 @ A ) @ ( B @ D ) ) @ E @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_evaln__elim__cases_I3_J) ).
thf(1567,plain,
! [A: loc,B: state > nat,C: com,D: state,E: nat,F: state] :
( ( evaln @ ( local @ A @ B @ C ) @ D @ E @ F )
=> ~ ! [G: state] :
( ( F
= ( update @ G @ ( loc_1 @ A ) @ ( getlocs @ D @ A ) ) )
=> ~ ( evaln @ C @ ( update @ D @ ( loc_1 @ A ) @ ( B @ D ) ) @ E @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(119,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( A != B )
| ( fequal1831255762_state @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com) ).
thf(1028,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( A != B )
| ( fequal1831255762_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(42,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ B @ ( semila848761471_nat_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_UnI2) ).
thf(753,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ B @ ( semila848761471_nat_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(308,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( C = A )
| ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_insert__compr__raw) ).
thf(1739,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( C = A )
| ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(15,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ~ ( member2058392318_state @ A @ B )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( finite1731015960_state @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_folding__one_Oeq__fold_H) ).
thf(669,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ~ ( member2058392318_state @ A @ B )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( finite1731015960_state @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(613,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] : ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_subset__insertI) ).
thf(2868,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] : ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(3,axiom,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( ( big_la43341705in_nat @ A )
= ( finite_fold1_nat @ semila972727038up_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_Sup__fin_OF__eq) ).
thf(635,plain,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( ( big_la43341705in_nat @ A )
= ( finite_fold1_nat @ semila972727038up_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(636,plain,
! [A: nat > $o] :
( ~ ( finite_finite_nat @ A )
| ( ( big_la43341705in_nat @ A )
= ( finite_fold1_nat @ semila972727038up_nat @ A ) ) ),
inference(cnf,[status(esa)],[635]) ).
thf(637,plain,
! [A: nat > $o] :
( ( ( finite_fold1_nat @ semila972727038up_nat @ A )
= ( big_la43341705in_nat @ A ) )
| ~ ( finite_finite_nat @ A ) ),
inference(lifteq,[status(thm)],[636]) ).
thf(324,axiom,
! [A: hoare_1167836817_state,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( image_1021683026_state
@ ^ [D: hoare_1775062406iple_a] : A
@ C )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_image__constant) ).
thf(1810,plain,
! [A: hoare_1167836817_state,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( image_1021683026_state
@ ^ [D: hoare_1775062406iple_a] : A
@ C )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(472,axiom,
! [A: hoare_1775062406iple_a] :
~ ! [B: x_a > state > $o,C: com,D: x_a > state > $o] :
( A
!= ( hoare_1766022166iple_a @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_triple_Oexhaust) ).
thf(2349,plain,
! [A: hoare_1775062406iple_a] :
~ ! [B: x_a > state > $o,C: com,D: x_a > state > $o] :
( A
!= ( hoare_1766022166iple_a @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(238,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1167836817_state > hoare_1775062406iple_a,C: hoare_1167836817_state > $o] :
( ( member2122167641iple_a @ A @ ( image_1802845250iple_a @ B @ C ) )
= ( ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_image__iff) ).
thf(1446,plain,
! [A: hoare_1775062406iple_a,B: hoare_1167836817_state > hoare_1775062406iple_a,C: hoare_1167836817_state > $o] :
( ( member2122167641iple_a @ A @ ( image_1802845250iple_a @ B @ C ) )
= ( ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(552,axiom,
! [A: hoare_1775062406iple_a > $o,B: com,C: x_a > state > $o,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ( hoare_1508237396rivs_a @ A
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [G: x_a,H: state] : ( H = F )
@ B
@ ^ [G: x_a] : ( C @ E ) )
@ bot_bo751897185le_a_o ) ) )
=> ( hoare_1508237396rivs_a @ A @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ B @ C ) @ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_escape) ).
thf(2649,plain,
! [A: hoare_1775062406iple_a > $o,B: com,C: x_a > state > $o,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ( hoare_1508237396rivs_a @ A
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [G: x_a,H: state] : ( H = F )
@ B
@ ^ [G: x_a] : ( C @ E ) )
@ bot_bo751897185le_a_o ) ) )
=> ( hoare_1508237396rivs_a @ A @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ B @ C ) @ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(30,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state] :
~ ( finite309220289_state @ A @ bot_bo70021908tate_o @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_empty__fold1SetE) ).
thf(706,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state] :
~ ( finite309220289_state @ A @ bot_bo70021908tate_o @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(195,axiom,
! [A: nat] :
( ( collect_nat @ ( fequal_nat @ A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_singleton__conv2) ).
thf(1292,plain,
! [A: nat] :
( ( collect_nat @ ( fequal_nat @ A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(96,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
= ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_subset__empty) ).
thf(933,plain,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
= ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(21,axiom,
! [A: nat > $o] :
( ( minus_minus_nat_o @ A @ A )
= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_Diff__cancel) ).
thf(686,plain,
! [A: nat > $o] :
( ( minus_minus_nat_o @ A @ A )
= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(493,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ bot_bo751897185le_a_o )
= ( A = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_subset__empty) ).
thf(2419,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ bot_bo751897185le_a_o )
= ( A = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(229,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ( member_nat @ B @ C )
=> ( ( minus_minus_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( minus_minus_nat_o @ A @ C ) ) )
& ( ~ ( member_nat @ B @ C )
=> ( ( minus_minus_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( insert_nat @ B @ ( minus_minus_nat_o @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_insert__Diff__if) ).
thf(1414,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ( member_nat @ B @ C )
=> ( ( minus_minus_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( minus_minus_nat_o @ A @ C ) ) )
& ( ~ ( member_nat @ B @ C )
=> ( ( minus_minus_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( insert_nat @ B @ ( minus_minus_nat_o @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(439,axiom,
! [A: nat,B: nat > $o,C: nat] :
( ( insert_nat @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_insert__code) ).
thf(2240,plain,
! [A: nat,B: nat > $o,C: nat] :
( ( insert_nat @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(524,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ A )
= ( ( A = bot_bo751897185le_a_o )
| ? [B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( A
= ( insert1281456128iple_a @ C @ B ) )
& ( finite2063573081iple_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_finite_Osimps) ).
thf(2551,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ A )
= ( ( A = bot_bo751897185le_a_o )
| ? [B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( A
= ( insert1281456128iple_a @ C @ B ) )
& ( finite2063573081iple_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(396,axiom,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_bot__apply) ).
thf(2085,plain,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(7,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( finite_fold_nat_nat @ semila972727038up_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_Sup__fin_Oeq__fold__idem_H) ).
thf(647,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( finite_fold_nat_nat @ semila972727038up_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
( finite856902323tate_o
@ ^ [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] : ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_comp__fun__idem__remove) ).
thf(701,plain,
( finite856902323tate_o
@ ^ [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] : ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(440,axiom,
! [A: state,B: nat,C: state] :
( ( evaln @ skip @ A @ B @ C )
=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_evaln__elim__cases_I1_J) ).
thf(2243,plain,
! [A: state,B: nat,C: state] :
( ( evaln @ skip @ A @ B @ C )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(35,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila848761471_nat_o @ B @ C ) )
=> ( ~ ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_UnE) ).
thf(721,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila848761471_nat_o @ B @ C ) )
=> ( ~ ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(357,axiom,
! [A: $o] :
( ( ord_less_eq_o @ A @ bot_bot_o )
= ( A = bot_bot_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_bot__unique) ).
thf(1947,plain,
! [A: $o] :
( ( ord_less_eq_o @ A @ bot_bot_o )
= ( A = bot_bot_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(600,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( ( ( member2122167641iple_a @ B @ A )
=> ( ord_le1143225901le_a_o @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) @ C ) )
& ( ~ ( member2122167641iple_a @ B @ A )
=> ( ord_le1143225901le_a_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_subset__insert__iff) ).
thf(2813,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( ( ( member2122167641iple_a @ B @ A )
=> ( ord_le1143225901le_a_o @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) @ C ) )
& ( ~ ( member2122167641iple_a @ B @ A )
=> ( ord_le1143225901le_a_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(584,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ ( insert1281456128iple_a @ A @ B ) @ ( insert1281456128iple_a @ A @ C ) )
= ( insert1281456128iple_a @ A @ ( semila966743401le_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_insert__inter__insert) ).
thf(2766,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ ( insert1281456128iple_a @ A @ B ) @ ( insert1281456128iple_a @ A @ C ) )
= ( insert1281456128iple_a @ A @ ( semila966743401le_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(52,axiom,
! [A: nat > $o] :
( ( semila848761471_nat_o @ A @ bot_bot_nat_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_sup__bot__right) ).
thf(779,plain,
! [A: nat > $o] :
( ( semila848761471_nat_o @ A @ bot_bot_nat_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(224,axiom,
! [A: nat] :
( ( the_elem_nat @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_the__elem__eq) ).
thf(1393,plain,
! [A: nat] :
( ( the_elem_nat @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(478,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ A @ bot_bo751897185le_a_o )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_Int__empty__right) ).
thf(2370,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ A @ bot_bo751897185le_a_o )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(503,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_singleton__iff) ).
thf(2450,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(405,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( insert2134838167_state @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_insert__code) ).
thf(2125,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( insert2134838167_state @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(513,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( minus_1944206118le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( minus_1944206118le_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_insert__Diff1) ).
thf(2487,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( minus_1944206118le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( minus_1944206118le_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(606,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ D @ E )
=> ( ( finite727644230iple_a @ A @ B @ E @ C )
=> ( finite727644230iple_a @ A @ B @ ( insert1281456128iple_a @ D @ E ) @ ( A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_fold__graph_OinsertI) ).
thf(2845,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ D @ E )
=> ( ( finite727644230iple_a @ A @ B @ E @ C )
=> ( finite727644230iple_a @ A @ B @ ( insert1281456128iple_a @ D @ E ) @ ( A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(539,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( bot_bo751897185le_a_o
!= ( insert1281456128iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_empty__not__insert) ).
thf(2598,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( bot_bo751897185le_a_o
!= ( insert1281456128iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(533,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( bot_bo751897185le_a_o
= ( collec676402587iple_a @ A ) )
= ( ! [B: hoare_1775062406iple_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_empty__Collect__eq) ).
thf(2581,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( bot_bo751897185le_a_o
= ( collec676402587iple_a @ A ) )
= ( ! [B: hoare_1775062406iple_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(508,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1167836817_state > $o] :
( ( ( B = bot_bo70021908tate_o )
=> ( ( image_1802845250iple_a
@ ^ [C: hoare_1167836817_state] : A
@ B )
= bot_bo751897185le_a_o ) )
& ( ( B != bot_bo70021908tate_o )
=> ( ( image_1802845250iple_a
@ ^ [C: hoare_1167836817_state] : A
@ B )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_image__constant__conv) ).
thf(2465,plain,
! [A: hoare_1775062406iple_a,B: hoare_1167836817_state > $o] :
( ( ( B = bot_bo70021908tate_o )
=> ( ( image_1802845250iple_a
@ ^ [C: hoare_1167836817_state] : A
@ B )
= bot_bo751897185le_a_o ) )
& ( ( B != bot_bo70021908tate_o )
=> ( ( image_1802845250iple_a
@ ^ [C: hoare_1167836817_state] : A
@ B )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(234,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o
@ ^ [C: hoare_1775062406iple_a] : ( member2122167641iple_a @ C @ A )
@ ^ [C: hoare_1775062406iple_a] : ( member2122167641iple_a @ C @ B ) )
= ( ord_le1143225901le_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_pred__subset__eq) ).
thf(1434,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o
@ ^ [C: hoare_1775062406iple_a] : ( member2122167641iple_a @ C @ A )
@ ^ [C: hoare_1775062406iple_a] : ( member2122167641iple_a @ C @ B ) )
= ( ord_le1143225901le_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(203,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( semila1947288293_nat_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_Int__insert__left__if0) ).
thf(1318,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( semila1947288293_nat_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(626,axiom,
( finite2120172977le_a_o
@ ^ [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] : ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_comp__fun__idem__remove) ).
thf(2926,plain,
( finite2120172977le_a_o
@ ^ [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] : ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(98,axiom,
! [A: nat > $o,B: nat > $o] :
( ~ ( fequal_nat_o @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T) ).
thf(938,plain,
! [A: nat > $o,B: nat > $o] :
( ~ ( fequal_nat_o @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(2206,plain,
( ( semila854092349_inf_o @ bot_bot_o @ $false )
= bot_bot_o ),
inference(instance,[status(thm)],[2204]) ).
thf(2208,plain,
( ( semila854092349_inf_o @ bot_bot_o @ $false )
= bot_bot_o ),
inference(lifteq,[status(thm)],[2206]) ).
thf(622,axiom,
! [A: hoare_1775062406iple_a] :
( ( collec676402587iple_a @ ( fequal1288209029iple_a @ A ) )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_singleton__conv2) ).
thf(2909,plain,
! [A: hoare_1775062406iple_a] :
( ( collec676402587iple_a @ ( fequal1288209029iple_a @ A ) )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(180,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( finite_finite_nat @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ C ) ) )
= ( finite_finite_nat @ ( minus_minus_nat_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_finite__Diff__insert) ).
thf(1241,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( finite_finite_nat @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ C ) ) )
= ( finite_finite_nat @ ( minus_minus_nat_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(568,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ A @ bot_bo751897185le_a_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_Un__empty__right) ).
thf(2702,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ A @ bot_bo751897185le_a_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(47,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ ( semila848761471_nat_o @ A @ B ) )
= ( ( finite_finite_nat @ A )
& ( finite_finite_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_finite__Un) ).
thf(765,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ ( semila848761471_nat_o @ A @ B ) )
= ( ( finite_finite_nat @ A )
& ( finite_finite_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(332,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > hoare_1775062406iple_a,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2122167641iple_a @ A @ ( image_1170193413iple_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_rev__image__eqI) ).
thf(1846,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > hoare_1775062406iple_a,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2122167641iple_a @ A @ ( image_1170193413iple_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(554,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ bot_bo751897185le_a_o )
=> ( A = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_le__bot) ).
thf(2662,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ bot_bo751897185le_a_o )
=> ( A = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(162,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ( ( semila1947288293_nat_o @ B @ A )
= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( semila848761471_nat_o @ B @ A ) )
= ( semila972727038up_nat @ ( big_la43341705in_nat @ B ) @ ( big_la43341705in_nat @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_Sup__fin_Ounion__disjoint) ).
thf(1185,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( B != bot_bot_nat_o )
=> ( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ( ( semila1947288293_nat_o @ B @ A )
= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( semila848761471_nat_o @ B @ A ) )
= ( semila972727038up_nat @ ( big_la43341705in_nat @ B ) @ ( big_la43341705in_nat @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(50,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_rev__finite__subset) ).
thf(773,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(57,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( finite_finite_nat @ ( minus_minus_nat_o @ A @ B ) )
= ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_finite__Diff2) ).
thf(794,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( finite_finite_nat @ ( minus_minus_nat_o @ A @ B ) )
= ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(523,axiom,
! [A: ( hoare_1775062406iple_a > $o ) > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ C )
=> ( ( ord_le1143225901le_a_o @ C @ B )
=> ( ( A @ bot_bo751897185le_a_o )
=> ( ! [D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ E )
=> ( ( member2122167641iple_a @ D @ B )
=> ( ~ ( member2122167641iple_a @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert1281456128iple_a @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_finite__subset__induct) ).
thf(2529,plain,
! [A: ( hoare_1775062406iple_a > $o ) > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ C )
=> ( ( ord_le1143225901le_a_o @ C @ B )
=> ( ( A @ bot_bo751897185le_a_o )
=> ( ! [D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ E )
=> ( ( member2122167641iple_a @ D @ B )
=> ( ~ ( member2122167641iple_a @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert1281456128iple_a @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(34,axiom,
! [A: nat > $o] :
( ( semila1947288293_nat_o @ bot_bot_nat_o @ A )
= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_Int__empty__left) ).
thf(718,plain,
! [A: nat > $o] :
( ( semila1947288293_nat_o @ bot_bot_nat_o @ A )
= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(92,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o
@ ^ [C: nat] : ( member_nat @ C @ A )
@ ^ [C: nat] : ( member_nat @ C @ B ) )
= ( ord_less_eq_nat_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_pred__subset__eq) ).
thf(906,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o
@ ^ [C: nat] : ( member_nat @ C @ A )
@ ^ [C: nat] : ( member_nat @ C @ B ) )
= ( ord_less_eq_nat_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(192,axiom,
! [A: state > nat,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o,F: loc,G: state] :
( ( hoare_123228589_state @ B
@ ( insert2134838167_state
@ ( hoare_908217195_state @ C @ D
@ ^ [H: state,I: state] : ( E @ H @ ( update @ I @ ( loc_1 @ F ) @ ( getlocs @ G @ F ) ) ) )
@ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ B
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [H: state,I: state] :
( ( G = I )
& ( C @ H @ ( update @ I @ ( loc_1 @ F ) @ ( A @ I ) ) ) )
@ ( local @ F @ A @ D )
@ E )
@ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_hoare__derivs_OLocal) ).
thf(1278,plain,
! [A: state > nat,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o,F: loc,G: state] :
( ( hoare_123228589_state @ B
@ ( insert2134838167_state
@ ( hoare_908217195_state @ C @ D
@ ^ [H: state,I: state] : ( E @ H @ ( update @ I @ ( loc_1 @ F ) @ ( getlocs @ G @ F ) ) ) )
@ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ B
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [H: state,I: state] :
( ( G = I )
& ( C @ H @ ( update @ I @ ( loc_1 @ F ) @ ( A @ I ) ) ) )
@ ( local @ F @ A @ D )
@ E )
@ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(147,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ C ) )
=> ~ ( ( member_nat @ A @ B )
=> ~ ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_IntE) ).
thf(1135,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ C ) )
=> ~ ( ( member_nat @ A @ B )
=> ~ ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(313,axiom,
! [A: hoare_1167836817_state > $o,B: nat,C: hoare_1167836817_state > nat,D: hoare_1167836817_state] :
( ( B
= ( C @ D ) )
=> ( ( member2058392318_state @ D @ A )
=> ( member_nat @ B @ ( image_1476618182te_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_image__eqI) ).
thf(1754,plain,
! [A: hoare_1167836817_state > $o,B: nat,C: hoare_1167836817_state > nat,D: hoare_1167836817_state] :
( ( B
= ( C @ D ) )
=> ( ( member2058392318_state @ D @ A )
=> ( member_nat @ B @ ( image_1476618182te_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(620,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( semila13410563le_a_o @ B @ A )
= ( finite1544171829le_a_o @ insert1281456128iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_union__fold__insert) ).
thf(2904,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( semila13410563le_a_o @ B @ A )
= ( finite1544171829le_a_o @ insert1281456128iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(136,axiom,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
=> ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_le__bot) ).
thf(1103,plain,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
=> ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(411,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( image_nat_nat
@ ^ [D: nat] : A
@ C )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_image__constant) ).
thf(2149,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( image_nat_nat
@ ^ [D: nat] : A
@ C )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(173,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila179895820tate_o @ A @ B )
= bot_bo70021908tate_o )
=> ( ( minus_2107060239tate_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_Diff__triv) ).
thf(1219,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila179895820tate_o @ A @ B )
= bot_bo70021908tate_o )
=> ( ( minus_2107060239tate_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(251,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ( ( insert2134838167_state @ A @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_insert__Diff) ).
thf(1483,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ( ( insert2134838167_state @ A @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(540,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_singletonE) ).
thf(2602,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(22,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ ( minus_minus_nat_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_finite__Diff) ).
thf(689,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ ( minus_minus_nat_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(480,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( hoare_1508237396rivs_a @ B @ C )
=> ( ( ord_le1143225901le_a_o @ A @ C )
=> ( hoare_1508237396rivs_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_weaken) ).
thf(2376,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( hoare_1508237396rivs_a @ B @ C )
=> ( ( ord_le1143225901le_a_o @ A @ C )
=> ( hoare_1508237396rivs_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(284,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ A @ B )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_Diff__insert__absorb) ).
thf(1631,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ A @ B )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(445,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ~ ( member2058392318_state @ B @ A )
=> ( ( ( insert2134838167_state @ B @ C )
= ( insert2134838167_state @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_insert__ident) ).
thf(2260,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ~ ( member2058392318_state @ B @ A )
=> ( ( ( insert2134838167_state @ B @ C )
= ( insert2134838167_state @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(105,axiom,
! [A: nat > $o,B: ( nat > $o ) > $o] :
( ( insert_nat_o @ A @ ( collect_nat_o @ B ) )
= ( collect_nat_o
@ ^ [C: nat > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_insert__Collect) ).
thf(965,plain,
! [A: nat > $o,B: ( nat > $o ) > $o] :
( ( insert_nat_o @ A @ ( collect_nat_o @ B ) )
= ( collect_nat_o
@ ^ [C: nat > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(40,axiom,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [B: nat > $o] : ( ord_less_eq_nat_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_finite__Collect__subsets) ).
thf(750,plain,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( finite_finite_nat_o
@ ( collect_nat_o
@ ^ [B: nat > $o] : ( ord_less_eq_nat_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(559,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( hoare_1508237396rivs_a @ B @ C )
=> ( ( hoare_1508237396rivs_a @ A @ B )
=> ( hoare_1508237396rivs_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cut) ).
thf(2677,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( hoare_1508237396rivs_a @ B @ C )
=> ( ( hoare_1508237396rivs_a @ A @ B )
=> ( hoare_1508237396rivs_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(419,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( semila1947288293_nat_o @ A @ B )
= bot_bot_nat_o )
= ( ! [C: nat] :
( ( member_nat @ C @ A )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_disjoint__iff__not__equal) ).
thf(2176,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( semila1947288293_nat_o @ A @ B )
= bot_bot_nat_o )
= ( ! [C: nat] :
( ( member_nat @ C @ A )
=> ! [D: nat] :
( ( member_nat @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(91,axiom,
! [A: nat > nat,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_nat_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_imageI) ).
thf(904,plain,
! [A: nat > nat,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_nat_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(328,axiom,
! [A: hoare_1167836817_state] :
~ ( member2058392318_state @ A @ bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_empty__iff) ).
thf(1833,plain,
! [A: hoare_1167836817_state] :
~ ( member2058392318_state @ A @ bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(576,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( ! [B: hoare_1775062406iple_a] :
~ ( member2122167641iple_a @ B @ A ) )
= ( A = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_all__not__in__conv) ).
thf(2727,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( ! [B: hoare_1775062406iple_a] :
~ ( member2122167641iple_a @ B @ A ) )
= ( A = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(24,axiom,
! [A: nat,B: nat > $o] :
( ( B != bot_bot_nat_o )
=> ( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( finite_fold1_nat @ times_times_nat @ ( insert_nat @ A @ B ) )
= ( times_times_nat @ A @ ( finite_fold1_nat @ times_times_nat @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_fold1__insert) ).
thf(694,plain,
! [A: nat,B: nat > $o] :
( ( B != bot_bot_nat_o )
=> ( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( finite_fold1_nat @ times_times_nat @ ( insert_nat @ A @ B ) )
= ( times_times_nat @ A @ ( finite_fold1_nat @ times_times_nat @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(349,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ C ) )
=> ( member2122167641iple_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_IntD2) ).
thf(1916,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ C ) )
=> ( member2122167641iple_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(611,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a] :
( ( finite1946188886iple_a @ A @ ( insert1281456128iple_a @ B @ C ) @ D )
=> ~ ! [E: hoare_1775062406iple_a,F: hoare_1775062406iple_a > $o] :
( ( ( insert1281456128iple_a @ B @ C )
= ( insert1281456128iple_a @ E @ F ) )
=> ( ( finite727644230iple_a @ A @ E @ F @ D )
=> ( member2122167641iple_a @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_insert__fold1SetE) ).
thf(2859,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a] :
( ( finite1946188886iple_a @ A @ ( insert1281456128iple_a @ B @ C ) @ D )
=> ~ ! [E: hoare_1775062406iple_a,F: hoare_1775062406iple_a > $o] :
( ( ( insert1281456128iple_a @ B @ C )
= ( insert1281456128iple_a @ E @ F ) )
=> ( ( finite727644230iple_a @ A @ E @ F @ D )
=> ( member2122167641iple_a @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(39,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( A @ B )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_2107060239tate_o @ D @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) ) ) ) ) )
=> ( A @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_finite__empty__induct) ).
thf(732,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( A @ B )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_2107060239tate_o @ D @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) ) ) ) ) )
=> ( A @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(591,axiom,
! [A: hoare_1775062406iple_a] :
( ( the_el1844711461iple_a @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_the__elem__eq) ).
thf(2789,plain,
! [A: hoare_1775062406iple_a] :
( ( the_el1844711461iple_a @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(1699,plain,
( ( ( semila10642723_sup_o @ $true @ $false )
= bot_bot_o )
= ( ( $true = bot_bot_o )
& ( $false = bot_bot_o ) ) ),
inference(instance,[status(thm)],[1696]) ).
thf(1700,plain,
( ( semila10642723_sup_o @ $true @ $false )
!= bot_bot_o ),
inference(simp,[status(thm)],[1699]) ).
thf(1706,plain,
( ( semila10642723_sup_o @ $true @ $false )
!= bot_bot_o ),
inference(lifteq,[status(thm)],[1700]) ).
thf(2981,plain,
( ~ ( semila10642723_sup_o @ $true @ $false )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[1706]) ).
thf(67,axiom,
! [A: state,B: com,C: state,D: state] :
( ( evalc @ B @ C @ D )
=> ( ( evalc @ B @ C @ A )
=> ( A = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_com__det) ).
thf(826,plain,
! [A: state,B: com,C: state,D: state] :
( ( evalc @ B @ C @ D )
=> ( ( evalc @ B @ C @ A )
=> ( A = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(597,axiom,
( bot_bot_nat_o_o
= ( collect_nat_o
@ ^ [A: nat > $o] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_empty__def) ).
thf(2806,plain,
( bot_bot_nat_o_o
= ( collect_nat_o
@ ^ [A: nat > $o] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(320,axiom,
! [A: hoare_1775062406iple_a,B: nat > hoare_1775062406iple_a,C: nat > $o] :
( ( member2122167641iple_a @ A @ ( image_43014529iple_a @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_image__iff) ).
thf(1795,plain,
! [A: hoare_1775062406iple_a,B: nat > hoare_1775062406iple_a,C: nat > $o] :
( ( member2122167641iple_a @ A @ ( image_43014529iple_a @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(572,axiom,
! [A: hoare_1775062406iple_a > hoare_1167836817_state] :
( ( image_1021683026_state @ A @ bot_bo751897185le_a_o )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_image__empty) ).
thf(2716,plain,
! [A: hoare_1775062406iple_a > hoare_1167836817_state] :
( ( image_1021683026_state @ A @ bot_bo751897185le_a_o )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(262,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: $o] :
( ( C
=> ( A
= ( the_Ho1155011127iple_a
@ ^ [D: hoare_1775062406iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) )
& ( ~ C
=> ( B
= ( the_Ho1155011127iple_a
@ ^ [D: hoare_1775062406iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_If__def) ).
thf(1520,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: $o] :
( ( C
=> ( A
= ( the_Ho1155011127iple_a
@ ^ [D: hoare_1775062406iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) )
& ( ~ C
=> ( B
= ( the_Ho1155011127iple_a
@ ^ [D: hoare_1775062406iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(632,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ord_le1143225901le_a_o @ ( insert1281456128iple_a @ A @ B ) @ ( insert1281456128iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_insert__mono) ).
thf(2959,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ B @ C )
=> ( ord_le1143225901le_a_o @ ( insert1281456128iple_a @ A @ B ) @ ( insert1281456128iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(558,axiom,
! [A: nat > hoare_1775062406iple_a,B: nat,C: nat > $o] :
( ( image_43014529iple_a @ A @ ( insert_nat @ B @ C ) )
= ( insert1281456128iple_a @ ( A @ B ) @ ( image_43014529iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_image__insert) ).
thf(2674,plain,
! [A: nat > hoare_1775062406iple_a,B: nat,C: nat > $o] :
( ( image_43014529iple_a @ A @ ( insert_nat @ B @ C ) )
= ( insert1281456128iple_a @ ( A @ B ) @ ( image_43014529iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(377,axiom,
! [A: nat > $o,B: nat > $o] :
( ( minus_minus_nat_o @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ~ ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_set__diff__eq) ).
thf(2016,plain,
! [A: nat > $o,B: nat > $o] :
( ( minus_minus_nat_o @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ~ ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(520,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a] :
( ( finite727644230iple_a @ A @ B @ C @ D )
= ( ( ( C = bot_bo751897185le_a_o )
& ( D = B ) )
| ? [E: hoare_1775062406iple_a,F: hoare_1775062406iple_a > $o,G: hoare_1775062406iple_a] :
( ( C
= ( insert1281456128iple_a @ E @ F ) )
& ( D
= ( A @ E @ G ) )
& ~ ( member2122167641iple_a @ E @ F )
& ( finite727644230iple_a @ A @ B @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_fold__graph_Osimps) ).
thf(2514,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a] :
( ( finite727644230iple_a @ A @ B @ C @ D )
= ( ( ( C = bot_bo751897185le_a_o )
& ( D = B ) )
| ? [E: hoare_1775062406iple_a,F: hoare_1775062406iple_a > $o,G: hoare_1775062406iple_a] :
( ( C
= ( insert1281456128iple_a @ E @ F ) )
& ( D
= ( A @ E @ G ) )
& ~ ( member2122167641iple_a @ E @ F )
& ( finite727644230iple_a @ A @ B @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(529,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ! [B: hoare_1775062406iple_a] :
~ ( member2122167641iple_a @ B @ A )
=> ( A = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_equals0I) ).
thf(2568,plain,
! [A: hoare_1775062406iple_a > $o] :
( ! [B: hoare_1775062406iple_a] :
~ ( member2122167641iple_a @ B @ A )
=> ( A = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(97,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( hoare_123228589_state @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_asm) ).
thf(936,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( hoare_123228589_state @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(433,axiom,
! [A: nat,B: hoare_1167836817_state > nat,C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( member2058392318_state @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_1476618182te_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_rev__image__eqI) ).
thf(2220,plain,
! [A: nat,B: hoare_1167836817_state > nat,C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( member2058392318_state @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_1476618182te_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(127,axiom,
! [A: hoare_1167836817_state] :
~ ! [B: state > state > $o,C: com,D: state > state > $o] :
( A
!= ( hoare_908217195_state @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_triple_Oexhaust) ).
thf(1058,plain,
! [A: hoare_1167836817_state] :
~ ! [B: state > state > $o,C: com,D: state > state > $o] :
( A
!= ( hoare_908217195_state @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(179,axiom,
! [A: hoare_1167836817_state > $o] : ( hoare_123228589_state @ A @ bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_empty) ).
thf(1239,plain,
! [A: hoare_1167836817_state > $o] : ( hoare_123228589_state @ A @ bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(501,axiom,
! [A: hoare_1775062406iple_a,B: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( B
= ( finite1790765286iple_a @ C ) )
=> ( ( B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_fold1__singleton__def) ).
thf(2442,plain,
! [A: hoare_1775062406iple_a,B: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( B
= ( finite1790765286iple_a @ C ) )
=> ( ( B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(132,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ C ) )
=> ( member_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_IntD1) ).
thf(1092,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ C ) )
=> ( member_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(416,axiom,
! [A: hoare_1167836817_state,B: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
( ( B
= ( finite1646097201_state @ C ) )
=> ( ( B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_fold1__singleton__def) ).
thf(2166,plain,
! [A: hoare_1167836817_state,B: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state] :
( ( B
= ( finite1646097201_state @ C ) )
=> ( ( B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(495,axiom,
! [A: hoare_1775062406iple_a > $o,B: x_a > state > $o,C: vname,D: state > nat] :
( hoare_1508237396rivs_a @ A
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [E: x_a,F: state] : ( B @ E @ ( update @ F @ C @ ( D @ F ) ) )
@ ( ass @ C @ D )
@ B )
@ bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Ass) ).
thf(2425,plain,
! [A: hoare_1775062406iple_a > $o,B: x_a > state > $o,C: vname,D: state > nat] :
( hoare_1508237396rivs_a @ A
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [E: x_a,F: state] : ( B @ E @ ( update @ F @ C @ ( D @ F ) ) )
@ ( ass @ C @ D )
@ B )
@ bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(29,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_finite__subset) ).
thf(704,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_nat_o @ A @ B )
=> ( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(295,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( A @ B )
=> ( ! [C: hoare_1775062406iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_Ho1155011127iple_a @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_the__equality) ).
thf(1675,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( A @ B )
=> ( ! [C: hoare_1775062406iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_Ho1155011127iple_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(16,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ C ) )
= ( ( member_nat @ A @ B )
& ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_Int__iff) ).
thf(672,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( semila1947288293_nat_o @ B @ C ) )
= ( ( member_nat @ A @ B )
& ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( finite_fold_nat_nat @ semila972727038up_nat @ A @ ( insert_nat @ B @ C ) )
= ( semila972727038up_nat @ B @ ( finite_fold_nat_nat @ semila972727038up_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_fold__sup__insert) ).
thf(641,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( finite_fold_nat_nat @ semila972727038up_nat @ A @ ( insert_nat @ B @ C ) )
= ( semila972727038up_nat @ B @ ( finite_fold_nat_nat @ semila972727038up_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(232,axiom,
! [A: nat > $o,B: nat] :
( ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( ( A = bot_bot_nat_o )
| ( A
= ( insert_nat @ B @ bot_bot_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_subset__singletonD) ).
thf(1428,plain,
! [A: nat > $o,B: nat] :
( ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( ( A = bot_bot_nat_o )
| ( A
= ( insert_nat @ B @ bot_bot_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(148,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) @ C )
=> ( ( member2058392318_state @ B @ A )
=> ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_diff__single__insert) ).
thf(1139,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) @ C )
=> ( ( member2058392318_state @ B @ A )
=> ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1501,plain,
( ( semila854092349_inf_o @ $false @ bot_bot_o )
= bot_bot_o ),
inference(instance,[status(thm)],[1499]) ).
thf(1503,plain,
( ( semila854092349_inf_o @ $false @ bot_bot_o )
= bot_bot_o ),
inference(lifteq,[status(thm)],[1501]) ).
thf(317,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ ( collec676402587iple_a @ C ) ) )
= ( ( member2122167641iple_a @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_Int__Collect) ).
thf(1786,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ ( collec676402587iple_a @ C ) ) )
= ( ( member2122167641iple_a @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(293,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( semila848761471_nat_o
@ ( collect_nat
@ ^ [C: nat] : ( C = A ) )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_insert__def) ).
thf(1669,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( semila848761471_nat_o
@ ( collect_nat
@ ^ [C: nat] : ( C = A ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(456,axiom,
! [A: loc,B: state > nat,C: com,D: vname,E: state > nat] :
( ( local @ A @ B @ C )
!= ( ass @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_com_Osimps_I23_J) ).
thf(2293,plain,
! [A: loc,B: state > nat,C: com,D: vname,E: state > nat] :
( ( local @ A @ B @ C )
!= ( ass @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(189,axiom,
finite389864113_nat_o @ insert_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_comp__fun__idem__insert) ).
thf(1271,plain,
finite389864113_nat_o @ insert_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(460,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a] :
( ( finite727644230iple_a @ A @ B @ C @ D )
=> ( ~ ( member2122167641iple_a @ B @ C )
=> ( finite1946188886iple_a @ A @ ( insert1281456128iple_a @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_fold1Set_Ointros) ).
thf(2308,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a] :
( ( finite727644230iple_a @ A @ B @ C @ D )
=> ( ~ ( member2122167641iple_a @ B @ C )
=> ( finite1946188886iple_a @ A @ ( insert1281456128iple_a @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(526,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ E )
=> ( ( finite727644230iple_a @ E @ B @ C @ D )
=> ( ( member2122167641iple_a @ A @ C )
=> ? [F: hoare_1775062406iple_a] :
( ( D
= ( E @ A @ F ) )
& ( finite727644230iple_a @ E @ B @ ( minus_1944206118le_a_o @ C @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_comp__fun__commute_Ofold__graph__insertE__aux) ).
thf(2557,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ E )
=> ( ( finite727644230iple_a @ E @ B @ C @ D )
=> ( ( member2122167641iple_a @ A @ C )
=> ? [F: hoare_1775062406iple_a] :
( ( D
= ( E @ A @ F ) )
& ( finite727644230iple_a @ E @ B @ ( minus_1944206118le_a_o @ C @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(60,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( semila1947288293_nat_o @ ( insert_nat @ A @ B ) @ ( insert_nat @ A @ C ) )
= ( insert_nat @ A @ ( semila1947288293_nat_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_insert__inter__insert) ).
thf(804,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( semila1947288293_nat_o @ ( insert_nat @ A @ B ) @ ( insert_nat @ A @ C ) )
= ( insert_nat @ A @ ( semila1947288293_nat_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(509,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a] :
( ( finite727644230iple_a @ A @ B @ bot_bo751897185le_a_o @ C )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_empty__fold__graphE) ).
thf(2474,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a] :
( ( finite727644230iple_a @ A @ B @ bot_bo751897185le_a_o @ C )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(101,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( minus_minus_nat_o @ B @ C ) )
=> ~ ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_DiffE) ).
thf(947,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( minus_minus_nat_o @ B @ C ) )
=> ~ ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(464,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a] :
( ( ( insert1281456128iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
= ( insert1281456128iple_a @ C @ ( insert1281456128iple_a @ D @ bot_bo751897185le_a_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_doubleton__eq__iff) ).
thf(2319,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a] :
( ( ( insert1281456128iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
= ( insert1281456128iple_a @ C @ ( insert1281456128iple_a @ D @ bot_bo751897185le_a_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(213,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( minus_2107060239tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_insert__Diff1) ).
thf(1356,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( minus_2107060239tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(394,axiom,
! [A: nat > $o] :
( ! [B: nat] :
~ ( member_nat @ B @ A )
=> ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_equals0I) ).
thf(2079,plain,
! [A: nat > $o] :
( ! [B: nat] :
~ ( member_nat @ B @ A )
=> ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(560,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ A )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_Diff__cancel) ).
thf(2679,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ A )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(69,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( hoare_123228589_state @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_weaken) ).
thf(831,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( hoare_123228589_state @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(550,axiom,
! [A: hoare_1775062406iple_a > $o,B: x_a > state > $o,C: com,D: x_a > state > $o,E: $o] :
( ( E
=> ( hoare_1508237396rivs_a @ A @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ B @ C @ D ) @ bot_bo751897185le_a_o ) ) )
=> ( hoare_1508237396rivs_a @ A
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [F: x_a,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_constant) ).
thf(2642,plain,
! [A: hoare_1775062406iple_a > $o,B: x_a > state > $o,C: com,D: x_a > state > $o,E: $o] :
( ( E
=> ( hoare_1508237396rivs_a @ A @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ B @ C @ D ) @ bot_bo751897185le_a_o ) ) )
=> ( hoare_1508237396rivs_a @ A
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [F: x_a,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(343,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ C )
=> ( ( finite2063573081iple_a @ B )
=> ( finite727644230iple_a @ C @ A @ B @ ( finite1842721992iple_a @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_comp__fun__commute_Ofold__graph__fold) ).
thf(1894,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ C )
=> ( ( finite2063573081iple_a @ B )
=> ( finite727644230iple_a @ C @ A @ B @ ( finite1842721992iple_a @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(113,axiom,
! [A: nat > $o] :
( ( semila1947288293_nat_o @ A @ bot_bot_nat_o )
= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_Int__empty__right) ).
thf(1011,plain,
! [A: nat > $o] :
( ( semila1947288293_nat_o @ A @ bot_bot_nat_o )
= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(211,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_Int__insert__left__if1) ).
thf(1349,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(109,axiom,
! [A: state > state > $o,B: state > state > $o,C: hoare_1167836817_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ E @ F ) @ bot_bo70021908tate_o ) )
=> ( ! [G: state,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: state] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ E @ A ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_conseq12) ).
thf(996,plain,
! [A: state > state > $o,B: state > state > $o,C: hoare_1167836817_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ E @ F ) @ bot_bo70021908tate_o ) )
=> ( ! [G: state,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: state] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ E @ A ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(150,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( minus_2107060239tate_o @ A @ B )
= ( finite291020855tate_o
@ ^ [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] : ( minus_2107060239tate_o @ D @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
@ A
@ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_minus__fold__remove) ).
thf(1144,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( minus_2107060239tate_o @ A @ B )
= ( finite291020855tate_o
@ ^ [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] : ( minus_2107060239tate_o @ D @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
@ A
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(604,axiom,
! [A: x_a > state > $o,B: hoare_1775062406iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ C @ D @ E ) @ bot_bo751897185le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ C @ D @ A ) @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_conseq2) ).
thf(2839,plain,
! [A: x_a > state > $o,B: hoare_1775062406iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ C @ D @ E ) @ bot_bo751897185le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ C @ D @ A ) @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(610,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ A @ ( minus_1944206118le_a_o @ B @ A ) )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_Diff__disjoint) ).
thf(2856,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ A @ ( minus_1944206118le_a_o @ B @ A ) )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(481,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( finite2063573081iple_a @ ( insert1281456128iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_finite_OinsertI) ).
thf(2378,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( finite2063573081iple_a @ ( insert1281456128iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(165,axiom,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_bot__least) ).
thf(1194,plain,
! [A: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(471,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( image_1802845250iple_a
@ ^ [D: hoare_1167836817_state] : A
@ C )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_image__constant) ).
thf(2346,plain,
! [A: hoare_1775062406iple_a,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( image_1802845250iple_a
@ ^ [D: hoare_1167836817_state] : A
@ C )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(19,axiom,
finite1084549118_state @ bot_bo70021908tate_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_finite_OemptyI) ).
thf(681,plain,
finite1084549118_state @ bot_bo70021908tate_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(334,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_Diff__insert2) ).
thf(1853,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(483,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
= ( semila13410563le_a_o @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_insert__is__Un) ).
thf(2383,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
= ( semila13410563le_a_o @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(546,axiom,
! [A: hoare_1167836817_state > hoare_1775062406iple_a,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( image_1802845250iple_a @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert1281456128iple_a @ ( A @ B ) @ ( image_1802845250iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_image__insert) ).
thf(2624,plain,
! [A: hoare_1167836817_state > hoare_1775062406iple_a,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( image_1802845250iple_a @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert1281456128iple_a @ ( A @ B ) @ ( image_1802845250iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(494,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( finite1842721992iple_a @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_folding__one__idem_Oeq__fold__idem_H) ).
thf(2422,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( finite1842721992iple_a @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(140,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( A != bot_bot_nat_o )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( ( semila972727038up_nat @ ( big_la43341705in_nat @ A ) @ ( big_la43341705in_nat @ B ) )
= ( big_la43341705in_nat @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_Sup__fin_Osubset__idem) ).
thf(1117,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( A != bot_bot_nat_o )
=> ( ( ord_less_eq_nat_o @ A @ B )
=> ( ( semila972727038up_nat @ ( big_la43341705in_nat @ A ) @ ( big_la43341705in_nat @ B ) )
= ( big_la43341705in_nat @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(441,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ C ) )
=> ( member2122167641iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_IntD1) ).
thf(2246,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ C ) )
=> ( member2122167641iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(254,axiom,
! [A: hoare_1167836817_state,B: hoare_1775062406iple_a > hoare_1167836817_state,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2058392318_state @ A @ ( image_1021683026_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_rev__image__eqI) ).
thf(1492,plain,
! [A: hoare_1167836817_state,B: hoare_1775062406iple_a > hoare_1167836817_state,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2058392318_state @ A @ ( image_1021683026_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(426,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) )
= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_insert__Diff__single) ).
thf(2197,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) )
= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(363,axiom,
! [A: nat > $o] :
( ( collect_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Collect__def) ).
thf(1969,plain,
! [A: nat > $o] :
( ( collect_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(390,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_doubleton__eq__iff) ).
thf(2065,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(158,axiom,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_empty__subsetI) ).
thf(1175,plain,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(421,axiom,
! [A: nat,B: nat > $o] : ( member_nat @ A @ ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insertI1) ).
thf(2182,plain,
! [A: nat,B: nat > $o] : ( member_nat @ A @ ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(470,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( semila13410563le_a_o @ A @ B )
= bot_bo751897185le_a_o )
= ( ( A = bot_bo751897185le_a_o )
& ( B = bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_sup__eq__bot__iff) ).
thf(2343,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( semila13410563le_a_o @ A @ B )
= bot_bo751897185le_a_o )
= ( ( A = bot_bo751897185le_a_o )
& ( B = bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(370,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ~ ( member2058392318_state @ B @ C )
=> ( B = A ) )
=> ( member2058392318_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_insertCI) ).
thf(1993,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ~ ( member2058392318_state @ B @ C )
=> ( B = A ) )
=> ( member2058392318_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(37,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( member_nat @ B @ A )
=> ( member_nat @ B @ ( semila1947288293_nat_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_IntI) ).
thf(726,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( member_nat @ B @ A )
=> ( member_nat @ B @ ( semila1947288293_nat_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(337,axiom,
! [A: state,B: nat] : ( evaln @ skip @ A @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_evaln_OSkip) ).
thf(1862,plain,
! [A: state,B: nat] : ( evaln @ skip @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(243,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( minus_1944206118le_a_o @ B @ C ) )
=> ( member2122167641iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_DiffD1) ).
thf(1460,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( minus_1944206118le_a_o @ B @ C ) )
=> ( member2122167641iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1948,plain,
( ( ord_less_eq_o @ $true @ bot_bot_o )
= ( $true = bot_bot_o ) ),
inference(instance,[status(thm)],[1947]) ).
thf(1949,plain,
( ( ord_less_eq_o @ $true @ bot_bot_o )
= bot_bot_o ),
inference(simp,[status(thm)],[1948]) ).
thf(1952,plain,
( ( ord_less_eq_o @ $true @ bot_bot_o )
= bot_bot_o ),
inference(lifteq,[status(thm)],[1949]) ).
thf(207,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ B @ ( semila13410563le_a_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_UnI1) ).
thf(1339,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ B @ ( semila13410563le_a_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(541,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) )
= ( insert1281456128iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_insert__Diff__single) ).
thf(2605,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ ( minus_1944206118le_a_o @ B @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ) )
= ( insert1281456128iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(625,axiom,
! [A: nat > hoare_1775062406iple_a,B: nat > $o] :
( ( ( image_43014529iple_a @ A @ B )
= bot_bo751897185le_a_o )
= ( B = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_image__is__empty) ).
thf(2923,plain,
! [A: nat > hoare_1775062406iple_a,B: nat > $o] :
( ( ( image_43014529iple_a @ A @ B )
= bot_bo751897185le_a_o )
= ( B = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(205,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ? [B: hoare_1775062406iple_a] :
( ( A @ B )
& ! [C: hoare_1775062406iple_a] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_Ho1155011127iple_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_theI_H) ).
thf(1325,plain,
! [A: hoare_1775062406iple_a > $o] :
( ? [B: hoare_1775062406iple_a] :
( ( A @ B )
& ! [C: hoare_1775062406iple_a] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_Ho1155011127iple_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( A != B )
| ( fequal_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(1149,plain,
! [A: nat,B: nat] :
( ( A != B )
| ( fequal_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(615,axiom,
! [A: ( hoare_1775062406iple_a > $o ) > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( A @ B )
=> ( ! [C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ D )
=> ( ( member2122167641iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_1944206118le_a_o @ D @ ( insert1281456128iple_a @ C @ bot_bo751897185le_a_o ) ) ) ) ) )
=> ( A @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_finite__empty__induct) ).
thf(2874,plain,
! [A: ( hoare_1775062406iple_a > $o ) > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( A @ B )
=> ( ! [C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ D )
=> ( ( member2122167641iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_1944206118le_a_o @ D @ ( insert1281456128iple_a @ C @ bot_bo751897185le_a_o ) ) ) ) ) )
=> ( A @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(628,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ bot_bo751897185le_a_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_Un__empty__left) ).
thf(2928,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ bot_bo751897185le_a_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(159,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat @ ( collect_nat @ A ) )
& ( finite_finite_nat @ ( collect_nat @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_finite__Collect__disjI) ).
thf(1177,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat @ ( collect_nat @ A ) )
& ( finite_finite_nat @ ( collect_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(220,axiom,
! [A: hoare_1775062406iple_a > $o,B: nat,C: hoare_1775062406iple_a > nat,D: hoare_1775062406iple_a] :
( ( B
= ( C @ D ) )
=> ( ( member2122167641iple_a @ D @ A )
=> ( member_nat @ B @ ( image_1806517641_a_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_image__eqI) ).
thf(1381,plain,
! [A: hoare_1775062406iple_a > $o,B: nat,C: hoare_1775062406iple_a > nat,D: hoare_1775062406iple_a] :
( ( B
= ( C @ D ) )
=> ( ( member2122167641iple_a @ D @ A )
=> ( member_nat @ B @ ( image_1806517641_a_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(532,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( insert1281456128iple_a @ B @ ( insert1281456128iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_insert__commute) ).
thf(2578,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( insert1281456128iple_a @ B @ ( insert1281456128iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(297,axiom,
! [A: nat > nat > nat,B: nat,C: nat] :
( ( finite_fold1Set_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) @ C )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_fold1Set__sing) ).
thf(1688,plain,
! [A: nat > nat > nat,B: nat,C: nat] :
( ( finite_fold1Set_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) @ C )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(157,axiom,
! [A: nat > $o,B: nat,C: nat > nat,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member_nat @ B @ ( image_nat_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_image__eqI) ).
thf(1171,plain,
! [A: nat > $o,B: nat,C: nat > nat,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member_nat @ B @ ( image_nat_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(393,axiom,
! [A: glb,B: loc] :
( ( glb_1 @ A )
!= ( loc_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_vname_Osimps_I3_J) ).
thf(2075,plain,
! [A: glb,B: loc] :
( ( glb_1 @ A )
!= ( loc_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(476,axiom,
! [A: com,B: x_a > state > $o,C: hoare_1775062406iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ E @ F ) @ bot_bo751897185le_a_o ) )
=> ( ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ F @ A @ B ) @ bot_bo751897185le_a_o ) )
=> ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ ( semi @ E @ A ) @ B ) @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_Comp) ).
thf(2365,plain,
! [A: com,B: x_a > state > $o,C: hoare_1775062406iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ E @ F ) @ bot_bo751897185le_a_o ) )
=> ( ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ F @ A @ B ) @ bot_bo751897185le_a_o ) )
=> ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ ( semi @ E @ A ) @ B ) @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(263,axiom,
! [A: nat,B: nat > $o] :
( ( ( B = bot_bot_nat_o )
=> ( ( image_nat_nat
@ ^ [C: nat] : A
@ B )
= bot_bot_nat_o ) )
& ( ( B != bot_bot_nat_o )
=> ( ( image_nat_nat
@ ^ [C: nat] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_image__constant__conv) ).
thf(1528,plain,
! [A: nat,B: nat > $o] :
( ( ( B = bot_bot_nat_o )
=> ( ( image_nat_nat
@ ^ [C: nat] : A
@ B )
= bot_bot_nat_o ) )
& ( ( B != bot_bot_nat_o )
=> ( ( image_nat_nat
@ ^ [C: nat] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1176,plain,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
inference(cnf,[status(esa)],[1175]) ).
thf(629,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ bot_bo751897185le_a_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_Diff__empty) ).
thf(2931,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ bot_bo751897185le_a_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(594,axiom,
! [A: hoare_1775062406iple_a > nat,B: hoare_1775062406iple_a > $o] :
( ( bot_bot_nat_o
= ( image_1806517641_a_nat @ A @ B ) )
= ( B = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_empty__is__image) ).
thf(2797,plain,
! [A: hoare_1775062406iple_a > nat,B: hoare_1775062406iple_a > $o] :
( ( bot_bot_nat_o
= ( image_1806517641_a_nat @ A @ B ) )
= ( B = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(379,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > hoare_1775062406iple_a,D: hoare_1775062406iple_a] :
( ( B
= ( C @ D ) )
=> ( ( member2122167641iple_a @ D @ A )
=> ( member2122167641iple_a @ B @ ( image_1170193413iple_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_image__eqI) ).
thf(2022,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > hoare_1775062406iple_a,D: hoare_1775062406iple_a] :
( ( B
= ( C @ D ) )
=> ( ( member2122167641iple_a @ D @ A )
=> ( member2122167641iple_a @ B @ ( image_1170193413iple_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(402,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1167836817_state > hoare_1775062406iple_a,C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( member2058392318_state @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2122167641iple_a @ A @ ( image_1802845250iple_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_rev__image__eqI) ).
thf(2101,plain,
! [A: hoare_1775062406iple_a,B: hoare_1167836817_state > hoare_1775062406iple_a,C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( member2058392318_state @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2122167641iple_a @ A @ ( image_1802845250iple_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(255,axiom,
! [A: nat,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( image_1476618182te_nat
@ ^ [D: hoare_1167836817_state] : A
@ C )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_image__constant) ).
thf(1496,plain,
! [A: nat,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( image_1476618182te_nat
@ ^ [D: hoare_1167836817_state] : A
@ C )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(413,axiom,
! [A: vname,B: state > nat] :
( ( ass @ A @ B )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_com_Osimps_I9_J) ).
thf(2156,plain,
! [A: vname,B: state > nat] :
( ( ass @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(2205,plain,
( ( semila854092349_inf_o @ bot_bot_o @ $true )
= bot_bot_o ),
inference(instance,[status(thm)],[2204]) ).
thf(2207,plain,
( ( semila854092349_inf_o @ bot_bot_o @ $true )
= bot_bot_o ),
inference(lifteq,[status(thm)],[2205]) ).
thf(9,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( member_nat @ A @ B )
=> ( ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ B ) )
= ( big_la43341705in_nat @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_Sup__fin_Oin__idem) ).
thf(653,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( member_nat @ A @ B )
=> ( ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ B ) )
= ( big_la43341705in_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(565,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( A != bot_bo751897185le_a_o )
= ( ? [B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( A
= ( insert1281456128iple_a @ B @ C ) )
& ~ ( member2122167641iple_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_nonempty__iff) ).
thf(2693,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( A != bot_bo751897185le_a_o )
= ( ? [B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( A
= ( insert1281456128iple_a @ B @ C ) )
& ~ ( member2122167641iple_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(11,axiom,
! [A: nat > $o,B: nat > nat] :
( ! [C: nat,D: nat] :
( ( B @ ( semila972727038up_nat @ C @ D ) )
= ( semila972727038up_nat @ ( B @ C ) @ ( B @ D ) ) )
=> ( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ( B @ ( big_la43341705in_nat @ A ) )
= ( big_la43341705in_nat @ ( image_nat_nat @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_Sup__fin_Ohom__commute) ).
thf(658,plain,
! [A: nat > $o,B: nat > nat] :
( ! [C: nat,D: nat] :
( ( B @ ( semila972727038up_nat @ C @ D ) )
= ( semila972727038up_nat @ ( B @ C ) @ ( B @ D ) ) )
=> ( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ( B @ ( big_la43341705in_nat @ A ) )
= ( big_la43341705in_nat @ ( image_nat_nat @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(517,axiom,
( bot_bot_nat_o
= ( collect_nat
@ ^ [A: nat] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_empty__def) ).
thf(2506,plain,
( bot_bot_nat_o
= ( collect_nat
@ ^ [A: nat] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(225,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( finite1842721992iple_a @ A @ B @ C )
= ( the_Ho1155011127iple_a @ ( finite727644230iple_a @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_fold__def) ).
thf(1396,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( finite1842721992iple_a @ A @ B @ C )
= ( the_Ho1155011127iple_a @ ( finite727644230iple_a @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(500,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ B @ C )
=> ( ( ord_le1143225901le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( ord_le1143225901le_a_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_subset__insert) ).
thf(2439,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ B @ C )
=> ( ( ord_le1143225901le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( ord_le1143225901le_a_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(430,axiom,
! [A: loc,B: state > nat,C: com] :
( ( local @ A @ B @ C )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_com_Osimps_I11_J) ).
thf(2212,plain,
! [A: loc,B: state > nat,C: com] :
( ( local @ A @ B @ C )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(417,axiom,
! [A: nat > $o] :
( ( collect_nat_o @ ( fequal_nat_o @ A ) )
= ( insert_nat_o @ A @ bot_bot_nat_o_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_singleton__conv2) ).
thf(2171,plain,
! [A: nat > $o] :
( ( collect_nat_o @ ( fequal_nat_o @ A ) )
= ( insert_nat_o @ A @ bot_bot_nat_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(172,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= A ) )
& ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
!= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_Sup__fin_Oinsert__remove) ).
thf(1213,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= A ) )
& ( ( ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) )
!= bot_bot_nat_o )
=> ( ( big_la43341705in_nat @ ( insert_nat @ A @ B ) )
= ( semila972727038up_nat @ A @ ( big_la43341705in_nat @ ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(48,axiom,
! [A: nat,B: nat > $o,C: nat > nat > nat,D: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ C @ D )
=> ( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( D @ ( insert_nat @ A @ B ) )
= ( finite_fold_nat_nat @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_folding__one_Oeq__fold_H) ).
thf(768,plain,
! [A: nat,B: nat > $o,C: nat > nat > nat,D: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ C @ D )
=> ( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( D @ ( insert_nat @ A @ B ) )
= ( finite_fold_nat_nat @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(537,axiom,
! [A: nat,B: x_a > state > $o,C: com,D: x_a > state > $o] :
( ( hoare_1462269968alid_a @ A @ ( hoare_1766022166iple_a @ B @ C @ D ) )
= ( ! [E: x_a,F: state] :
( ( B @ E @ F )
=> ! [G: state] :
( ( evaln @ C @ F @ A @ G )
=> ( D @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_triple__valid__def2) ).
thf(2592,plain,
! [A: nat,B: x_a > state > $o,C: com,D: x_a > state > $o] :
( ( hoare_1462269968alid_a @ A @ ( hoare_1766022166iple_a @ B @ C @ D ) )
= ( ! [E: x_a,F: state] :
( ( B @ E @ F )
=> ! [G: state] :
( ( evaln @ C @ F @ A @ G )
=> ( D @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(581,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( insert1281456128iple_a @ B @ ( semila966743401le_a_o @ A @ C ) ) ) )
& ( ~ ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( semila966743401le_a_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_Int__insert__left) ).
thf(2752,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( insert1281456128iple_a @ B @ ( semila966743401le_a_o @ A @ C ) ) ) )
& ( ~ ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( semila966743401le_a_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(485,axiom,
! [A: x_a > state > $o,B: x_a > state > $o,C: hoare_1775062406iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ E @ F ) @ bot_bo751897185le_a_o ) )
=> ( ! [G: x_a,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: x_a] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ B @ E @ A ) @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_conseq12) ).
thf(2390,plain,
! [A: x_a > state > $o,B: x_a > state > $o,C: hoare_1775062406iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ E @ F ) @ bot_bo751897185le_a_o ) )
=> ( ! [G: x_a,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: x_a] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_1508237396rivs_a @ C @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ B @ E @ A ) @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(183,axiom,
! [A: loc,B: state > nat,C: com] :
( skip
!= ( local @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_com_Osimps_I10_J) ).
thf(1250,plain,
! [A: loc,B: state > nat,C: com] :
( skip
!= ( local @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(373,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ E )
=> ( ( finite727644230iple_a @ E @ B @ C @ D )
=> ( ( finite727644230iple_a @ E @ B @ C @ A )
=> ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_comp__fun__commute_Ofold__graph__determ) ).
thf(2005,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ E )
=> ( ( finite727644230iple_a @ E @ B @ C @ D )
=> ( ( finite727644230iple_a @ E @ B @ C @ A )
=> ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(388,axiom,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( ( A @ B )
=> ( ( collect_nat_o
@ ^ [C: nat > $o] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_nat_o @ B @ bot_bot_nat_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat_o
@ ^ [C: nat > $o] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_nat_o_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Collect__conv__if2) ).
thf(2054,plain,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( ( A @ B )
=> ( ( collect_nat_o
@ ^ [C: nat > $o] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_nat_o @ B @ bot_bot_nat_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat_o
@ ^ [C: nat > $o] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_nat_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(341,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( insert_nat @ B @ ( semila1947288293_nat_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_Int__insert__right__if1) ).
thf(1873,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( insert_nat @ B @ ( semila1947288293_nat_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(245,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( ord_le827224136tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_subset__insert) ).
thf(1467,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( ord_le827224136tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(449,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila179895820tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ! [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ A )
=> ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_disjoint__iff__not__equal) ).
thf(2271,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila179895820tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ! [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ A )
=> ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(13,axiom,
! [A: nat > $o,B: nat > $o] :
( ( semila1947288293_nat_o @ A @ ( minus_minus_nat_o @ B @ A ) )
= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_Diff__disjoint) ).
thf(663,plain,
! [A: nat > $o,B: nat > $o] :
( ( semila1947288293_nat_o @ A @ ( minus_minus_nat_o @ B @ A ) )
= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(437,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_mem__def) ).
thf(2234,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(259,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ~ ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ B @ A ) )
=> ( member2122167641iple_a @ B @ ( semila13410563le_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_UnCI) ).
thf(1509,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ~ ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ B @ A ) )
=> ( member2122167641iple_a @ B @ ( semila13410563le_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(627,axiom,
finite2063573081iple_a @ bot_bo751897185le_a_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_finite_OemptyI) ).
thf(2927,plain,
finite2063573081iple_a @ bot_bo751897185le_a_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(369,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ D )
=> ( ( finite727644230iple_a @ D @ A @ B @ C )
=> ( ( finite1842721992iple_a @ D @ A @ B )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_comp__fun__commute_Ofold__equality) ).
thf(1990,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ D )
=> ( ( finite727644230iple_a @ D @ A @ B @ C )
=> ( ( finite1842721992iple_a @ D @ A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(106,axiom,
! [A: state,B: state] :
( ( evalc @ skip @ A @ B )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_evalc__elim__cases_I1_J) ).
thf(968,plain,
! [A: state,B: state] :
( ( evalc @ skip @ A @ B )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(71,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ bot_bo70021908tate_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_Un__empty__right) ).
thf(836,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ bot_bo70021908tate_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(124,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ bot_bo70021908tate_o )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_inf__bot__right) ).
thf(1049,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ bot_bo70021908tate_o )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(17,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( semila848761471_nat_o @ A @ B )
= bot_bot_nat_o )
= ( ( A = bot_bot_nat_o )
& ( B = bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_sup__eq__bot__iff) ).
thf(675,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( semila848761471_nat_o @ A @ B )
= bot_bot_nat_o )
= ( ( A = bot_bot_nat_o )
& ( B = bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(601,axiom,
! [A: ( hoare_1775062406iple_a > $o ) > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( A @ bot_bo751897185le_a_o )
=> ( ! [C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ D )
=> ( ~ ( member2122167641iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert1281456128iple_a @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_finite__induct) ).
thf(2816,plain,
! [A: ( hoare_1775062406iple_a > $o ) > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( A @ bot_bo751897185le_a_o )
=> ( ! [C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ D )
=> ( ~ ( member2122167641iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert1281456128iple_a @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(314,axiom,
! [A: hoare_1167836817_state > $o] :
( ( the_el323660082_state @ A )
= ( the_Ho310147232_state
@ ^ [B: hoare_1167836817_state] :
( A
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_the__elem__def) ).
thf(1758,plain,
! [A: hoare_1167836817_state > $o] :
( ( the_el323660082_state @ A )
= ( the_Ho310147232_state
@ ^ [B: hoare_1167836817_state] :
( A
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(404,axiom,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( A @ bot_bot_nat_o )
=> ( ! [C: nat,D: nat > $o] :
( ( finite_finite_nat @ D )
=> ( ~ ( member_nat @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_nat @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_finite__induct) ).
thf(2107,plain,
! [A: ( nat > $o ) > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( A @ bot_bot_nat_o )
=> ( ! [C: nat,D: nat > $o] :
( ( finite_finite_nat @ D )
=> ( ~ ( member_nat @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_nat @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(168,axiom,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_bot__least) ).
thf(1203,plain,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(170,axiom,
! [A: nat > nat > nat,B: nat] :
~ ( finite_fold1Set_nat @ A @ bot_bot_nat_o @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_empty__fold1SetE) ).
thf(1208,plain,
! [A: nat > nat > nat,B: nat] :
~ ( finite_fold1Set_nat @ A @ bot_bot_nat_o @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(100,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( semila1947288293_nat_o @ A @ B )
= bot_bot_nat_o )
=> ( ( minus_minus_nat_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_Diff__triv) ).
thf(944,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( semila1947288293_nat_o @ A @ B )
= bot_bot_nat_o )
=> ( ( minus_minus_nat_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(555,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
=> ( ( insert1281456128iple_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_insert__absorb) ).
thf(2665,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
=> ( ( insert1281456128iple_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(94,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > hoare_1167836817_state,D: hoare_1167836817_state] :
( ( B
= ( C @ D ) )
=> ( ( member2058392318_state @ D @ A )
=> ( member2058392318_state @ B @ ( image_31595733_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_image__eqI) ).
thf(927,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > hoare_1167836817_state,D: hoare_1167836817_state] :
( ( B
= ( C @ D ) )
=> ( ( member2058392318_state @ D @ A )
=> ( member2058392318_state @ B @ ( image_31595733_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(382,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( semila179895820tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_Int__insert__right__if0) ).
thf(2037,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( semila179895820tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(516,axiom,
! [A: hoare_1775062406iple_a > nat,B: hoare_1775062406iple_a > $o] :
( ( ( image_1806517641_a_nat @ A @ B )
= bot_bot_nat_o )
= ( B = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_image__is__empty) ).
thf(2503,plain,
! [A: hoare_1775062406iple_a > nat,B: hoare_1775062406iple_a > $o] :
( ( ( image_1806517641_a_nat @ A @ B )
= bot_bot_nat_o )
= ( B = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(296,axiom,
! [A: com,B: com,C: state,D: nat,E: state] :
( ( evaln @ ( semi @ A @ B ) @ C @ D @ E )
=> ~ ! [F: state] :
( ( evaln @ A @ C @ D @ F )
=> ~ ( evaln @ B @ F @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_evaln__elim__cases_I4_J) ).
thf(1684,plain,
! [A: com,B: com,C: state,D: nat,E: state] :
( ( evaln @ ( semi @ A @ B ) @ C @ D @ E )
=> ~ ! [F: state] :
( ( evaln @ A @ C @ D @ F )
=> ~ ( evaln @ B @ F @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(321,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ~ ( member_nat @ B @ C )
=> ( B = A ) )
=> ( member_nat @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_insertCI) ).
thf(1798,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ~ ( member_nat @ B @ C )
=> ( B = A ) )
=> ( member_nat @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(32,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ bot_bo70021908tate_o )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_Int__empty__right) ).
thf(712,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ bot_bo70021908tate_o )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(261,axiom,
! [A: nat,B: nat > $o] :
( bot_bot_nat_o
!= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_empty__not__insert) ).
thf(1516,plain,
! [A: nat,B: nat > $o] :
( bot_bot_nat_o
!= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(639,plain,
! [B: nat > $o,A: nat > $o] :
( ~ ( finite_finite_nat @ B )
| ( ( semila848761471_nat_o @ B @ A )
= ( finite326637109_nat_o @ insert_nat @ A @ B ) ) ),
inference(cnf,[status(esa)],[638]) ).
thf(640,plain,
! [B: nat > $o,A: nat > $o] :
( ( ( finite326637109_nat_o @ insert_nat @ A @ B )
= ( semila848761471_nat_o @ B @ A ) )
| ~ ( finite_finite_nat @ B ) ),
inference(lifteq,[status(thm)],[639]) ).
thf(131,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le827224136tate_o @ C @ B )
=> ( ( A @ bot_bo70021908tate_o )
=> ( ! [D: hoare_1167836817_state,E: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ E )
=> ( ( member2058392318_state @ D @ B )
=> ( ~ ( member2058392318_state @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert2134838167_state @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_finite__subset__induct) ).
thf(1070,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le827224136tate_o @ C @ B )
=> ( ( A @ bot_bo70021908tate_o )
=> ( ! [D: hoare_1167836817_state,E: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ E )
=> ( ( member2058392318_state @ D @ B )
=> ( ~ ( member2058392318_state @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert2134838167_state @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(175,axiom,
! [A: state] : ( evalc @ skip @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_evalc_OSkip) ).
thf(1225,plain,
! [A: state] : ( evalc @ skip @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(2191,plain,
( ( semila10642723_sup_o @ $true @ bot_bot_o )
= $true ),
inference(instance,[status(thm)],[2190]) ).
thf(2192,plain,
semila10642723_sup_o @ $true @ bot_bot_o,
inference(simp,[status(thm)],[2191]) ).
thf(107,axiom,
! [A: ( nat > $o ) > $o,B: nat > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ B )
=> ( ( A @ bot_bot_nat_o )
=> ( ! [D: nat,E: nat > $o] :
( ( finite_finite_nat @ E )
=> ( ( member_nat @ D @ B )
=> ( ~ ( member_nat @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_nat @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_finite__subset__induct) ).
thf(971,plain,
! [A: ( nat > $o ) > $o,B: nat > $o,C: nat > $o] :
( ( finite_finite_nat @ C )
=> ( ( ord_less_eq_nat_o @ C @ B )
=> ( ( A @ bot_bot_nat_o )
=> ( ! [D: nat,E: nat > $o] :
( ( finite_finite_nat @ E )
=> ( ( member_nat @ D @ B )
=> ( ~ ( member_nat @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_nat @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(355,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_singletonE) ).
thf(1941,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(108,axiom,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ! [B: nat,C: nat] : ( member_nat @ ( semila972727038up_nat @ B @ C ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_nat_o ) ) )
=> ( member_nat @ ( big_la43341705in_nat @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_Sup__fin_Oclosed) ).
thf(993,plain,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ! [B: nat,C: nat] : ( member_nat @ ( semila972727038up_nat @ B @ C ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_nat_o ) ) )
=> ( member_nat @ ( big_la43341705in_nat @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(267,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( insert_nat @ B @ ( semila1947288293_nat_o @ A @ C ) ) ) )
& ( ~ ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( semila1947288293_nat_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_Int__insert__left) ).
thf(1547,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( insert_nat @ B @ ( semila1947288293_nat_o @ A @ C ) ) ) )
& ( ~ ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( semila1947288293_nat_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(311,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ A )
| ( member2122167641iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_Un__def) ).
thf(1748,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( semila13410563le_a_o @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ A )
| ( member2122167641iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(487,axiom,
! [A: hoare_1775062406iple_a > nat,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( image_1806517641_a_nat @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( insert_nat @ ( A @ B ) @ ( image_1806517641_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_image__insert) ).
thf(2397,plain,
! [A: hoare_1775062406iple_a > nat,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( image_1806517641_a_nat @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( insert_nat @ ( A @ B ) @ ( image_1806517641_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ~ ( fequal_nat @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(1025,plain,
! [A: nat,B: nat] :
( ~ ( fequal_nat @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(484,axiom,
! [A: x_a > state > $o,B: hoare_1775062406iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ C @ D @ E ) @ bot_bo751897185le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ A @ D @ E ) @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_conseq1) ).
thf(2386,plain,
! [A: x_a > state > $o,B: hoare_1775062406iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ C @ D @ E ) @ bot_bo751897185le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ A @ D @ E ) @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(490,axiom,
! [A: hoare_1775062406iple_a > $o] : ( ord_le1143225901le_a_o @ bot_bo751897185le_a_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_bot__least) ).
thf(2407,plain,
! [A: hoare_1775062406iple_a > $o] : ( ord_le1143225901le_a_o @ bot_bo751897185le_a_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(187,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_insertI2) ).
thf(1267,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(608,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C = A )
| ( member2122167641iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_insert__compr) ).
thf(2850,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C = A )
| ( member2122167641iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(414,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ B @ C )
=> ( ( C @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_folding__one_Osingleton) ).
thf(2160,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ B @ C )
=> ( ( C @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(434,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( minus_1944206118le_a_o @ B @ C ) )
=> ~ ( ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_DiffE) ).
thf(2224,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( minus_1944206118le_a_o @ B @ C ) )
=> ~ ( ( member2122167641iple_a @ A @ B )
=> ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(163,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ B @ ( semila848761471_nat_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_UnI1) ).
thf(1188,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member_nat @ B @ ( semila848761471_nat_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(121,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ord_less_eq_nat_o @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) ) @ C )
=> ( ( member_nat @ B @ A )
=> ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_diff__single__insert) ).
thf(1038,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ord_less_eq_nat_o @ ( minus_minus_nat_o @ A @ ( insert_nat @ B @ bot_bot_nat_o ) ) @ C )
=> ( ( member_nat @ B @ A )
=> ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(465,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( the_el1844711461iple_a @ A )
= ( the_Ho1155011127iple_a
@ ^ [B: hoare_1775062406iple_a] :
( A
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_the__elem__def) ).
thf(2322,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( the_el1844711461iple_a @ A )
= ( the_Ho1155011127iple_a
@ ^ [B: hoare_1775062406iple_a] :
( A
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(102,axiom,
! [A: nat > nat > nat,B: nat > $o,C: nat] :
( ( finite_fold1Set_nat @ A @ B @ C )
=> ( B != bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_fold1Set__nonempty) ).
thf(951,plain,
! [A: nat > nat > nat,B: nat > $o,C: nat] :
( ( finite_fold1Set_nat @ A @ B @ C )
=> ( B != bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(302,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( image_31595733_state
@ ^ [D: hoare_1167836817_state] : A
@ C )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_image__constant) ).
thf(1711,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( image_31595733_state
@ ^ [D: hoare_1167836817_state] : A
@ C )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(325,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ~ ( member_nat @ B @ A )
=> ( ( ( insert_nat @ B @ C )
= ( insert_nat @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_insert__ident) ).
thf(1813,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ~ ( member_nat @ B @ A )
=> ( ( ( insert_nat @ B @ C )
= ( insert_nat @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(240,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_Int__insert__right__if1) ).
thf(1452,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(286,axiom,
! [A: hoare_1167836817_state] :
~ ( member2058392318_state @ A @ bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_emptyE) ).
thf(1637,plain,
! [A: hoare_1167836817_state] :
~ ( member2058392318_state @ A @ bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(624,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( semila966743401le_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_Int__insert__left__if0) ).
thf(2920,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ ( insert1281456128iple_a @ B @ A ) @ C )
= ( semila966743401le_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(56,axiom,
! [A: nat > $o,B: nat > $o,C: nat] :
( ( semila1947288293_nat_o
@ ^ [D: nat] : ( member_nat @ D @ A )
@ ^ [D: nat] : ( member_nat @ D @ B )
@ C )
= ( member_nat @ C @ ( semila1947288293_nat_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_inf__Int__eq) ).
thf(791,plain,
! [A: nat > $o,B: nat > $o,C: nat] :
( ( semila1947288293_nat_o
@ ^ [D: nat] : ( member_nat @ D @ A )
@ ^ [D: nat] : ( member_nat @ D @ B )
@ C )
= ( member_nat @ C @ ( semila1947288293_nat_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(1979,plain,
( ( semila10642723_sup_o @ bot_bot_o @ $true )
= $true ),
inference(instance,[status(thm)],[1978]) ).
thf(1980,plain,
semila10642723_sup_o @ bot_bot_o @ $true,
inference(simp,[status(thm)],[1979]) ).
thf(406,axiom,
! [A: nat,B: hoare_1775062406iple_a > nat,C: hoare_1775062406iple_a > $o] :
( ( member_nat @ A @ ( image_1806517641_a_nat @ B @ C ) )
= ( ? [D: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_image__iff) ).
thf(2128,plain,
! [A: nat,B: hoare_1775062406iple_a > nat,C: hoare_1775062406iple_a > $o] :
( ( member_nat @ A @ ( image_1806517641_a_nat @ B @ C ) )
= ( ? [D: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(145,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_subsetD) ).
thf(1130,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(275,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ! [C: hoare_1167836817_state] : ( A @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ( D != bot_bo70021908tate_o )
=> ( ~ ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert2134838167_state @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_finite__ne__induct) ).
thf(1579,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ! [C: hoare_1167836817_state] : ( A @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ( D != bot_bo70021908tate_o )
=> ( ~ ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert2134838167_state @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(206,axiom,
! [A: hoare_1167836817_state > $o] :
( ( bot_bo70021908tate_o
= ( collec1027672124_state @ A ) )
= ( ! [B: hoare_1167836817_state] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_empty__Collect__eq) ).
thf(1336,plain,
! [A: hoare_1167836817_state > $o] :
( ( bot_bo70021908tate_o
= ( collec1027672124_state @ A ) )
= ( ! [B: hoare_1167836817_state] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(642,plain,
! [C: nat > $o,B: nat,A: nat] :
( ~ ( finite_finite_nat @ C )
| ( ( finite_fold_nat_nat @ semila972727038up_nat @ A @ ( insert_nat @ B @ C ) )
= ( semila972727038up_nat @ B @ ( finite_fold_nat_nat @ semila972727038up_nat @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[641]) ).
thf(643,plain,
! [C: nat > $o,B: nat,A: nat] :
( ( ( finite_fold_nat_nat @ semila972727038up_nat @ A @ ( insert_nat @ B @ C ) )
= ( semila972727038up_nat @ B @ ( finite_fold_nat_nat @ semila972727038up_nat @ A @ C ) ) )
| ~ ( finite_finite_nat @ C ) ),
inference(lifteq,[status(thm)],[642]) ).
thf(266,axiom,
! [A: nat > $o,B: hoare_1167836817_state,C: nat > hoare_1167836817_state,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member2058392318_state @ B @ ( image_2121260246_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_image__eqI) ).
thf(1543,plain,
! [A: nat > $o,B: hoare_1167836817_state,C: nat > hoare_1167836817_state,D: nat] :
( ( B
= ( C @ D ) )
=> ( ( member_nat @ D @ A )
=> ( member2058392318_state @ B @ ( image_2121260246_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(185,axiom,
! [A: com,B: state,C: loc,D: state > nat,E: state] :
( ( evalc @ A @ ( update @ B @ ( loc_1 @ C ) @ ( D @ B ) ) @ E )
=> ( evalc @ ( local @ C @ D @ A ) @ B @ ( update @ E @ ( loc_1 @ C ) @ ( getlocs @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_evalc_OLocal) ).
thf(1257,plain,
! [A: com,B: state,C: loc,D: state > nat,E: state] :
( ( evalc @ A @ ( update @ B @ ( loc_1 @ C ) @ ( D @ B ) ) @ E )
=> ( evalc @ ( local @ C @ D @ A ) @ B @ ( update @ E @ ( loc_1 @ C ) @ ( getlocs @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(149,axiom,
! [A: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ A )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_Diff__cancel) ).
thf(1141,plain,
! [A: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ A )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(78,axiom,
! [A: nat > $o] :
( ( semila848761471_nat_o @ bot_bot_nat_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_sup__bot__left) ).
thf(864,plain,
! [A: nat > $o] :
( ( semila848761471_nat_o @ bot_bot_nat_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(257,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ C ) )
= ( ( member2122167641iple_a @ A @ B )
& ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_Int__iff) ).
thf(1504,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ C ) )
= ( ( member2122167641iple_a @ A @ B )
& ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(519,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ bot_bo751897185le_a_o @ A )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_Int__empty__left) ).
thf(2511,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ bot_bo751897185le_a_o @ A )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(534,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( finite1790765286iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_fold1__singleton) ).
thf(2584,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( finite1790765286iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(10,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ ( insert_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_finite_OinsertI) ).
thf(656,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ ( insert_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(117,axiom,
! [A: com,B: state,C: nat,D: state] :
( ( evaln @ A @ B @ C @ D )
=> ( evalc @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_evaln__evalc) ).
thf(1023,plain,
! [A: com,B: state,C: nat,D: state] :
( ( evaln @ A @ B @ C @ D )
=> ( evalc @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(452,axiom,
! [A: loc,B: state > nat,C: com,D: com,E: com] :
( ( local @ A @ B @ C )
!= ( semi @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_com_Osimps_I34_J) ).
thf(2279,plain,
! [A: loc,B: state > nat,C: com,D: com,E: com] :
( ( local @ A @ B @ C )
!= ( semi @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(364,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( insert_nat @ B @ ( semila1947288293_nat_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_Int__insert__left__if1) ).
thf(1972,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ ( insert_nat @ B @ A ) @ C )
= ( insert_nat @ B @ ( semila1947288293_nat_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(125,axiom,
! [A: nat > $o] :
( ( semila848761471_nat_o @ A @ bot_bot_nat_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_Un__empty__right) ).
thf(1052,plain,
! [A: nat > $o] :
( ( semila848761471_nat_o @ A @ bot_bot_nat_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(570,axiom,
! [A: hoare_1775062406iple_a] :
( ( bot_bo751897185le_a_o @ A )
= ( member2122167641iple_a @ A @ bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_bot__empty__eq) ).
thf(2711,plain,
! [A: hoare_1775062406iple_a] :
( ( bot_bo751897185le_a_o @ A )
= ( member2122167641iple_a @ A @ bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(574,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) @ C )
=> ( ( member2122167641iple_a @ B @ A )
=> ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_diff__single__insert) ).
thf(2722,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) @ C )
=> ( ( member2122167641iple_a @ B @ A )
=> ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(112,axiom,
! [A: nat > $o,B: nat > $o] :
( ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila1947288293_nat_o @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_Collect__conj__eq) ).
thf(1008,plain,
! [A: nat > $o,B: nat > $o] :
( ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila1947288293_nat_o @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(304,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( minus_2107060239tate_o @ A @ C ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( minus_2107060239tate_o @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_insert__Diff__if) ).
thf(1717,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( minus_2107060239tate_o @ A @ C ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( minus_2107060239tate_o @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(381,axiom,
! [A: $o] :
( ( ord_less_eq_o @ A @ bot_bot_o )
=> ( A = bot_bot_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_le__bot) ).
thf(2030,plain,
! [A: $o] :
( ( ord_less_eq_o @ A @ bot_bot_o )
=> ( A = bot_bot_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(218,axiom,
! [A: nat,B: ( nat > $o ) > nat,C: nat > nat > nat] :
( ( B
= ( finite_fold1_nat @ C ) )
=> ( ( B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_fold1__singleton__def) ).
thf(1372,plain,
! [A: nat,B: ( nat > $o ) > nat,C: nat > nat > nat] :
( ( B
= ( finite_fold1_nat @ C ) )
=> ( ( B @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(616,axiom,
! [A: hoare_1167836817_state > hoare_1775062406iple_a,B: hoare_1167836817_state > $o] :
( ( ( image_1802845250iple_a @ A @ B )
= bot_bo751897185le_a_o )
= ( B = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_image__is__empty) ).
thf(2892,plain,
! [A: hoare_1167836817_state > hoare_1775062406iple_a,B: hoare_1167836817_state > $o] :
( ( ( image_1802845250iple_a @ A @ B )
= bot_bo751897185le_a_o )
= ( B = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(2807,plain,
( ( collect_nat_o
@ ^ [A: nat > $o] : $false )
= bot_bot_nat_o_o ),
inference(lifteq,[status(thm)],[2806]) ).
thf(190,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( semila1947288293_nat_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_Int__insert__right__if0) ).
thf(1272,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( semila1947288293_nat_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(447,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( minus_1944206118le_a_o @ B @ C ) )
=> ~ ( member2122167641iple_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_DiffD2) ).
thf(2266,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( minus_1944206118le_a_o @ B @ C ) )
=> ~ ( member2122167641iple_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(82,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ~ ( member_nat @ B @ A )
=> ( member_nat @ B @ ( minus_minus_nat_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_DiffI) ).
thf(876,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ~ ( member_nat @ B @ A )
=> ( member_nat @ B @ ( minus_minus_nat_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(612,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ A @ B )
=> ( ( minus_1944206118le_a_o @ ( insert1281456128iple_a @ A @ B ) @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_Diff__insert__absorb) ).
thf(2865,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ A @ B )
=> ( ( minus_1944206118le_a_o @ ( insert1281456128iple_a @ A @ B ) @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(330,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1167836817_state,C: hoare_1775062406iple_a > hoare_1167836817_state,D: hoare_1775062406iple_a] :
( ( B
= ( C @ D ) )
=> ( ( member2122167641iple_a @ D @ A )
=> ( member2058392318_state @ B @ ( image_1021683026_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_image__eqI) ).
thf(1839,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1167836817_state,C: hoare_1775062406iple_a > hoare_1167836817_state,D: hoare_1775062406iple_a] :
( ( B
= ( C @ D ) )
=> ( ( member2122167641iple_a @ D @ A )
=> ( member2058392318_state @ B @ ( image_1021683026_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(350,axiom,
! [A: com,B: com,C: vname,D: state > nat] :
( ( semi @ A @ B )
!= ( ass @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_com_Osimps_I25_J) ).
thf(1918,plain,
! [A: com,B: com,C: vname,D: state > nat] :
( ( semi @ A @ B )
!= ( ass @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(511,axiom,
! [A: x_a > state > $o,B: hoare_1775062406iple_a > $o,C: com,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ? [G: x_a > state > $o,H: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ G @ C @ H ) @ bot_bo751897185le_a_o ) )
& ! [I: state] :
( ! [J: x_a] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ C @ A ) @ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_conseq) ).
thf(2479,plain,
! [A: x_a > state > $o,B: hoare_1775062406iple_a > $o,C: com,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ? [G: x_a > state > $o,H: x_a > state > $o] :
( ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ G @ C @ H ) @ bot_bo751897185le_a_o ) )
& ! [I: state] :
( ! [J: x_a] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_1508237396rivs_a @ B @ ( insert1281456128iple_a @ ( hoare_1766022166iple_a @ D @ C @ A ) @ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(397,axiom,
! [A: hoare_1167836817_state > hoare_1775062406iple_a,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2122167641iple_a @ ( A @ B ) @ ( image_1802845250iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_imageI) ).
thf(2088,plain,
! [A: hoare_1167836817_state > hoare_1775062406iple_a,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2122167641iple_a @ ( A @ B ) @ ( image_1802845250iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(385,axiom,
! [A: hoare_1167836817_state > $o,B: state > state > $o] : ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ skip @ B ) @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_hoare__derivs_OSkip) ).
thf(2045,plain,
! [A: hoare_1167836817_state > $o,B: state > state > $o] : ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ skip @ B ) @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(160,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( semila1172322802tate_o @ B @ A )
= ( finite291020855tate_o @ insert2134838167_state @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_union__fold__insert) ).
thf(1180,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( semila1172322802tate_o @ B @ A )
= ( finite291020855tate_o @ insert2134838167_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(362,axiom,
! [A: vname,B: state > nat,C: state,D: nat,E: state] :
( ( evaln @ ( ass @ A @ B ) @ C @ D @ E )
=> ( E
= ( update @ C @ A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_evaln__elim__cases_I2_J) ).
thf(1966,plain,
! [A: vname,B: state > nat,C: state,D: nat,E: state] :
( ( evaln @ ( ass @ A @ B ) @ C @ D @ E )
=> ( E
= ( update @ C @ A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(95,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_in__mono) ).
thf(931,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ B @ C )
=> ( ( member_nat @ A @ B )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(566,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ bot_bo751897185le_a_o @ A )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_inf__bot__left) ).
thf(2696,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( semila966743401le_a_o @ bot_bo751897185le_a_o @ A )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(614,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( B = bot_bo751897185le_a_o )
=> ~ ( member2122167641iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_equals0D) ).
thf(2870,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( B = bot_bo751897185le_a_o )
=> ~ ( member2122167641iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(461,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( finite1946188886iple_a @ A @ B @ C )
=> ( B != bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_fold1Set__nonempty) ).
thf(2310,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( finite1946188886iple_a @ A @ B @ C )
=> ( B != bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(2193,plain,
( ( semila10642723_sup_o @ $false @ bot_bot_o )
= $false ),
inference(instance,[status(thm)],[2190]) ).
thf(2194,plain,
~ ( semila10642723_sup_o @ $false @ bot_bot_o ),
inference(simp,[status(thm)],[2193]) ).
thf(466,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o )
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_singleton__inject) ).
thf(2325,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o )
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(143,axiom,
finite_finite_nat @ bot_bot_nat_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_finite_OemptyI) ).
thf(1126,plain,
finite_finite_nat @ bot_bot_nat_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(74,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ ( collect_nat @ B ) )
| ( finite_finite_nat @ ( collect_nat @ A ) ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_finite__Collect__conjI) ).
thf(845,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ ( collect_nat @ B ) )
| ( finite_finite_nat @ ( collect_nat @ A ) ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(582,axiom,
! [A: hoare_1775062406iple_a > hoare_1167836817_state,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( image_1021683026_state @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( insert2134838167_state @ ( A @ B ) @ ( image_1021683026_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_image__insert) ).
thf(2760,plain,
! [A: hoare_1775062406iple_a > hoare_1167836817_state,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( image_1021683026_state @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( insert2134838167_state @ ( A @ B ) @ ( image_1021683026_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(154,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( ( partia715677851_state @ B @ A )
= B ) )
& ( ~ ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( ( partia715677851_state @ B @ A )
= ( the_Ho310147232_state
@ ^ [C: hoare_1167836817_state] : ( member2058392318_state @ C @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_flat__lub__def) ).
thf(1157,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( ( partia715677851_state @ B @ A )
= B ) )
& ( ~ ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( ( partia715677851_state @ B @ A )
= ( the_Ho310147232_state
@ ^ [C: hoare_1167836817_state] : ( member2058392318_state @ C @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(204,axiom,
! [A: loc,B: glb] :
( ( loc_1 @ A )
!= ( glb_1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_vname_Osimps_I4_J) ).
thf(1321,plain,
! [A: loc,B: glb] :
( ( loc_1 @ A )
!= ( glb_1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(348,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( minus_minus_nat_o @ A @ ( insert_nat @ B @ C ) )
= ( minus_minus_nat_o @ ( minus_minus_nat_o @ A @ C ) @ ( insert_nat @ B @ bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_Diff__insert) ).
thf(1913,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( minus_minus_nat_o @ A @ ( insert_nat @ B @ C ) )
= ( minus_minus_nat_o @ ( minus_minus_nat_o @ A @ C ) @ ( insert_nat @ B @ bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(86,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ~ ( fequal1831255762_state @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com) ).
thf(891,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ~ ( fequal1831255762_state @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(429,axiom,
! [A: hoare_1167836817_state,B: hoare_1775062406iple_a > hoare_1167836817_state,C: hoare_1775062406iple_a > $o] :
( ( member2058392318_state @ A @ ( image_1021683026_state @ B @ C ) )
= ( ? [D: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_image__iff) ).
thf(2209,plain,
! [A: hoare_1167836817_state,B: hoare_1775062406iple_a > hoare_1167836817_state,C: hoare_1775062406iple_a > $o] :
( ( member2058392318_state @ A @ ( image_1021683026_state @ B @ C ) )
= ( ? [D: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(514,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
=> ? [C: hoare_1775062406iple_a > $o] :
( ( B
= ( insert1281456128iple_a @ A @ C ) )
& ~ ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_mk__disjoint__insert) ).
thf(2490,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
=> ? [C: hoare_1775062406iple_a > $o] :
( ( B
= ( insert1281456128iple_a @ A @ C ) )
& ~ ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(423,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ! [B: hoare_1167836817_state] :
~ ( member2058392318_state @ B @ A ) )
= ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_all__not__in__conv) ).
thf(2187,plain,
! [A: hoare_1167836817_state > $o] :
( ( ! [B: hoare_1167836817_state] :
~ ( member2058392318_state @ B @ A ) )
= ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(223,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( image_1170193413iple_a
@ ^ [B: hoare_1775062406iple_a] : B
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_image__ident) ).
thf(1390,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( image_1170193413iple_a
@ ^ [B: hoare_1775062406iple_a] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(459,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = A )
| ( member2058392318_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_insert__compr__raw) ).
thf(2305,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = A )
| ( member2058392318_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(392,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
!= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_insert__not__empty) ).
thf(2071,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
!= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(587,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ? [C: hoare_1775062406iple_a] : ( finite1946188886iple_a @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_finite__nonempty__imp__fold1Set) ).
thf(2775,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ? [C: hoare_1775062406iple_a] : ( finite1946188886iple_a @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(592,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ B )
=> ( hoare_1508237396rivs_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_asm) ).
thf(2792,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ord_le1143225901le_a_o @ A @ B )
=> ( hoare_1508237396rivs_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(323,axiom,
! [A: nat,B: nat] :
( ( member_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_singletonE) ).
thf(1807,plain,
! [A: nat,B: nat] :
( ( member_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(49,axiom,
! [A: nat > $o,B: nat] : ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_subset__insertI) ).
thf(771,plain,
! [A: nat > $o,B: nat] : ( ord_less_eq_nat_o @ A @ ( insert_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(621,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ B @ ( insert1281456128iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_insertI2) ).
thf(2907,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member2122167641iple_a @ B @ ( insert1281456128iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(2591,plain,
( ( collec676402587iple_a
@ ^ [A: hoare_1775062406iple_a] : $false )
= bot_bo751897185le_a_o ),
inference(lifteq,[status(thm)],[2590]) ).
thf(289,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( A @ B )
=> ( ! [C: hoare_1775062406iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_Ho1155011127iple_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_theI) ).
thf(1646,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( A @ B )
=> ( ! [C: hoare_1775062406iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_Ho1155011127iple_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(26,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ ( A @ B ) @ ( image_31595733_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_imageI) ).
thf(699,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ ( A @ B ) @ ( image_31595733_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(408,axiom,
! [A: loc,B: loc] :
( ( ( loc_1 @ A )
= ( loc_1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_vname_Osimps_I2_J) ).
thf(2135,plain,
! [A: loc,B: loc] :
( ( ( loc_1 @ A )
= ( loc_1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(525,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( minus_1944206118le_a_o @ A @ B )
= ( finite1544171829le_a_o
@ ^ [C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] : ( minus_1944206118le_a_o @ D @ ( insert1281456128iple_a @ C @ bot_bo751897185le_a_o ) )
@ A
@ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_minus__fold__remove) ).
thf(2554,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( minus_1944206118le_a_o @ A @ B )
= ( finite1544171829le_a_o
@ ^ [C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] : ( minus_1944206118le_a_o @ D @ ( insert1281456128iple_a @ C @ bot_bo751897185le_a_o ) )
@ A
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(128,axiom,
! [A: com,B: state,C: state] :
( ( evalc @ A @ B @ C )
=> ? [D: nat] : ( evaln @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_evalc__evaln) ).
thf(1062,plain,
! [A: com,B: state,C: state] :
( ( evalc @ A @ B @ C )
=> ? [D: nat] : ( evaln @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(250,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( ord_le1143225901le_a_o @ C @ A )
=> ( member2122167641iple_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_set__rev__mp) ).
thf(1481,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( ord_le1143225901le_a_o @ C @ A )
=> ( member2122167641iple_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(2004,plain,
ord_less_eq_o @ bot_bot_o @ $false,
inference(instance,[status(thm)],[2002]) ).
thf(310,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( ( insert2134838167_state @ A @ bot_bo70021908tate_o )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_singleton__inject) ).
thf(1745,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( ( insert2134838167_state @ A @ bot_bo70021908tate_o )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(380,axiom,
! [A: com,B: com,C: loc,D: state > nat,E: com] :
( ( semi @ A @ B )
!= ( local @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_com_Osimps_I35_J) ).
thf(2026,plain,
! [A: com,B: com,C: loc,D: state > nat,E: com] :
( ( semi @ A @ B )
!= ( local @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(542,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( ( A @ B )
=> ( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Collect__conv__if) ).
thf(2608,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( ( A @ B )
=> ( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(181,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_Int__empty__left) ).
thf(1244,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(104,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( member_nat @ C @ B )
=> ( member_nat @ C @ A ) )
=> ( ord_less_eq_nat_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_subsetI) ).
thf(961,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( member_nat @ C @ B )
=> ( member_nat @ C @ A ) )
=> ( ord_less_eq_nat_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(63,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite1084549118_state @ ( insert2134838167_state @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_finite_OinsertI) ).
thf(813,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite1084549118_state @ ( insert2134838167_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(221,axiom,
! [A: hoare_1775062406iple_a > nat,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_1806517641_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_imageI) ).
thf(1385,plain,
! [A: hoare_1775062406iple_a > nat,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( member_nat @ ( A @ B ) @ ( image_1806517641_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(418,axiom,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: vname,D: state > nat] :
( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [E: state,F: state] : ( B @ E @ ( update @ F @ C @ ( D @ F ) ) )
@ ( ass @ C @ D )
@ B )
@ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Ass) ).
thf(2174,plain,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: vname,D: state > nat] :
( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [E: state,F: state] : ( B @ E @ ( update @ F @ C @ ( D @ F ) ) )
@ ( ass @ C @ D )
@ B )
@ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(453,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( C = A )
| ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_insert__compr) ).
thf(2283,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( collect_nat
@ ^ [C: nat] :
( ( C = A )
| ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(248,axiom,
! [A: nat > $o] :
( ( bot_bot_nat_o
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_empty__Collect__eq) ).
thf(1476,plain,
! [A: nat > $o] :
( ( bot_bot_nat_o
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(208,axiom,
! [A: nat > hoare_1775062406iple_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member2122167641iple_a @ ( A @ B ) @ ( image_43014529iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_imageI) ).
thf(1341,plain,
! [A: nat > hoare_1775062406iple_a,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( member2122167641iple_a @ ( A @ B ) @ ( image_43014529iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(401,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_mem__def) ).
thf(2098,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(609,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
= ( semila13410563le_a_o
@ ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] : ( C = A ) )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_insert__def) ).
thf(2853,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ B )
= ( semila13410563le_a_o
@ ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] : ( C = A ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(455,axiom,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= ( member2058392318_state @ A @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_bot__empty__eq) ).
thf(2290,plain,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= ( member2058392318_state @ A @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(443,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( A != B )
| ( fequal1288209029iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_) ).
thf(2251,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ( A != B )
| ( fequal1288209029iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(630,axiom,
! [A: ( hoare_1775062406iple_a > $o ) > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ( ! [C: hoare_1775062406iple_a] : ( A @ ( insert1281456128iple_a @ C @ bot_bo751897185le_a_o ) )
=> ( ! [C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ D )
=> ( ( D != bot_bo751897185le_a_o )
=> ( ~ ( member2122167641iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert1281456128iple_a @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_finite__ne__induct) ).
thf(2934,plain,
! [A: ( hoare_1775062406iple_a > $o ) > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ( ! [C: hoare_1775062406iple_a] : ( A @ ( insert1281456128iple_a @ C @ bot_bo751897185le_a_o ) )
=> ( ! [C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a @ D )
=> ( ( D != bot_bo751897185le_a_o )
=> ( ~ ( member2122167641iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert1281456128iple_a @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(412,axiom,
! [A: vname,B: state > nat,C: com,D: com] :
( ( ass @ A @ B )
!= ( semi @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_com_Osimps_I24_J) ).
thf(2152,plain,
! [A: vname,B: state > nat,C: com,D: com] :
( ( ass @ A @ B )
!= ( semi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(502,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( insert1281456128iple_a @ ( A @ B ) @ ( image_1170193413iple_a @ A @ C ) )
= ( image_1170193413iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_insert__image) ).
thf(2447,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ B @ C )
=> ( ( insert1281456128iple_a @ ( A @ B ) @ ( image_1170193413iple_a @ A @ C ) )
= ( image_1170193413iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(631,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( ( A = B )
| ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_insert__iff) ).
thf(2956,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( ( A = B )
| ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(590,axiom,
! [A: hoare_1775062406iple_a > hoare_1167836817_state,B: hoare_1775062406iple_a > $o] :
( ( bot_bo70021908tate_o
= ( image_1021683026_state @ A @ B ) )
= ( B = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_empty__is__image) ).
thf(2786,plain,
! [A: hoare_1775062406iple_a > hoare_1167836817_state,B: hoare_1775062406iple_a > $o] :
( ( bot_bo70021908tate_o
= ( image_1021683026_state @ A @ B ) )
= ( B = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(623,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( ( A @ B )
=> ( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Collect__conv__if2) ).
thf(2912,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( ( A @ B )
=> ( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(507,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > hoare_1775062406iple_a,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ! [E: hoare_1775062406iple_a,F: hoare_1775062406iple_a] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite2063573081iple_a @ A )
=> ( ( A != bot_bo751897185le_a_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_1170193413iple_a @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_folding__one__idem_Ohom__commute) ).
thf(2462,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > hoare_1775062406iple_a,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ! [E: hoare_1775062406iple_a,F: hoare_1775062406iple_a] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite2063573081iple_a @ A )
=> ( ( A != bot_bo751897185le_a_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_1170193413iple_a @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(278,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state,D: hoare_1167836817_state] :
( ( ( insert2134838167_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= ( insert2134838167_state @ C @ ( insert2134838167_state @ D @ bot_bo70021908tate_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_doubleton__eq__iff) ).
thf(1607,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state,D: hoare_1167836817_state] :
( ( ( insert2134838167_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= ( insert2134838167_state @ C @ ( insert2134838167_state @ D @ bot_bo70021908tate_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(260,axiom,
! [A: nat > nat > nat,B: nat] :
( ( finite_fold1_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_fold1__singleton) ).
thf(1513,plain,
! [A: nat > nat > nat,B: nat] :
( ( finite_fold1_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(400,axiom,
! [A: nat > $o,B: nat > nat > nat,C: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ B @ C )
=> ( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ! [D: nat,E: nat] : ( member_nat @ ( B @ D @ E ) @ ( insert_nat @ D @ ( insert_nat @ E @ bot_bot_nat_o ) ) )
=> ( member_nat @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_folding__one_Oclosed) ).
thf(2095,plain,
! [A: nat > $o,B: nat > nat > nat,C: ( nat > $o ) > nat] :
( ( finite988810631ne_nat @ B @ C )
=> ( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ! [D: nat,E: nat] : ( member_nat @ ( B @ D @ E ) @ ( insert_nat @ D @ ( insert_nat @ E @ bot_bot_nat_o ) ) )
=> ( member_nat @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(462,axiom,
finite2120172977le_a_o @ insert1281456128iple_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_comp__fun__idem__insert) ).
thf(2315,plain,
finite2120172977le_a_o @ insert1281456128iple_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(579,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ E )
=> ( ( finite727644230iple_a @ E @ A @ ( insert1281456128iple_a @ B @ C ) @ D )
=> ( ~ ( member2122167641iple_a @ B @ C )
=> ~ ! [F: hoare_1775062406iple_a] :
( ( D
= ( E @ B @ F ) )
=> ~ ( finite727644230iple_a @ E @ A @ C @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_comp__fun__commute_Ofold__graph__insertE) ).
thf(2739,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o,D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a] :
( ( finite2064891473iple_a @ E )
=> ( ( finite727644230iple_a @ E @ A @ ( insert1281456128iple_a @ B @ C ) @ D )
=> ( ~ ( member2122167641iple_a @ B @ C )
=> ~ ! [F: hoare_1775062406iple_a] :
( ( D
= ( E @ B @ F ) )
=> ~ ( finite727644230iple_a @ E @ A @ C @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(378,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila13410563le_a_o @ ( collec676402587iple_a @ A ) @ ( collec676402587iple_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_Collect__disj__eq) ).
thf(2019,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila13410563le_a_o @ ( collec676402587iple_a @ A ) @ ( collec676402587iple_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(89,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert2134838167_state @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_Un__insert__right) ).
thf(899,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert2134838167_state @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(291,axiom,
! [A: hoare_1775062406iple_a,B: nat > hoare_1775062406iple_a,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2122167641iple_a @ A @ ( image_43014529iple_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_rev__image__eqI) ).
thf(1661,plain,
! [A: hoare_1775062406iple_a,B: nat > hoare_1775062406iple_a,C: nat,D: nat > $o] :
( ( member_nat @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2122167641iple_a @ A @ ( image_43014529iple_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(2033,plain,
( ( ord_less_eq_o @ $false @ bot_bot_o )
=> ( $false = bot_bot_o ) ),
inference(instance,[status(thm)],[2030]) ).
thf(2034,plain,
( ( ord_less_eq_o @ $false @ bot_bot_o )
=> ~ bot_bot_o ),
inference(simp,[status(thm)],[2033]) ).
thf(2036,plain,
( ~ ( ord_less_eq_o @ $false @ bot_bot_o )
| ~ bot_bot_o ),
inference(cnf,[status(esa)],[2034]) ).
thf(200,axiom,
! [A: nat,B: hoare_1775062406iple_a > nat,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_1806517641_a_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_rev__image__eqI) ).
thf(1309,plain,
! [A: nat,B: hoare_1775062406iple_a > nat,C: hoare_1775062406iple_a,D: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_nat @ A @ ( image_1806517641_a_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(2003,plain,
ord_less_eq_o @ bot_bot_o @ $true,
inference(instance,[status(thm)],[2002]) ).
thf(359,axiom,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
= ( ( A = bot_bot_nat_o )
| ? [B: nat > $o,C: nat] :
( ( A
= ( insert_nat @ C @ B ) )
& ( finite_finite_nat @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_finite_Osimps) ).
thf(1957,plain,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
= ( ( A = bot_bot_nat_o )
| ? [B: nat > $o,C: nat] :
( ( A
= ( insert_nat @ C @ B ) )
& ( finite_finite_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(444,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ~ ! [C: nat > $o] :
( ( B
= ( insert_nat @ A @ C ) )
=> ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Set_Oset__insert) ).
thf(2255,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ~ ! [C: nat > $o] :
( ( B
= ( insert_nat @ A @ C ) )
=> ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(65,axiom,
! [A: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_empty__Diff) ).
thf(818,plain,
! [A: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(342,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( A @ bot_bo70021908tate_o )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ~ ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert2134838167_state @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_finite__induct) ).
thf(1876,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( A @ bot_bo70021908tate_o )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ~ ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert2134838167_state @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(387,axiom,
! [A: com,B: state,C: nat,D: state,E: com,F: state,G: nat,H: state] :
( ( evaln @ E @ F @ G @ H )
=> ( ( evaln @ A @ B @ C @ D )
=> ? [I: nat] :
( ( evaln @ E @ F @ I @ H )
& ( evaln @ A @ B @ I @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_evaln__max2) ).
thf(2050,plain,
! [A: com,B: state,C: nat,D: state,E: com,F: state,G: nat,H: state] :
( ( evaln @ E @ F @ G @ H )
=> ( ( evaln @ A @ B @ C @ D )
=> ? [I: nat] :
( ( evaln @ E @ F @ I @ H )
& ( evaln @ A @ B @ I @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(79,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
=> ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_le__bot) ).
thf(867,plain,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
=> ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(288,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ C ) )
=> ~ ( ( member2122167641iple_a @ A @ B )
=> ~ ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_IntE) ).
thf(1642,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila966743401le_a_o @ B @ C ) )
=> ~ ( ( member2122167641iple_a @ A @ B )
=> ~ ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(41,axiom,
( finite389864113_nat_o
@ ^ [A: nat,B: nat > $o] : ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_comp__fun__idem__remove) ).
thf(752,plain,
( finite389864113_nat_o
@ ^ [A: nat,B: nat > $o] : ( minus_minus_nat_o @ B @ ( insert_nat @ A @ bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(458,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( insert2134838167_state @ A @ B ) )
= ( insert2134838167_state @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_insert__absorb2) ).
thf(2302,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( insert2134838167_state @ A @ B ) )
= ( insert2134838167_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(521,axiom,
! [A: hoare_1167836817_state > hoare_1775062406iple_a,B: hoare_1167836817_state > $o] :
( ( bot_bo751897185le_a_o
= ( image_1802845250iple_a @ A @ B ) )
= ( B = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_empty__is__image) ).
thf(2517,plain,
! [A: hoare_1167836817_state > hoare_1775062406iple_a,B: hoare_1167836817_state > $o] :
( ( bot_bo751897185le_a_o
= ( image_1802845250iple_a @ A @ B ) )
= ( B = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(305,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state] :
( ( finite309220289_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) @ C )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_fold1Set__sing) ).
thf(1725,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state] :
( ( finite309220289_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) @ C )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(193,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ( ( insert2134838167_state @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_insert__absorb) ).
thf(1280,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ( ( insert2134838167_state @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(70,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ bot_bo70021908tate_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_sup__bot__right) ).
thf(833,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ bot_bo70021908tate_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(573,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( ( A = bot_bo751897185le_a_o )
| ( A
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_subset__singletonD) ).
thf(2719,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a] :
( ( ord_le1143225901le_a_o @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) )
=> ( ( A = bot_bo751897185le_a_o )
| ( A
= ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(134,axiom,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ! [B: nat,C: nat] : ( member_nat @ ( times_times_nat @ B @ C ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_nat_o ) ) )
=> ( member_nat @ ( finite_fold1_nat @ times_times_nat @ A ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_fold1__in) ).
thf(1097,plain,
! [A: nat > $o] :
( ( finite_finite_nat @ A )
=> ( ( A != bot_bot_nat_o )
=> ( ! [B: nat,C: nat] : ( member_nat @ ( times_times_nat @ B @ C ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_nat_o ) ) )
=> ( member_nat @ ( finite_fold1_nat @ times_times_nat @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(535,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ B @ C )
=> ( ~ ( member2122167641iple_a @ B @ A )
=> ( ( ( insert1281456128iple_a @ B @ C )
= ( insert1281456128iple_a @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_insert__ident) ).
thf(2587,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ B @ C )
=> ( ~ ( member2122167641iple_a @ B @ A )
=> ( ( ( insert1281456128iple_a @ B @ C )
= ( insert1281456128iple_a @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(578,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,C: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ B @ C )
=> ( ( finite2063573081iple_a @ A )
=> ( ( A != bot_bo751897185le_a_o )
=> ( ! [D: hoare_1775062406iple_a,E: hoare_1775062406iple_a] : ( member2122167641iple_a @ ( B @ D @ E ) @ ( insert1281456128iple_a @ D @ ( insert1281456128iple_a @ E @ bot_bo751897185le_a_o ) ) )
=> ( member2122167641iple_a @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_folding__one_Oclosed) ).
thf(2736,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,C: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ B @ C )
=> ( ( finite2063573081iple_a @ A )
=> ( ( A != bot_bo751897185le_a_o )
=> ( ! [D: hoare_1775062406iple_a,E: hoare_1775062406iple_a] : ( member2122167641iple_a @ ( B @ D @ E ) @ ( insert1281456128iple_a @ D @ ( insert1281456128iple_a @ E @ bot_bo751897185le_a_o ) ) )
=> ( member2122167641iple_a @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(374,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ~ ( fequal1288209029iple_a @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_) ).
thf(2008,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a] :
( ~ ( fequal1288209029iple_a @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(368,axiom,
! [A: vname,B: state > nat,C: loc,D: state > nat,E: com] :
( ( ass @ A @ B )
!= ( local @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_com_Osimps_I22_J) ).
thf(1986,plain,
! [A: vname,B: state > nat,C: loc,D: state > nat,E: com] :
( ( ass @ A @ B )
!= ( local @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(336,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a
@ ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite2063573081iple_a @ ( collec676402587iple_a @ A ) )
& ( finite2063573081iple_a @ ( collec676402587iple_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_finite__Collect__disjI) ).
thf(1859,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( finite2063573081iple_a
@ ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite2063573081iple_a @ ( collec676402587iple_a @ A ) )
& ( finite2063573081iple_a @ ( collec676402587iple_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(595,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( semila966743401le_a_o @ A @ B )
= bot_bo751897185le_a_o )
= ( ! [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ A )
=> ! [D: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_disjoint__iff__not__equal) ).
thf(2800,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( semila966743401le_a_o @ A @ B )
= bot_bo751897185le_a_o )
= ( ! [C: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ C @ A )
=> ! [D: hoare_1775062406iple_a] :
( ( member2122167641iple_a @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(59,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( semila848761471_nat_o @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( semila848761471_nat_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_Un__insert__right) ).
thf(801,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( semila848761471_nat_o @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( semila848761471_nat_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(326,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B = C )
& ( A @ C ) ) )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_Collect__conv__if2) ).
thf(1816,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B = C )
& ( A @ C ) ) )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(290,axiom,
! [A: hoare_1167836817_state > $o] :
( ! [B: hoare_1167836817_state] :
~ ( member2058392318_state @ B @ A )
=> ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_equals0I) ).
thf(1657,plain,
! [A: hoare_1167836817_state > $o] :
( ! [B: hoare_1167836817_state] :
~ ( member2058392318_state @ B @ A )
=> ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(61,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( ( ( member2058392318_state @ B @ A )
=> ( ord_le827224136tate_o @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) @ C ) )
& ( ~ ( member2058392318_state @ B @ A )
=> ( ord_le827224136tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_subset__insert__iff) ).
thf(807,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( ( ( member2058392318_state @ B @ A )
=> ( ord_le827224136tate_o @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) @ C ) )
& ( ~ ( member2058392318_state @ B @ A )
=> ( ord_le827224136tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(270,axiom,
! [A: vname,B: state > nat,C: state,D: state] :
( ( evalc @ ( ass @ A @ B ) @ C @ D )
=> ( D
= ( update @ C @ A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_evalc__elim__cases_I2_J) ).
thf(1561,plain,
! [A: vname,B: state > nat,C: state,D: state] :
( ( evalc @ ( ass @ A @ B ) @ C @ D )
=> ( D
= ( update @ C @ A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(318,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ~ ( member2058392318_state @ A @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_folding__one_Oinsert) ).
thf(1789,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ~ ( member2058392318_state @ A @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(633,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( A != bot_bo751897185le_a_o )
=> ( ( ord_le1143225901le_a_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_folding__one__idem_Osubset__idem) ).
thf(2961,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( A != bot_bo751897185le_a_o )
=> ( ( ord_le1143225901le_a_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(489,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ( ( finite2063573081iple_a @ A )
=> ( ( A != bot_bo751897185le_a_o )
=> ( ( D @ ( semila13410563le_a_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_folding__one__idem_Ounion__idem) ).
thf(2404,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite1358382848iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ( B != bot_bo751897185le_a_o )
=> ( ( finite2063573081iple_a @ A )
=> ( ( A != bot_bo751897185le_a_o )
=> ( ( D @ ( semila13410563le_a_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(571,axiom,
! [A: state > nat,B: hoare_1775062406iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o,F: loc,G: state] :
( ( hoare_1508237396rivs_a @ B
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a @ C @ D
@ ^ [H: x_a,I: state] : ( E @ H @ ( update @ I @ ( loc_1 @ F ) @ ( getlocs @ G @ F ) ) ) )
@ bot_bo751897185le_a_o ) )
=> ( hoare_1508237396rivs_a @ B
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [H: x_a,I: state] :
( ( G = I )
& ( C @ H @ ( update @ I @ ( loc_1 @ F ) @ ( A @ I ) ) ) )
@ ( local @ F @ A @ D )
@ E )
@ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_hoare__derivs_OLocal) ).
thf(2714,plain,
! [A: state > nat,B: hoare_1775062406iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o,F: loc,G: state] :
( ( hoare_1508237396rivs_a @ B
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a @ C @ D
@ ^ [H: x_a,I: state] : ( E @ H @ ( update @ I @ ( loc_1 @ F ) @ ( getlocs @ G @ F ) ) ) )
@ bot_bo751897185le_a_o ) )
=> ( hoare_1508237396rivs_a @ B
@ ( insert1281456128iple_a
@ ( hoare_1766022166iple_a
@ ^ [H: x_a,I: state] :
( ( G = I )
& ( C @ H @ ( update @ I @ ( loc_1 @ F ) @ ( A @ I ) ) ) )
@ ( local @ F @ A @ D )
@ E )
@ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(544,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( semila966743401le_a_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_Int__insert__right__if0) ).
thf(2619,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ~ ( member2122167641iple_a @ B @ C )
=> ( ( semila966743401le_a_o @ C @ ( insert1281456128iple_a @ B @ A ) )
= ( semila966743401le_a_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(383,axiom,
! [A: vname,B: state > nat,C: state] : ( evalc @ ( ass @ A @ B ) @ C @ ( update @ C @ A @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_evalc_OAssign) ).
thf(2040,plain,
! [A: vname,B: state > nat,C: state] : ( evalc @ ( ass @ A @ B ) @ C @ ( update @ C @ A @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(589,axiom,
! [A: hoare_1775062406iple_a] :
~ ( member2122167641iple_a @ A @ bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_empty__iff) ).
thf(2783,plain,
! [A: hoare_1775062406iple_a] :
~ ( member2122167641iple_a @ A @ bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(309,axiom,
! [A: hoare_1775062406iple_a] :
( ( the_Ho1155011127iple_a @ ( fequal1288209029iple_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_the__sym__eq__trivial) ).
thf(1742,plain,
! [A: hoare_1775062406iple_a] :
( ( the_Ho1155011127iple_a @ ( fequal1288209029iple_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(299,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( ( A = bot_bo70021908tate_o )
| ( A
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_subset__singletonD) ).
thf(1693,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( ( A = bot_bo70021908tate_o )
| ( A
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(530,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( semila13410563le_a_o @ A @ B )
= bot_bo751897185le_a_o )
= ( ( A = bot_bo751897185le_a_o )
& ( B = bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_Un__empty) ).
thf(2572,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( ( semila13410563le_a_o @ A @ B )
= bot_bo751897185le_a_o )
= ( ( A = bot_bo751897185le_a_o )
& ( B = bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(88,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( member_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_set__rev__mp) ).
thf(897,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( member_nat @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ A )
=> ( member_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(492,axiom,
! [A: hoare_1775062406iple_a > $o] : ( hoare_1508237396rivs_a @ A @ bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).
thf(2417,plain,
! [A: hoare_1775062406iple_a > $o] : ( hoare_1508237396rivs_a @ A @ bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(247,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( ord_less_eq_nat_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_subset__insert) ).
thf(1473,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ~ ( member_nat @ B @ C )
=> ( ( ord_less_eq_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( ord_less_eq_nat_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(469,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ ( collec676402587iple_a @ B ) )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_insert__Collect) ).
thf(2340,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ ( collec676402587iple_a @ B ) )
= ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(556,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ ( insert1281456128iple_a @ A @ B ) )
= ( insert1281456128iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_insert__absorb2) ).
thf(2668,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o] :
( ( insert1281456128iple_a @ A @ ( insert1281456128iple_a @ A @ B ) )
= ( insert1281456128iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(155,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( minus_minus_nat_o @ A @ B )
= ( finite326637109_nat_o
@ ^ [C: nat,D: nat > $o] : ( minus_minus_nat_o @ D @ ( insert_nat @ C @ bot_bot_nat_o ) )
@ A
@ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_minus__fold__remove) ).
thf(1165,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ( minus_minus_nat_o @ A @ B )
= ( finite326637109_nat_o
@ ^ [C: nat,D: nat > $o] : ( minus_minus_nat_o @ D @ ( insert_nat @ C @ bot_bot_nat_o ) )
@ A
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(210,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ ( insert_nat @ A @ B ) @ C )
= ( ( member_nat @ A @ C )
& ( ord_less_eq_nat_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_insert__subset) ).
thf(1346,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_nat_o @ ( insert_nat @ A @ B ) @ C )
= ( ( member_nat @ A @ C )
& ( ord_less_eq_nat_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(279,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = B )
& ( A @ C ) ) )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Collect__conv__if) ).
thf(1610,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = B )
& ( A @ C ) ) )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(38,axiom,
! [A: nat > $o,B: nat > $o] :
( ( A != B )
| ( fequal_nat_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T) ).
thf(728,plain,
! [A: nat > $o,B: nat > $o] :
( ( A != B )
| ( fequal_nat_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(178,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( insert2134838167_state @ A @ B ) @ C )
= ( insert2134838167_state @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_Un__insert__left) ).
thf(1236,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( insert2134838167_state @ A @ B ) @ C )
= ( insert2134838167_state @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(497,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( minus_1944206118le_a_o @ ( minus_1944206118le_a_o @ A @ C ) @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_Diff__insert) ).
thf(2430,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ A @ ( insert1281456128iple_a @ B @ C ) )
= ( minus_1944206118le_a_o @ ( minus_1944206118le_a_o @ A @ C ) @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(6,axiom,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( finite_fold1_nat @ times_times_nat @ ( insert_nat @ A @ B ) )
= ( finite_fold_nat_nat @ times_times_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_fold1__eq__fold) ).
thf(644,plain,
! [A: nat,B: nat > $o] :
( ( finite_finite_nat @ B )
=> ( ~ ( member_nat @ A @ B )
=> ( ( finite_fold1_nat @ times_times_nat @ ( insert_nat @ A @ B ) )
= ( finite_fold_nat_nat @ times_times_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,axiom,
! [A: nat > $o] :
( ( image_nat_nat
@ ^ [B: nat] : B
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_image__ident) ).
thf(723,plain,
! [A: nat > $o] :
( ( image_nat_nat
@ ^ [B: nat] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(2507,plain,
( ( collect_nat
@ ^ [A: nat] : $false )
= bot_bot_nat_o ),
inference(lifteq,[status(thm)],[2506]) ).
thf(352,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert2134838167_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_insert__commute) ).
thf(1925,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert2134838167_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(197,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( semila848761471_nat_o @ ( insert_nat @ A @ bot_bot_nat_o ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_insert__is__Un) ).
thf(1299,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= ( semila848761471_nat_o @ ( insert_nat @ A @ bot_bot_nat_o ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(141,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( minus_minus_nat_o @ B @ C ) )
=> ( member_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_DiffD1) ).
thf(1120,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( minus_minus_nat_o @ B @ C ) )
=> ( member_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(409,axiom,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Collect__conv__if2) ).
thf(2138,plain,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(473,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ~ ( member2122167641iple_a @ A @ B )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( finite1842721992iple_a @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_folding__one_Oeq__fold_H) ).
thf(2353,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,D: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ C @ D )
=> ( ( finite2063573081iple_a @ B )
=> ( ~ ( member2122167641iple_a @ A @ B )
=> ( ( D @ ( insert1281456128iple_a @ A @ B ) )
= ( finite1842721992iple_a @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(72,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ bot_bo70021908tate_o @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_Un__empty__left) ).
thf(839,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ bot_bo70021908tate_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(599,axiom,
! [A: hoare_1775062406iple_a > nat] :
( ( image_1806517641_a_nat @ A @ bot_bo751897185le_a_o )
= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_image__empty) ).
thf(2810,plain,
! [A: hoare_1775062406iple_a > nat] :
( ( image_1806517641_a_nat @ A @ bot_bo751897185le_a_o )
= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(212,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( bot_bo70021908tate_o
!= ( insert2134838167_state @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_empty__not__insert) ).
thf(1352,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( bot_bo70021908tate_o
!= ( insert2134838167_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(596,axiom,
! [A: hoare_1775062406iple_a > hoare_1167836817_state,B: hoare_1775062406iple_a > $o] :
( ( ( image_1021683026_state @ A @ B )
= bot_bo70021908tate_o )
= ( B = bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_image__is__empty) ).
thf(2803,plain,
! [A: hoare_1775062406iple_a > hoare_1167836817_state,B: hoare_1775062406iple_a > $o] :
( ( ( image_1021683026_state @ A @ B )
= bot_bo70021908tate_o )
= ( B = bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(77,axiom,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ E ) @ bot_bo70021908tate_o ) )
=> ( ! [F: state,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ A ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_conseq2) ).
thf(860,plain,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ E ) @ bot_bo70021908tate_o ) )
=> ( ! [F: state,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ A ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(607,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( ( collec676402587iple_a @ A )
= bot_bo751897185le_a_o )
= ( ! [B: hoare_1775062406iple_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__empty__eq) ).
thf(2847,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( ( collec676402587iple_a @ A )
= bot_bo751897185le_a_o )
= ( ! [B: hoare_1775062406iple_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(618,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( ? [B: hoare_1775062406iple_a] : ( member2122167641iple_a @ B @ A ) )
= ( A != bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_ex__in__conv) ).
thf(2898,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( ? [B: hoare_1775062406iple_a] : ( member2122167641iple_a @ B @ A ) )
= ( A != bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(264,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila13410563le_a_o @ B @ C ) )
= ( ( member2122167641iple_a @ A @ B )
| ( member2122167641iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_Un__iff) ).
thf(1537,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a > $o] :
( ( member2122167641iple_a @ A @ ( semila13410563le_a_o @ B @ C ) )
= ( ( member2122167641iple_a @ A @ B )
| ( member2122167641iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(563,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( finite1946188886iple_a @ A @ B @ C )
= ( ? [D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > $o,F: hoare_1775062406iple_a] :
( ( B
= ( insert1281456128iple_a @ D @ E ) )
& ( C = F )
& ( finite727644230iple_a @ A @ D @ E @ F )
& ~ ( member2122167641iple_a @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_fold1Set_Osimps) ).
thf(2687,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a > $o,C: hoare_1775062406iple_a] :
( ( finite1946188886iple_a @ A @ B @ C )
= ( ? [D: hoare_1775062406iple_a,E: hoare_1775062406iple_a > $o,F: hoare_1775062406iple_a] :
( ( B
= ( insert1281456128iple_a @ D @ E ) )
& ( C = F )
& ( finite727644230iple_a @ A @ D @ E @ F )
& ~ ( member2122167641iple_a @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(233,axiom,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila966743401le_a_o @ ( collec676402587iple_a @ A ) @ ( collec676402587iple_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_Collect__conj__eq) ).
thf(1431,plain,
! [A: hoare_1775062406iple_a > $o,B: hoare_1775062406iple_a > $o] :
( ( collec676402587iple_a
@ ^ [C: hoare_1775062406iple_a] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila966743401le_a_o @ ( collec676402587iple_a @ A ) @ ( collec676402587iple_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(111,axiom,
! [A: com,B: com,C: state,D: state] :
( ( evalc @ ( semi @ A @ B ) @ C @ D )
=> ~ ! [E: state] :
( ( evalc @ A @ C @ E )
=> ~ ( evalc @ B @ E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_evalc__elim__cases_I4_J) ).
thf(1004,plain,
! [A: com,B: com,C: state,D: state] :
( ( evalc @ ( semi @ A @ B ) @ C @ D )
=> ~ ! [E: state] :
( ( evalc @ A @ C @ E )
=> ~ ( evalc @ B @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(346,axiom,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( insert_nat @ B @ ( semila1947288293_nat_o @ C @ A ) ) ) )
& ( ~ ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( semila1947288293_nat_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_Int__insert__right) ).
thf(1902,plain,
! [A: nat > $o,B: nat,C: nat > $o] :
( ( ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( insert_nat @ B @ ( semila1947288293_nat_o @ C @ A ) ) ) )
& ( ~ ( member_nat @ B @ C )
=> ( ( semila1947288293_nat_o @ C @ ( insert_nat @ B @ A ) )
= ( semila1947288293_nat_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(23,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ ( minus_2107060239tate_o @ B @ A ) )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_Diff__disjoint) ).
thf(691,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ ( minus_2107060239tate_o @ B @ A ) )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(512,axiom,
! [A: hoare_1775062406iple_a] :
~ ( member2122167641iple_a @ A @ bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_emptyE) ).
thf(2484,plain,
! [A: hoare_1775062406iple_a] :
~ ( member2122167641iple_a @ A @ bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(567,axiom,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,C: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ B @ C )
=> ( ( C @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_folding__one_Osingleton) ).
thf(2699,plain,
! [A: hoare_1775062406iple_a,B: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,C: ( hoare_1775062406iple_a > $o ) > hoare_1775062406iple_a] :
( ( finite2078349315iple_a @ B @ C )
=> ( ( C @ ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(226,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ A @ C ) ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( semila179895820tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_Int__insert__left) ).
thf(1399,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ A @ C ) ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( semila179895820tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(281,axiom,
! [A: loc,B: state > nat,C: com,D: loc,E: state > nat,F: com] :
( ( ( local @ A @ B @ C )
= ( local @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_com_Osimps_I2_J) ).
thf(1621,plain,
! [A: loc,B: state > nat,C: com,D: loc,E: state > nat,F: com] :
( ( ( local @ A @ B @ C )
= ( local @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(499,axiom,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a] :
( ( finite1946188886iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) @ C )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_fold1Set__sing) ).
thf(2436,plain,
! [A: hoare_1775062406iple_a > hoare_1775062406iple_a > hoare_1775062406iple_a,B: hoare_1775062406iple_a,C: hoare_1775062406iple_a] :
( ( finite1946188886iple_a @ A @ ( insert1281456128iple_a @ B @ bot_bo751897185le_a_o ) @ C )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(43,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( minus_minus_nat_o @ B @ C ) )
=> ~ ( member_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_DiffD2) ).
thf(755,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ( member_nat @ A @ ( minus_minus_nat_o @ B @ C ) )
=> ~ ( member_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(504,axiom,
! [A: x_a > state > $o,B: com,C: x_a > state > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( ( hoare_1766022166iple_a @ A @ B @ C )
= ( hoare_1766022166iple_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_triple_Oinject) ).
thf(2453,plain,
! [A: x_a > state > $o,B: com,C: x_a > state > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( ( hoare_1766022166iple_a @ A @ B @ C )
= ( hoare_1766022166iple_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(602,axiom,
! [A: hoare_1775062406iple_a] :
( ( collec676402587iple_a
@ ^ [B: hoare_1775062406iple_a] : ( B = A ) )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_singleton__conv) ).
thf(2834,plain,
! [A: hoare_1775062406iple_a] :
( ( collec676402587iple_a
@ ^ [B: hoare_1775062406iple_a] : ( B = A ) )
= ( insert1281456128iple_a @ A @ bot_bo751897185le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(239,axiom,
! [A: hoare_1167836817_state] :
( ( the_el323660082_state @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_the__elem__eq) ).
thf(1449,plain,
! [A: hoare_1167836817_state] :
( ( the_el323660082_state @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(84,axiom,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
= ( A = bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_subset__empty) ).
thf(882,plain,
! [A: nat > $o] :
( ( ord_less_eq_nat_o @ A @ bot_bot_nat_o )
= ( A = bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(356,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) )
= ( insert2134838167_state @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_insert__Diff__single) ).
thf(1944,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) )
= ( insert2134838167_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(217,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ? [C: nat > $o] :
( ( B
= ( insert_nat @ A @ C ) )
& ~ ( member_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_mk__disjoint__insert) ).
thf(1367,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ B )
=> ? [C: nat > $o] :
( ( B
= ( insert_nat @ A @ C ) )
& ~ ( member_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(564,axiom,
! [A: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ bot_bo751897185le_a_o @ A )
= bot_bo751897185le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_empty__Diff) ).
thf(2690,plain,
! [A: hoare_1775062406iple_a > $o] :
( ( minus_1944206118le_a_o @ bot_bo751897185le_a_o @ A )
= bot_bo751897185le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(244,axiom,
! [A: nat,B: nat > $o] :
( ( B = bot_bot_nat_o )
=> ~ ( member_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_equals0D) ).
thf(1463,plain,
! [A: nat,B: nat > $o] :
( ( B = bot_bot_nat_o )
=> ~ ( member_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(457,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ~ ! [C: hoare_1167836817_state > $o] :
( ( B
= ( insert2134838167_state @ A @ C ) )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Set_Oset__insert) ).
thf(2297,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ~ ! [C: hoare_1167836817_state > $o] :
( ( B
= ( insert2134838167_state @ A @ C ) )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(51,axiom,
! [A: hoare_1167836817_state > $o,B: com,C: state > state > $o,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [G: state,H: state] : ( H = F )
@ B
@ ^ [G: state] : ( C @ E ) )
@ bot_bo70021908tate_o ) ) )
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ B @ C ) @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_escape) ).
thf(775,plain,
! [A: hoare_1167836817_state > $o,B: com,C: state > state > $o,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [G: state,H: state] : ( H = F )
@ B
@ ^ [G: state] : ( C @ E ) )
@ bot_bo70021908tate_o ) ) )
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ B @ C ) @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(114,axiom,
! [A: hoare_1167836817_state > $o] :
( ( image_31595733_state
@ ^ [B: hoare_1167836817_state] : B
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_image__ident) ).
thf(1014,plain,
! [A: hoare_1167836817_state > $o] :
( ( image_31595733_state
@ ^ [B: hoare_1167836817_state] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(340,axiom,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= ( member_nat @ A @ bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_bot__empty__eq) ).
thf(1870,plain,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= ( member_nat @ A @ bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(4512,plain,
$false,
inference(e,[status(thm)],[2163,1665,2630,1411,2131,2778,2263,1559,909,1899,941,2331,2744,1190,1168,760,1315,2595,1850,2427,1982,666,1295,1211,762,2808,2495,1443,1618,2590,1422,1728,1437,1486,2231,2622,2395,2062,2671,2014,873,1205,2837,1269,878,2380,2195,715,1275,1233,2627,2459,1761,1640,2901,2042,2146,1458,2575,1867,2184,1999,797,2316,1954,2844,1507,1222,1196,2216,1001,709,1359,1601,2400,1254,829,1095,1127,2763,782,1441,885,1046,1628,1055,1709,2328,1792,785,2217,2682,1313,2562,1132,2356,2274,702,1577,1455,638,1147,1247,870,1479,1115,1100,1922,902,2373,1572,2520,2730,2989,1362,1963,2456,2616,1714,2105,2090,1864,1978,1020,1960,821,1489,2237,1302,2794,1040,1109,1183,1283,2508,1843,1377,634,956,2772,2002,849,1696,2367,1928,1896,2190,2286,2639,1975,1564,1604,2011,2204,678,1691,661,2646,1306,1199,1153,810,2047,1783,1470,2093,2083,1067,1736,1387,894,1343,2249,2277,1123,815,2705,2409,1502,1751,1824,788,1032,1365,2565,1555,2179,1836,757,2769,2433,2477,2068,1624,2200,830,682,1407,1634,2228,1910,842,2653,1106,1936,697,1983,1259,650,1804,2895,2359,1064,1227,1856,1425,1672,1540,2724,2268,857,1017,2685,1567,1028,753,1739,669,2868,637,1810,2349,1446,2649,706,1292,933,686,2419,1414,2240,2551,2085,647,701,2243,721,1947,2813,2766,779,1393,2370,2450,2125,2487,2845,2598,2581,2465,1434,1318,2926,938,2208,2909,1241,2702,765,1846,2662,1185,773,794,2529,718,906,1278,1135,1754,2904,1103,2149,1219,1483,2602,689,2376,1631,2260,965,750,2677,2176,904,1833,2727,694,1916,2859,732,2789,2981,826,2806,1795,2716,1520,2959,2674,2016,2514,2568,936,2220,1058,1239,2442,1092,2166,2425,704,1675,672,641,1428,1139,1503,1786,1669,1707,2293,1271,2308,2557,804,2474,947,2319,1356,2079,2679,831,2642,1894,1011,1349,996,1144,2839,2856,2378,1194,2346,681,1853,2383,2624,2422,1117,2246,1492,2197,1969,2065,1175,2182,2343,1993,726,1862,1460,1952,1339,2605,2923,1325,1149,2874,2928,1177,1381,2578,1688,1171,2075,2365,1528,1176,2931,2797,2022,2101,1496,2156,2207,653,2693,658,2506,1396,2439,2212,2171,1213,768,2592,2752,2390,1250,2005,2054,1873,1467,2271,663,2234,1509,2927,1990,968,836,1049,675,2816,1758,2107,1203,1208,944,2665,927,2037,2503,1684,1798,712,1516,640,1070,1225,2192,971,1941,993,1547,1748,2397,1025,2386,2407,1267,2850,2160,2224,1188,1038,2322,951,1711,1499,1813,1452,1637,2920,791,1980,2128,1130,1579,1336,643,1543,1257,1141,864,1504,2511,2584,656,1023,2279,2843,1972,1052,2711,2722,1008,1717,2030,1372,2892,2807,1272,2266,876,2865,1839,1918,2479,2088,2045,1180,1966,931,2696,2870,2310,2194,2325,1126,845,2760,1157,1321,1913,891,2209,2490,2187,1390,2305,2071,2775,2792,1807,771,2907,2591,1646,699,2135,2554,1062,1481,2004,1745,2026,2608,1244,961,813,1385,2174,2283,1476,1341,2098,2853,2290,2251,2934,2152,2447,2956,2786,2912,2462,1706,1607,1513,2095,2315,2739,2019,899,1661,2036,1309,2003,1957,2255,818,1876,2050,867,1642,752,2302,2517,1725,1280,833,2719,1097,2587,2736,2008,1986,1859,2800,801,1816,1657,807,1561,1789,2961,2404,2714,2619,2040,2783,1742,1693,2572,897,2417,635,1473,2340,2668,1165,1346,1610,728,1236,2430,644,723,2507,1925,1299,1120,2138,2353,839,2810,1352,2803,860,2847,2898,1537,2687,1431,1004,1902,691,2484,2699,1399,1621,2436,755,2453,2834,1449,882,1944,1367,2690,1463,2297,775,1014,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470^2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n013.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 16:04:21 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.80/1.33 % [INFO] Parsing done (517ms).
% 2.80/1.34 % [INFO] Running in sequential loop mode.
% 4.16/1.74 % [INFO] eprover registered as external prover.
% 4.16/1.75 % [INFO] Scanning for conjecture ...
% 4.66/1.95 % [INFO] Found a conjecture (or negated_conjecture) and 710 axioms. Running axiom selection ...
% 5.54/2.20 % [INFO] Axiom selection finished. Selected 631 axioms (removed 79 axioms).
% 6.66/2.57 % [INFO] Problem is higher-order (TPTP THF).
% 6.66/2.59 % [INFO] Type checking passed.
% 6.66/2.59 % [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 ...
% 70.56/16.10 % External prover 'e' found a proof!
% 70.56/16.10 % [INFO] Killing All external provers ...
% 70.56/16.10 % Time passed: 15741ms (effective reasoning time: 14753ms)
% 70.56/16.10 % 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)>
% 70.56/16.11 % Axioms used in derivation (631): fact_651_Int__insert__right__if0, fact_386_insert__Diff__single, fact_679_disjoint__iff__not__equal, fact_683_Int__empty__left, fact_153_nonempty__iff, fact_158_bot__empty__eq, fact_624_IntE, fact_375_insert__Diff1, fact_664_inf__Int__eq, fact_47_Collect__empty__eq, fact_421_fold1__singleton, fact_251_hoare__derivs_OLocal, fact_291_evaln__elim__cases_I3_J, fact_614_Sup__fin_Ounion__idem, fact_307_folding__one_Oinsert, fact_426_fold__def, fact_391_Diff__insert2, fact_686_inf__bot__left, fact_258_com_Osimps_I11_J, fact_402_folding__one__idem_Ohom__commute, fact_468_subset__insert, fact_380_insert__Diff, fact_202_imageI, fact_450_UnE, fact_579_union__fold__insert, fact_656_insert__inter__insert, fact_273_fold1Set_Ointros, fact_552_bot__unique, fact_270_evaln_OLocal, fact_429_folding__one_Oeq__fold_H, fact_511_Un__empty, fact_236_image__insert, fact_667_Int__Collect, fact_695_Diff__triv, fact_152_com_Osimps_I3_J, fact_22_insertCI, fact_463_subset__insertI, fact_111_doubleton__eq__iff, fact_67_insert__absorb, fact_447_subsetD, fact_321_finite__insert, fact_440_fold1__in, fact_192_rev__image__eqI, fact_494_sup__eq__bot__iff, fact_453_empty__subsetI, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com, fact_144_equals0I, fact_577_insert__is__Un, fact_359_DiffD1, fact_242_If__def, fact_532_set__rev__mp, fact_559_le__bot, fact_3_triple_Oinject, fact_277_evalc_OSemi, fact_137_Set_Oset__insert, fact_503_Un__empty__left, fact_172_image__constant, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_264_fold1Set__nonempty, fact_238_image__insert, fact_274_evaln_OSemi, fact_247_folding__one_Osingleton, fact_423_fold1__singleton__def, fact_80_insert__iff, fact_378_insert__Diff__if, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com, fact_229_empty__is__image, fact_175_image__constant, fact_205_imageI, fact_469_subset__insert, fact_49_Collect__empty__eq, fact_623_IntE, fact_414_comp__fun__commute_Ofold__graph__determ, fact_454_empty__subsetI, fact_314_finite_OinsertI, fact_571_asm, fact_82_insert__commute, fact_209_image__iff, fact_173_image__constant, fact_437_minus__fold__remove, fact_180_image__eqI, fact_419_fold1__singleton, fact_10_escape, fact_476_insert__mono, fact_492_sup__eq__bot__iff, fact_263_fold1Set__nonempty, fact_288_fold__graph_OemptyI, fact_507_Un__empty__right, fact_134_triple_Oexhaust, fact_149_the__elem__def, fact_688_inf__bot__left, fact_504_Un__empty__left, fact_219_image__is__empty, fact_422_fold1__singleton__def, fact_162_image__constant__conv, fact_545_sup__Un__eq, fact_248_folding__one_Osingleton, fact_696_Diff__triv, fact_142_equals0I, fact_672_Int__iff, fact_92_insert__compr, fact_392_Diff__insert, fact_0_empty, fact_565_Un__insert__left, fact_553_bot__unique, fact_388_insert__Diff__single, fact_138_Set_Oset__insert, fact_677_disjoint__iff__not__equal, fact_255_com_Osimps_I35_J, fact_93_insert__compr, fact_14_conseq1, fact_543_pred__subset__eq, fact_285_com__det, fact_620_Sup__fin_Ounion__disjoint, fact_89_insert__Collect, fact_313_finite_OemptyI, fact_583_subset__singletonD, fact_593_folding__one__idem_Ounion__idem, fact_289_fold__graph_OinsertI, fact_316_finite_OinsertI, fact_330_finite__nonempty__imp__fold1Set, fact_530_set__mp, fact_371_empty__Diff, fact_350_folding__one_Oinsert__remove, fact_425_comp__fun__commute_Ofold__equality, fact_618_Sup__fin_Ohom__commute, fact_446_subsetD, fact_110_doubleton__eq__iff, fact_20_insertE, fact_39_Collect__conv__if, fact_77_insert__code, fact_685_Int__empty__left, fact_315_finite_OinsertI, fact_5_cut, fact_505_Un__empty__left, fact_578_fold__sup__insert, fact_385_Diff__insert__absorb, fact_262_empty__fold1SetE, fact_310_finite__Collect__conjI, fact_113_singleton__iff, fact_580_union__fold__insert, fact_569_weaken, fact_212_image__iff, fact_183_image__eqI, fact_179_image__eqI, fact_200_imageI, fact_78_insert__code, fact_324_vname_Osimps_I3_J, fact_118_empty__not__insert, fact_131_hoare__derivs_OSkip, fact_71_insertI2, fact_97_insertI1, fact_412_comp__fun__idem__insert, fact_286_evaln__evalc, fact_397_finite__Diff__insert, fact_337_finite__imp__fold__graph, fact_508_Un__empty__right, fact_83_insert__commute, fact_129_bot__fun__def, fact_464_subset__insertI, fact_539_Un__iff, fact_457_subset__empty, fact_322_finite__insert, fact_331_finite__induct, fact_119_empty__not__insert, fact_130_hoare__derivs_OSkip, fact_1_empty, fact_500_sup__bot__left, fact_140_mk__disjoint__insert, fact_64_empty__def, fact_57_ex__in__conv, fact_531_set__rev__mp, fact_575_insert__is__Un, fact_335_finite_Osimps, fact_444_folding__one__idem_Osubset__idem, fact_472_subset__insertI2, fact_17_conseq12, fact_562_Un__insert__right, fact_420_fold1__singleton, fact_603_flat__lub__def, fact_370_empty__Diff, fact_366_Diff__cancel, fact_234_insert__image, fact_40_Collect__conv__if, fact_308_folding__one_Oinsert, fact_343_finite__ne__induct, fact_697_Diff__disjoint, fact_650_Int__insert__left__if0, fact_33_singleton__conv, fact_544_pred__subset__eq, fact_374_insert__Diff1, fact_459_subset__empty, fact_104_singleton__inject, fact_102_insert__compr__raw, fact_373_finite__Diff2, fact_448_UnCI, fact_348_folding__one_Oinsert__remove, fact_41_Collect__conv__if, fact_133_Comp, fact_462_subset__insertI, fact_65_empty__def, fact_224_image__empty, fact_346_folding__one_Oremove, fact_491_sup__eq__bot__iff, fact_377_insert__Diff__if, fact_275_evaln_OSkip, fact_393_Diff__insert, fact_123_the__elem__eq, fact_60_all__not__in__conv, fact_379_insert__Diff__if, fact_21_insertCI, fact_439_minus__fold__remove, fact_644_Int__insert__left__if1, fact_306_folding__one_Oinsert, fact_203_imageI, fact_309_finite__Collect__conjI, fact_214_com_Osimps_I24_J, fact_384_Diff__insert__absorb, fact_529_set__mp, fact_298_evalc__evaln, fact_654_insert__inter__insert, fact_418_fold1__eq__fold, fact_125_bot__apply, fact_126_bot__apply, fact_13_conseq2, fact_280_evaln_OAssign, fact_382_insert__Diff, fact_658_Int__insert__left, fact_387_insert__Diff__single, fact_116_insert__not__empty, fact_221_image__is__empty, fact_361_Diff__iff, fact_48_Collect__empty__eq, fact_150_the__elem__def, fact_204_imageI, fact_302_fold__graph_Osimps, fact_266_theI, fact_55_empty__Collect__eq, fact_206_imageI, fact_502_sup__bot__left, fact_438_minus__fold__remove, fact_470_subset__insert, fact_127_bot__fun__def, fact_220_image__is__empty, fact_689_inf__bot__left, fact_597_finite__subset__induct, fact_510_Un__empty, fact_389_Diff__insert2, fact_680_Int__empty__right, fact_96_insertI1, fact_431_folding__one_Oeq__fold_H, fact_171_image__constant, fact_293_evaln__elim__cases_I4_J, fact_177_image__eqI, fact_90_insert__Collect, fact_182_image__eqI, fact_595_finite__subset__induct, fact_235_insert__image, fact_283_evalc__elim__cases_I2_J, fact_292_evalc__elim__cases_I4_J, fact_76_insert__code, fact_460_rev__finite__subset, help_fequal_1_1_fequal_000tc__Nat__Onat_T, fact_143_equals0I, fact_584_subset__singletonD, fact_673_IntD1, fact_305_triple__valid__def2, fact_184_image__eqI, fact_461_finite__subset, fact_663_inf__Int__eq, fact_345_folding__one_Oremove, fact_156_bot__empty__eq, fact_165_image__constant__conv, fact_195_rev__image__eqI, fact_466_insert__subset, fact_253_com_Osimps_I2_J, fact_167_image__constant__conv, fact_451_UnE, fact_257_com_Osimps_I22_J, fact_16_conseq12, fact_290_evalc__elim__cases_I3_J, fact_157_bot__empty__eq, fact_240_the__sym__eq__trivial, fact_645_Int__insert__right__if1, fact_232_Collect__def, fact_404_finite__empty__induct, fact_407_comp__fun__idem__remove, fact_228_empty__is__image, fact_261_empty__fold1SetE, fact_245_fold1Set__sing, fact_497_sup__bot__right, fact_44_equals0D, fact_534_in__mono, fact_151_the__elem__def, fact_557_le__bot, fact_160_Ass, fact_28_singleton__conv2, fact_659_Int__insert__left, fact_609_Sup__fin_Oin__idem, fact_608_Sup__fin_Osingleton, fact_296_insert__fold1SetE, fact_501_sup__bot__left, fact_73_insert__ident, fact_252_vname_Osimps_I2_J, fact_621_IntI, fact_662_Int__insert__right, fact_669_Int__def, fact_613_Sup__fin_Osubset__idem, fact_547_bot__least, fact_109_doubleton__eq__iff, fact_85_insert__absorb2, fact_161_image__constant__conv, fact_19_insertE, fact_265_fold1Set__nonempty, fact_347_folding__one_Oremove, fact_84_insert__commute, fact_146_conseq, fact_282_evalc_OAssign, fact_148_com_Osimps_I12_J, fact_567_Un__insert__left, fact_61_all__not__in__conv, fact_243_fold1Set__sing, fact_540_Un__iff, fact_590_subset__insert__iff, fact_352_DiffE, fact_617_Sup__fin_Oinsert__remove, fact_320_finite__insert, fact_681_Int__empty__right, fact_191_rev__image__eqI, fact_223_image__empty, fact_201_imageI, fact_383_Diff__insert__absorb, fact_303_evaln__max2, fact_554_bot__unique, fact_694_Diff__triv, fact_189_rev__image__eqI, fact_278_evalc_OSkip, fact_225_image__empty, fact_671_Int__iff, fact_166_image__constant__conv, fact_369_Diff__empty, fact_222_image__empty, fact_467_insert__subset, fact_334_finite_Osimps, fact_395_finite__Diff__insert, fact_53_empty__Collect__eq, fact_661_Int__insert__right, fact_356_DiffD2, fact_527_Collect__disj__eq, fact_27_singleton__conv2, fact_589_subset__insert__iff, fact_18_insertE, fact_108_singletonE, fact_536_UnI2, fact_368_Diff__empty, fact_95_insert__compr, fact_199_imageI, fact_168_image__constant, fact_586_diff__single__insert, fact_66_empty__def, fact_103_singleton__inject, fact_287_empty__fold__graphE, fact_121_the__elem__eq, fact_699_Diff__disjoint, fact_424_fold1__singleton__def, fact_215_com_Osimps_I25_J, fact_56_empty__Collect__eq, fact_498_sup__bot__right, fact_112_singleton__iff, fact_568_weaken, fact_54_empty__Collect__eq, fact_682_Int__empty__right, fact_194_rev__image__eqI, fact_208_image__iff, fact_655_insert__inter__insert, fact_147_com_Osimps_I13_J, fact_79_insert__iff, fact_585_diff__single__insert, fact_169_image__constant, fact_372_empty__Diff, fact_124_bot__apply, fact_535_UnI2, fact_155_nonempty__iff, fact_106_singletonE, fact_653_Int__insert__right__if0, fact_301_fold1Set_Osimps, fact_403_finite__empty__induct, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_, fact_26_emptyE, fact_237_image__insert, fact_652_Int__insert__right__if0, fact_327_folding__one_Oclosed, fact_394_Diff__insert, fact_185_image__ident, fact_588_subset__insert__iff, fact_351_DiffE, fact_43_equals0D, fact_596_finite__subset__induct, fact_281_evaln__elim__cases_I2_J, fact_670_Int__def, fact_312_finite_OemptyI, fact_360_Diff__iff, fact_602_flat__lub__def, fact_693_inf__bot__right, fact_250_hoare__derivs_OLocal, fact_8_constant, fact_625_finite__Int, fact_52_empty__iff, fact_676_IntD2, fact_163_image__constant__conv, fact_541_Un__def, fact_256_com_Osimps_I23_J, fact_279_evalc__elim__cases_I1_J, fact_29_singleton__conv2, fact_471_subset__insertI2, fact_512_finite__Un, fact_452_empty__subsetI, fact_495_sup__bot__right, fact_216_com_Osimps_I8_J, fact_187_image__ident, fact_506_Un__empty__right, fact_691_inf__bot__right, fact_38_Collect__conv__if2, fact_59_ex__in__conv, fact_87_insert__absorb2, fact_376_insert__Diff1, fact_24_emptyE, fact_190_rev__image__eqI, fact_239_image__insert, fact_367_Diff__empty, fact_186_image__ident, fact_698_Diff__disjoint, fact_145_conseq, fact_88_insert__Collect, fact_647_Int__insert__right__if1, fact_63_empty__def, fact_58_ex__in__conv, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_It__a_J_, fact_319_vname_Osimps_I1_J, fact_354_DiffI, fact_196_rev__image__eqI, fact_496_sup__bot__right, fact_37_Collect__conv__if2, fact_610_Sup__fin_OF__eq, fact_405_finite__empty__induct, fact_207_image__iff, fact_105_singleton__inject, fact_328_finite__nonempty__imp__fold1Set, fact_311_finite_OemptyI, fact_34_singleton__conv, fact_141_mk__disjoint__insert, fact_317_finite__Collect__disjI, fact_619_Sup__fin_Oclosed, fact_428_folding__one_Oeq__fold, fact_117_insert__not__empty, fact_364_Diff__cancel, fact_574_insert__def, fact_599_subsetI, fact_2_triple_Oinject, fact_357_DiffD2, fact_260_empty__fold1SetE, fact_336_finite_Osimps, fact_51_empty__iff, fact_32_singleton__conv, fact_362_set__diff__eq, fact_72_insertI2, fact_576_insert__is__Un, fact_690_inf__bot__right, fact_564_Un__insert__right, fact_558_le__bot, fact_493_sup__eq__bot__iff, fact_528_Collect__disj__eq, fact_318_finite__Collect__disjI, fact_358_DiffD1, fact_427_folding__one_Oeq__fold, fact_381_insert__Diff, fact_114_singleton__iff, fact_416_comp__fun__commute_Ofold__graph__insertE, fact_408_comp__fun__idem__remove, fact_434_folding__one__idem_Oeq__fold__idem_H, fact_674_IntD1, fact_396_finite__Diff__insert, fact_533_in__mono, fact_612_Sup__fin_Oinsert, fact_231_mem__def, fact_259_com_Osimps_I10_J, fact_45_equals0D, fact_665_Collect__conj__eq, fact_581_union__fold__insert, fact_68_insert__absorb, fact_546_sup__Un__eq, fact_122_the__elem__eq, fact_668_Int__Collect, fact_210_image__iff, fact_465_insert__subset, fact_473_subset__insertI2, fact_98_insertI1, fact_413_comp__fun__idem__insert, fact_254_com_Osimps_I34_J, fact_538_UnI1, fact_499_sup__bot__left, fact_435_comp__fun__commute_Ofold__graph__fold, fact_178_image__eqI, fact_643_Int__insert__left__if1, fact_197_rev__image__eqI, fact_198_imageI, fact_573_insert__def, fact_249_folding__one_Osingleton, fact_174_image__constant, fact_233_Collect__def, fact_340_folding__one__idem_Oinsert__idem, fact_649_Int__insert__left__if0, fact_128_bot__fun__def, fact_100_insert__compr__raw, fact_107_singletonE, fact_604_flat__lub__def, fact_69_insert__absorb, fact_398_folding__one__idem_Oin__idem, fact_42_Collect__conv__if, fact_267_the1__equality, fact_678_disjoint__iff__not__equal, fact_560_le__bot, fact_74_insert__ident, fact_227_empty__is__image, fact_136_Set_Oset__insert, fact_458_subset__empty, fact_75_insert__ident, fact_326_folding__one_Oclosed, fact_349_folding__one_Oinsert__remove, fact_11_escape, fact_99_insert__compr__raw, fact_537_UnI1, fact_411_comp__fun__idem__insert, fact_135_triple_Oexhaust, fact_4_cut, fact_15_conseq1, fact_390_Diff__insert2, fact_666_Collect__conj__eq, fact_35_Collect__conv__if2, fact_329_finite__nonempty__imp__fold1Set, fact_342_finite__ne__induct, fact_284_eval__eq, fact_31_singleton__conv, fact_660_Int__insert__right, fact_365_Diff__cancel, help_fequal_2_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T, fact_430_folding__one_Oeq__fold_H, fact_154_nonempty__iff, fact_355_finite__Diff, fact_406_comp__fun__idem__remove, fact_332_finite__induct, fact_687_inf__bot__left, fact_269_evalc_OLocal, fact_509_Un__empty, fact_323_vname_Osimps_I4_J, fact_615_Sup__fin_Oeq__fold__idem_H, fact_230_mem__def, fact_363_set__diff__eq, fact_622_IntI, fact_566_Un__insert__left, fact_353_DiffI, fact_648_Int__insert__left__if0, fact_241_the__eq__trivial, fact_226_empty__is__image, fact_325_folding__one_Oclosed, fact_159_Ass, fact_692_inf__bot__right, fact_555_bot__unique, fact_9_constant, fact_30_singleton__conv2, fact_193_rev__image__eqI, fact_684_Int__empty__left, fact_139_mk__disjoint__insert, fact_513_finite__UnI, fact_217_com_Osimps_I9_J, fact_582_subset__singletonD, fact_6_hoare__derivs_Oinsert, fact_86_insert__absorb2, fact_563_Un__insert__right, fact_164_image__constant__conv, fact_91_insert__Collect, fact_62_all__not__in__conv, fact_611_Sup__fin_Oinsert__idem, fact_548_bot__least, fact_25_emptyE, fact_616_Sup__fin_Oeq__fold_H, fact_409_comp__fun__commute_Ofold__graph__insertE__aux, fact_657_Int__insert__left, fact_244_fold1Set__sing, fact_46_Collect__empty__eq, fact_598_subsetI, fact_475_insert__mono, fact_213_image__iff, fact_455_finite__Collect__subsets, fact_341_finite__ne__induct, help_fequal_1_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T, fact_188_com_Osimps_I1_J, fact_570_asm, fact_417_fold1__insert, fact_572_insert__def, fact_211_image__iff, fact_542_Un__def, fact_115_insert__not__empty, fact_276_evaln__elim__cases_I1_J, fact_170_image__constant, fact_246_the__equality, fact_36_Collect__conv__if2, fact_436_fold1__def, fact_550_bot__least, fact_120_empty__not__insert, fact_218_image__is__empty, fact_587_diff__single__insert, fact_642_Int__insert__left__if1, fact_181_image__eqI, fact_474_insert__mono, fact_607_Sup__fin_Oremove, fact_176_image__eqI, fact_344_vname_Oexhaust, fact_12_conseq2, fact_549_bot__least, fact_268_theI_H, fact_50_empty__iff, fact_23_insertCI, fact_449_UnCI, fact_7_hoare__derivs_Oinsert, fact_646_Int__insert__right__if1, fact_81_insert__iff, fact_675_IntD2, fact_333_finite__induct, fact_132_Comp, fact_70_insertI2
% 70.56/16.11 % No. of inferences in proof: 1310
% 70.56/16.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15741 ms resp. 14753 ms w/o parsing
% 64.23/16.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 64.23/16.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------