%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW474^3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:15 AM UTC 2026
% Result : Theorem 145.50s 46.13s
% Output : Refutation 135.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 838
% Syntax : Number of formulae : 1872 ( 806 unt; 0 typ; 5 def)
% Number of atoms : 8212 (1751 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 14720 ( 651 ~; 179 |; 303 &;11938 @)
% ( 0 <=>;1649 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 3785 (3785 >; 0 *; 0 +; 0 <<)
% Number of symbols : 129 ( 126 usr; 21 con; 0-5 aty)
% Number of variables : 4912 ( 370 ^;4399 !; 138 ?;4912 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(com_type,type,
com: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(state_type,type,
state: $tType ).
thf(hoare_1708887482_state_type,type,
hoare_1708887482_state: $tType ).
thf(option_com_type,type,
option_com: $tType ).
thf(option_pname_type,type,
option_pname: $tType ).
thf(option1624383643_state_type,type,
option1624383643_state: $tType ).
thf(wt_decl,type,
wt: com > $o ).
thf(wT_bodies_decl,type,
wT_bodies: $o ).
thf(body_decl,type,
body: pname > option_com ).
thf(body_1_decl,type,
body_1: pname > com ).
thf(skip_decl,type,
skip: com ).
thf(semi_decl,type,
semi: com > com > com ).
thf(while_decl,type,
while: ( state > $o ) > com > com ).
thf(finite138924780name_o_decl,type,
finite138924780name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > $o ).
thf(finite2034616076tate_o_decl,type,
finite2034616076tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o ).
thf(finite662762081tate_o_decl,type,
finite662762081tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o ).
thf(finite297249702name_o_decl,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(finite1329924456tate_o_decl,type,
finite1329924456tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(finite1625599783_state_decl,type,
finite1625599783_state: ( hoare_1708887482_state > $o ) > $o ).
thf(finite603803317name_o_decl,type,
finite603803317name_o: ( pname > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(finite96880613tate_o_decl,type,
finite96880613tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(finite309095018_state_decl,type,
finite309095018_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(finite2139561282_pname_decl,type,
finite2139561282_pname: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( pname > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > hoare_1708887482_state > $o ).
thf(finite1282449217_pname_decl,type,
finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(finite1615457021_state_decl,type,
finite1615457021_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
thf(finite89670078_pname_decl,type,
finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(finite1347568576_state_decl,type,
finite1347568576_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o ).
thf(fun_up1986763201_state_decl,type,
fun_up1986763201_state: ( pname > hoare_1708887482_state ) > pname > hoare_1708887482_state > pname > hoare_1708887482_state ).
thf(fun_up879233478on_com_decl,type,
fun_up879233478on_com: ( pname > option_com ) > pname > option_com > pname > option_com ).
thf(inj_on11367768on_com_decl,type,
inj_on11367768on_com: ( com > option_com ) > ( com > $o ) > $o ).
thf(inj_on1553129421_state_decl,type,
inj_on1553129421_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > $o ).
thf(inj_on737724108_pname_decl,type,
inj_on737724108_pname: ( pname > option_pname ) > ( pname > $o ) > $o ).
thf(inj_on1945914667_pname_decl,type,
inj_on1945914667_pname: ( hoare_1708887482_state > pname ) > ( hoare_1708887482_state > $o ) > $o ).
thf(inj_on632008595_state_decl,type,
inj_on632008595_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > $o ).
thf(inj_on945311362_state_decl,type,
inj_on945311362_state: ( hoare_1708887482_state > option1624383643_state ) > ( hoare_1708887482_state > $o ) > $o ).
thf(overri1496249029on_com_decl,type,
overri1496249029on_com: ( pname > option_com ) > ( pname > option_com ) > ( pname > $o ) > pname > option_com ).
thf(minus_minus_pname_o_decl,type,
minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(minus_2056855718tate_o_decl,type,
minus_2056855718tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(the_Ho851197897_state_decl,type,
the_Ho851197897_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(hoare_Mirabelle_MGT_decl,type,
hoare_Mirabelle_MGT: com > hoare_1708887482_state ).
thf(hoare_90032982_state_decl,type,
hoare_90032982_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(hoare_496444244_state_decl,type,
hoare_496444244_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(hoare_1160767572gleton_decl,type,
hoare_1160767572gleton: $o ).
thf(hoare_858012674_state_decl,type,
hoare_858012674_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1708887482_state ).
thf(if_Hoa1374726218_state_decl,type,
if_Hoa1374726218_state: $o > hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ).
thf(if_option_com_decl,type,
if_option_com: $o > option_com > option_com > option_com ).
thf(semila1673364395name_o_decl,type,
semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(semila129691299tate_o_decl,type,
semila129691299tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(semila1780557381name_o_decl,type,
semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(semila1122118281tate_o_decl,type,
semila1122118281tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(dom_com_com_decl,type,
dom_com_com: ( com > option_com ) > com > $o ).
thf(dom_pname_com_decl,type,
dom_pname_com: ( pname > option_com ) > pname > $o ).
thf(dom_pname_pname_decl,type,
dom_pname_pname: ( pname > option_pname ) > pname > $o ).
thf(dom_pn1412407212_state_decl,type,
dom_pn1412407212_state: ( pname > option1624383643_state ) > pname > $o ).
thf(dom_Ho1805192458_pname_decl,type,
dom_Ho1805192458_pname: ( hoare_1708887482_state > option_pname ) > hoare_1708887482_state > $o ).
thf(dom_Ho1703271284_state_decl,type,
dom_Ho1703271284_state: ( hoare_1708887482_state > option1624383643_state ) > hoare_1708887482_state > $o ).
thf(restri1382200118me_com_decl,type,
restri1382200118me_com: ( pname > option_com ) > ( pname > $o ) > pname > option_com ).
thf(evalc_decl,type,
evalc: com > state > state > $o ).
thf(is_none_pname_decl,type,
is_none_pname: option_pname > $o ).
thf(is_non163157940_state_decl,type,
is_non163157940_state: option1624383643_state > $o ).
thf(none_com_decl,type,
none_com: option_com ).
thf(none_H1106584047_state_decl,type,
none_H1106584047_state: option1624383643_state ).
thf(some_com_decl,type,
some_com: com > option_com ).
thf(some_pname_decl,type,
some_pname: pname > option_pname ).
thf(some_H1974565227_state_decl,type,
some_H1974565227_state: hoare_1708887482_state > option1624383643_state ).
thf(set_com_decl,type,
set_com: option_com > com > $o ).
thf(set_pname_decl,type,
set_pname: option_pname > pname > $o ).
thf(set_Ho525251890_state_decl,type,
set_Ho525251890_state: option1624383643_state > hoare_1708887482_state > $o ).
thf(the_com_decl,type,
the_com: option_com > com ).
thf(the_pname_1_decl,type,
the_pname_1: option_pname > pname ).
thf(the_Ho963921505_state_decl,type,
the_Ho963921505_state: option1624383643_state > hoare_1708887482_state ).
thf(bot_bot_com_o_decl,type,
bot_bot_com_o: com > $o ).
thf(bot_bot_pname_o_decl,type,
bot_bot_pname_o: pname > $o ).
thf(bot_bo19817387tate_o_decl,type,
bot_bo19817387tate_o: hoare_1708887482_state > $o ).
thf(bot_bot_o_decl,type,
bot_bot_o: $o ).
thf(ord_le1205211808me_o_o_decl,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(ord_le1728773982te_o_o_decl,type,
ord_le1728773982te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o ).
thf(ord_less_eq_pname_o_decl,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(ord_le777019615tate_o_decl,type,
ord_le777019615tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(top_top_com_o_decl,type,
top_top_com_o: com > $o ).
thf(top_top_pname_o_decl,type,
top_top_pname_o: pname > $o ).
thf(top_to832624271tate_o_decl,type,
top_to832624271tate_o: hoare_1708887482_state > $o ).
thf(partia1256728516_state_decl,type,
partia1256728516_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(collect_pname_o_decl,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(collec219771562tate_o_decl,type,
collec219771562tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(collect_com_decl,type,
collect_com: ( com > $o ) > com > $o ).
thf(collect_pname_decl,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(collec1568722789_state_decl,type,
collec1568722789_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(image_pname_o_pname_decl,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(image_1922967206_state_decl,type,
image_1922967206_state: ( ( pname > $o ) > hoare_1708887482_state ) > ( ( pname > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(image_2051418740_pname_decl,type,
image_2051418740_pname: ( ( hoare_1708887482_state > $o ) > pname ) > ( ( hoare_1708887482_state > $o ) > $o ) > pname > $o ).
thf(image_27005066_state_decl,type,
image_27005066_state: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ).
thf(image_com_pname_decl,type,
image_com_pname: ( com > pname ) > ( com > $o ) > pname > $o ).
thf(image_934102463_state_decl,type,
image_934102463_state: ( com > hoare_1708887482_state ) > ( com > $o ) > hoare_1708887482_state > $o ).
thf(image_pname_pname_o_decl,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(image_425134806tate_o_decl,type,
image_425134806tate_o: ( pname > hoare_1708887482_state > $o ) > ( pname > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(image_pname_com_decl,type,
image_pname_com: ( pname > com ) > ( pname > $o ) > com > $o ).
thf(image_pname_pname_decl,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(image_1116629049_state_decl,type,
image_1116629049_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > hoare_1708887482_state > $o ).
thf(image_1552895654name_o_decl,type,
image_1552895654name_o: ( hoare_1708887482_state > pname > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > $o ).
thf(image_1551509096tate_o_decl,type,
image_1551509096tate_o: ( hoare_1708887482_state > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o ).
thf(image_1509414295_pname_decl,type,
image_1509414295_pname: ( hoare_1708887482_state > pname ) > ( hoare_1708887482_state > $o ) > pname > $o ).
thf(image_757158439_state_decl,type,
image_757158439_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(insert_pname_decl,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(insert528405184_state_decl,type,
insert528405184_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ).
thf(the_elem_pname_decl,type,
the_elem_pname: ( pname > $o ) > pname ).
thf(the_el864710747_state_decl,type,
the_el864710747_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state ).
thf(vimage1943311875_state_decl,type,
vimage1943311875_state: ( pname > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > pname > $o ).
thf(fequal_pname_decl,type,
fequal_pname: pname > pname > $o ).
thf(fequal_state_decl,type,
fequal_state: state > state > $o ).
thf(fequal224822779_state_decl,type,
fequal224822779_state: hoare_1708887482_state > hoare_1708887482_state > $o ).
thf(member_com_decl,type,
member_com: com > ( com > $o ) > $o ).
thf(member_pname_decl,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(member451959335_state_decl,type,
member451959335_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > $o ).
thf(fa_decl,type,
fa: hoare_1708887482_state > $o ).
thf(pn_decl,type,
pn: pname ).
thf(y_decl,type,
y: com ).
thf(sk1_decl,type,
sk1: ( pname > $o ) > ( pname > $o ) > ( pname > pname ) > pname > $o ).
thf(sk2_decl,type,
sk2: ( ( pname > $o ) > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > pname > $o ) > hoare_1708887482_state > $o ).
thf(sk3_decl,type,
sk3: ( pname > $o ) > ( pname > $o ) > ( pname > pname ) > pname ).
thf(sk137_decl,type,
sk137: state ).
thf(sk138_decl,type,
sk138: state ).
thf(sk139_decl,type,
sk139: hoare_1708887482_state ).
thf(sk140_decl,type,
sk140: pname ).
thf(sk141_decl,type,
sk141: pname ).
thf(sk144_decl,type,
sk144: com ).
thf(sk145_decl,type,
sk145: hoare_1708887482_state ).
thf(sk146_decl,type,
sk146: hoare_1708887482_state ).
thf(sk147_decl,type,
sk147: hoare_1708887482_state ).
thf(sk148_decl,type,
sk148: hoare_1708887482_state ).
thf(sk152_decl,type,
sk152: hoare_1708887482_state ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: pname > $o,B: pname > $o,C: pname > pname] :
@+[D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( A
= ( image_pname_pname @ C @ D ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: ( pname > $o ) > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > pname > $o] :
@+[D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ B )
& ( finite1625599783_state @ D )
& ( A
= ( image_1552895654name_o @ C @ D ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: pname > $o,B: pname > $o,C: pname > pname] :
@+[D: pname] :
~ ( ( member_pname @ D @ A )
=> ( member_pname @ ( C @ D ) @ B ) ) ) ) ).
thf(sk137_def,definition,
( sk137
= ( @+[A: state] :
? [B: state] : ( A != B ) ) ) ).
thf(sk138_def,definition,
( sk138
= ( @+[A: state] : ( sk137 != A ) ) ) ).
thf(662,axiom,
! [A: pname > $o,B: pname] :
( ( ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_pname @ B @ bot_bot_pname_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_Collect__conv__if2) ).
thf(3021,plain,
! [A: pname > $o,B: pname] :
( ( ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_pname @ B @ bot_bot_pname_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(155,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1625599783_state @ ( collec1568722789_state @ A ) )
& ( finite1625599783_state @ ( collec1568722789_state @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_finite__Collect__disjI) ).
thf(1337,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1625599783_state @ ( collec1568722789_state @ A ) )
& ( finite1625599783_state @ ( collec1568722789_state @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(177,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_Sup__fin_Oidem) ).
thf(1411,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(530,axiom,
( bot_bot_pname_o
= ( collect_pname
@ ^ [A: pname] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_empty__def) ).
thf(2580,plain,
( bot_bot_pname_o
= ( collect_pname
@ ^ [A: pname] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(2581,plain,
( ( collect_pname
@ ^ [A: pname] : $false )
= bot_bot_pname_o ),
inference(lifteq,[status(thm)],[2580]) ).
thf(472,axiom,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_bot__apply) ).
thf(2396,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(2397,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[2396]) ).
thf(2398,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[2397]) ).
thf(3883,plain,
( ( collect_pname
@ ^ [A: pname] : $false )
= ( ^ [A: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[2581,2398]) ).
thf(248,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1780557381name_o @ B @ C ) )
=> ( ~ ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_UnE) ).
thf(1633,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1780557381name_o @ B @ C ) )
=> ( ~ ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(226,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_sup__inf__distrib1) ).
thf(1559,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(275,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ C @ B ) @ ( minus_2056855718tate_o @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_Diff__mono) ).
thf(1729,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ C @ B ) @ ( minus_2056855718tate_o @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(494,axiom,
! [A: pname > hoare_1708887482_state,B: pname,C: pname > $o] :
( ( inj_on1553129421_state @ A @ ( insert_pname @ B @ C ) )
= ( ( inj_on1553129421_state @ A @ C )
& ~ ( member451959335_state @ ( A @ B ) @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ C @ ( insert_pname @ B @ bot_bot_pname_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_inj__on__insert) ).
thf(2463,plain,
! [A: pname > hoare_1708887482_state,B: pname,C: pname > $o] :
( ( inj_on1553129421_state @ A @ ( insert_pname @ B @ C ) )
= ( ( inj_on1553129421_state @ A @ C )
& ~ ( member451959335_state @ ( A @ B ) @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ C @ ( insert_pname @ B @ bot_bot_pname_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(522,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_sup__ge1) ).
thf(2559,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(700,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ C ) )
= ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_Diff__insert2) ).
thf(3172,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ C ) )
= ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(541,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_equalityI) ).
thf(2612,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(58,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) )
= ( minus_minus_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1039_Diff__insert2) ).
thf(1024,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) )
= ( minus_minus_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(100,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( insert_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite_OinsertI) ).
thf(1168,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( insert_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(445,axiom,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_insertI1) ).
thf(2306,plain,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(388,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ C )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ C ) @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_939_sup__inf__distrib2) ).
thf(2131,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ C )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ C ) @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(357,axiom,
! [A: com > hoare_1708887482_state] :
( ( image_934102463_state @ A @ bot_bot_com_o )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_image__empty) ).
thf(2031,plain,
! [A: com > hoare_1708887482_state] :
( ( image_934102463_state @ A @ bot_bot_com_o )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(122,axiom,
! [A: pname > $o,B: hoare_1708887482_state > pname,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_1509414295_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_finite__surj) ).
thf(1237,plain,
! [A: pname > $o,B: hoare_1708887482_state > pname,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_1509414295_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(5,axiom,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_finite__subset__image) ).
thf(841,plain,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(842,plain,
! [C: pname > $o,B: pname > $o,A: pname > pname] :
( ( ~ ( finite_finite_pname @ C )
| ~ ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
| ( ord_less_eq_pname_o @ ( sk1 @ C @ B @ A ) @ B ) )
& ( ~ ( finite_finite_pname @ C )
| ~ ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
| ( finite_finite_pname @ ( sk1 @ C @ B @ A ) ) )
& ( ~ ( finite_finite_pname @ C )
| ~ ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
| ( C
= ( image_pname_pname @ A @ ( sk1 @ C @ B @ A ) ) ) ) ),
inference(cnf,[status(esa)],[841]) ).
thf(845,plain,
! [C: pname > $o,B: pname > $o,A: pname > pname] :
( ~ ( finite_finite_pname @ C )
| ~ ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
| ( C
= ( image_pname_pname @ A @ ( sk1 @ C @ B @ A ) ) ) ),
inference(cnfConj,[status(thm)],[842]) ).
thf(846,plain,
! [C: pname > $o,B: pname > $o,A: pname > pname] :
( ( C
= ( image_pname_pname @ A @ ( sk1 @ C @ B @ A ) ) )
| ~ ( finite_finite_pname @ C )
| ~ ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) ) ),
inference(lifteq,[status(thm)],[845]) ).
thf(86,axiom,
! [A: hoare_1708887482_state] : ( member451959335_state @ A @ top_to832624271tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_UNIV__I) ).
thf(1122,plain,
! [A: hoare_1708887482_state] : ( member451959335_state @ A @ top_to832624271tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1123,plain,
! [A: hoare_1708887482_state] : ( member451959335_state @ A @ top_to832624271tate_o ),
inference(cnf,[status(esa)],[1122]) ).
thf(741,axiom,
! [A: hoare_1708887482_state] :
~ ( member451959335_state @ A @ bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_emptyE) ).
thf(3348,plain,
! [A: hoare_1708887482_state] :
~ ( member451959335_state @ A @ bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(3349,plain,
~ ? [A: hoare_1708887482_state] : ( member451959335_state @ A @ bot_bo19817387tate_o ),
inference(miniscope,[status(thm)],[3348]) ).
thf(3350,plain,
! [A: hoare_1708887482_state] :
~ ( member451959335_state @ A @ bot_bo19817387tate_o ),
inference(cnf,[status(esa)],[3349]) ).
thf(4080,plain,
! [B: hoare_1708887482_state,A: hoare_1708887482_state] :
( ~ $true
| ( ( member451959335_state @ A @ top_to832624271tate_o )
!= ( member451959335_state @ B @ bot_bo19817387tate_o ) ) ),
inference(paramod_ordered,[status(thm)],[1123,3350]) ).
thf(4081,plain,
! [B: hoare_1708887482_state,A: hoare_1708887482_state] :
( ( member451959335_state @ A @ top_to832624271tate_o )
!= ( member451959335_state @ B @ bot_bo19817387tate_o ) ),
inference(simp,[status(thm)],[4080]) ).
thf(4082,plain,
! [B: hoare_1708887482_state,A: hoare_1708887482_state] :
( ( A != B )
| ( top_to832624271tate_o != bot_bo19817387tate_o ) ),
inference(simp,[status(thm)],[4081]) ).
thf(4083,plain,
top_to832624271tate_o != bot_bo19817387tate_o,
inference(simp,[status(thm)],[4082]) ).
thf(712,axiom,
! [A: hoare_1708887482_state] :
( ( bot_bo19817387tate_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_bot__fun__def) ).
thf(3232,plain,
! [A: hoare_1708887482_state] :
( ( bot_bo19817387tate_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(3233,plain,
! [A: hoare_1708887482_state] :
( ( bot_bo19817387tate_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[3232]) ).
thf(3234,plain,
! [A: hoare_1708887482_state] :
( ( bot_bo19817387tate_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[3233]) ).
thf(4151,plain,
( top_to832624271tate_o
!= ( ^ [A: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[4083,3234]) ).
thf(4155,plain,
( ( top_to832624271tate_o @ sk147 )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[4151]) ).
thf(4183,plain,
( ( top_to832624271tate_o @ sk147 )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[4155]) ).
thf(630,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila129691299tate_o @ ( collec1568722789_state @ A ) @ ( collec1568722789_state @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_862_Collect__conj__eq) ).
thf(2921,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila129691299tate_o @ ( collec1568722789_state @ A ) @ ( collec1568722789_state @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(689,axiom,
! [A: hoare_1708887482_state > $o] : ( hoare_90032982_state @ A @ bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
thf(3135,plain,
! [A: hoare_1708887482_state > $o] : ( hoare_90032982_state @ A @ bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(3136,plain,
! [A: hoare_1708887482_state > $o] : ( hoare_90032982_state @ A @ bot_bo19817387tate_o ),
inference(cnf,[status(esa)],[3135]) ).
thf(1,conjecture,
( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7) ).
thf(2,negated_conjecture,
~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(835,plain,
~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4116,plain,
! [A: hoare_1708887482_state > $o] :
( ~ $true
| ( ( hoare_90032982_state @ A @ bot_bo19817387tate_o )
!= ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [B: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ B ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ) ) ),
inference(paramod_ordered,[status(thm)],[3136,835]) ).
thf(4117,plain,
! [A: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ A @ bot_bo19817387tate_o )
!= ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [B: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ B ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) ) ),
inference(simp,[status(thm)],[4116]) ).
thf(4126,plain,
! [A: hoare_1708887482_state > $o] :
( ( A
!= ( image_1116629049_state
@ ^ [B: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ B ) )
@ ( dom_pname_com @ body ) ) )
| ( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o )
!= bot_bo19817387tate_o ) ),
inference(simp,[status(thm)],[4117]) ).
thf(4134,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o )
!= bot_bo19817387tate_o ),
inference(simp,[status(thm)],[4126]) ).
thf(4136,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o @ sk146 )
!= ( bot_bo19817387tate_o @ sk146 ) ),
inference(func_ext,[status(esa)],[4134]) ).
thf(4288,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk146 )
!= bot_bot_o ),
inference(rewrite,[status(thm)],[4136,3234]) ).
thf(4290,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk146 )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[4288]) ).
thf(409,axiom,
! [A: pname] : ( member_pname @ A @ top_top_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_UNIV__I) ).
thf(2201,plain,
! [A: pname] : ( member_pname @ A @ top_top_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(2202,plain,
! [A: pname] : ( member_pname @ A @ top_top_pname_o ),
inference(cnf,[status(esa)],[2201]) ).
thf(129,axiom,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_equals0D) ).
thf(1255,plain,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1256,plain,
! [B: pname > $o,A: pname] :
( ( B != bot_bot_pname_o )
| ~ ( member_pname @ A @ B ) ),
inference(cnf,[status(esa)],[1255]) ).
thf(1257,plain,
! [B: pname > $o,A: pname] :
( ( B != bot_bot_pname_o )
| ~ ( member_pname @ A @ B ) ),
inference(lifteq,[status(thm)],[1256]) ).
thf(1258,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(simp,[status(thm)],[1257]) ).
thf(3817,plain,
! [B: pname,A: pname] :
( ~ $true
| ( ( member_pname @ A @ top_top_pname_o )
!= ( member_pname @ B @ bot_bot_pname_o ) ) ),
inference(paramod_ordered,[status(thm)],[2202,1258]) ).
thf(3818,plain,
! [B: pname,A: pname] :
( ( member_pname @ A @ top_top_pname_o )
!= ( member_pname @ B @ bot_bot_pname_o ) ),
inference(simp,[status(thm)],[3817]) ).
thf(3819,plain,
! [B: pname,A: pname] :
( ( A != B )
| ( top_top_pname_o != bot_bot_pname_o ) ),
inference(simp,[status(thm)],[3818]) ).
thf(3820,plain,
top_top_pname_o != bot_bot_pname_o,
inference(simp,[status(thm)],[3819]) ).
thf(3880,plain,
( top_top_pname_o
!= ( ^ [A: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[3820,2398]) ).
thf(3892,plain,
( ( top_top_pname_o @ sk141 )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[3880]) ).
thf(3979,plain,
( ~ ( top_top_pname_o @ sk141 )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[3892]) ).
thf(310,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_insert__mono) ).
thf(1840,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(816,axiom,
! [A: hoare_1708887482_state] :
( ( bot_bo19817387tate_o @ A )
= ( member451959335_state @ A @ bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_bot__empty__eq) ).
thf(3581,plain,
! [A: hoare_1708887482_state] :
( ( bot_bo19817387tate_o @ A )
= ( member451959335_state @ A @ bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(483,axiom,
! [A: hoare_1708887482_state,B: com > hoare_1708887482_state,C: com,D: com > $o] :
( ( member_com @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member451959335_state @ A @ ( image_934102463_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_rev__image__eqI) ).
thf(2427,plain,
! [A: hoare_1708887482_state,B: com > hoare_1708887482_state,C: com,D: com > $o] :
( ( member_com @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member451959335_state @ A @ ( image_934102463_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(500,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ? [C: pname > $o] :
( ( B
= ( insert_pname @ A @ C ) )
& ~ ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_749_mk__disjoint__insert) ).
thf(2480,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ? [C: pname > $o] :
( ( B
= ( insert_pname @ A @ C ) )
& ~ ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(104,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ C )
= ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) ) )
= ( ord_less_eq_pname_o @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_Un__Int__assoc__eq) ).
thf(1179,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ C )
= ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) ) )
= ( ord_less_eq_pname_o @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(452,axiom,
! [A: pname > $o] : ( inj_on737724108_pname @ some_pname @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_inj__Some) ).
thf(2330,plain,
! [A: pname > $o] : ( inj_on737724108_pname @ some_pname @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(2331,plain,
! [A: pname > $o] : ( inj_on737724108_pname @ some_pname @ A ),
inference(cnf,[status(esa)],[2330]) ).
thf(339,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [D: pname,E: pname > $o] :
( ( finite_finite_pname @ E )
=> ( ( member_pname @ D @ B )
=> ( ~ ( member_pname @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_pname @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_finite__subset__induct) ).
thf(1950,plain,
! [A: ( pname > $o ) > $o,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [D: pname,E: pname > $o] :
( ( finite_finite_pname @ E )
=> ( ( member_pname @ D @ B )
=> ( ~ ( member_pname @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_pname @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(224,axiom,
! [A: hoare_1708887482_state > $o,B: pname > hoare_1708887482_state,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le777019615tate_o @ A @ ( image_1116629049_state @ B @ C ) )
=> ( finite1625599783_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_finite__surj) ).
thf(1549,plain,
! [A: hoare_1708887482_state > $o,B: pname > hoare_1708887482_state,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le777019615tate_o @ A @ ( image_1116629049_state @ B @ C ) )
=> ( finite1625599783_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(371,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ~ ( fequal224822779_state @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com) ).
thf(2077,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ~ ( fequal224822779_state @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(283,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( ( semila1673364395name_o @ B @ A )
= bot_bot_pname_o )
=> ( ( D @ ( semila1780557381name_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_folding__one_Ounion__disjoint) ).
thf(1750,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( ( semila1673364395name_o @ B @ A )
= bot_bot_pname_o )
=> ( ( D @ ( semila1780557381name_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(52,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ C @ B ) @ ( minus_minus_pname_o @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_Diff__mono) ).
thf(1005,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ C @ B ) @ ( minus_minus_pname_o @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(730,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( member451959335_state @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_singletonE) ).
thf(3317,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( member451959335_state @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(419,axiom,
! [A: pname > $o,B: ( pname > $o ) > pname,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_pname_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_finite__surj) ).
thf(2231,plain,
! [A: pname > $o,B: ( pname > $o ) > pname,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_pname_o_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(467,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( semila1780557381name_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_le__supI1) ).
thf(2381,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( semila1780557381name_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(788,axiom,
( ( set_Ho525251890_state @ none_H1106584047_state )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_Option_Oset_Osimps_I1_J) ).
thf(3498,plain,
( ( set_Ho525251890_state @ none_H1106584047_state )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(267,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_Un__upper2) ).
thf(1692,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(536,axiom,
! [A: com] : ( member_com @ A @ top_top_com_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1195_UNIV__I) ).
thf(2601,plain,
! [A: com] : ( member_com @ A @ top_top_com_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(2602,plain,
! [A: com] : ( member_com @ A @ top_top_com_o ),
inference(cnf,[status(esa)],[2601]) ).
thf(417,axiom,
! [A: com] :
~ ( member_com @ A @ bot_bot_com_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_empty__iff) ).
thf(2225,plain,
! [A: com] :
~ ( member_com @ A @ bot_bot_com_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(2226,plain,
~ ? [A: com] : ( member_com @ A @ bot_bot_com_o ),
inference(miniscope,[status(thm)],[2225]) ).
thf(2227,plain,
! [A: com] :
~ ( member_com @ A @ bot_bot_com_o ),
inference(cnf,[status(esa)],[2226]) ).
thf(314,axiom,
! [A: com] :
( ( bot_bot_com_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_bot__apply) ).
thf(1861,plain,
! [A: com] :
( ( bot_bot_com_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(1862,plain,
! [A: com] :
( ( bot_bot_com_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[1861]) ).
thf(1863,plain,
! [A: com] :
( ( bot_bot_com_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[1862]) ).
thf(3874,plain,
! [A: com] :
~ ( member_com @ A
@ ^ [B: com] : bot_bot_o ),
inference(rewrite,[status(thm)],[2227,1863]) ).
thf(4033,plain,
! [B: com,A: com] :
( ~ $true
| ( ( member_com @ A @ top_top_com_o )
!= ( member_com @ B
@ ^ [C: com] : bot_bot_o ) ) ),
inference(paramod_ordered,[status(thm)],[2602,3874]) ).
thf(4034,plain,
! [B: com,A: com] :
( ( member_com @ A @ top_top_com_o )
!= ( member_com @ B
@ ^ [C: com] : bot_bot_o ) ),
inference(simp,[status(thm)],[4033]) ).
thf(4035,plain,
! [B: com,A: com] :
( ( A != B )
| ( top_top_com_o
!= ( ^ [C: com] : bot_bot_o ) ) ),
inference(simp,[status(thm)],[4034]) ).
thf(4036,plain,
( top_top_com_o
!= ( ^ [A: com] : bot_bot_o ) ),
inference(simp,[status(thm)],[4035]) ).
thf(4037,plain,
( ( top_top_com_o @ sk144 )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[4036]) ).
thf(509,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila129691299tate_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_Int__absorb1) ).
thf(2512,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila129691299tate_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(215,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_equalityI) ).
thf(1522,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(547,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( ( ord_le777019615tate_o @ A @ C )
& ( ord_le777019615tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_le__sup__iff) ).
thf(2644,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( ( ord_le777019615tate_o @ A @ C )
& ( ord_le777019615tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(588,axiom,
! [A: option_com] :
( ( ! [B: com] :
( A
!= ( some_com @ B ) ) )
= ( A = none_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_not__Some__eq) ).
thf(2776,plain,
! [A: option_com] :
( ( ! [B: com] :
( A
!= ( some_com @ B ) ) )
= ( A = none_com ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(762,axiom,
! [A: pname > state > state > $o,B: pname > state > state > $o,C: hoare_1708887482_state > $o,D: pname > state > state > $o,E: pname > com,F: pname > state > state > $o,G: pname > $o] :
( ( finite_finite_pname @ G )
=> ( ! [H: pname] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) ) @ bot_bo19817387tate_o ) ) )
=> ( ( hoare_90032982_state @ C
@ ( image_1116629049_state
@ ^ [H: pname] : ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) )
@ G ) )
=> ( hoare_90032982_state @ C
@ ( image_1116629049_state
@ ^ [H: pname] : ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) )
@ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_finite__pointwise) ).
thf(3417,plain,
! [A: pname > state > state > $o,B: pname > state > state > $o,C: hoare_1708887482_state > $o,D: pname > state > state > $o,E: pname > com,F: pname > state > state > $o,G: pname > $o] :
( ( finite_finite_pname @ G )
=> ( ! [H: pname] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) ) @ bot_bo19817387tate_o ) ) )
=> ( ( hoare_90032982_state @ C
@ ( image_1116629049_state
@ ^ [H: pname] : ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) )
@ G ) )
=> ( hoare_90032982_state @ C
@ ( image_1116629049_state
@ ^ [H: pname] : ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) )
@ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(514,axiom,
! [A: hoare_1708887482_state] :
( ( some_H1974565227_state @ A )
!= none_H1106584047_state ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_option_Osimps_I3_J) ).
thf(2527,plain,
! [A: hoare_1708887482_state] :
( ( some_H1974565227_state @ A )
!= none_H1106584047_state ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(667,axiom,
! [A: hoare_1708887482_state > $o] :
( ( ? [B: hoare_1708887482_state] : ( member451959335_state @ B @ A ) )
= ( A != bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_ex__in__conv) ).
thf(3040,plain,
! [A: hoare_1708887482_state > $o] :
( ( ? [B: hoare_1708887482_state] : ( member451959335_state @ B @ A ) )
= ( A != bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(695,axiom,
! [A: hoare_1708887482_state,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_1116629049_state
@ ^ [C: pname] : A
@ B )
= bot_bo19817387tate_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_1116629049_state
@ ^ [C: pname] : A
@ B )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_image__constant__conv) ).
thf(3153,plain,
! [A: hoare_1708887482_state,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_1116629049_state
@ ^ [C: pname] : A
@ B )
= bot_bo19817387tate_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_1116629049_state
@ ^ [C: pname] : A
@ B )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(230,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_order__eq__iff) ).
thf(1569,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(425,axiom,
! [A: com] :
( ( bot_bot_com_o @ A )
= ( member_com @ A @ bot_bot_com_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_bot__empty__eq) ).
thf(2248,plain,
! [A: com] :
( ( bot_bot_com_o @ A )
= ( member_com @ A @ bot_bot_com_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(608,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ bot_bot_pname_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_Un__empty__right) ).
thf(2837,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ bot_bot_pname_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(91,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_order__refl) ).
thf(1142,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(134,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_894_le__infI2) ).
thf(1269,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(298,axiom,
! [A: option1624383643_state] :
( ( A != none_H1106584047_state )
=> ~ ! [B: hoare_1708887482_state] :
( A
!= ( some_H1974565227_state @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_option_Oexhaust) ).
thf(1793,plain,
! [A: option1624383643_state] :
( ( A != none_H1106584047_state )
=> ~ ! [B: hoare_1708887482_state] :
( A
!= ( some_H1974565227_state @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(757,axiom,
! [A: hoare_1708887482_state > $o,B: state > state > $o,C: state > $o,D: com] :
( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [E: state,F: state] :
( ( B @ E @ F )
& ~ ( C @ F ) )
@ ( while @ C @ D )
@ B )
@ bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_LoopF) ).
thf(3402,plain,
! [A: hoare_1708887482_state > $o,B: state > state > $o,C: state > $o,D: com] :
( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [E: state,F: state] :
( ( B @ E @ F )
& ~ ( C @ F ) )
@ ( while @ C @ D )
@ B )
@ bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(64,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1673364395name_o @ A @ ( minus_minus_pname_o @ B @ A ) )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_Diff__disjoint) ).
thf(1041,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1673364395name_o @ A @ ( minus_minus_pname_o @ B @ A ) )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(10,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) ) )
= ( finite_finite_pname @ ( minus_minus_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_finite__Diff__insert) ).
thf(861,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) ) )
= ( finite_finite_pname @ ( minus_minus_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(241,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_sup_Oleft__idem) ).
thf(1608,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(255,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ C ) )
= ( ( ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C ) )
& ( ~ ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_subset__insert__iff) ).
thf(1655,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ C ) )
= ( ( ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C ) )
& ( ~ ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(766,axiom,
! [A: hoare_1708887482_state > $o] :
( ( A != bot_bo19817387tate_o )
= ( ? [B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( A
= ( insert528405184_state @ B @ C ) )
& ~ ( member451959335_state @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_nonempty__iff) ).
thf(3429,plain,
! [A: hoare_1708887482_state > $o] :
( ( A != bot_bo19817387tate_o )
= ( ? [B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( A
= ( insert528405184_state @ B @ C ) )
& ~ ( member451959335_state @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(350,axiom,
! [A: pname > $o,B: pname > option_com,C: pname] :
( ( ( B @ C )
= none_com )
=> ( ( minus_minus_pname_o @ ( dom_pname_com @ B ) @ ( insert_pname @ C @ A ) )
= ( minus_minus_pname_o @ ( dom_pname_com @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_dom__minus) ).
thf(1999,plain,
! [A: pname > $o,B: pname > option_com,C: pname] :
( ( ( B @ C )
= none_com )
=> ( ( minus_minus_pname_o @ ( dom_pname_com @ B ) @ ( insert_pname @ C @ A ) )
= ( minus_minus_pname_o @ ( dom_pname_com @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(121,axiom,
! [A: com,B: pname > com,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_com @ A @ ( image_pname_com @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_rev__image__eqI) ).
thf(1233,plain,
! [A: com,B: pname > com,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_com @ A @ ( image_pname_com @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(704,axiom,
! [A: hoare_1708887482_state,B: com > $o] :
( ( ( B = bot_bot_com_o )
=> ( ( image_934102463_state
@ ^ [C: com] : A
@ B )
= bot_bo19817387tate_o ) )
& ( ( B != bot_bot_com_o )
=> ( ( image_934102463_state
@ ^ [C: com] : A
@ B )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_image__constant__conv) ).
thf(3199,plain,
! [A: hoare_1708887482_state,B: com > $o] :
( ( ( B = bot_bot_com_o )
=> ( ( image_934102463_state
@ ^ [C: com] : A
@ B )
= bot_bo19817387tate_o ) )
& ( ( B != bot_bot_com_o )
=> ( ( image_934102463_state
@ ^ [C: com] : A
@ B )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(3200,plain,
( ! [A: hoare_1708887482_state,B: com > $o] :
( ( B = bot_bot_com_o )
=> ( ( image_934102463_state
@ ^ [C: com] : A
@ B )
= bot_bo19817387tate_o ) )
& ! [A: hoare_1708887482_state,B: com > $o] :
( ( B != bot_bot_com_o )
=> ( ( image_934102463_state
@ ^ [C: com] : A
@ B )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ),
inference(miniscope,[status(thm)],[3199]) ).
thf(3201,plain,
! [D: com > $o,C: hoare_1708887482_state,B: com > $o,A: hoare_1708887482_state] :
( ( ( B != bot_bot_com_o )
| ( ( image_934102463_state
@ ^ [E: com] : A
@ B )
= bot_bo19817387tate_o ) )
& ( ( D = bot_bot_com_o )
| ( ( image_934102463_state
@ ^ [E: com] : C
@ D )
= ( insert528405184_state @ C @ bot_bo19817387tate_o ) ) ) ),
inference(cnf,[status(esa)],[3200]) ).
thf(3202,plain,
! [B: com > $o,A: hoare_1708887482_state] :
( ( B != bot_bot_com_o )
| ( ( image_934102463_state
@ ^ [C: com] : A
@ B )
= bot_bo19817387tate_o ) ),
inference(cnfConj,[status(thm)],[3201]) ).
thf(3204,plain,
! [B: com > $o,A: hoare_1708887482_state] :
( ( B != bot_bot_com_o )
| ( ( image_934102463_state
@ ^ [C: com] : A
@ B )
= bot_bo19817387tate_o ) ),
inference(lifteq,[status(thm)],[3202]) ).
thf(3205,plain,
! [A: hoare_1708887482_state] :
( ( image_934102463_state
@ ^ [B: com] : A
@ bot_bot_com_o )
= bot_bo19817387tate_o ),
inference(simp,[status(thm)],[3204]) ).
thf(4564,plain,
! [A: hoare_1708887482_state] :
( ( image_934102463_state
@ ^ [B: com] : A
@ ^ [B: com] : bot_bot_o )
= ( ^ [B: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[3205,3234,1863]) ).
thf(398,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C = A )
| ( member451959335_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_insert__compr__raw) ).
thf(2168,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C = A )
| ( member451959335_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(714,axiom,
! [A: pname,B: state > $o,C: com] :
( ( body_1 @ A )
!= ( while @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_705_com_Osimps_I59_J) ).
thf(3253,plain,
! [A: pname,B: state > $o,C: com] :
( ( body_1 @ A )
!= ( while @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(611,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_sup__idem) ).
thf(2844,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(814,axiom,
~ ( member451959335_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(3577,plain,
~ ( member451959335_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(721,axiom,
! [A: hoare_1708887482_state > $o,B: com] :
( ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ B ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [C: state,D: state] :
! [E: state] :
( ( evalc @ B @ D @ E )
=> ( C = E ) )
@ B
@ fequal_state )
@ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_MGT__alternI) ).
thf(3276,plain,
! [A: hoare_1708887482_state > $o,B: com] :
( ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ B ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [C: state,D: state] :
! [E: state] :
( ( evalc @ B @ D @ E )
=> ( C = E ) )
@ B
@ fequal_state )
@ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(71,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
= ( ( A = B )
| ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_insert__iff) ).
thf(1078,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
= ( ( A = B )
| ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(296,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1673364395name_o
@ ^ [D: pname] : ( member_pname @ D @ A )
@ ^ [D: pname] : ( member_pname @ D @ B )
@ C )
= ( member_pname @ C @ ( semila1673364395name_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_821_inf__Int__eq) ).
thf(1788,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1673364395name_o
@ ^ [D: pname] : ( member_pname @ D @ A )
@ ^ [D: pname] : ( member_pname @ D @ B )
@ C )
= ( member_pname @ C @ ( semila1673364395name_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(739,axiom,
( ( dom_pname_com
@ ^ [A: pname] : none_com )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_dom__empty) ).
thf(3344,plain,
( ( dom_pname_com
@ ^ [A: pname] : none_com )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(3345,plain,
( ( dom_pname_com
@ ^ [A: pname] : none_com )
= bot_bot_pname_o ),
inference(lifteq,[status(thm)],[3344]) ).
thf(3645,plain,
( ~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ bot_bot_pname_o )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
| ( ( dom_pname_com @ body )
!= ( dom_pname_com
@ ^ [A: pname] : none_com ) ) ),
inference(paramod_ordered,[status(thm)],[3345,835]) ).
thf(3647,plain,
( ~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ bot_bot_pname_o )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
| ( ( ^ [A: pname] : body )
!= ( ^ [A: pname,B: pname] : none_com ) )
| ( ( ^ [A: pname] : A )
!= ( ^ [A: pname] : A ) ) ),
inference(simp,[status(thm)],[3645]) ).
thf(3649,plain,
( ~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ bot_bot_pname_o )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
| ( ( ^ [A: pname] : body )
!= ( ^ [A: pname,B: pname] : none_com ) ) ),
inference(simp,[status(thm)],[3647]) ).
thf(3875,plain,
( ~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ^ [A: pname] : bot_bot_o )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )
| ( ( ^ [A: pname] : body )
!= ( ^ [A: pname,B: pname] : none_com ) ) ),
inference(rewrite,[status(thm)],[3649,2398]) ).
thf(4150,plain,
( ~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ^ [A: pname] : bot_bot_o )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o ) )
| ( ( ^ [A: pname] : body )
!= ( ^ [A: pname,B: pname] : none_com ) ) ),
inference(rewrite,[status(thm)],[3875,3234]) ).
thf(742,axiom,
! [A: pname > hoare_1708887482_state] :
( ( image_1116629049_state @ A @ bot_bot_pname_o )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_image__empty) ).
thf(3351,plain,
! [A: pname > hoare_1708887482_state] :
( ( image_1116629049_state @ A @ bot_bot_pname_o )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(3352,plain,
! [A: pname > hoare_1708887482_state] :
( ( image_1116629049_state @ A @ bot_bot_pname_o )
= bot_bo19817387tate_o ),
inference(cnf,[status(esa)],[3351]) ).
thf(3353,plain,
! [A: pname > hoare_1708887482_state] :
( ( image_1116629049_state @ A @ bot_bot_pname_o )
= bot_bo19817387tate_o ),
inference(lifteq,[status(thm)],[3352]) ).
thf(4572,plain,
! [A: pname > hoare_1708887482_state] :
( ( image_1116629049_state @ A
@ ^ [B: pname] : bot_bot_o )
= ( ^ [B: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[3353,3234,2398]) ).
thf(4575,plain,
( ~ ( hoare_90032982_state
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o ) )
| ( ( ^ [A: pname] : body )
!= ( ^ [A: pname,B: pname] : none_com ) ) ),
inference(rewrite,[status(thm)],[4150,4572]) ).
thf(146,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_IntD1) ).
thf(1310,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(577,axiom,
! [A: state > state > $o,B: com,C: state > state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( ( hoare_858012674_state @ A @ B @ C )
= ( hoare_858012674_state @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_triple_Oinject) ).
thf(2740,plain,
! [A: state > state > $o,B: com,C: state > state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( ( hoare_858012674_state @ A @ B @ C )
= ( hoare_858012674_state @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(629,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1780557381name_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_subset__Un__eq) ).
thf(2918,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1780557381name_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(316,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( image_1509414295_pname @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1780557381name_o @ ( image_1509414295_pname @ A @ B ) @ ( image_1509414295_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_image__Un) ).
thf(1867,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( image_1509414295_pname @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1780557381name_o @ ( image_1509414295_pname @ A @ B ) @ ( image_1509414295_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(701,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ~ ( member451959335_state @ A @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_folding__one_Oinsert) ).
thf(3175,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ~ ( member451959335_state @ A @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(489,axiom,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_ex__in__conv) ).
thf(2448,plain,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(634,axiom,
! [A: com > $o] :
( ! [B: com] :
~ ( member_com @ B @ A )
=> ( A = bot_bot_com_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_equals0I) ).
thf(2933,plain,
! [A: com > $o] :
( ! [B: com] :
~ ( member_com @ B @ A )
=> ( A = bot_bot_com_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(318,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_le__infI1) ).
thf(1872,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(568,axiom,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
=> ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_le__bot) ).
thf(2712,plain,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
=> ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(761,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( insert528405184_state @ B @ C ) )
= ( insert528405184_state @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_Un__insert__right) ).
thf(3414,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( insert528405184_state @ B @ C ) )
= ( insert528405184_state @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(157,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( C = A )
=> ( ord_le777019615tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_ord__le__eq__trans) ).
thf(1342,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( C = A )
=> ( ord_le777019615tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(159,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( finite1625599783_state @ A )
=> ( ( ( semila129691299tate_o @ B @ A )
!= bot_bo19817387tate_o )
=> ( ( C @ ( D @ ( semila1122118281tate_o @ B @ A ) ) @ ( D @ ( semila129691299tate_o @ B @ A ) ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_folding__one_Ounion__inter) ).
thf(1354,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( finite1625599783_state @ A )
=> ( ( ( semila129691299tate_o @ B @ A )
!= bot_bo19817387tate_o )
=> ( ( C @ ( D @ ( semila1122118281tate_o @ B @ A ) ) @ ( D @ ( semila129691299tate_o @ B @ A ) ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',fact_771_evalc__elim__cases_I4_J) ).
thf(2146,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)],[393]) ).
thf(833,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ A @ B )
=> ( hoare_496444244_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_hoare__sound) ).
thf(3629,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ A @ B )
=> ( hoare_496444244_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(803,axiom,
! [A: com] :
( hoare_1160767572gleton
=> ( wT_bodies
=> ( ( wt @ A )
=> ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo19817387tate_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_MGF) ).
thf(3545,plain,
! [A: com] :
( hoare_1160767572gleton
=> ( wT_bodies
=> ( ( wt @ A )
=> ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo19817387tate_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(334,axiom,
! [A: hoare_1708887482_state > pname] :
( ( image_1509414295_pname @ A @ bot_bo19817387tate_o )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_image__empty) ).
thf(1935,plain,
! [A: hoare_1708887482_state > pname] :
( ( image_1509414295_pname @ A @ bot_bo19817387tate_o )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(252,axiom,
! [A: hoare_1708887482_state > $o] :
( ( collec1568722789_state @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Collect__def) ).
thf(1645,plain,
! [A: hoare_1708887482_state > $o] :
( ( collec1568722789_state @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(400,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_Sup__fin_Oidem) ).
thf(2173,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(125,axiom,
finite_finite_pname @ bot_bot_pname_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_finite_OemptyI) ).
thf(1244,plain,
finite_finite_pname @ bot_bot_pname_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(3878,plain,
( finite_finite_pname
@ ^ [A: pname] : bot_bot_o ),
inference(rewrite,[status(thm)],[1244,2398]) ).
thf(515,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_inf__sup__distrib1) ).
thf(2531,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(646,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_Int__lower2) ).
thf(2972,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(361,axiom,
! [A: pname,B: pname] :
( ( member_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_singletonE) ).
thf(2046,plain,
! [A: pname,B: pname] :
( ( member_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(503,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( minus_2056855718tate_o @ B @ C ) )
=> ~ ( member451959335_state @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_DiffD2) ).
thf(2491,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( minus_2056855718tate_o @ B @ C ) )
=> ~ ( member451959335_state @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(521,axiom,
! [A: pname,B: pname > $o,C: option_pname] :
( ! [D: pname] :
( ( member_pname @ D @ ( set_pname @ C ) )
=> ( B @ D ) )
=> ( ( C
= ( some_pname @ A ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_ospec) ).
thf(2548,plain,
! [A: pname,B: pname > $o,C: option_pname] :
( ! [D: pname] :
( ( member_pname @ D @ ( set_pname @ C ) )
=> ( B @ D ) )
=> ( ( C
= ( some_pname @ A ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(294,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_set__eq__subset) ).
thf(1782,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(18,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( minus_minus_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ B ) @ ( minus_minus_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_Diff__Int) ).
thf(885,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( minus_minus_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ B ) @ ( minus_minus_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(675,axiom,
! [A: hoare_1708887482_state > $o,B: com,C: state > state > $o,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [G: state,H: state] : ( H = F )
@ B
@ ^ [G: state] : ( C @ E ) )
@ bot_bo19817387tate_o ) ) )
=> ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ D @ B @ C ) @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_escape) ).
thf(3088,plain,
! [A: hoare_1708887482_state > $o,B: com,C: state > state > $o,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [G: state,H: state] : ( H = F )
@ B
@ ^ [G: state] : ( C @ E ) )
@ bot_bo19817387tate_o ) ) )
=> ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ D @ B @ C ) @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(691,axiom,
! [A: state > state > $o,B: hoare_1708887482_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ C @ D @ E ) @ bot_bo19817387tate_o ) )
=> ( ! [F: state,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ C @ D @ A ) @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_conseq2) ).
thf(3140,plain,
! [A: state > state > $o,B: hoare_1708887482_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ C @ D @ E ) @ bot_bo19817387tate_o ) )
=> ( ! [F: state,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ C @ D @ A ) @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(198,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( B @ C )
=> ( semila1780557381name_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_sup1I2) ).
thf(1475,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( B @ C )
=> ( semila1780557381name_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(368,axiom,
! [A: pname > pname > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_pigeonhole__infinite) ).
thf(2067,plain,
! [A: pname > pname > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(604,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ C ) )
=> ( member451959335_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_IntD1) ).
thf(2825,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ C ) )
=> ( member451959335_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(601,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_Diff__subset) ).
thf(2819,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(4084,plain,
( ( top_to832624271tate_o @ sk145 )
!= ( bot_bo19817387tate_o @ sk145 ) ),
inference(func_ext,[status(esa)],[4083]) ).
thf(4145,plain,
( ( top_to832624271tate_o @ sk145 )
!= bot_bot_o ),
inference(rewrite,[status(thm)],[4084,3234]) ).
thf(4156,plain,
( ~ ( top_to832624271tate_o @ sk145 )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[4145]) ).
thf(300,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_inf__sup__ord_I2_J) ).
thf(1803,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(201,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_Int__lower1) ).
thf(1482,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(822,axiom,
( bot_bo19817387tate_o
= ( collec1568722789_state
@ ^ [A: hoare_1708887482_state] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_empty__def) ).
thf(3597,plain,
( bot_bo19817387tate_o
= ( collec1568722789_state
@ ^ [A: hoare_1708887482_state] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(3578,plain,
~ ( member451959335_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ),
inference(polarity_switch,[status(thm)],[3577]) ).
thf(3683,plain,
! [A: hoare_1708887482_state] :
( ~ $true
| ( ( member451959335_state @ A @ top_to832624271tate_o )
!= ( member451959335_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ) ),
inference(paramod_ordered,[status(thm)],[1123,3578]) ).
thf(3684,plain,
! [A: hoare_1708887482_state] :
( ( member451959335_state @ A @ top_to832624271tate_o )
!= ( member451959335_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) ),
inference(simp,[status(thm)],[3683]) ).
thf(3685,plain,
! [A: hoare_1708887482_state] :
( ( A
!= ( hoare_Mirabelle_MGT @ y ) )
| ( fa != top_to832624271tate_o ) ),
inference(simp,[status(thm)],[3684]) ).
thf(3686,plain,
fa != top_to832624271tate_o,
inference(simp,[status(thm)],[3685]) ).
thf(3687,plain,
( ( fa @ sk139 )
!= ( top_to832624271tate_o @ sk139 ) ),
inference(func_ext,[status(esa)],[3686]) ).
thf(3688,plain,
( ~ ( fa @ sk139 )
| ~ ( top_to832624271tate_o @ sk139 ) ),
inference(bool_ext,[status(thm)],[3687]) ).
thf(619,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_le__infI1) ).
thf(2869,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(246,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_insert__absorb) ).
thf(1628,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(771,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( insert528405184_state @ B @ C ) )
= ( ( A = B )
| ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_insert__iff) ).
thf(3442,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( insert528405184_state @ B @ C ) )
= ( ( A = B )
| ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(537,axiom,
! [A: option1624383643_state] :
( ( ! [B: hoare_1708887482_state] :
( A
!= ( some_H1974565227_state @ B ) ) )
= ( A = none_H1106584047_state ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_not__Some__eq) ).
thf(2603,plain,
! [A: option1624383643_state] :
( ( ! [B: hoare_1708887482_state] :
( A
!= ( some_H1974565227_state @ B ) ) )
= ( A = none_H1106584047_state ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(663,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( semila1122118281tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_sup__commute) ).
thf(3029,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( semila1122118281tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(599,axiom,
! [A: pname > hoare_1708887482_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member451959335_state @ ( A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_imageI) ).
thf(2814,plain,
! [A: pname > hoare_1708887482_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member451959335_state @ ( A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(787,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
= ( semila1122118281tate_o @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_insert__is__Un) ).
thf(3495,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
= ( semila1122118281tate_o @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(506,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( ord_le777019615tate_o @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_le__infI) ).
thf(2501,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( ord_le777019615tate_o @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(210,axiom,
finite2034616076tate_o @ semila1122118281tate_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_comp__fun__idem__sup) ).
thf(1511,plain,
finite2034616076tate_o @ semila1122118281tate_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(147,axiom,
! [A: com > $o,B: hoare_1708887482_state,C: com > hoare_1708887482_state,D: com] :
( ( B
= ( C @ D ) )
=> ( ( member_com @ D @ A )
=> ( member451959335_state @ B @ ( image_934102463_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_image__eqI) ).
thf(1313,plain,
! [A: com > $o,B: hoare_1708887482_state,C: com > hoare_1708887482_state,D: com] :
( ( B
= ( C @ D ) )
=> ( ( member_com @ D @ A )
=> ( member451959335_state @ B @ ( image_934102463_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(502,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( semila129691299tate_o @ A @ B )
= bot_bo19817387tate_o )
=> ( ( minus_2056855718tate_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_Diff__triv) ).
thf(2488,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( semila129691299tate_o @ A @ B )
= bot_bo19817387tate_o )
=> ( ( minus_2056855718tate_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(347,axiom,
! [A: com,B: state > $o,C: state] :
( ~ ( B @ C )
=> ( evalc @ ( while @ B @ A ) @ C @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_evalc_OWhileFalse) ).
thf(1992,plain,
! [A: com,B: state > $o,C: state] :
( ~ ( B @ C )
=> ( evalc @ ( while @ B @ A ) @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(563,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( minus_2056855718tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( minus_2056855718tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_insert__Diff1) ).
thf(2698,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( minus_2056855718tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( minus_2056855718tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(688,axiom,
! [A: hoare_1708887482_state > option_pname,B: hoare_1708887482_state,C: pname] :
( ( ( A @ B )
= ( some_pname @ C ) )
=> ( ( insert528405184_state @ B @ ( dom_Ho1805192458_pname @ A ) )
= ( dom_Ho1805192458_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_insert__dom) ).
thf(3131,plain,
! [A: hoare_1708887482_state > option_pname,B: hoare_1708887482_state,C: pname] :
( ( ( A @ B )
= ( some_pname @ C ) )
=> ( ( insert528405184_state @ B @ ( dom_Ho1805192458_pname @ A ) )
= ( dom_Ho1805192458_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(683,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] : ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_subset__insertI) ).
thf(3116,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] : ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(552,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_sup__left__commute) ).
thf(2667,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(455,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ B )
| ( finite_finite_pname @ A ) )
=> ( finite_finite_pname @ ( semila1673364395name_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_finite__Int) ).
thf(2339,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ B )
| ( finite_finite_pname @ A ) )
=> ( finite_finite_pname @ ( semila1673364395name_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(3689,plain,
( ( fa @ sk139 )
| ( top_to832624271tate_o @ sk139 ) ),
inference(bool_ext,[status(thm)],[3687]) ).
thf(829,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( finite1625599783_state @ ( insert528405184_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite_OinsertI) ).
thf(3617,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( finite1625599783_state @ ( insert528405184_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(488,axiom,
! [A: hoare_1708887482_state > option1624383643_state,B: hoare_1708887482_state,C: hoare_1708887482_state] :
( ( ( A @ B )
= ( some_H1974565227_state @ C ) )
=> ( member451959335_state @ B @ ( dom_Ho1703271284_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_domI) ).
thf(2444,plain,
! [A: hoare_1708887482_state > option1624383643_state,B: hoare_1708887482_state,C: hoare_1708887482_state] :
( ( ( A @ B )
= ( some_H1974565227_state @ C ) )
=> ( member451959335_state @ B @ ( dom_Ho1703271284_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(132,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ ( minus_2056855718tate_o @ B @ A ) )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_Diff__disjoint) ).
thf(1264,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ ( minus_2056855718tate_o @ B @ A ) )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(681,axiom,
( ( body @ pn )
= ( some_com @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(3111,plain,
( ( body @ pn )
= ( some_com @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(3112,plain,
( ( some_com @ y )
= ( body @ pn ) ),
inference(lifteq,[status(thm)],[3111]) ).
thf(176,axiom,
! [A: com] :
( none_com
!= ( some_com @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1106_option_Osimps_I2_J) ).
thf(1407,plain,
! [A: com] :
( none_com
!= ( some_com @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1408,plain,
~ ? [A: com] :
( none_com
= ( some_com @ A ) ),
inference(miniscope,[status(thm)],[1407]) ).
thf(1409,plain,
! [A: com] :
( none_com
!= ( some_com @ A ) ),
inference(cnf,[status(esa)],[1408]) ).
thf(1410,plain,
! [A: com] :
( ( some_com @ A )
!= none_com ),
inference(lifteq,[status(thm)],[1409]) ).
thf(3652,plain,
! [A: com] :
( ( ( body @ pn )
!= none_com )
| ( ( some_com @ y )
!= ( some_com @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3112,1410]) ).
thf(3653,plain,
( ( body @ pn )
!= none_com ),
inference(pattern_uni,[status(thm)],[3652:[bind(A,$thf( y ))]]) ).
thf(4,axiom,
! [A: pname,B: pname] :
( ~ ( fequal_pname @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
thf(838,plain,
! [A: pname,B: pname] :
( ~ ( fequal_pname @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(686,axiom,
! [A: hoare_1708887482_state > $o] :
( ( ( collec1568722789_state @ A )
= bot_bo19817387tate_o )
= ( ! [B: hoare_1708887482_state] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Collect__empty__eq) ).
thf(3125,plain,
! [A: hoare_1708887482_state > $o] :
( ( ( collec1568722789_state @ A )
= bot_bo19817387tate_o )
= ( ! [B: hoare_1708887482_state] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(306,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_pname_pname
@ ^ [D: pname] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_image__constant) ).
thf(1826,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_pname_pname
@ ^ [D: pname] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(32,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( minus_minus_pname_o @ A @ C ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( minus_minus_pname_o @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_insert__Diff__if) ).
thf(934,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( minus_minus_pname_o @ A @ C ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( minus_minus_pname_o @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(108,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( member451959335_state @ B @ A )
=> ( member451959335_state @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_805_IntI) ).
thf(1191,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( member451959335_state @ B @ A )
=> ( member451959335_state @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(495,axiom,
! [A: pname > option_com,B: pname > option_com,C: pname > $o] :
( ( dom_pname_com @ ( overri1496249029on_com @ A @ B @ C ) )
= ( semila1780557381name_o
@ ( minus_minus_pname_o @ ( dom_pname_com @ A )
@ ( collect_pname
@ ^ [D: pname] : ( member_pname @ D @ ( minus_minus_pname_o @ C @ ( dom_pname_com @ B ) ) ) ) )
@ ( collect_pname
@ ^ [D: pname] : ( member_pname @ D @ ( semila1673364395name_o @ C @ ( dom_pname_com @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_dom__override__on) ).
thf(2466,plain,
! [A: pname > option_com,B: pname > option_com,C: pname > $o] :
( ( dom_pname_com @ ( overri1496249029on_com @ A @ B @ C ) )
= ( semila1780557381name_o
@ ( minus_minus_pname_o @ ( dom_pname_com @ A )
@ ( collect_pname
@ ^ [D: pname] : ( member_pname @ D @ ( minus_minus_pname_o @ C @ ( dom_pname_com @ B ) ) ) ) )
@ ( collect_pname
@ ^ [D: pname] : ( member_pname @ D @ ( semila1673364395name_o @ C @ ( dom_pname_com @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(386,axiom,
! [A: pname,B: pname > option1624383643_state] :
( ( member_pname @ A @ ( dom_pn1412407212_state @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( B @ A )
= ( some_H1974565227_state @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_domD) ).
thf(2126,plain,
! [A: pname,B: pname > option1624383643_state] :
( ( member_pname @ A @ ( dom_pn1412407212_state @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( B @ A )
= ( some_H1974565227_state @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(89,axiom,
! [A: pname > option_pname,B: pname,C: pname] :
( ( ( A @ B )
= ( some_pname @ C ) )
=> ( member_pname @ B @ ( dom_pname_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_domI) ).
thf(1132,plain,
! [A: pname > option_pname,B: pname,C: pname] :
( ( ( A @ B )
= ( some_pname @ C ) )
=> ( member_pname @ B @ ( dom_pname_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(668,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] :
( ( ( A @ B )
=> ( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C = B )
& ( A @ C ) ) )
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_Collect__conv__if) ).
thf(3043,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] :
( ( ( A @ B )
=> ( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C = B )
& ( A @ C ) ) )
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(527,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_sup__absorb2) ).
thf(2571,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(461,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: option1624383643_state] :
( ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ ( set_Ho525251890_state @ C ) )
=> ( B @ D ) )
=> ( ( C
= ( some_H1974565227_state @ A ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_ospec) ).
thf(2356,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: option1624383643_state] :
( ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ ( set_Ho525251890_state @ C ) )
=> ( B @ D ) )
=> ( ( C
= ( some_H1974565227_state @ A ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(93,axiom,
! [A: pname,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( image_1509414295_pname
@ ^ [D: hoare_1708887482_state] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_image__constant) ).
thf(1147,plain,
! [A: pname,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( image_1509414295_pname
@ ^ [D: hoare_1708887482_state] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(362,axiom,
! [A: com,B: com,C: state > $o,D: com] :
( ( semi @ A @ B )
!= ( while @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_com_Osimps_I46_J) ).
thf(2049,plain,
! [A: com,B: com,C: state > $o,D: com] :
( ( semi @ A @ B )
!= ( while @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(200,axiom,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_bot__unique) ).
thf(1479,plain,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(231,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( insert_pname @ B @ A ) )
= ( ord_less_eq_pname_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_subset__insert) ).
thf(1572,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( insert_pname @ B @ A ) )
= ( ord_less_eq_pname_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(708,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ~ ( member451959335_state @ B @ C )
=> ( B = A ) )
=> ( member451959335_state @ B @ ( insert528405184_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_insertCI) ).
thf(3216,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ~ ( member451959335_state @ B @ C )
=> ( B = A ) )
=> ( member451959335_state @ B @ ( insert528405184_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(779,axiom,
! [A: pname,B: com,C: com] :
( ( body_1 @ A )
!= ( semi @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_com_Osimps_I49_J) ).
thf(3470,plain,
! [A: pname,B: com,C: com] :
( ( body_1 @ A )
!= ( semi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(332,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ C @ A ) @ ( semila1122118281tate_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_sup__mono) ).
thf(1931,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ C @ A ) @ ( semila1122118281tate_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(355,axiom,
! [A: pname > $o,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ! [D: pname,E: pname] : ( member_pname @ ( B @ D @ E ) @ ( insert_pname @ D @ ( insert_pname @ E @ bot_bot_pname_o ) ) )
=> ( member_pname @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_737_folding__one_Oclosed) ).
thf(2024,plain,
! [A: pname > $o,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ! [D: pname,E: pname] : ( member_pname @ ( B @ D @ E ) @ ( insert_pname @ D @ ( insert_pname @ E @ bot_bot_pname_o ) ) )
=> ( member_pname @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(291,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( minus_2056855718tate_o @ B @ C ) )
=> ( member451959335_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_DiffD1) ).
thf(1773,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( minus_2056855718tate_o @ B @ C ) )
=> ( member451959335_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(305,axiom,
! [A: com,B: com > $o,C: option_com] :
( ! [D: com] :
( ( member_com @ D @ ( set_com @ C ) )
=> ( B @ D ) )
=> ( ( C
= ( some_com @ A ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_ospec) ).
thf(1815,plain,
! [A: com,B: com > $o,C: option_com] :
( ! [D: com] :
( ( member_com @ D @ ( set_com @ C ) )
=> ( B @ D ) )
=> ( ( C
= ( some_com @ A ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(470,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ! [D: pname > $o,E: pname > $o,F: pname > $o] :
( ( semila1780557381name_o @ D @ ( semila1673364395name_o @ E @ F ) )
= ( semila1673364395name_o @ ( semila1780557381name_o @ D @ E ) @ ( semila1780557381name_o @ D @ F ) ) )
=> ( ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_distrib__imp2) ).
thf(2388,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ! [D: pname > $o,E: pname > $o,F: pname > $o] :
( ( semila1780557381name_o @ D @ ( semila1673364395name_o @ E @ F ) )
= ( semila1673364395name_o @ ( semila1780557381name_o @ D @ E ) @ ( semila1780557381name_o @ D @ F ) ) )
=> ( ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(313,axiom,
! [A: state > $o,B: com,C: state,D: state] :
( ( evalc @ ( while @ A @ B ) @ C @ D )
=> ( ( ( D = C )
=> ( A @ C ) )
=> ~ ( ( A @ C )
=> ! [E: state] :
( ( evalc @ B @ C @ E )
=> ~ ( evalc @ ( while @ A @ B ) @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_evalc__WHILE__case) ).
thf(1847,plain,
! [A: state > $o,B: com,C: state,D: state] :
( ( evalc @ ( while @ A @ B ) @ C @ D )
=> ( ( ( D = C )
=> ( A @ C ) )
=> ~ ( ( A @ C )
=> ! [E: state] :
( ( evalc @ B @ C @ E )
=> ~ ( evalc @ ( while @ A @ B ) @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(74,axiom,
! [A: pname > $o,B: pname > hoare_1708887482_state,C: pname > hoare_1708887482_state,D: pname > $o] :
( ( image_1116629049_state
@ ^ [E: pname] : ( if_Hoa1374726218_state @ ( A @ E ) @ ( B @ E ) @ ( C @ E ) )
@ D )
= ( semila1122118281tate_o @ ( image_1116629049_state @ B @ ( semila1673364395name_o @ D @ ( collect_pname @ A ) ) )
@ ( image_1116629049_state @ C
@ ( semila1673364395name_o @ D
@ ( collect_pname
@ ^ [E: pname] :
~ ( A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_if__image__distrib) ).
thf(1087,plain,
! [A: pname > $o,B: pname > hoare_1708887482_state,C: pname > hoare_1708887482_state,D: pname > $o] :
( ( image_1116629049_state
@ ^ [E: pname] : ( if_Hoa1374726218_state @ ( A @ E ) @ ( B @ E ) @ ( C @ E ) )
@ D )
= ( semila1122118281tate_o @ ( image_1116629049_state @ B @ ( semila1673364395name_o @ D @ ( collect_pname @ A ) ) )
@ ( image_1116629049_state @ C
@ ( semila1673364395name_o @ D
@ ( collect_pname
@ ^ [E: pname] :
~ ( A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(212,axiom,
! [A: com,B: com] :
( ( wt @ B )
=> ( ( wt @ A )
=> ( wt @ ( semi @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_WT_OSemi) ).
thf(1514,plain,
! [A: com,B: com] :
( ( wt @ B )
=> ( ( wt @ A )
=> ( wt @ ( semi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(12,axiom,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_pname_pname @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_image__subsetI) ).
thf(867,plain,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_pname_pname @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(868,plain,
! [C: pname > $o,B: pname > $o,A: pname > pname] :
( ( ( member_pname @ ( sk3 @ C @ B @ A ) @ C )
| ( ord_less_eq_pname_o @ ( image_pname_pname @ A @ C ) @ B ) )
& ( ~ ( member_pname @ ( A @ ( sk3 @ C @ B @ A ) ) @ B )
| ( ord_less_eq_pname_o @ ( image_pname_pname @ A @ C ) @ B ) ) ),
inference(cnf,[status(esa)],[867]) ).
thf(870,plain,
! [C: pname > $o,B: pname > $o,A: pname > pname] :
( ~ ( member_pname @ ( A @ ( sk3 @ C @ B @ A ) ) @ B )
| ( ord_less_eq_pname_o @ ( image_pname_pname @ A @ C ) @ B ) ),
inference(cnfConj,[status(thm)],[868]) ).
thf(325,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( semila1122118281tate_o
@ ^ [D: hoare_1708887482_state] : ( member451959335_state @ D @ A )
@ ^ [D: hoare_1708887482_state] : ( member451959335_state @ D @ B )
@ C )
= ( member451959335_state @ C @ ( semila1122118281tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_sup__Un__eq) ).
thf(1890,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( semila1122118281tate_o
@ ^ [D: hoare_1708887482_state] : ( member451959335_state @ D @ A )
@ ^ [D: hoare_1708887482_state] : ( member451959335_state @ D @ B )
@ C )
= ( member451959335_state @ C @ ( semila1122118281tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(512,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( finite1625599783_state @ ( collec1568722789_state @ B ) )
| ( finite1625599783_state @ ( collec1568722789_state @ A ) ) )
=> ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_finite__Collect__conjI) ).
thf(2520,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( finite1625599783_state @ ( collec1568722789_state @ B ) )
| ( finite1625599783_state @ ( collec1568722789_state @ A ) ) )
=> ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(4141,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o )
!= ( ^ [A: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[4134,3234]) ).
thf(824,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( finite309095018_state @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_folding__one__idem_Oeq__fold__idem_H) ).
thf(3602,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( finite309095018_state @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(807,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( insert528405184_state @ B @ C ) )
=> ( ( A != B )
=> ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_insertE) ).
thf(3557,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( insert528405184_state @ B @ C ) )
=> ( ( A != B )
=> ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(223,axiom,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_inf__bot__right) ).
thf(1546,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1547,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
inference(cnf,[status(esa)],[1546]) ).
thf(1548,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
inference(lifteq,[status(thm)],[1547]) ).
thf(4400,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ A
@ ^ [B: pname] : bot_bot_o )
= ( ^ [B: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1548,2398]) ).
thf(416,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1780557381name_o @ A @ B )
= bot_bot_pname_o )
= ( ( A = bot_bot_pname_o )
& ( B = bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_Un__empty) ).
thf(2222,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1780557381name_o @ A @ B )
= bot_bot_pname_o )
= ( ( A = bot_bot_pname_o )
& ( B = bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(732,axiom,
finite_finite_pname @ ( dom_pname_com @ body ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_finite__dom__body) ).
thf(3322,plain,
finite_finite_pname @ ( dom_pname_com @ body ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(258,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( ~ ( B @ C )
=> ( A @ C ) )
=> ( semila1122118281tate_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_sup1CI) ).
thf(1664,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( ~ ( B @ C )
=> ( A @ C ) )
=> ( semila1122118281tate_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(189,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( semila1780557381name_o @ B @ A )
= ( finite603803317name_o @ insert_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_union__fold__insert) ).
thf(1450,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( semila1780557381name_o @ B @ A )
= ( finite603803317name_o @ insert_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(490,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ C ) )
=> ~ ( ( member451959335_state @ A @ B )
=> ~ ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_IntE) ).
thf(2451,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ C ) )
=> ~ ( ( member451959335_state @ A @ B )
=> ~ ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(67,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( minus_minus_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_insert__Diff1) ).
thf(1051,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( minus_minus_pname_o @ ( insert_pname @ B @ A ) @ C )
= ( minus_minus_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(338,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ! [C: hoare_1708887482_state] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le777019615tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_predicate1I) ).
thf(1946,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ! [C: hoare_1708887482_state] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le777019615tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(194,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_Un__least) ).
thf(1465,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(3821,plain,
( ( top_top_pname_o @ sk140 )
!= ( bot_bot_pname_o @ sk140 ) ),
inference(func_ext,[status(esa)],[3820]) ).
thf(3823,plain,
( ~ ( top_top_pname_o @ sk140 )
| ~ ( bot_bot_pname_o @ sk140 ) ),
inference(bool_ext,[status(thm)],[3821]) ).
thf(3887,plain,
( ~ ( top_top_pname_o @ sk140 )
| ~ bot_bot_o ),
inference(rewrite,[status(thm)],[3823,2398]) ).
thf(356,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
=> ( ord_le777019615tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_equalityD2) ).
thf(2027,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
=> ( ord_le777019615tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(165,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ~ ( member451959335_state @ B @ C )
=> ( member451959335_state @ B @ A ) )
=> ( member451959335_state @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_UnCI) ).
thf(1373,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ~ ( member451959335_state @ B @ C )
=> ( member451959335_state @ B @ A ) )
=> ( member451959335_state @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(468,axiom,
( bot_bot_com_o
= ( collect_com
@ ^ [A: com] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_empty__def) ).
thf(2383,plain,
( bot_bot_com_o
= ( collect_com
@ ^ [A: com] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(2384,plain,
( ( collect_com
@ ^ [A: com] : $false )
= bot_bot_com_o ),
inference(lifteq,[status(thm)],[2383]) ).
thf(3724,plain,
( ( collect_com
@ ^ [A: com] : $false )
= ( ^ [A: com] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[2384,1863]) ).
thf(729,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ! [C: hoare_1708887482_state] : ( A @ ( insert528405184_state @ C @ bot_bo19817387tate_o ) )
=> ( ! [C: hoare_1708887482_state,D: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ D )
=> ( ( D != bot_bo19817387tate_o )
=> ( ~ ( member451959335_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert528405184_state @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_finite__ne__induct) ).
thf(3295,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ! [C: hoare_1708887482_state] : ( A @ ( insert528405184_state @ C @ bot_bo19817387tate_o ) )
=> ( ! [C: hoare_1708887482_state,D: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ D )
=> ( ( D != bot_bo19817387tate_o )
=> ( ~ ( member451959335_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert528405184_state @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(591,axiom,
! [A: option_com] :
( ( A != none_com )
=> ~ ! [B: com] :
( A
!= ( some_com @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1184_option_Oexhaust) ).
thf(2782,plain,
! [A: option_com] :
( ( A != none_com )
=> ~ ! [B: com] :
( A
!= ( some_com @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(81,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_subsetD) ).
thf(1109,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(496,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_inf__sup__aci_I5_J) ).
thf(2469,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(264,axiom,
! [A: hoare_1708887482_state,B: pname > hoare_1708887482_state,C: pname > $o] :
( ( member451959335_state @ A @ ( image_1116629049_state @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_imageE) ).
thf(1682,plain,
! [A: hoare_1708887482_state,B: pname > hoare_1708887482_state,C: pname > $o] :
( ( member451959335_state @ A @ ( image_1116629049_state @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(90,axiom,
! [A: ( pname > $o ) > hoare_1708887482_state,B: ( pname > $o ) > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le777019615tate_o @ C @ ( image_1922967206_state @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_1922967206_state @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_finite__subset__image) ).
thf(1136,plain,
! [A: ( pname > $o ) > hoare_1708887482_state,B: ( pname > $o ) > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le777019615tate_o @ C @ ( image_1922967206_state @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_1922967206_state @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(769,axiom,
! [A: state > state > $o,B: state > state > $o,C: com] :
( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C ) @ bot_bo19817387tate_o ) )
=> ( ( hoare_496444244_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ A @ C @ B ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ A @ C @ B ) @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_MGF__complete) ).
thf(3438,plain,
! [A: state > state > $o,B: state > state > $o,C: com] :
( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C ) @ bot_bo19817387tate_o ) )
=> ( ( hoare_496444244_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ A @ C @ B ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ A @ C @ B ) @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(3598,plain,
( ( collec1568722789_state
@ ^ [A: hoare_1708887482_state] : $false )
= bot_bo19817387tate_o ),
inference(lifteq,[status(thm)],[3597]) ).
thf(4147,plain,
( ( collec1568722789_state
@ ^ [A: hoare_1708887482_state] : $false )
= ( ^ [A: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[3598,3234]) ).
thf(315,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1780557381name_o
@ ^ [D: pname] : ( member_pname @ D @ A )
@ ^ [D: pname] : ( member_pname @ D @ B )
@ C )
= ( member_pname @ C @ ( semila1780557381name_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_sup__Un__eq) ).
thf(1864,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1780557381name_o
@ ^ [D: pname] : ( member_pname @ D @ A )
@ ^ [D: pname] : ( member_pname @ D @ B )
@ C )
= ( member_pname @ C @ ( semila1780557381name_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(168,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_sup__least) ).
thf(1383,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(427,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( ord_le777019615tate_o @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_inf__greatest) ).
thf(2254,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( ord_le777019615tate_o @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(518,axiom,
! [A: state,B: state] :
( ~ ( fequal_state @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Ostate_T) ).
thf(2540,plain,
! [A: state,B: state] :
( ~ ( fequal_state @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(358,axiom,
! [A: com > hoare_1708887482_state,B: com,C: com > $o] :
( ( member_com @ B @ C )
=> ( member451959335_state @ ( A @ B ) @ ( image_934102463_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_imageI) ).
thf(2034,plain,
! [A: com > hoare_1708887482_state,B: com,C: com > $o] :
( ( member_com @ B @ C )
=> ( member451959335_state @ ( A @ B ) @ ( image_934102463_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(234,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A @ B ) @ C )
= ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_Diff__subset__conv) ).
thf(1581,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A @ B ) @ C )
= ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(454,axiom,
! [A: pname,B: com > pname,C: com,D: com > $o] :
( ( member_com @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_pname @ A @ ( image_com_pname @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_rev__image__eqI) ).
thf(2335,plain,
! [A: pname,B: com > pname,C: com,D: com > $o] :
( ( member_com @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_pname @ A @ ( image_com_pname @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(353,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_xt1_I4_J) ).
thf(2017,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(23,axiom,
! [A: pname > $o] :
( ( minus_minus_pname_o @ A @ A )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_941_Diff__cancel) ).
thf(905,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o @ A @ A )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(462,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( semila1122118281tate_o @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_sup1E) ).
thf(2367,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( semila1122118281tate_o @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(166,axiom,
! [A: pname,B: pname > option_pname] :
( ( member_pname @ A @ ( dom_pname_pname @ B ) )
=> ? [C: pname] :
( ( B @ A )
= ( some_pname @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_domD) ).
thf(1377,plain,
! [A: pname,B: pname > option_pname] :
( ( member_pname @ A @ ( dom_pname_pname @ B ) )
=> ? [C: pname] :
( ( B @ A )
= ( some_pname @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(437,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( semila1122118281tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_sup_Ocommute) ).
thf(2281,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( semila1122118281tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(115,axiom,
! [A: com > hoare_1708887482_state,B: com,C: com > $o] :
( ( member_com @ B @ C )
=> ( ( insert528405184_state @ ( A @ B ) @ ( image_934102463_state @ A @ C ) )
= ( image_934102463_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_insert__image) ).
thf(1215,plain,
! [A: com > hoare_1708887482_state,B: com,C: com > $o] :
( ( member_com @ B @ C )
=> ( ( insert528405184_state @ ( A @ B ) @ ( image_934102463_state @ A @ C ) )
= ( image_934102463_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(69,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( if_Hoa1374726218_state @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate) ).
thf(1072,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( if_Hoa1374726218_state @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(390,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ A @ ( minus_2056855718tate_o @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_Diff__partition) ).
thf(2137,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ A @ ( minus_2056855718tate_o @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(4038,plain,
( ~ ( top_top_com_o @ sk144 )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[4037]) ).
thf(471,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_ord__eq__le__trans) ).
thf(2392,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(753,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( member451959335_state @ B @ ( insert528405184_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_insertI2) ).
thf(3389,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( member451959335_state @ B @ ( insert528405184_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(44,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le1728773982te_o_o @ A @ ( image_1551509096tate_o @ B @ C ) )
=> ( finite1329924456tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_finite__surj) ).
thf(981,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le1728773982te_o_o @ A @ ( image_1551509096tate_o @ B @ C ) )
=> ( finite1329924456tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(327,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_set__mp) ).
thf(1896,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(15,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ B )
=> ( ( ord_le1728773982te_o_o @ A @ B )
=> ( finite1329924456tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_rev__finite__subset) ).
thf(877,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ B )
=> ( ( ord_le1728773982te_o_o @ A @ B )
=> ( finite1329924456tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(763,axiom,
! [A: pname > option_com,B: pname > $o] :
( ( dom_pname_com @ ( restri1382200118me_com @ A @ B ) )
= ( semila1673364395name_o @ ( dom_pname_com @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1190_dom__restrict) ).
thf(3421,plain,
! [A: pname > option_com,B: pname > $o] :
( ( dom_pname_com @ ( restri1382200118me_com @ A @ B ) )
= ( semila1673364395name_o @ ( dom_pname_com @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(11,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ ( minus_minus_pname_o @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_Diff__partition) ).
thf(864,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ ( minus_minus_pname_o @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(865,plain,
! [B: pname > $o,A: pname > $o] :
( ~ ( ord_less_eq_pname_o @ A @ B )
| ( ( semila1780557381name_o @ A @ ( minus_minus_pname_o @ B @ A ) )
= B ) ),
inference(cnf,[status(esa)],[864]) ).
thf(866,plain,
! [B: pname > $o,A: pname > $o] :
( ( ( semila1780557381name_o @ A @ ( minus_minus_pname_o @ B @ A ) )
= B )
| ~ ( ord_less_eq_pname_o @ A @ B ) ),
inference(lifteq,[status(thm)],[865]) ).
thf(323,axiom,
( ( set_com @ none_com )
= bot_bot_com_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_Option_Oset_Osimps_I1_J) ).
thf(1886,plain,
( ( set_com @ none_com )
= bot_bot_com_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(351,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ A )
| ( member451959335_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_Un__def) ).
thf(2002,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ A )
| ( member451959335_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(678,axiom,
( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(3105,plain,
( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(4148,plain,
~ ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[835,3234]) ).
thf(4519,plain,
( ~ $true
| ( ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o ) )
!= ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ) ) ),
inference(paramod_ordered,[status(thm)],[3105,4148]) ).
thf(4520,plain,
( ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o ) )
!= ( hoare_90032982_state
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ) ),
inference(simp,[status(thm)],[4519]) ).
thf(4524,plain,
( ( ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
!= ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) ) )
| ( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o )
!= fa ) ),
inference(simp,[status(thm)],[4520]) ).
thf(4527,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o )
!= fa ),
inference(simp,[status(thm)],[4524]) ).
thf(4529,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk152 )
!= ( fa @ sk152 ) ),
inference(func_ext,[status(esa)],[4527]) ).
thf(4532,plain,
( bot_bot_o
| ~ ( fa @ sk152 )
| ( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk152 )
!= ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk146 ) ) ),
inference(paramod_ordered,[status(thm)],[4290,4529]) ).
thf(4534,plain,
( bot_bot_o
| ~ ( fa @ sk152 )
| ( ( hoare_Mirabelle_MGT @ y )
!= ( hoare_Mirabelle_MGT @ y ) )
| ( ( ^ [A: hoare_1708887482_state] : bot_bot_o )
!= ( ^ [A: hoare_1708887482_state] : bot_bot_o ) )
| ( sk152 != sk146 ) ),
inference(simp,[status(thm)],[4532]) ).
thf(4536,plain,
( bot_bot_o
| ~ ( fa @ sk152 )
| ( sk152 != sk146 ) ),
inference(simp,[status(thm)],[4534]) ).
thf(380,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( insert_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_Int__insert__right) ).
thf(2103,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( insert_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(580,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_sup_Oidem) ).
thf(2750,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(337,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_sup__absorb1) ).
thf(1943,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(112,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_Int__greatest) ).
thf(1201,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(819,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ C ) )
= ( ( ( member451959335_state @ B @ A )
=> ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) @ C ) )
& ( ~ ( member451959335_state @ B @ A )
=> ( ord_le777019615tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_subset__insert__iff) ).
thf(3588,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ C ) )
= ( ( ( member451959335_state @ B @ A )
=> ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) @ C ) )
& ( ~ ( member451959335_state @ B @ A )
=> ( ord_le777019615tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(7,axiom,
! [A: pname > $o] :
( ( minus_minus_pname_o @ A @ bot_bot_pname_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_Diff__empty) ).
thf(849,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o @ A @ bot_bot_pname_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(570,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( B @ C )
=> ( semila1122118281tate_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_sup1I2) ).
thf(2718,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( B @ C )
=> ( semila1122118281tate_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(410,axiom,
! [A: pname] :
~ ( is_none_pname @ ( some_pname @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_is__none__code_I2_J) ).
thf(2203,plain,
! [A: pname] :
~ ( is_none_pname @ ( some_pname @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(2204,plain,
~ ? [A: pname] : ( is_none_pname @ ( some_pname @ A ) ),
inference(miniscope,[status(thm)],[2203]) ).
thf(2205,plain,
! [A: pname] :
~ ( is_none_pname @ ( some_pname @ A ) ),
inference(cnf,[status(esa)],[2204]) ).
thf(269,axiom,
! [A: hoare_1708887482_state > $o,B: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,C: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ C )
=> ( ( ord_le777019615tate_o @ A @ ( image_27005066_state @ B @ C ) )
=> ( finite1625599783_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_finite__surj) ).
thf(1696,plain,
! [A: hoare_1708887482_state > $o,B: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,C: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ C )
=> ( ( ord_le777019615tate_o @ A @ ( image_27005066_state @ B @ C ) )
=> ( finite1625599783_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(650,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_le__supI) ).
thf(2982,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(585,axiom,
! [A: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ( A @ C )
= B )
=> ( ! [E: hoare_1708887482_state > $o,F: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ F @ E )
=> ( ord_le777019615tate_o @ ( A @ F ) @ ( A @ E ) ) )
=> ( ord_le777019615tate_o @ B @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_xt1_I16_J) ).
thf(2762,plain,
! [A: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ( A @ C )
= B )
=> ( ! [E: hoare_1708887482_state > $o,F: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ F @ E )
=> ( ord_le777019615tate_o @ ( A @ F ) @ ( A @ E ) ) )
=> ( ord_le777019615tate_o @ B @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(749,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( minus_2056855718tate_o @ A @ B )
= ( finite96880613tate_o
@ ^ [C: hoare_1708887482_state,D: hoare_1708887482_state > $o] : ( minus_2056855718tate_o @ D @ ( insert528405184_state @ C @ bot_bo19817387tate_o ) )
@ A
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_minus__fold__remove) ).
thf(3378,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( minus_2056855718tate_o @ A @ B )
= ( finite96880613tate_o
@ ^ [C: hoare_1708887482_state,D: hoare_1708887482_state > $o] : ( minus_2056855718tate_o @ D @ ( insert528405184_state @ C @ bot_bo19817387tate_o ) )
@ A
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(254,axiom,
! [A: pname > hoare_1708887482_state > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite1329924456tate_o @ ( image_425134806tate_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_pigeonhole__infinite) ).
thf(1651,plain,
! [A: pname > hoare_1708887482_state > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite1329924456tate_o @ ( image_425134806tate_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(711,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) )
= ( insert528405184_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_insert__Diff__single) ).
thf(3229,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) )
= ( insert528405184_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(114,axiom,
! [A: pname,B: hoare_1708887482_state > $o] :
( ( ( B = bot_bo19817387tate_o )
=> ( ( image_1509414295_pname
@ ^ [C: hoare_1708887482_state] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bo19817387tate_o )
=> ( ( image_1509414295_pname
@ ^ [C: hoare_1708887482_state] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_image__constant__conv) ).
thf(1206,plain,
! [A: pname,B: hoare_1708887482_state > $o] :
( ( ( B = bot_bo19817387tate_o )
=> ( ( image_1509414295_pname
@ ^ [C: hoare_1708887482_state] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bo19817387tate_o )
=> ( ( image_1509414295_pname
@ ^ [C: hoare_1708887482_state] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(528,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o] :
( ( bot_bot_pname_o
= ( image_1509414295_pname @ A @ B ) )
= ( B = bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_empty__is__image) ).
thf(2574,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o] :
( ( bot_bot_pname_o
= ( image_1509414295_pname @ A @ B ) )
= ( B = bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(4531,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk152 )
| ( fa @ sk152 ) ),
inference(bool_ext,[status(thm)],[4529]) ).
thf(397,axiom,
! [A: pname > option1624383643_state,B: pname,C: hoare_1708887482_state] :
( ( ( A @ B )
= ( some_H1974565227_state @ C ) )
=> ( member_pname @ B @ ( dom_pn1412407212_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_domI) ).
thf(2164,plain,
! [A: pname > option1624383643_state,B: pname,C: hoare_1708887482_state] :
( ( ( A @ B )
= ( some_H1974565227_state @ C ) )
=> ( member_pname @ B @ ( dom_pn1412407212_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(383,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_empty__iff) ).
thf(2118,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(196,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ~ ( member451959335_state @ A @ B )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( finite309095018_state @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_folding__one_Oeq__fold_H) ).
thf(1470,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ~ ( member451959335_state @ A @ B )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( finite309095018_state @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(546,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1673364395name_o @ A @ B )
= bot_bot_pname_o )
= ( ! [C: pname] :
( ( member_pname @ C @ A )
=> ! [D: pname] :
( ( member_pname @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_disjoint__iff__not__equal) ).
thf(2641,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1673364395name_o @ A @ B )
= bot_bot_pname_o )
= ( ! [C: pname] :
( ( member_pname @ C @ A )
=> ! [D: pname] :
( ( member_pname @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(33,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_Diff__subset) ).
thf(942,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(820,axiom,
! [A: hoare_1708887482_state] :
~ ( member451959335_state @ A @ bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_empty__iff) ).
thf(3591,plain,
! [A: hoare_1708887482_state] :
~ ( member451959335_state @ A @ bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(699,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ ( insert528405184_state @ A @ B ) )
= ( finite1625599783_state @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_finite__insert) ).
thf(3169,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ ( insert528405184_state @ A @ B ) )
= ( finite1625599783_state @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(717,axiom,
! [A: pname,B: hoare_1708887482_state > $o,C: pname > state > state > $o,D: pname > state > state > $o,E: pname > $o] :
( ( hoare_90032982_state
@ ( semila1122118281tate_o @ B
@ ( image_1116629049_state
@ ^ [F: pname] : ( hoare_858012674_state @ ( C @ F ) @ ( body_1 @ F ) @ ( D @ F ) )
@ E ) )
@ ( image_1116629049_state
@ ^ [F: pname] : ( hoare_858012674_state @ ( C @ F ) @ ( the_com @ ( body @ F ) ) @ ( D @ F ) )
@ E ) )
=> ( ( member_pname @ A @ E )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ ( C @ A ) @ ( body_1 @ A ) @ ( D @ A ) ) @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_Body1) ).
thf(3265,plain,
! [A: pname,B: hoare_1708887482_state > $o,C: pname > state > state > $o,D: pname > state > state > $o,E: pname > $o] :
( ( hoare_90032982_state
@ ( semila1122118281tate_o @ B
@ ( image_1116629049_state
@ ^ [F: pname] : ( hoare_858012674_state @ ( C @ F ) @ ( body_1 @ F ) @ ( D @ F ) )
@ E ) )
@ ( image_1116629049_state
@ ^ [F: pname] : ( hoare_858012674_state @ ( C @ F ) @ ( the_com @ ( body @ F ) ) @ ( D @ F ) )
@ E ) )
=> ( ( member_pname @ A @ E )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ ( C @ A ) @ ( body_1 @ A ) @ ( D @ A ) ) @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(442,axiom,
! [A: pname > $o,B: hoare_1708887482_state,C: pname > hoare_1708887482_state,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member451959335_state @ B @ ( image_1116629049_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_image__eqI) ).
thf(2296,plain,
! [A: pname > $o,B: hoare_1708887482_state,C: pname > hoare_1708887482_state,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member451959335_state @ B @ ( image_1116629049_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(670,axiom,
! [A: hoare_1708887482_state > $o] :
( ( the_el864710747_state @ A )
= ( the_Ho851197897_state
@ ^ [B: hoare_1708887482_state] :
( A
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_the__elem__def) ).
thf(3054,plain,
! [A: hoare_1708887482_state > $o] :
( ( the_el864710747_state @ A )
= ( the_Ho851197897_state
@ ^ [B: hoare_1708887482_state] :
( A
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(373,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ C @ A ) @ ( semila129691299tate_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_inf__mono) ).
thf(2083,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ C @ A ) @ ( semila129691299tate_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(278,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o] :
( ~ ( finite1625599783_state @ B )
=> ( ( finite_finite_pname @ ( image_1509414295_pname @ A @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
& ~ ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_pigeonhole__infinite) ).
thf(1736,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o] :
( ~ ( finite1625599783_state @ B )
=> ( ( finite_finite_pname @ ( image_1509414295_pname @ A @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
& ~ ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(505,axiom,
! [A: hoare_1708887482_state,B: com > hoare_1708887482_state,C: com > $o] :
( ( member451959335_state @ A @ ( image_934102463_state @ B @ C ) )
=> ~ ! [D: com] :
( ( A
= ( B @ D ) )
=> ~ ( member_com @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_imageE) ).
thf(2496,plain,
! [A: hoare_1708887482_state,B: com > hoare_1708887482_state,C: com > $o] :
( ( member451959335_state @ A @ ( image_934102463_state @ B @ C ) )
=> ~ ! [D: com] :
( ( A
= ( B @ D ) )
=> ~ ( member_com @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(289,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila129691299tate_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_inf__absorb1) ).
thf(1768,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila129691299tate_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(625,axiom,
! [A: com > option_com,B: com,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( member_com @ B @ ( dom_com_com @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_domI) ).
thf(2905,plain,
! [A: com > option_com,B: com,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( member_com @ B @ ( dom_com_com @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(805,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ bot_bo19817387tate_o @ A )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_Int__empty__left) ).
thf(3550,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ bot_bo19817387tate_o @ A )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(587,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_folding__one__idem_Oin__idem) ).
thf(2773,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(66,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ! [C: pname > $o] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le1205211808me_o_o @ ( collect_pname_o @ B ) @ ( collect_pname_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_Collect__mono) ).
thf(1047,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ! [C: pname > $o] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le1205211808me_o_o @ ( collect_pname_o @ B ) @ ( collect_pname_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(666,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( image_1116629049_state @ A @ B )
= ( finite2139561282_pname @ semila1122118281tate_o
@ ^ [C: pname] : ( insert528405184_state @ ( A @ C ) @ bot_bo19817387tate_o )
@ bot_bo19817387tate_o
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_image__eq__fold__image) ).
thf(3037,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( image_1116629049_state @ A @ B )
= ( finite2139561282_pname @ semila1122118281tate_o
@ ^ [C: pname] : ( insert528405184_state @ ( A @ C ) @ bot_bo19817387tate_o )
@ bot_bo19817387tate_o
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(98,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ bot_bot_pname_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_sup__bot__left) ).
thf(1163,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ bot_bot_pname_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(136,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( finite1625599783_state @ ( minus_2056855718tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_finite__Diff) ).
thf(1274,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( finite1625599783_state @ ( minus_2056855718tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(533,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C = A )
| ( member451959335_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_insert__compr) ).
thf(2589,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C = A )
| ( member451959335_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(431,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( ~ ( B @ C )
=> ( A @ C ) )
=> ( semila1780557381name_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_sup1CI) ).
thf(2264,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( ~ ( B @ C )
=> ( A @ C ) )
=> ( semila1780557381name_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(273,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_inf__sup__aci_I6_J) ).
thf(1723,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(57,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
= ( ( member_pname @ A @ B )
& ~ ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_Diff__iff) ).
thf(1021,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
= ( ( member_pname @ A @ B )
& ~ ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(214,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( semila1122118281tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_Un__commute) ).
thf(1519,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( semila1122118281tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(207,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ( member_pname @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_IntD2) ).
thf(1502,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ( member_pname @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(645,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
=> ( ( A != B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_insertE) ).
thf(2969,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ A @ ( insert_pname @ B @ C ) )
=> ( ( A != B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(635,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( ord_le777019615tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_order__trans) ).
thf(2937,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( ord_le777019615tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(538,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_inf__le2) ).
thf(2606,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(4158,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk148 )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[4141]) ).
thf(4160,plain,
( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk148 )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[4158]) ).
thf(322,axiom,
! [A: pname > $o,B: pname > $o,C: pname > hoare_1708887482_state,D: pname > $o] :
( ( inj_on1553129421_state @ C @ D )
=> ( ( ord_less_eq_pname_o @ B @ D )
=> ( ( ord_less_eq_pname_o @ A @ D )
=> ( ( image_1116629049_state @ C @ ( minus_minus_pname_o @ B @ A ) )
= ( minus_2056855718tate_o @ ( image_1116629049_state @ C @ B ) @ ( image_1116629049_state @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_inj__on__image__set__diff) ).
thf(1883,plain,
! [A: pname > $o,B: pname > $o,C: pname > hoare_1708887482_state,D: pname > $o] :
( ( inj_on1553129421_state @ C @ D )
=> ( ( ord_less_eq_pname_o @ B @ D )
=> ( ( ord_less_eq_pname_o @ A @ D )
=> ( ( image_1116629049_state @ C @ ( minus_minus_pname_o @ B @ A ) )
= ( minus_2056855718tate_o @ ( image_1116629049_state @ C @ B ) @ ( image_1116629049_state @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(38,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: pname > hoare_1708887482_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le1728773982te_o_o @ A @ ( image_425134806tate_o @ B @ C ) )
=> ( finite1329924456tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_finite__surj) ).
thf(957,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: pname > hoare_1708887482_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le1728773982te_o_o @ A @ ( image_425134806tate_o @ B @ C ) )
=> ( finite1329924456tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(118,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ! [D: hoare_1708887482_state > $o,E: hoare_1708887482_state > $o,F: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ D @ ( semila1122118281tate_o @ E @ F ) )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ D @ E ) @ ( semila129691299tate_o @ D @ F ) ) )
=> ( ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1081_distrib__imp1) ).
thf(1223,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ! [D: hoare_1708887482_state > $o,E: hoare_1708887482_state > $o,F: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ D @ ( semila1122118281tate_o @ E @ F ) )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ D @ E ) @ ( semila129691299tate_o @ D @ F ) ) )
=> ( ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(394,axiom,
! [A: hoare_1708887482_state > $o,B: pname > $o] :
( ( B != bot_bot_pname_o )
=> ( ( ? [C: pname > hoare_1708887482_state] :
( ( inj_on1553129421_state @ C @ B )
& ( ord_le777019615tate_o @ ( image_1116629049_state @ C @ B ) @ A ) ) )
= ( ? [C: hoare_1708887482_state > pname] :
( ( image_1509414295_pname @ C @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1183_inj__on__iff__surj) ).
thf(2150,plain,
! [A: hoare_1708887482_state > $o,B: pname > $o] :
( ( B != bot_bot_pname_o )
=> ( ( ? [C: pname > hoare_1708887482_state] :
( ( inj_on1553129421_state @ C @ B )
& ( ord_le777019615tate_o @ ( image_1116629049_state @ C @ B ) @ A ) ) )
= ( ? [C: hoare_1708887482_state > pname] :
( ( image_1509414295_pname @ C @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(164,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_Un__Int__distrib) ).
thf(1370,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(78,axiom,
( hoare_1160767572gleton
= ( ? [A: state,B: state] : ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_state__not__singleton__def) ).
thf(1101,plain,
( hoare_1160767572gleton
= ( ? [A: state,B: state] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1102,plain,
( hoare_1160767572gleton
= ( ? [A: state,B: state] : ( A != B ) ) ),
inference(lifteq,[status(thm)],[1101]) ).
thf(160,axiom,
hoare_1160767572gleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1357,plain,
hoare_1160767572gleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(3680,plain,
? [A: state,B: state] : ( A != B ),
inference(rewrite,[status(thm)],[1102,1357]) ).
thf(3681,plain,
sk137 != sk138,
inference(cnf,[status(esa)],[3680]) ).
thf(3682,plain,
sk138 != sk137,
inference(lifteq,[status(thm)],[3681]) ).
thf(719,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( semila1122118281tate_o @ B @ A )
= ( finite96880613tate_o @ insert528405184_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_union__fold__insert) ).
thf(3271,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( semila1122118281tate_o @ B @ A )
= ( finite96880613tate_o @ insert528405184_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(3980,plain,
( ( top_top_pname_o @ sk141 )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[3892]) ).
thf(553,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_Un__least) ).
thf(2670,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(485,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_sup__inf__distrib1) ).
thf(2433,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(16,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ B ) @ ( semila1673364395name_o @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_Un__Diff__Int) ).
thf(879,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ B ) @ ( semila1673364395name_o @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(690,axiom,
! [A: pname,B: pname > option_com] :
( ( member_pname @ A @ ( dom_pname_com @ B ) )
= ( ( B @ A )
!= none_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_domIff) ).
thf(3137,plain,
! [A: pname,B: pname > option_com] :
( ( member_pname @ A @ ( dom_pname_com @ B ) )
= ( ( B @ A )
!= none_com ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(324,axiom,
! [A: state > $o,B: com] :
( ( wt @ B )
=> ( wt @ ( while @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_707_While) ).
thf(1888,plain,
! [A: state > $o,B: com] :
( ( wt @ B )
=> ( wt @ ( while @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(265,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_sup__ge2) ).
thf(1687,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(245,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
=> ~ ( ( ord_le777019615tate_o @ A @ C )
=> ~ ( ord_le777019615tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_le__supE) ).
thf(1624,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
=> ~ ( ( ord_le777019615tate_o @ A @ C )
=> ~ ( ord_le777019615tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(402,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
=> ~ ( ( ord_le777019615tate_o @ A @ B )
=> ~ ( ord_le777019615tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_le__infE) ).
thf(2179,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
=> ~ ( ( ord_le777019615tate_o @ A @ B )
=> ~ ( ord_le777019615tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(692,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] :
( ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( ( A = bot_bo19817387tate_o )
| ( A
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_subset__singletonD) ).
thf(3144,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] :
( ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( ( A = bot_bo19817387tate_o )
| ( A
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(140,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( A != bot_bot_pname_o )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_folding__one__idem_Osubset__idem) ).
thf(1291,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( A != bot_bot_pname_o )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(279,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_subsetD) ).
thf(1740,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(772,axiom,
! [A: pname > option_com] :
( ( dom_pname_com @ A )
= ( collect_pname
@ ^ [B: pname] :
( ( A @ B )
!= none_com ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1118_dom__def) ).
thf(3445,plain,
! [A: pname > option_com] :
( ( dom_pname_com @ A )
= ( collect_pname
@ ^ [B: pname] :
( ( A @ B )
!= none_com ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(80,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
= ( ( member_pname @ A @ B )
& ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_Int__iff) ).
thf(1106,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
= ( ( member_pname @ A @ B )
& ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(724,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( hoare_90032982_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_thin) ).
thf(3282,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( hoare_90032982_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(641,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_insert__ident) ).
thf(2958,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( ( ( insert_pname @ B @ C )
= ( insert_pname @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(181,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( minus_2056855718tate_o @ B @ C ) )
=> ~ ( ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_DiffE) ).
thf(1423,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( minus_2056855718tate_o @ B @ C ) )
=> ~ ( ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(335,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B @ A )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_predicate1D) ).
thf(1938,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B @ A )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(6,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( member_pname @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_DiffD2) ).
thf(847,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( member_pname @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(583,axiom,
! [A: hoare_1708887482_state > $o,B: ( pname > $o ) > hoare_1708887482_state,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le777019615tate_o @ A @ ( image_1922967206_state @ B @ C ) )
=> ( finite1625599783_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_finite__surj) ).
thf(2758,plain,
! [A: hoare_1708887482_state > $o,B: ( pname > $o ) > hoare_1708887482_state,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le777019615tate_o @ A @ ( image_1922967206_state @ B @ C ) )
=> ( finite1625599783_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(8,axiom,
! [A: pname > $o] :
( ( minus_minus_pname_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_empty__Diff) ).
thf(852,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(453,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_sup__assoc) ).
thf(2332,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(799,axiom,
! [A: pname] :
( skip
!= ( body_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_com_Osimps_I18_J) ).
thf(3532,plain,
! [A: pname] :
( skip
!= ( body_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(3533,plain,
~ ? [A: pname] :
( skip
= ( body_1 @ A ) ),
inference(miniscope,[status(thm)],[3532]) ).
thf(3534,plain,
! [A: pname] :
( skip
!= ( body_1 @ A ) ),
inference(cnf,[status(esa)],[3533]) ).
thf(3535,plain,
! [A: pname] :
( ( body_1 @ A )
!= skip ),
inference(lifteq,[status(thm)],[3534]) ).
thf(309,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( B = C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( ord_le777019615tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_xt1_I3_J) ).
thf(1836,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( B = C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( ord_le777019615tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(59,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_folding__one_Oinsert__remove) ).
thf(1027,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(451,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) )
= ( insert_pname @ A @ ( semila1673364395name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_insert__inter__insert) ).
thf(2327,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) )
= ( insert_pname @ A @ ( semila1673364395name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(413,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_le__infI) ).
thf(2213,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(110,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_rev__finite__subset) ).
thf(1195,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(448,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( B @ C )
=> ( semila1780557381name_o @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_sup1I1) ).
thf(2313,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( B @ C )
=> ( semila1780557381name_o @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(88,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_equalityD2) ).
thf(1128,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(171,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_insert__Diff) ).
thf(1392,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(418,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( ord_le777019615tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_subset__insert) ).
thf(2228,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( ord_le777019615tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(174,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ C ) ) @ ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_distrib__inf__le) ).
thf(1402,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ C ) ) @ ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(219,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( semila129691299tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_Int__insert__left__if0) ).
thf(1534,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( semila129691299tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(151,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( insert_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_Int__insert__right__if1) ).
thf(1328,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( insert_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(85,axiom,
! [A: hoare_1708887482_state > $o] : ( inj_on945311362_state @ some_H1974565227_state @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1104_inj__Some) ).
thf(1120,plain,
! [A: hoare_1708887482_state > $o] : ( inj_on945311362_state @ some_H1974565227_state @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1121,plain,
! [A: hoare_1708887482_state > $o] : ( inj_on945311362_state @ some_H1974565227_state @ A ),
inference(cnf,[status(esa)],[1120]) ).
thf(869,plain,
! [C: pname > $o,B: pname > $o,A: pname > pname] :
( ( member_pname @ ( sk3 @ C @ B @ A ) @ C )
| ( ord_less_eq_pname_o @ ( image_pname_pname @ A @ C ) @ B ) ),
inference(cnfConj,[status(thm)],[868]) ).
thf(285,axiom,
! [A: hoare_1708887482_state > hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ~ ( finite1625599783_state @ B )
=> ( ( finite1329924456tate_o @ ( image_1551509096tate_o @ A @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
& ~ ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_pigeonhole__infinite) ).
thf(1755,plain,
! [A: hoare_1708887482_state > hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ~ ( finite1625599783_state @ B )
=> ( ( finite1329924456tate_o @ ( image_1551509096tate_o @ A @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
& ~ ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(545,axiom,
! [A: pname] :
( ( set_pname @ ( some_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_Option_Oset_Osimps_I2_J) ).
thf(2638,plain,
! [A: pname] :
( ( set_pname @ ( some_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(47,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( minus_minus_pname_o @ B @ A ) )
= ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_Un__Diff__cancel) ).
thf(989,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( minus_minus_pname_o @ B @ A ) )
= ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(778,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ ( insert528405184_state @ A @ B ) )
= ( insert528405184_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_insert__absorb2) ).
thf(3467,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ ( insert528405184_state @ A @ B ) )
= ( insert528405184_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(443,axiom,
! [A: com,B: com] :
( ( ( some_com @ A )
= ( some_com @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_option_Oinject) ).
thf(2300,plain,
! [A: com,B: com] :
( ( ( some_com @ A )
= ( some_com @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(14,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( minus_minus_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ C ) @ ( minus_minus_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_Un__Diff) ).
thf(874,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( minus_minus_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ C ) @ ( minus_minus_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(609,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C )
=> ( ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_diff__single__insert) ).
thf(2840,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) ) @ C )
=> ( ( member_pname @ B @ A )
=> ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(382,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_inf__sup__aci_I6_J) ).
thf(2115,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(286,axiom,
! [A: hoare_1708887482_state] :
( none_H1106584047_state
!= ( some_H1974565227_state @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_option_Osimps_I2_J) ).
thf(1759,plain,
! [A: hoare_1708887482_state] :
( none_H1106584047_state
!= ( some_H1974565227_state @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(1760,plain,
~ ? [A: hoare_1708887482_state] :
( none_H1106584047_state
= ( some_H1974565227_state @ A ) ),
inference(miniscope,[status(thm)],[1759]) ).
thf(1761,plain,
! [A: hoare_1708887482_state] :
( none_H1106584047_state
!= ( some_H1974565227_state @ A ) ),
inference(cnf,[status(esa)],[1760]) ).
thf(1762,plain,
! [A: hoare_1708887482_state] :
( ( some_H1974565227_state @ A )
!= none_H1106584047_state ),
inference(lifteq,[status(thm)],[1761]) ).
thf(510,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
= ( ( ord_le777019615tate_o @ A @ B )
& ( ord_le777019615tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_set__eq__subset) ).
thf(2515,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
= ( ( ord_le777019615tate_o @ A @ B )
& ( ord_le777019615tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(379,axiom,
! [A: pname > $o,B: pname > $o] :
( ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila1780557381name_o @ ( collect_pname @ A ) @ ( collect_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_Collect__disj__eq) ).
thf(2100,plain,
! [A: pname > $o,B: pname > $o] :
( ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila1780557381name_o @ ( collect_pname @ A ) @ ( collect_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(130,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_Int__lower2) ).
thf(1259,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(685,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ C ) )
= ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A @ C ) @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_Diff__insert) ).
thf(3122,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ C ) )
= ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A @ C ) @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(529,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1673364395name_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
& ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_Int__def) ).
thf(2577,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1673364395name_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
& ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(750,axiom,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ bot_bo19817387tate_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_Diff__empty) ).
thf(3381,plain,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ bot_bo19817387tate_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(82,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ C ) )
= ( ( member451959335_state @ A @ B )
& ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_Int__iff) ).
thf(1111,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ C ) )
= ( ( member451959335_state @ A @ B )
& ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(119,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > option_pname] :
( ( member451959335_state @ A @ ( dom_Ho1805192458_pname @ B ) )
=> ? [C: pname] :
( ( B @ A )
= ( some_pname @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_domD) ).
thf(1227,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > option_pname] :
( ( member451959335_state @ A @ ( dom_Ho1805192458_pname @ B ) )
=> ? [C: pname] :
( ( B @ A )
= ( some_pname @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(206,axiom,
( hoare_1160767572gleton
=> ! [A: state] :
~ ! [B: state] : ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_single__stateE) ).
thf(1498,plain,
( hoare_1160767572gleton
=> ! [A: state] :
~ ! [B: state] : ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(236,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1780557381name_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_le__iff__sup) ).
thf(1587,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1780557381name_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(508,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( semila129691299tate_o @ A @ B )
= bot_bo19817387tate_o )
= ( ! [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ A )
=> ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_disjoint__iff__not__equal) ).
thf(2509,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( semila129691299tate_o @ A @ B )
= bot_bo19817387tate_o )
= ( ! [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ A )
=> ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(261,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ bot_bot_pname_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_sup__bot__right) ).
thf(1672,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ bot_bot_pname_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(221,axiom,
! [A: pname,B: pname] :
( ( ( insert_pname @ A @ bot_bot_pname_o )
= ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_singleton__inject) ).
thf(1540,plain,
! [A: pname,B: pname] :
( ( ( insert_pname @ A @ bot_bot_pname_o )
= ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(794,axiom,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_bot__least) ).
thf(3518,plain,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(572,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1673364395name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_inf__sup__absorb) ).
thf(2724,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1673364395name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(272,axiom,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_less_eq_pname_o @ ( collect_pname @ B ) @ ( collect_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_Collect__mono) ).
thf(1719,plain,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_less_eq_pname_o @ ( collect_pname @ B ) @ ( collect_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(616,axiom,
! [A: pname,B: com > pname,C: com > $o] :
( ( member_pname @ A @ ( image_com_pname @ B @ C ) )
=> ~ ! [D: com] :
( ( A
= ( B @ D ) )
=> ~ ( member_com @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_imageE) ).
thf(2858,plain,
! [A: pname,B: com > pname,C: com > $o] :
( ( member_pname @ A @ ( image_com_pname @ B @ C ) )
=> ~ ! [D: com] :
( ( A
= ( B @ D ) )
=> ~ ( member_com @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(517,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_mem__def) ).
thf(2537,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(432,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_Int__lower1) ).
thf(2268,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(770,axiom,
! [A: state > state > $o,B: pname,C: state > state > $o,D: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_858012674_state @ A @ ( body_1 @ B ) @ C ) @ D ) @ ( insert528405184_state @ ( hoare_858012674_state @ A @ ( the_com @ ( body @ B ) ) @ C ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ D @ ( insert528405184_state @ ( hoare_858012674_state @ A @ ( body_1 @ B ) @ C ) @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_BodyN) ).
thf(3440,plain,
! [A: state > state > $o,B: pname,C: state > state > $o,D: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_858012674_state @ A @ ( body_1 @ B ) @ C ) @ D ) @ ( insert528405184_state @ ( hoare_858012674_state @ A @ ( the_com @ ( body @ B ) ) @ C ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ D @ ( insert528405184_state @ ( hoare_858012674_state @ A @ ( body_1 @ B ) @ C ) @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(661,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( insert528405184_state @ A @ B ) @ C )
= ( ( member451959335_state @ A @ C )
& ( ord_le777019615tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_insert__subset) ).
thf(3018,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( insert528405184_state @ A @ B ) @ C )
= ( ( member451959335_state @ A @ C )
& ( ord_le777019615tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(9,axiom,
! [A: hoare_1708887482_state > pname > $o,B: hoare_1708887482_state > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) )
=> ? [D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ B )
& ( finite1625599783_state @ D )
& ( C
= ( image_1552895654name_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_finite__subset__image) ).
thf(855,plain,
! [A: hoare_1708887482_state > pname > $o,B: hoare_1708887482_state > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) )
=> ? [D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ B )
& ( finite1625599783_state @ D )
& ( C
= ( image_1552895654name_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(856,plain,
! [C: ( pname > $o ) > $o,B: hoare_1708887482_state > $o,A: hoare_1708887482_state > pname > $o] :
( ( ~ ( finite297249702name_o @ C )
| ~ ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) )
| ( ord_le777019615tate_o @ ( sk2 @ C @ B @ A ) @ B ) )
& ( ~ ( finite297249702name_o @ C )
| ~ ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) )
| ( finite1625599783_state @ ( sk2 @ C @ B @ A ) ) )
& ( ~ ( finite297249702name_o @ C )
| ~ ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) )
| ( C
= ( image_1552895654name_o @ A @ ( sk2 @ C @ B @ A ) ) ) ) ),
inference(cnf,[status(esa)],[855]) ).
thf(857,plain,
! [C: ( pname > $o ) > $o,B: hoare_1708887482_state > $o,A: hoare_1708887482_state > pname > $o] :
( ~ ( finite297249702name_o @ C )
| ~ ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) )
| ( ord_le777019615tate_o @ ( sk2 @ C @ B @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[856]) ).
thf(229,axiom,
! [A: state > $o,B: com] :
( ( wt @ ( while @ A @ B ) )
=> ( wt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_WTs__elim__cases_I6_J) ).
thf(1567,plain,
! [A: state > $o,B: com] :
( ( wt @ ( while @ A @ B ) )
=> ( wt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(493,axiom,
! [A: pname,B: pname] :
( ( member_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_singleton__iff) ).
thf(2460,plain,
! [A: pname,B: pname] :
( ( member_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(97,axiom,
! [A: pname] :
( ( the_elem_pname @ ( insert_pname @ A @ bot_bot_pname_o ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_the__elem__eq) ).
thf(1160,plain,
! [A: pname] :
( ( the_elem_pname @ ( insert_pname @ A @ bot_bot_pname_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(734,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
=> ( ( insert528405184_state @ A @ ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_insert__Diff) ).
thf(3326,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
=> ( ( insert528405184_state @ A @ ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(162,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ C )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ C ) @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_Un__Int__distrib2) ).
thf(1361,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ C )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ C ) @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(850,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o @ A @ bot_bot_pname_o )
= A ),
inference(cnf,[status(esa)],[849]) ).
thf(851,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o @ A @ bot_bot_pname_o )
= A ),
inference(lifteq,[status(thm)],[850]) ).
thf(3922,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o @ A
@ ^ [B: pname] : bot_bot_o )
= A ),
inference(rewrite,[status(thm)],[851,2398]) ).
thf(656,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_sup_Oidem) ).
thf(3000,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(105,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1780557381name_o @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_sup1E) ).
thf(1182,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1780557381name_o @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(491,axiom,
! [A: ( pname > $o ) > hoare_1708887482_state,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite1625599783_state @ ( image_1922967206_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(2455,plain,
! [A: ( pname > $o ) > hoare_1708887482_state,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite1625599783_state @ ( image_1922967206_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(372,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
= ( semila1122118281tate_o
@ ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] : ( C = A ) )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_insert__def) ).
thf(2080,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
= ( semila1122118281tate_o
@ ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] : ( C = A ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(235,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_com_Osimps_I3_J) ).
thf(1584,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)],[235]) ).
thf(664,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ C ) )
=> ( member451959335_state @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_IntD2) ).
thf(3032,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ C ) )
=> ( member451959335_state @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(458,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_inf__sup__ord_I3_J) ).
thf(2349,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1887,plain,
( ( set_com @ none_com )
= bot_bot_com_o ),
inference(lifteq,[status(thm)],[1886]) ).
thf(3723,plain,
( ( set_com @ none_com )
= ( ^ [A: com] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1887,1863]) ).
thf(812,axiom,
! [A: com] :
( ( hoare_Mirabelle_MGT @ A )
= ( hoare_858012674_state @ fequal_state @ A @ ( evalc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_762_MGT__def) ).
thf(3573,plain,
! [A: com] :
( ( hoare_Mirabelle_MGT @ A )
= ( hoare_858012674_state @ fequal_state @ A @ ( evalc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(759,axiom,
! [A: hoare_1708887482_state > $o] :
( ! [B: hoare_1708887482_state] :
~ ( member451959335_state @ B @ A )
=> ( A = bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_equals0I) ).
thf(3407,plain,
! [A: hoare_1708887482_state > $o] :
( ! [B: hoare_1708887482_state] :
~ ( member451959335_state @ B @ A )
=> ( A = bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(523,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_Int__Un__distrib) ).
thf(2561,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(706,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( bot_bo19817387tate_o
= ( image_1116629049_state @ A @ B ) )
= ( B = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_empty__is__image) ).
thf(3210,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( bot_bo19817387tate_o
= ( image_1116629049_state @ A @ B ) )
= ( B = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(22,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ! [C: hoare_1708887482_state > $o] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le1728773982te_o_o @ ( collec219771562tate_o @ B ) @ ( collec219771562tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_Collect__mono) ).
thf(901,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ! [C: hoare_1708887482_state > $o] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le1728773982te_o_o @ ( collec219771562tate_o @ B ) @ ( collec219771562tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(480,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_le777019615tate_o @ ( image_1116629049_state @ A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_image__mono) ).
thf(2419,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_le777019615tate_o @ ( image_1116629049_state @ A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(70,axiom,
! [A: option_com,B: option_com] :
( ( if_option_com @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) ).
thf(1075,plain,
! [A: option_com,B: option_com] :
( ( if_option_com @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(178,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
= ( ( semila129691299tate_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_le__iff__inf) ).
thf(1414,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
= ( ( semila129691299tate_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(363,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ C @ A ) @ ( semila1122118281tate_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_Un__mono) ).
thf(2053,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ C @ A ) @ ( semila1122118281tate_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(311,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
= ( ( semila1122118281tate_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_le__iff__sup) ).
thf(1842,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
= ( ( semila1122118281tate_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(303,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_Un__commute) ).
thf(1810,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(297,axiom,
! [A: hoare_1708887482_state > hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( ord_le777019615tate_o @ B @ ( image_757158439_state @ A @ B ) )
=> ( inj_on632008595_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_finite__surj__inj) ).
thf(1791,plain,
! [A: hoare_1708887482_state > hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( ord_le777019615tate_o @ B @ ( image_757158439_state @ A @ B ) )
=> ( inj_on632008595_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(55,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o
@ ( collect_pname_o
@ ^ [C: pname > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite297249702name_o @ ( collect_pname_o @ A ) )
& ( finite297249702name_o @ ( collect_pname_o @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_finite__Collect__disjI) ).
thf(1016,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o
@ ( collect_pname_o
@ ^ [C: pname > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite297249702name_o @ ( collect_pname_o @ A ) )
& ( finite297249702name_o @ ( collect_pname_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(374,axiom,
finite138924780name_o @ semila1780557381name_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_comp__fun__idem__sup) ).
thf(2085,plain,
finite138924780name_o @ semila1780557381name_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(497,axiom,
! [A: pname] :
( ( collect_pname @ ( fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_singleton__conv2) ).
thf(2472,plain,
! [A: pname] :
( ( collect_pname @ ( fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(549,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ bot_bot_pname_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_Un__empty__left) ).
thf(2649,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ bot_bot_pname_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(63,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ( ord_le1205211808me_o_o @ A @ B )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_rev__finite__subset) ).
thf(1039,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( ( ord_le1205211808me_o_o @ A @ B )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4530,plain,
( ~ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk152 )
| ~ ( fa @ sk152 ) ),
inference(bool_ext,[status(thm)],[4529]) ).
thf(180,axiom,
! [A: com > $o,B: pname,C: com > pname,D: com] :
( ( B
= ( C @ D ) )
=> ( ( member_com @ D @ A )
=> ( member_pname @ B @ ( image_com_pname @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_image__eqI) ).
thf(1419,plain,
! [A: com > $o,B: pname,C: com > pname,D: com] :
( ( B
= ( C @ D ) )
=> ( ( member_com @ D @ A )
=> ( member_pname @ B @ ( image_com_pname @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(3,axiom,
! [A: pname > $o,B: pname > pname,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_pname_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_finite__surj) ).
thf(836,plain,
! [A: pname > $o,B: pname > pname,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_pname_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(837,plain,
! [C: pname > $o,B: pname > pname,A: pname > $o] :
( ~ ( finite_finite_pname @ C )
| ~ ( ord_less_eq_pname_o @ A @ ( image_pname_pname @ B @ C ) )
| ( finite_finite_pname @ A ) ),
inference(cnf,[status(esa)],[836]) ).
thf(83,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( A != bot_bo19817387tate_o )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_folding__one__idem_Osubset__idem) ).
thf(1114,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( A != bot_bo19817387tate_o )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(784,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ bot_bo19817387tate_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_sup__bot__right) ).
thf(3486,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ bot_bo19817387tate_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(191,axiom,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_com_Osimps_I13_J) ).
thf(1456,plain,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(535,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_inf__sup__aci_I7_J) ).
thf(2598,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(709,axiom,
! [A: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ bot_bo19817387tate_o )
=> ( A = bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_le__bot) ).
thf(3222,plain,
! [A: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ bot_bo19817387tate_o )
=> ( A = bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(344,axiom,
! [A: pname > $o] :
( ( ( collect_pname @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Collect__empty__eq) ).
thf(1984,plain,
! [A: pname > $o] :
( ( ( collect_pname @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(51,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ( minus_minus_pname_o @ C @ ( minus_minus_pname_o @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_double__diff) ).
thf(1002,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ( minus_minus_pname_o @ C @ ( minus_minus_pname_o @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(319,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_Un__assoc) ).
thf(1874,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(183,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( ord_le777019615tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_subset__trans) ).
thf(1429,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( ord_le777019615tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(737,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] :
( ( ( A @ B )
=> ( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( B = C )
& ( A @ C ) ) )
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_Collect__conv__if2) ).
thf(3333,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] :
( ( ( A @ B )
=> ( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( B = C )
& ( A @ C ) ) )
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(744,axiom,
( finite662762081tate_o
@ ^ [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] : ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_comp__fun__idem__remove) ).
thf(3362,plain,
( finite662762081tate_o
@ ^ [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] : ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(4152,plain,
( finite662762081tate_o
@ ^ [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( minus_2056855718tate_o @ B
@ ( insert528405184_state @ A
@ ^ [C: hoare_1708887482_state] : bot_bot_o ) ) ),
inference(rewrite,[status(thm)],[3362,3234]) ).
thf(434,axiom,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_Int__empty__right) ).
thf(2272,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(216,axiom,
! [A: hoare_1708887482_state] :
( ( the_Ho963921505_state @ ( some_H1974565227_state @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_the_Osimps) ).
thf(1525,plain,
! [A: hoare_1708887482_state] :
( ( the_Ho963921505_state @ ( some_H1974565227_state @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(292,axiom,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_Collect__def) ).
thf(1776,plain,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(131,axiom,
! [A: hoare_1708887482_state] :
~ ( is_non163157940_state @ ( some_H1974565227_state @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_is__none__code_I2_J) ).
thf(1261,plain,
! [A: hoare_1708887482_state] :
~ ( is_non163157940_state @ ( some_H1974565227_state @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1262,plain,
~ ? [A: hoare_1708887482_state] : ( is_non163157940_state @ ( some_H1974565227_state @ A ) ),
inference(miniscope,[status(thm)],[1261]) ).
thf(1263,plain,
! [A: hoare_1708887482_state] :
~ ( is_non163157940_state @ ( some_H1974565227_state @ A ) ),
inference(cnf,[status(esa)],[1262]) ).
thf(827,axiom,
! [A: pname,B: pname] :
( ( ( body_1 @ A )
= ( body_1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_com_Osimps_I6_J) ).
thf(3611,plain,
! [A: pname,B: pname] :
( ( ( body_1 @ A )
= ( body_1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(94,axiom,
! [A: com > hoare_1708887482_state,B: hoare_1708887482_state > $o,C: com > $o] :
( ! [D: com] :
( ( member_com @ D @ C )
=> ( member451959335_state @ ( A @ D ) @ B ) )
=> ( ord_le777019615tate_o @ ( image_934102463_state @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_image__subsetI) ).
thf(1150,plain,
! [A: com > hoare_1708887482_state,B: hoare_1708887482_state > $o,C: com > $o] :
( ! [D: com] :
( ( member_com @ D @ C )
=> ( member451959335_state @ ( A @ D ) @ B ) )
=> ( ord_le777019615tate_o @ ( image_934102463_state @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(127,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A @ B ) @ ( minus_2056855718tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_Diff__Int) ).
thf(1249,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A @ B ) @ ( minus_2056855718tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(142,axiom,
! [A: com > pname,B: pname > $o,C: com > $o] :
( ! [D: com] :
( ( member_com @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_com_pname @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_image__subsetI) ).
thf(1297,plain,
! [A: com > pname,B: pname > $o,C: com > $o] :
( ! [D: com] :
( ( member_com @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_com_pname @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(557,axiom,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ ( insert_pname @ A @ B ) )
= ( finite_finite_pname @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_finite__insert) ).
thf(2681,plain,
! [A: pname,B: pname > $o] :
( ( finite_finite_pname @ ( insert_pname @ A @ B ) )
= ( finite_finite_pname @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(802,axiom,
! [A: state > $o,B: com,C: pname] :
( ( while @ A @ B )
!= ( body_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_com_Osimps_I58_J) ).
thf(3541,plain,
! [A: state > $o,B: com,C: pname] :
( ( while @ A @ B )
!= ( body_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(743,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] :
( ( ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( ( partia1256728516_state @ B @ A )
= B ) )
& ( ~ ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( ( partia1256728516_state @ B @ A )
= ( the_Ho851197897_state
@ ^ [C: hoare_1708887482_state] : ( member451959335_state @ C @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_flat__lub__def) ).
thf(3354,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state] :
( ( ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( ( partia1256728516_state @ B @ A )
= B ) )
& ( ~ ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( ( partia1256728516_state @ B @ A )
= ( the_Ho851197897_state
@ ^ [C: hoare_1708887482_state] : ( member451959335_state @ C @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(395,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( semila129691299tate_o
@ ^ [D: hoare_1708887482_state] : ( member451959335_state @ D @ A )
@ ^ [D: hoare_1708887482_state] : ( member451959335_state @ D @ B )
@ C )
= ( member451959335_state @ C @ ( semila129691299tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_inf__Int__eq) ).
thf(2153,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( semila129691299tate_o
@ ^ [D: hoare_1708887482_state] : ( member451959335_state @ D @ A )
@ ^ [D: hoare_1708887482_state] : ( member451959335_state @ D @ B )
@ C )
= ( member451959335_state @ C @ ( semila129691299tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(259,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_Un__upper2) ).
thf(1668,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(341,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_insert__compr__raw) ).
thf(1974,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(680,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ B @ ( insert528405184_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_subset__insertI2) ).
thf(3109,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ B @ ( insert528405184_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(658,axiom,
! [A: ( pname > $o ) > pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ( A @ C )
= B )
=> ( ! [E: pname > $o,F: pname > $o] :
( ( ord_less_eq_pname_o @ F @ E )
=> ( ord_less_eq_pname_o @ ( A @ F ) @ ( A @ E ) ) )
=> ( ord_less_eq_pname_o @ B @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_xt1_I16_J) ).
thf(3005,plain,
! [A: ( pname > $o ) > pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ( A @ C )
= B )
=> ( ! [E: pname > $o,F: pname > $o] :
( ( ord_less_eq_pname_o @ F @ E )
=> ( ord_less_eq_pname_o @ ( A @ F ) @ ( A @ E ) ) )
=> ( ord_less_eq_pname_o @ B @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(391,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( insert_pname @ A @ B ) @ C )
= ( insert_pname @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_Un__insert__left) ).
thf(2140,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( insert_pname @ A @ B ) @ C )
= ( insert_pname @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(582,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_inf__sup__ord_I1_J) ).
thf(2756,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(696,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( hoare_90032982_state @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_weaken) ).
thf(3162,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( hoare_90032982_state @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(781,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ bot_bo19817387tate_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_Un__empty__left) ).
thf(3476,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ bot_bo19817387tate_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(593,axiom,
! [A: state > $o,B: com] :
( ( while @ A @ B )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_com_Osimps_I17_J) ).
thf(2788,plain,
! [A: state > $o,B: com] :
( ( while @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(710,axiom,
! [A: com,B: com,C: pname] :
( ( semi @ A @ B )
!= ( body_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_com_Osimps_I48_J) ).
thf(3225,plain,
! [A: com,B: com,C: pname] :
( ( semi @ A @ B )
!= ( body_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(293,axiom,
! [A: com > hoare_1708887482_state,B: com > $o] :
( ( ( image_934102463_state @ A @ B )
= bot_bo19817387tate_o )
= ( B = bot_bot_com_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_image__is__empty) ).
thf(1779,plain,
! [A: com > hoare_1708887482_state,B: com > $o] :
( ( ( image_934102463_state @ A @ B )
= bot_bo19817387tate_o )
= ( B = bot_bot_com_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(723,axiom,
! [A: hoare_1708887482_state > $o] :
( ( bot_bo19817387tate_o
= ( collec1568722789_state @ A ) )
= ( ! [B: hoare_1708887482_state] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_empty__Collect__eq) ).
thf(3279,plain,
! [A: hoare_1708887482_state > $o] :
( ( bot_bo19817387tate_o
= ( collec1568722789_state @ A ) )
= ( ! [B: hoare_1708887482_state] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(27,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( member_pname @ B @ ( minus_minus_pname_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_DiffI) ).
thf(921,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( member_pname @ B @ ( minus_minus_pname_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(101,axiom,
! [A: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ A )
=> ( finite1329924456tate_o
@ ( collec219771562tate_o
@ ^ [B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__Collect__subsets) ).
thf(1170,plain,
! [A: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ A )
=> ( finite1329924456tate_o
@ ( collec219771562tate_o
@ ^ [B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(791,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ A @ ( insert528405184_state @ B @ C ) )
=> ( ( hoare_90032982_state @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
& ( hoare_90032982_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_derivs__insertD) ).
thf(3508,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ A @ ( insert528405184_state @ B @ C ) )
=> ( ( hoare_90032982_state @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
& ( hoare_90032982_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(693,axiom,
! [A: hoare_1708887482_state] :
( ( collec1568722789_state @ ( fequal224822779_state @ A ) )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_singleton__conv2) ).
thf(3147,plain,
! [A: hoare_1708887482_state] :
( ( collec1568722789_state @ ( fequal224822779_state @ A ) )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(775,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( bot_bo19817387tate_o
!= ( insert528405184_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_empty__not__insert) ).
thf(3454,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( bot_bo19817387tate_o
!= ( insert528405184_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(124,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_sup_Oassoc) ).
thf(1241,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(365,axiom,
! [A: com > hoare_1708887482_state,B: com > $o] :
( ( bot_bo19817387tate_o
= ( image_934102463_state @ A @ B ) )
= ( B = bot_bot_com_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_empty__is__image) ).
thf(2057,plain,
! [A: com > hoare_1708887482_state,B: com > $o] :
( ( bot_bo19817387tate_o
= ( image_934102463_state @ A @ B ) )
= ( B = bot_bot_com_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(68,axiom,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_o_pname @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_pname_o_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_finite__subset__image) ).
thf(1054,plain,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_o_pname @ A @ B ) )
=> ? [D: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ D @ B )
& ( finite297249702name_o @ D )
& ( C
= ( image_pname_o_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(643,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ C )
= ( ( member_pname @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_insert__subset) ).
thf(2963,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( insert_pname @ A @ B ) @ C )
= ( ( member_pname @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(61,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ A @ B )
=> ( ( finite297249702name_o @ B )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_finite__subset) ).
thf(1035,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ A @ B )
=> ( ( finite297249702name_o @ B )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(628,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_insert__absorb2) ).
thf(2915,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(487,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( member_pname @ B @ A ) )
=> ( member_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_UnCI) ).
thf(2440,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( member_pname @ B @ A ) )
=> ( member_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(405,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1780557381name_o @ B @ C ) )
= ( ( member_pname @ A @ B )
| ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_Un__iff) ).
thf(2189,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1780557381name_o @ B @ C ) )
= ( ( member_pname @ A @ B )
| ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(654,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( finite1625599783_state @ ( image_1116629049_state @ A @ B ) )
=> ( ( inj_on1553129421_state @ A @ B )
=> ( finite_finite_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_finite__imageD) ).
thf(2995,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( finite1625599783_state @ ( image_1116629049_state @ A @ B ) )
=> ( ( inj_on1553129421_state @ A @ B )
=> ( finite_finite_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(482,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( B = C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( ord_le777019615tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_ord__eq__le__trans) ).
thf(2423,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( B = C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( ord_le777019615tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(19,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( minus_minus_pname_o @ A @ B )
= ( finite603803317name_o
@ ^ [C: pname,D: pname > $o] : ( minus_minus_pname_o @ D @ ( insert_pname @ C @ bot_bot_pname_o ) )
@ A
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_minus__fold__remove) ).
thf(888,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( minus_minus_pname_o @ A @ B )
= ( finite603803317name_o
@ ^ [C: pname,D: pname > $o] : ( minus_minus_pname_o @ D @ ( insert_pname @ C @ bot_bot_pname_o ) )
@ A
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(29,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( minus_minus_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_818_finite__Diff) ).
thf(926,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( minus_minus_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(626,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ! [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
=> ( member451959335_state @ C @ A ) )
=> ( ord_le777019615tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_subsetI) ).
thf(2909,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ! [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
=> ( member451959335_state @ C @ A ) )
=> ( ord_le777019615tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(253,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ ( semila1122118281tate_o @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
=> ( A @ D ) )
& ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ C )
=> ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_ball__Un) ).
thf(1648,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ ( semila1122118281tate_o @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
=> ( A @ D ) )
& ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ C )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(40,axiom,
! [A: ( pname > $o ) > $o] :
( ( collect_pname_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Collect__def) ).
thf(965,plain,
! [A: ( pname > $o ) > $o] :
( ( collect_pname_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(478,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_sup__absorb2) ).
thf(2413,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(435,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_Un__absorb) ).
thf(2275,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(532,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
=> ( ord_le777019615tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_equalityD1) ).
thf(2585,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
=> ( ord_le777019615tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(715,axiom,
! [A: hoare_1708887482_state > $o] :
( ( ! [B: hoare_1708887482_state] :
~ ( member451959335_state @ B @ A ) )
= ( A = bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_all__not__in__conv) ).
thf(3257,plain,
! [A: hoare_1708887482_state > $o] :
( ( ! [B: hoare_1708887482_state] :
~ ( member451959335_state @ B @ A ) )
= ( A = bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(727,axiom,
! [A: pname,B: pname > option_com] :
( ( member_pname @ A @ ( dom_pname_com @ B ) )
=> ? [C: com] :
( ( B @ A )
= ( some_com @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_domD) ).
thf(3289,plain,
! [A: pname,B: pname > option_com] :
( ( member_pname @ A @ ( dom_pname_com @ B ) )
=> ? [C: com] :
( ( B @ A )
= ( some_com @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(247,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_Un__upper1) ).
thf(1631,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(384,axiom,
! [A: hoare_1708887482_state > hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( finite1329924456tate_o @ ( image_1551509096tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(2121,plain,
! [A: hoare_1708887482_state > hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( finite1329924456tate_o @ ( image_1551509096tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(421,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ ( semila1122118281tate_o @ A @ B ) )
= ( ( finite1625599783_state @ A )
& ( finite1625599783_state @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_finite__Un) ).
thf(2235,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ ( semila1122118281tate_o @ A @ B ) )
= ( ( finite1625599783_state @ A )
& ( finite1625599783_state @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(556,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_912_le__infE) ).
thf(2677,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(401,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_Un__assoc) ).
thf(2176,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(270,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ B )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_minus_pname_o @ D @ ( insert_pname @ C @ bot_bot_pname_o ) ) ) ) ) )
=> ( A @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_finite__empty__induct) ).
thf(1698,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ B )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_minus_pname_o @ D @ ( insert_pname @ C @ bot_bot_pname_o ) ) ) ) ) )
=> ( A @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(79,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_inf__sup__aci_I8_J) ).
thf(1103,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(672,axiom,
! [A: pname] :
( ( ( body @ A )
!= none_com )
=> ( wt @ ( body_1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_WT_OBody) ).
thf(3079,plain,
! [A: pname] :
( ( ( body @ A )
!= none_com )
=> ( wt @ ( body_1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(637,axiom,
! [A: pname > $o] :
( ( A != bot_bot_pname_o )
= ( ? [B: pname,C: pname > $o] :
( ( A
= ( insert_pname @ B @ C ) )
& ~ ( member_pname @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_nonempty__iff) ).
thf(2941,plain,
! [A: pname > $o] :
( ( A != bot_bot_pname_o )
= ( ? [B: pname,C: pname > $o] :
( ( A
= ( insert_pname @ B @ C ) )
& ~ ( member_pname @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(143,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ A )
& ~ ( member451959335_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_set__diff__eq) ).
thf(1301,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ A )
& ~ ( member451959335_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(238,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_equalityE) ).
thf(1595,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(796,axiom,
! [A: hoare_1708887482_state] :
( ( set_Ho525251890_state @ ( some_H1974565227_state @ A ) )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_Option_Oset_Osimps_I2_J) ).
thf(3523,plain,
! [A: hoare_1708887482_state] :
( ( set_Ho525251890_state @ ( some_H1974565227_state @ A ) )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(720,axiom,
! [A: hoare_1708887482_state > $o,B: pname > $o] :
( ( hoare_90032982_state
@ ( semila1122118281tate_o @ A
@ ( image_1116629049_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ C ) )
@ B ) )
@ ( image_1116629049_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ C ) ) )
@ B ) )
=> ( ( finite_finite_pname @ B )
=> ( hoare_90032982_state @ A
@ ( image_1116629049_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ C ) )
@ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_MGT__Body) ).
thf(3274,plain,
! [A: hoare_1708887482_state > $o,B: pname > $o] :
( ( hoare_90032982_state
@ ( semila1122118281tate_o @ A
@ ( image_1116629049_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ C ) )
@ B ) )
@ ( image_1116629049_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ C ) ) )
@ B ) )
=> ( ( finite_finite_pname @ B )
=> ( hoare_90032982_state @ A
@ ( image_1116629049_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ C ) )
@ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(853,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(cnf,[status(esa)],[852]) ).
thf(854,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(lifteq,[status(thm)],[853]) ).
thf(4017,plain,
! [A: pname > $o] :
( ( minus_minus_pname_o
@ ^ [B: pname] : bot_bot_o
@ A )
= ( ^ [B: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[854,2398]) ).
thf(513,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_sup__commute) ).
thf(2524,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(755,axiom,
! [A: hoare_1708887482_state > option1624383643_state,B: hoare_1708887482_state,C: hoare_1708887482_state] :
( ( ( A @ B )
= ( some_H1974565227_state @ C ) )
=> ( ( insert528405184_state @ B @ ( dom_Ho1703271284_state @ A ) )
= ( dom_Ho1703271284_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_insert__dom) ).
thf(3396,plain,
! [A: hoare_1708887482_state > option1624383643_state,B: hoare_1708887482_state,C: hoare_1708887482_state] :
( ( ( A @ B )
= ( some_H1974565227_state @ C ) )
=> ( ( insert528405184_state @ B @ ( dom_Ho1703271284_state @ A ) )
= ( dom_Ho1703271284_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(308,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ C )
= ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) )
= ( ord_le777019615tate_o @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_Un__Int__assoc__eq) ).
thf(1833,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ C )
= ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) ) )
= ( ord_le777019615tate_o @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(53,axiom,
! [A: pname,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( C @ ( insert_pname @ A @ bot_bot_pname_o ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_folding__one_Osingleton) ).
thf(1007,plain,
! [A: pname,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( C @ ( insert_pname @ A @ bot_bot_pname_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(170,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_sup_Oleft__idem) ).
thf(1389,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(843,plain,
! [C: pname > $o,B: pname > $o,A: pname > pname] :
( ~ ( finite_finite_pname @ C )
| ~ ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
| ( ord_less_eq_pname_o @ ( sk1 @ C @ B @ A ) @ B ) ),
inference(cnfConj,[status(thm)],[842]) ).
thf(4159,plain,
( ~ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk148 )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[4158]) ).
thf(244,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_xt1_I3_J) ).
thf(1620,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(555,axiom,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= ( member_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_bot__empty__eq) ).
thf(2674,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= ( member_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(597,axiom,
! [A: com,B: pname > com,C: pname > $o] :
( ( member_com @ A @ ( image_pname_com @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_imageE) ).
thf(2806,plain,
! [A: com,B: pname > com,C: pname > $o] :
( ( member_com @ A @ ( image_pname_com @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(776,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ bot_bo19817387tate_o @ A )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_inf__bot__left) ).
thf(3458,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ bot_bo19817387tate_o @ A )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(758,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ bot_bo19817387tate_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_sup__bot__left) ).
thf(3404,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ bot_bo19817387tate_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(87,axiom,
! [A: com,B: com] :
( ( wt @ ( semi @ A @ B ) )
=> ~ ( ( wt @ A )
=> ~ ( wt @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_WTs__elim__cases_I4_J) ).
thf(1124,plain,
! [A: com,B: com] :
( ( wt @ ( semi @ A @ B ) )
=> ~ ( ( wt @ A )
=> ~ ( wt @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(707,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] :
( ( inj_on1553129421_state @ A @ ( semila1780557381name_o @ B @ C ) )
=> ( ( ( image_1116629049_state @ A @ B )
= ( image_1116629049_state @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_inj__on__Un__image__eq__iff) ).
thf(3213,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] :
( ( inj_on1553129421_state @ A @ ( semila1780557381name_o @ B @ C ) )
=> ( ( ( image_1116629049_state @ A @ B )
= ( image_1116629049_state @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(800,axiom,
! [A: hoare_1708887482_state,B: com,C: com > $o] :
( ( member_com @ B @ C )
=> ( ( image_934102463_state
@ ^ [D: com] : A
@ C )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_image__constant) ).
thf(3536,plain,
! [A: hoare_1708887482_state,B: com,C: com > $o] :
( ( member_com @ B @ C )
=> ( ( image_934102463_state
@ ^ [D: com] : A
@ C )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(95,axiom,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_all__not__in__conv) ).
thf(1154,plain,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(43,axiom,
! [A: hoare_1708887482_state > hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ C )
=> ( ( ord_le1728773982te_o_o @ C @ ( image_1551509096tate_o @ A @ B ) )
=> ? [D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ B )
& ( finite1625599783_state @ D )
& ( C
= ( image_1551509096tate_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_finite__subset__image) ).
thf(975,plain,
! [A: hoare_1708887482_state > hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ C )
=> ( ( ord_le1728773982te_o_o @ C @ ( image_1551509096tate_o @ A @ B ) )
=> ? [D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ B )
& ( finite1625599783_state @ D )
& ( C
= ( image_1551509096tate_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(752,axiom,
! [A: pname > hoare_1708887482_state,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( image_1116629049_state @ A @ ( vimage1943311875_state @ A @ B ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1189_image__vimage__subset) ).
thf(3387,plain,
! [A: pname > hoare_1708887482_state,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( image_1116629049_state @ A @ ( vimage1943311875_state @ A @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(782,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( B = bot_bo19817387tate_o )
=> ~ ( member451959335_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_equals0D) ).
thf(3479,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( B = bot_bo19817387tate_o )
=> ~ ( member451959335_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(3480,plain,
! [B: hoare_1708887482_state > $o,A: hoare_1708887482_state] :
( ( B != bot_bo19817387tate_o )
| ~ ( member451959335_state @ A @ B ) ),
inference(cnf,[status(esa)],[3479]) ).
thf(3481,plain,
! [B: hoare_1708887482_state > $o,A: hoare_1708887482_state] :
( ( B != bot_bo19817387tate_o )
| ~ ( member451959335_state @ A @ B ) ),
inference(lifteq,[status(thm)],[3480]) ).
thf(3482,plain,
! [A: hoare_1708887482_state] :
~ ( member451959335_state @ A @ bot_bo19817387tate_o ),
inference(simp,[status(thm)],[3481]) ).
thf(4268,plain,
! [A: hoare_1708887482_state] :
~ ( member451959335_state @ A
@ ^ [B: hoare_1708887482_state] : bot_bot_o ),
inference(rewrite,[status(thm)],[3482,3234]) ).
thf(573,axiom,
! [A: pname,B: pname > $o] :
( bot_bot_pname_o
!= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_empty__not__insert) ).
thf(2727,plain,
! [A: pname,B: pname > $o] :
( bot_bot_pname_o
!= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(790,axiom,
! [A: pname > option_com,B: pname,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( ( insert_pname @ B @ ( dom_pname_com @ A ) )
= ( dom_pname_com @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_insert__dom) ).
thf(3504,plain,
! [A: pname > option_com,B: pname,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( ( insert_pname @ B @ ( dom_pname_com @ A ) )
= ( dom_pname_com @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(562,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_inf__sup__absorb) ).
thf(2695,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(203,axiom,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( member_pname @ C @ B )
=> ( member_pname @ C @ A ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_subsetI) ).
thf(1488,plain,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( member_pname @ C @ B )
=> ( member_pname @ C @ A ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(389,axiom,
! [A: state > $o,B: com,C: state > $o,D: com] :
( ( ( while @ A @ B )
= ( while @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_704_com_Osimps_I5_J) ).
thf(2134,plain,
! [A: state > $o,B: com,C: state > $o,D: com] :
( ( ( while @ A @ B )
= ( while @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(823,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( ( insert528405184_state @ A @ bot_bo19817387tate_o )
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_singleton__inject) ).
thf(3599,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( ( insert528405184_state @ A @ bot_bo19817387tate_o )
= ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(182,axiom,
! [A: com > $o] : ( inj_on11367768on_com @ some_com @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_inj__Some) ).
thf(1427,plain,
! [A: com > $o] : ( inj_on11367768on_com @ some_com @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1428,plain,
! [A: com > $o] : ( inj_on11367768on_com @ some_com @ A ),
inference(cnf,[status(esa)],[1427]) ).
thf(4533,plain,
( bot_bot_o
| ~ ( fa @ sk152 )
| ( ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk152 )
!= ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk148 ) ) ),
inference(paramod_ordered,[status(thm)],[4160,4529]) ).
thf(4535,plain,
( bot_bot_o
| ~ ( fa @ sk152 )
| ( ( hoare_Mirabelle_MGT @ y )
!= ( hoare_Mirabelle_MGT @ y ) )
| ( ( ^ [A: hoare_1708887482_state] : bot_bot_o )
!= ( ^ [A: hoare_1708887482_state] : bot_bot_o ) )
| ( sk152 != sk148 ) ),
inference(simp,[status(thm)],[4533]) ).
thf(4537,plain,
( bot_bot_o
| ~ ( fa @ sk152 )
| ( sk152 != sk148 ) ),
inference(simp,[status(thm)],[4535]) ).
thf(684,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
!= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_insert__not__empty) ).
thf(3118,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ B )
!= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(576,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_subset__trans) ).
thf(2738,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(705,axiom,
! [A: pname,B: state,C: state] :
( ( evalc @ ( the_com @ ( body @ A ) ) @ B @ C )
=> ( evalc @ ( body_1 @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_evalc_OBody) ).
thf(3208,plain,
! [A: pname,B: state,C: state] :
( ( evalc @ ( the_com @ ( body @ A ) ) @ B @ C )
=> ( evalc @ ( body_1 @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(153,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_folding__one_Oinsert) ).
thf(1332,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(364,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_in__mono) ).
thf(2055,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(632,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_empty__subsetI) ).
thf(2928,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(2929,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(cnf,[status(esa)],[2928]) ).
thf(4060,plain,
! [A: pname > $o] :
( ord_less_eq_pname_o
@ ^ [B: pname] : bot_bot_o
@ A ),
inference(rewrite,[status(thm)],[2929,2398]) ).
thf(492,axiom,
! [A: com,B: com > option_com] :
( ( member_com @ A @ ( dom_com_com @ B ) )
=> ? [C: com] :
( ( B @ A )
= ( some_com @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_domD) ).
thf(2457,plain,
! [A: com,B: com > option_com] :
( ( member_com @ A @ ( dom_com_com @ B ) )
=> ? [C: com] :
( ( B @ A )
= ( some_com @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(786,axiom,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_empty__subsetI) ).
thf(3493,plain,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(3494,plain,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A ),
inference(cnf,[status(esa)],[3493]) ).
thf(4273,plain,
! [A: hoare_1708887482_state > $o] :
( ord_le777019615tate_o
@ ^ [B: hoare_1708887482_state] : bot_bot_o
@ A ),
inference(rewrite,[status(thm)],[3494,3234]) ).
thf(35,axiom,
! [A: pname > $o,B: pname > $o] :
( ( minus_minus_pname_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
& ~ ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_set__diff__eq) ).
thf(947,plain,
! [A: pname > $o,B: pname > $o] :
( ( minus_minus_pname_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
& ~ ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(810,axiom,
! [A: pname,B: hoare_1708887482_state,C: pname > hoare_1708887482_state,D: pname > $o] :
( ( inj_on1553129421_state @ C @ D )
=> ( ~ ( member451959335_state @ B @ ( image_1116629049_state @ C @ D ) )
=> ( inj_on1553129421_state @ ( fun_up1986763201_state @ C @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_inj__on__fun__updI) ).
thf(3568,plain,
! [A: pname,B: hoare_1708887482_state,C: pname > hoare_1708887482_state,D: pname > $o] :
( ( inj_on1553129421_state @ C @ D )
=> ( ~ ( member451959335_state @ B @ ( image_1116629049_state @ C @ D ) )
=> ( inj_on1553129421_state @ ( fun_up1986763201_state @ C @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(450,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( B
= ( C @ D ) )
=> ( ( ord_le777019615tate_o @ A @ D )
=> ( ! [E: hoare_1708887482_state > $o,F: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ F @ E )
=> ( ord_le777019615tate_o @ ( C @ F ) @ ( C @ E ) ) )
=> ( ord_le777019615tate_o @ ( C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_xt1_I15_J) ).
thf(2319,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( B
= ( C @ D ) )
=> ( ( ord_le777019615tate_o @ A @ D )
=> ( ! [E: hoare_1708887482_state > $o,F: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ F @ E )
=> ( ord_le777019615tate_o @ ( C @ F ) @ ( C @ E ) ) )
=> ( ord_le777019615tate_o @ ( C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(262,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( semila1780557381name_o
@ ( collect_pname
@ ^ [C: pname] : ( C = A ) )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_insert__def) ).
thf(1675,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( semila1780557381name_o
@ ( collect_pname
@ ^ [C: pname] : ( C = A ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(441,axiom,
! [A: state,B: com,C: state,D: state] :
( ( evalc @ B @ C @ D )
=> ( ( evalc @ B @ C @ A )
=> ( A = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_770_com__det) ).
thf(2293,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)],[441]) ).
thf(669,axiom,
! [A: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ A )
= ( ( A = bot_bo19817387tate_o )
| ? [B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( A
= ( insert528405184_state @ C @ B ) )
& ( finite1625599783_state @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_finite_Osimps) ).
thf(3051,plain,
! [A: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ A )
= ( ( A = bot_bo19817387tate_o )
| ? [B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( A
= ( insert528405184_state @ C @ B ) )
& ( finite1625599783_state @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(135,axiom,
! [A: com] :
( ( the_com @ ( some_com @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_the_Osimps) ).
thf(1271,plain,
! [A: com] :
( ( the_com @ ( some_com @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(446,axiom,
! [A: com > $o] :
( ( ! [B: com] :
~ ( member_com @ B @ A ) )
= ( A = bot_bot_com_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_all__not__in__conv) ).
thf(2308,plain,
! [A: com > $o] :
( ( ! [B: com] :
~ ( member_com @ B @ A ) )
= ( A = bot_bot_com_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(249,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_equalityD1) ).
thf(1635,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(277,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_emptyE) ).
thf(1733,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(821,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > hoare_1708887482_state,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ! [E: hoare_1708887482_state,F: hoare_1708887482_state] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite1625599783_state @ A )
=> ( ( A != bot_bo19817387tate_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_757158439_state @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_folding__one__idem_Ohom__commute) ).
thf(3594,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > hoare_1708887482_state,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ! [E: hoare_1708887482_state,F: hoare_1708887482_state] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite1625599783_state @ A )
=> ( ( A != bot_bo19817387tate_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_757158439_state @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(123,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_le__infI2) ).
thf(1239,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(349,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_bot__least) ).
thf(1997,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(581,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ? [D: pname] :
( ( member_pname @ D @ ( semila1780557381name_o @ B @ C ) )
& ( A @ D ) ) )
= ( ? [D: pname] :
( ( member_pname @ D @ B )
& ( A @ D ) )
| ? [D: pname] :
( ( member_pname @ D @ C )
& ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_bex__Un) ).
thf(2753,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ? [D: pname] :
( ( member_pname @ D @ ( semila1780557381name_o @ B @ C ) )
& ( A @ D ) ) )
= ( ? [D: pname] :
( ( member_pname @ D @ B )
& ( A @ D ) )
| ? [D: pname] :
( ( member_pname @ D @ C )
& ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(768,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) @ C )
=> ( ( member451959335_state @ B @ A )
=> ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_diff__single__insert) ).
thf(3436,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) ) @ C )
=> ( ( member451959335_state @ B @ A )
=> ( ord_le777019615tate_o @ A @ ( insert528405184_state @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(830,axiom,
! [A: pname] :
( ( wt @ ( body_1 @ A ) )
=> ~ ! [B: com] :
( ( body @ A )
!= ( some_com @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_WTs__elim__cases_I7_J) ).
thf(3619,plain,
! [A: pname] :
( ( wt @ ( body_1 @ A ) )
=> ~ ! [B: com] :
( ( body @ A )
!= ( some_com @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(815,axiom,
! [A: hoare_1708887482_state > $o,B: state > state > $o,C: pname,D: state > state > $o] :
( ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ B @ ( the_com @ ( body @ C ) ) @ D ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ B @ ( body_1 @ C ) @ D ) @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_weak__Body) ).
thf(3579,plain,
! [A: hoare_1708887482_state > $o,B: state > state > $o,C: pname,D: state > state > $o] :
( ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ B @ ( the_com @ ( body @ C ) ) @ D ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ B @ ( body_1 @ C ) @ D ) @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(288,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1673364395name_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_le__iff__inf) ).
thf(1765,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1673364395name_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(75,axiom,
! [A: hoare_1708887482_state > pname,B: pname > $o,C: hoare_1708887482_state > $o] :
( ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_1509414295_pname @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_image__subsetI) ).
thf(1090,plain,
! [A: hoare_1708887482_state > pname,B: pname > $o,C: hoare_1708887482_state > $o] :
( ! [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_1509414295_pname @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(447,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ A ) @ ( semila1673364395name_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_Int__mono) ).
thf(2311,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ A ) @ ( semila1673364395name_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(834,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ ( insert528405184_state @ A @ B ) @ ( insert528405184_state @ A @ C ) )
= ( insert528405184_state @ A @ ( semila129691299tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_insert__inter__insert) ).
thf(3631,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ ( insert528405184_state @ A @ B ) @ ( insert528405184_state @ A @ C ) )
= ( insert528405184_state @ A @ ( semila129691299tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(499,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] : ( ord_le777019615tate_o @ ( image_1116629049_state @ A @ ( semila1673364395name_o @ B @ C ) ) @ ( semila129691299tate_o @ ( image_1116629049_state @ A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_image__Int__subset) ).
thf(2478,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] : ( ord_le777019615tate_o @ ( image_1116629049_state @ A @ ( semila1673364395name_o @ B @ C ) ) @ ( semila129691299tate_o @ ( image_1116629049_state @ A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(504,axiom,
! [A: option_com] :
( ( A != none_com )
= ( ? [B: com] :
( A
= ( some_com @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_not__None__eq) ).
thf(2493,plain,
! [A: option_com] :
( ( A != none_com )
= ( ? [B: com] :
( A
= ( some_com @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(84,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_Un__left__commute) ).
thf(1117,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(378,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_sup_Oassoc) ).
thf(2097,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(679,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( member451959335_state @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_singleton__iff) ).
thf(3106,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( member451959335_state @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(92,axiom,
! [A: pname > option_com,B: pname] :
( ( ( dom_pname_com @ A )
= ( insert_pname @ B @ bot_bot_pname_o ) )
= ( ? [C: com] :
( A
= ( fun_up879233478on_com
@ ^ [D: pname] : none_com
@ B
@ ( some_com @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1096_dom__eq__singleton__conv) ).
thf(1144,plain,
! [A: pname > option_com,B: pname] :
( ( ( dom_pname_com @ A )
= ( insert_pname @ B @ bot_bot_pname_o ) )
= ( ? [C: com] :
( A
= ( fun_up879233478on_com
@ ^ [D: pname] : none_com
@ B
@ ( some_com @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(290,axiom,
! [A: hoare_1708887482_state > pname > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( finite297249702name_o @ ( image_1552895654name_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(1771,plain,
! [A: hoare_1708887482_state > pname > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( finite297249702name_o @ ( image_1552895654name_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(789,axiom,
! [A: ( hoare_1708887482_state > $o ) > state > state > $o,B: ( hoare_1708887482_state > $o ) > state > state > $o,C: hoare_1708887482_state > $o,D: ( hoare_1708887482_state > $o ) > state > state > $o,E: ( hoare_1708887482_state > $o ) > com,F: ( hoare_1708887482_state > $o ) > state > state > $o,G: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ G )
=> ( ! [H: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) ) @ bot_bo19817387tate_o ) ) )
=> ( ( hoare_90032982_state @ C
@ ( image_27005066_state
@ ^ [H: hoare_1708887482_state > $o] : ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) )
@ G ) )
=> ( hoare_90032982_state @ C
@ ( image_27005066_state
@ ^ [H: hoare_1708887482_state > $o] : ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) )
@ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_finite__pointwise) ).
thf(3500,plain,
! [A: ( hoare_1708887482_state > $o ) > state > state > $o,B: ( hoare_1708887482_state > $o ) > state > state > $o,C: hoare_1708887482_state > $o,D: ( hoare_1708887482_state > $o ) > state > state > $o,E: ( hoare_1708887482_state > $o ) > com,F: ( hoare_1708887482_state > $o ) > state > state > $o,G: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ G )
=> ( ! [H: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) ) @ bot_bo19817387tate_o ) ) )
=> ( ( hoare_90032982_state @ C
@ ( image_27005066_state
@ ^ [H: hoare_1708887482_state > $o] : ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) )
@ G ) )
=> ( hoare_90032982_state @ C
@ ( image_27005066_state
@ ^ [H: hoare_1708887482_state > $o] : ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) )
@ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(751,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,C: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ B @ C )
=> ( ( finite1625599783_state @ A )
=> ( ( A != bot_bo19817387tate_o )
=> ( ! [D: hoare_1708887482_state,E: hoare_1708887482_state] : ( member451959335_state @ ( B @ D @ E ) @ ( insert528405184_state @ D @ ( insert528405184_state @ E @ bot_bo19817387tate_o ) ) )
=> ( member451959335_state @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_folding__one_Oclosed) ).
thf(3384,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,C: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ B @ C )
=> ( ( finite1625599783_state @ A )
=> ( ( A != bot_bo19817387tate_o )
=> ( ! [D: hoare_1708887482_state,E: hoare_1708887482_state] : ( member451959335_state @ ( B @ D @ E ) @ ( insert528405184_state @ D @ ( insert528405184_state @ E @ bot_bo19817387tate_o ) ) )
=> ( member451959335_state @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(145,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ( finite1625599783_state @ A )
=> ( ( A != bot_bo19817387tate_o )
=> ( ( D @ ( semila1122118281tate_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_folding__one__idem_Ounion__idem) ).
thf(1307,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ( finite1625599783_state @ A )
=> ( ( A != bot_bo19817387tate_o )
=> ( ( D @ ( semila1122118281tate_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(726,axiom,
! [A: pname > hoare_1708887482_state,B: pname] : ( member451959335_state @ ( A @ B ) @ ( image_1116629049_state @ A @ top_top_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1198_rangeI) ).
thf(3287,plain,
! [A: pname > hoare_1708887482_state,B: pname] : ( member451959335_state @ ( A @ B ) @ ( image_1116629049_state @ A @ top_top_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(793,axiom,
! [A: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ bot_bo19817387tate_o )
= ( A = bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_subset__empty) ).
thf(3515,plain,
! [A: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ bot_bo19817387tate_o )
= ( A = bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(49,axiom,
! [A: pname > pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_pname_pname @ A @ C ) )
= ( image_pname_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_insert__image) ).
thf(996,plain,
! [A: pname > pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_pname_pname @ A @ C ) )
= ( image_pname_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(438,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ C ) ) )
= ( finite1625599783_state @ ( minus_2056855718tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_finite__Diff__insert) ).
thf(2284,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ ( minus_2056855718tate_o @ A @ ( insert528405184_state @ B @ C ) ) )
= ( finite1625599783_state @ ( minus_2056855718tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(333,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( finite1625599783_state @ A )
=> ( finite1625599783_state @ ( semila1122118281tate_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_finite__UnI) ).
thf(1933,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( finite1625599783_state @ A )
=> ( finite1625599783_state @ ( semila1122118281tate_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(204,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] :
( ( image_1116629049_state @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1122118281tate_o @ ( image_1116629049_state @ A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_image__Un) ).
thf(1492,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] :
( ( image_1116629049_state @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1122118281tate_o @ ( image_1116629049_state @ A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(239,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ C @ A ) @ ( semila1780557381name_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_sup__mono) ).
thf(1603,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ C @ A ) @ ( semila1780557381name_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(640,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( semila1673364395name_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_Int__insert__right__if0) ).
thf(2955,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( semila1673364395name_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(424,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( member451959335_state @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_UnI2) ).
thf(2246,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( member451959335_state @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(466,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( semila1780557381name_o @ ( insert_pname @ A @ bot_bot_pname_o ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_insert__is__Un) ).
thf(2378,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( semila1780557381name_o @ ( insert_pname @ A @ bot_bot_pname_o ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(622,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_insert__commute) ).
thf(2896,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(818,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ ( insert528405184_state @ A @ B ) @ ( insert528405184_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_insert__mono) ).
thf(3586,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ ( insert528405184_state @ A @ B ) @ ( insert528405184_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(620,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ A )
& ( member451959335_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_Int__def) ).
thf(2871,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ B )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ A )
& ( member451959335_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(148,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_insert__not__empty) ).
thf(1317,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1318,plain,
~ ? [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= bot_bot_pname_o ),
inference(miniscope,[status(thm)],[1317]) ).
thf(1319,plain,
! [B: pname > $o,A: pname] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
inference(cnf,[status(esa)],[1318]) ).
thf(1320,plain,
! [B: pname > $o,A: pname] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
inference(lifteq,[status(thm)],[1319]) ).
thf(4509,plain,
! [B: pname > $o,A: pname] :
( ( insert_pname @ A @ B )
!= ( ^ [C: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1320,2398]) ).
thf(862,plain,
! [C: pname > $o,B: pname,A: pname > $o] :
( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) ) )
= ( finite_finite_pname @ ( minus_minus_pname_o @ A @ C ) ) ),
inference(cnf,[status(esa)],[861]) ).
thf(863,plain,
! [C: pname > $o,B: pname,A: pname > $o] :
( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) ) )
= ( finite_finite_pname @ ( minus_minus_pname_o @ A @ C ) ) ),
inference(lifteq,[status(thm)],[862]) ).
thf(103,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ! [D: hoare_1708887482_state > $o,E: hoare_1708887482_state > $o,F: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ D @ ( semila129691299tate_o @ E @ F ) )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ D @ E ) @ ( semila1122118281tate_o @ D @ F ) ) )
=> ( ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_distrib__imp2) ).
thf(1175,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ! [D: hoare_1708887482_state > $o,E: hoare_1708887482_state > $o,F: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ D @ ( semila129691299tate_o @ E @ F ) )
= ( semila129691299tate_o @ ( semila1122118281tate_o @ D @ E ) @ ( semila1122118281tate_o @ D @ F ) ) )
=> ( ( semila129691299tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(320,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_le__inf__iff) ).
thf(1877,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(540,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_set__mp) ).
thf(2610,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(858,plain,
! [C: ( pname > $o ) > $o,B: hoare_1708887482_state > $o,A: hoare_1708887482_state > pname > $o] :
( ~ ( finite297249702name_o @ C )
| ~ ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) )
| ( finite1625599783_state @ ( sk2 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[856]) ).
thf(381,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
=> ( ord_le777019615tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_order__eq__refl) ).
thf(2111,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
=> ( ord_le777019615tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(590,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_subset__insertI2) ).
thf(2780,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(698,axiom,
! [A: state > state > $o,B: hoare_1708887482_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ C @ D @ E ) @ bot_bo19817387tate_o ) )
=> ( ! [F: state,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ A @ D @ E ) @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_conseq1) ).
thf(3165,plain,
! [A: state > state > $o,B: hoare_1708887482_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ C @ D @ E ) @ bot_bo19817387tate_o ) )
=> ( ! [F: state,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ A @ D @ E ) @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(848,plain,
! [C: pname > $o,B: pname > $o,A: pname] :
( ~ ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
| ~ ( member_pname @ A @ C ) ),
inference(cnf,[status(esa)],[847]) ).
thf(774,axiom,
! [A: pname > option_com] :
( ( ( dom_pname_com @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
( ( A @ B )
= none_com ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_dom__eq__empty__conv) ).
thf(3451,plain,
! [A: pname > option_com] :
( ( ( dom_pname_com @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
( ( A @ B )
= none_com ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(621,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ! [C: pname] : ( A @ ( insert_pname @ C @ bot_bot_pname_o ) )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( D != bot_bot_pname_o )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_finite__ne__induct) ).
thf(2874,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ! [C: pname] : ( A @ ( insert_pname @ C @ bot_bot_pname_o ) )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( D != bot_bot_pname_o )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(26,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_792_folding__one_Oremove) ).
thf(915,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(783,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state,D: hoare_1708887482_state] :
( ( ( insert528405184_state @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
= ( insert528405184_state @ C @ ( insert528405184_state @ D @ bot_bo19817387tate_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_doubleton__eq__iff) ).
thf(3483,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state,D: hoare_1708887482_state] :
( ( ( insert528405184_state @ A @ ( insert528405184_state @ B @ bot_bo19817387tate_o ) )
= ( insert528405184_state @ C @ ( insert528405184_state @ D @ bot_bo19817387tate_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(436,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_Un__absorb2) ).
thf(2278,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(647,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_Un__absorb) ).
thf(2974,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(567,axiom,
! [A: com > pname,B: com,C: com > $o] :
( ( member_com @ B @ C )
=> ( member_pname @ ( A @ B ) @ ( image_com_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_imageI) ).
thf(2710,plain,
! [A: com > pname,B: com,C: com > $o] :
( ( member_com @ B @ C )
=> ( member_pname @ ( A @ B ) @ ( image_com_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',fact_767_evalc_OSemi) ).
thf(2129,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)],[387]) ).
thf(456,axiom,
! [A: com] :
( ( some_com @ A )
!= none_com ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1109_option_Osimps_I3_J) ).
thf(2343,plain,
! [A: com] :
( ( some_com @ A )
!= none_com ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(430,axiom,
! [A: pname,B: option_pname] :
( ( member_pname @ A @ ( set_pname @ B ) )
= ( B
= ( some_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_elem__set) ).
thf(2261,plain,
! [A: pname,B: option_pname] :
( ( member_pname @ A @ ( set_pname @ B ) )
= ( B
= ( some_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(276,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( B @ A )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_predicate1D) ).
thf(1731,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( B @ A )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(665,axiom,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ bot_bo19817387tate_o @ A )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_empty__Diff) ).
thf(3034,plain,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ bot_bo19817387tate_o @ A )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(477,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_inf__sup__aci_I7_J) ).
thf(2410,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(150,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( ( minus_2056855718tate_o @ C @ ( minus_2056855718tate_o @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_double__diff) ).
thf(1325,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( ( minus_2056855718tate_o @ C @ ( minus_2056855718tate_o @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(828,axiom,
! [A: option1624383643_state] :
( ( ( set_Ho525251890_state @ A )
= bot_bo19817387tate_o )
= ( A = none_H1106584047_state ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_set__empty__eq) ).
thf(3614,plain,
! [A: option1624383643_state] :
( ( ( set_Ho525251890_state @ A )
= bot_bo19817387tate_o )
= ( A = none_H1106584047_state ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(192,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o
@ ^ [C: pname] : ( member_pname @ C @ A )
@ ^ [C: pname] : ( member_pname @ C @ B ) )
= ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_pred__subset__eq) ).
thf(1460,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o
@ ^ [C: pname] : ( member_pname @ C @ A )
@ ^ [C: pname] : ( member_pname @ C @ B ) )
= ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(548,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( image_1509414295_pname @ A @ B ) @ ( image_1509414295_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_image__mono) ).
thf(2647,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( image_1509414295_pname @ A @ B ) @ ( image_1509414295_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(694,axiom,
! [A: hoare_1708887482_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_1116629049_state
@ ^ [D: pname] : A
@ C )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_image__constant) ).
thf(3150,plain,
! [A: hoare_1708887482_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_1116629049_state
@ ^ [D: pname] : A
@ C )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(610,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ B @ C ) ) @ ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_distrib__sup__le) ).
thf(2842,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ B @ C ) ) @ ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(25,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( minus_minus_pname_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1673364395name_o @ ( minus_minus_pname_o @ A @ B ) @ ( minus_minus_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_868_Diff__Un) ).
thf(912,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( minus_minus_pname_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1673364395name_o @ ( minus_minus_pname_o @ A @ B ) @ ( minus_minus_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(474,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( insert528405184_state @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_Int__insert__right__if1) ).
thf(2401,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( insert528405184_state @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(607,axiom,
! [A: pname > hoare_1708887482_state > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1329924456tate_o @ ( image_425134806tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(2835,plain,
! [A: pname > hoare_1708887482_state > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1329924456tate_o @ ( image_425134806tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(375,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( member451959335_state @ A @ B )
=> ( ( ( ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= bot_bo19817387tate_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
!= bot_bo19817387tate_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_folding__one_Oremove) ).
thf(2086,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( member451959335_state @ A @ B )
=> ( ( ( ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= bot_bo19817387tate_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
!= bot_bo19817387tate_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(46,axiom,
! [A: com > $o] :
( ( bot_bot_com_o
= ( collect_com @ A ) )
= ( ! [B: com] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_empty__Collect__eq) ).
thf(986,plain,
! [A: com > $o] :
( ( bot_bot_com_o
= ( collect_com @ A ) )
= ( ! [B: com] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(660,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_finite__subset) ).
thf(3016,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(534,axiom,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite_finite_pname @ ( image_pname_o_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(2592,plain,
! [A: ( pname > $o ) > pname,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite_finite_pname @ ( image_pname_o_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(199,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( finite1625599783_state @ B )
=> ( finite1625599783_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_finite__subset) ).
thf(1477,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( finite1625599783_state @ B )
=> ( finite1625599783_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(444,axiom,
! [A: pname] :
( ( the_pname_1 @ ( some_pname @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_the_Osimps) ).
thf(2303,plain,
! [A: pname] :
( ( the_pname_1 @ ( some_pname @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(227,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_sup__absorb1) ).
thf(1562,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(801,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( hoare_90032982_state @ B @ ( insert528405184_state @ C @ bot_bo19817387tate_o ) )
=> ( ( hoare_90032982_state @ B @ A )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).
thf(3539,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( hoare_90032982_state @ B @ ( insert528405184_state @ C @ bot_bo19817387tate_o ) )
=> ( ( hoare_90032982_state @ B @ A )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(586,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1673364395name_o @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_sup__inf__absorb) ).
thf(2770,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1673364395name_o @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(45,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ B ) )
= ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_finite__Diff2) ).
thf(983,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( minus_minus_pname_o @ A @ B ) )
= ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(39,axiom,
! [A: ( hoare_1708887482_state > $o ) > pname,B: ( hoare_1708887482_state > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_2051418740_pname @ A @ B ) )
=> ? [D: ( hoare_1708887482_state > $o ) > $o] :
( ( ord_le1728773982te_o_o @ D @ B )
& ( finite1329924456tate_o @ D )
& ( C
= ( image_2051418740_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_finite__subset__image) ).
thf(959,plain,
! [A: ( hoare_1708887482_state > $o ) > pname,B: ( hoare_1708887482_state > $o ) > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_2051418740_pname @ A @ B ) )
=> ? [D: ( hoare_1708887482_state > $o ) > $o] :
( ( ord_le1728773982te_o_o @ D @ B )
& ( finite1329924456tate_o @ D )
& ( C
= ( image_2051418740_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(399,axiom,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_subset__insertI) ).
thf(2171,plain,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(65,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_DiffD1) ).
thf(1044,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(126,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_ord__le__eq__trans) ).
thf(1245,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(187,axiom,
! [A: com,B: option_com] :
( ( member_com @ A @ ( set_com @ B ) )
= ( B
= ( some_com @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_elem__set) ).
thf(1445,plain,
! [A: com,B: option_com] :
( ( member_com @ A @ ( set_com @ B ) )
= ( B
= ( some_com @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(217,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A @ C ) @ ( minus_2056855718tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_Un__Diff) ).
thf(1528,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A @ C ) @ ( minus_2056855718tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(367,axiom,
! [A: hoare_1708887482_state > $o,B: pname > hoare_1708887482_state,C: pname > $o] :
( ( ord_le777019615tate_o @ A @ ( image_1116629049_state @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_1116629049_state @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_subset__image__iff) ).
thf(2064,plain,
! [A: hoare_1708887482_state > $o,B: pname > hoare_1708887482_state,C: pname > $o] :
( ( ord_le777019615tate_o @ A @ ( image_1116629049_state @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_1116629049_state @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(463,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_1509414295_pname @ A @ C ) )
= ( image_1509414295_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_insert__image) ).
thf(2369,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_1509414295_pname @ A @ C ) )
= ( image_1509414295_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(543,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_xt1_I5_J) ).
thf(2633,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(745,axiom,
! [A: hoare_1708887482_state > $o,B: com] :
( hoare_1160767572gleton
=> ( ( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [C: state,D: state] :
! [E: state] :
( ( evalc @ B @ D @ E )
=> ( C = E ) )
@ B
@ fequal_state )
@ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ B ) @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_757_MGT__alternD) ).
thf(3363,plain,
! [A: hoare_1708887482_state > $o,B: com] :
( hoare_1160767572gleton
=> ( ( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [C: state,D: state] :
! [E: state] :
( ( evalc @ B @ D @ E )
=> ( C = E ) )
@ B
@ fequal_state )
@ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ B ) @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(274,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_pname @ ( collect_pname @ A ) )
& ( finite_finite_pname @ ( collect_pname @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_finite__Collect__disjI) ).
thf(1726,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_pname @ ( collect_pname @ A ) )
& ( finite_finite_pname @ ( collect_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(163,axiom,
! [A: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,B: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ B )
=> ( finite1625599783_state @ ( image_27005066_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(1364,plain,
! [A: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,B: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ B )
=> ( finite1625599783_state @ ( image_27005066_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(792,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ bot_bo19817387tate_o )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_Int__empty__right) ).
thf(3512,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ bot_bo19817387tate_o )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(702,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( A @ bot_bo19817387tate_o )
=> ( ! [C: hoare_1708887482_state,D: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ D )
=> ( ~ ( member451959335_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert528405184_state @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_finite__induct) ).
thf(3178,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( A @ bot_bo19817387tate_o )
=> ( ! [C: hoare_1708887482_state,D: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ D )
=> ( ~ ( member451959335_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert528405184_state @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(396,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ( member451959335_state @ B @ C )
=> ( ( minus_2056855718tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( minus_2056855718tate_o @ A @ C ) ) )
& ( ~ ( member451959335_state @ B @ C )
=> ( ( minus_2056855718tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( insert528405184_state @ B @ ( minus_2056855718tate_o @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_insert__Diff__if) ).
thf(2156,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ( member451959335_state @ B @ C )
=> ( ( minus_2056855718tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( minus_2056855718tate_o @ A @ C ) ) )
& ( ~ ( member451959335_state @ B @ C )
=> ( ( minus_2056855718tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( insert528405184_state @ B @ ( minus_2056855718tate_o @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(3824,plain,
( ( top_top_pname_o @ sk140 )
| ( bot_bot_pname_o @ sk140 ) ),
inference(bool_ext,[status(thm)],[3821]) ).
thf(3876,plain,
( ( top_top_pname_o @ sk140 )
| bot_bot_o ),
inference(rewrite,[status(thm)],[3824,2398]) ).
thf(268,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_rev__predicate1D) ).
thf(1694,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(561,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_order__trans) ).
thf(2693,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(651,axiom,
! [A: com,B: com > $o] :
( ( B = bot_bot_com_o )
=> ~ ( member_com @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_equals0D) ).
thf(2984,plain,
! [A: com,B: com > $o] :
( ( B = bot_bot_com_o )
=> ~ ( member_com @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(301,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( member451959335_state @ B @ ( semila1122118281tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_UnI1) ).
thf(1805,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( member451959335_state @ B @ ( semila1122118281tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(600,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_inf__absorb2) ).
thf(2816,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(639,axiom,
! [A: hoare_1708887482_state,B: pname > hoare_1708887482_state,C: pname > $o] :
( ( member451959335_state @ A @ ( image_1116629049_state @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_image__iff) ).
thf(2952,plain,
! [A: hoare_1708887482_state,B: pname > hoare_1708887482_state,C: pname > $o] :
( ( member451959335_state @ A @ ( image_1116629049_state @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(99,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ C @ A ) @ ( semila1780557381name_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_Un__mono) ).
thf(1166,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ C @ A ) @ ( semila1780557381name_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(113,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ A )
=> ( ( ( semila1673364395name_o @ B @ A )
!= bot_bot_pname_o )
=> ( ( C @ ( D @ ( semila1780557381name_o @ B @ A ) ) @ ( D @ ( semila1673364395name_o @ B @ A ) ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_folding__one_Ounion__inter) ).
thf(1203,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ A )
=> ( ( ( semila1673364395name_o @ B @ A )
!= bot_bot_pname_o )
=> ( ( C @ ( D @ ( semila1780557381name_o @ B @ A ) ) @ ( D @ ( semila1673364395name_o @ B @ A ) ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(195,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ ( semila1780557381name_o @ A @ B ) )
= ( ( finite_finite_pname @ A )
& ( finite_finite_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_finite__Un) ).
thf(1467,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ ( semila1780557381name_o @ A @ B ) )
= ( ( finite_finite_pname @ A )
& ( finite_finite_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(550,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila1122118281tate_o @ ( collec1568722789_state @ A ) @ ( collec1568722789_state @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_Collect__disj__eq) ).
thf(2652,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila1122118281tate_o @ ( collec1568722789_state @ A ) @ ( collec1568722789_state @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(330,axiom,
! [A: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,B: ( hoare_1708887482_state > $o ) > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le777019615tate_o @ C @ ( image_27005066_state @ A @ B ) )
=> ? [D: ( hoare_1708887482_state > $o ) > $o] :
( ( ord_le1728773982te_o_o @ D @ B )
& ( finite1329924456tate_o @ D )
& ( C
= ( image_27005066_state @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_finite__subset__image) ).
thf(1905,plain,
! [A: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,B: ( hoare_1708887482_state > $o ) > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le777019615tate_o @ C @ ( image_27005066_state @ A @ B ) )
=> ? [D: ( hoare_1708887482_state > $o ) > $o] :
( ( ord_le1728773982te_o_o @ D @ B )
& ( finite1329924456tate_o @ D )
& ( C
= ( image_27005066_state @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(507,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_1509414295_pname @ A @ B ) )
=> ? [D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ B )
& ( finite1625599783_state @ D )
& ( C
= ( image_1509414295_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_finite__subset__image) ).
thf(2503,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_1509414295_pname @ A @ B ) )
=> ? [D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ B )
& ( finite1625599783_state @ D )
& ( C
= ( image_1509414295_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(72,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila129691299tate_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_inf__absorb2) ).
thf(1081,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila129691299tate_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(156,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_sup__ge1) ).
thf(1340,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(722,axiom,
( ord_le777019615tate_o @ fa
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) )
@ ( dom_pname_com @ body ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(3278,plain,
( ord_le777019615tate_o @ fa
@ ( image_1116629049_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) )
@ ( dom_pname_com @ body ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(41,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_DiffE) ).
thf(968,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(531,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( semila1122118281tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_inf__sup__aci_I5_J) ).
thf(2582,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ B )
= ( semila1122118281tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(352,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o,C: pname > hoare_1708887482_state,D: pname > $o] :
? [E: pname > $o] :
( ( ord_less_eq_pname_o @ E @ D )
& ! [F: pname] :
( ( member_pname @ F @ E )
=> ~ ( member_pname @ F @ ( image_1509414295_pname @ A @ ( minus_2056855718tate_o @ B @ ( image_1116629049_state @ C @ E ) ) ) ) )
& ? [F: pname > hoare_1708887482_state] :
( ! [G: pname] :
( ( member_pname @ G @ E )
=> ( ( F @ G )
= ( C @ G ) ) )
& ! [G: pname] :
( ( member_pname @ G @ ( minus_minus_pname_o @ D @ E ) )
=> ( ( member451959335_state @ ( F @ G ) @ ( minus_2056855718tate_o @ B @ ( image_1116629049_state @ C @ E ) ) )
& ( G
= ( A @ ( F @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_Cantor__Bernstein__aux) ).
thf(2005,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o,C: pname > hoare_1708887482_state,D: pname > $o] :
? [E: pname > $o] :
( ( ord_less_eq_pname_o @ E @ D )
& ! [F: pname] :
( ( member_pname @ F @ E )
=> ~ ( member_pname @ F @ ( image_1509414295_pname @ A @ ( minus_2056855718tate_o @ B @ ( image_1116629049_state @ C @ E ) ) ) ) )
& ? [F: pname > hoare_1708887482_state] :
( ! [G: pname] :
( ( member_pname @ G @ E )
=> ( ( F @ G )
= ( C @ G ) ) )
& ! [G: pname] :
( ( member_pname @ G @ ( minus_minus_pname_o @ D @ E ) )
=> ( ( member451959335_state @ ( F @ G ) @ ( minus_2056855718tate_o @ B @ ( image_1116629049_state @ C @ E ) ) )
& ( G
= ( A @ ( F @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(3881,plain,
( ( top_top_pname_o @ sk140 )
!= bot_bot_o ),
inference(rewrite,[status(thm)],[3821,2398]) ).
thf(144,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_Un__absorb1) ).
thf(1304,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila1122118281tate_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(765,axiom,
! [A: com,B: state > state > $o,C: hoare_1708887482_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ D @ E @ F ) @ bot_bo19817387tate_o ) )
=> ( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ F @ A @ B ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ D @ ( semi @ E @ A ) @ B ) @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_Comp) ).
thf(3427,plain,
! [A: com,B: state > state > $o,C: hoare_1708887482_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ D @ E @ F ) @ bot_bo19817387tate_o ) )
=> ( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ F @ A @ B ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ D @ ( semi @ E @ A ) @ B ) @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(813,axiom,
finite1625599783_state @ bot_bo19817387tate_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite_OemptyI) ).
thf(3576,plain,
finite1625599783_state @ bot_bo19817387tate_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(34,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ B ) @ B )
= ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_Un__Diff__cancel2) ).
thf(944,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ B ) @ B )
= ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(346,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_inf__sup__ord_I2_J) ).
thf(1990,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(558,axiom,
! [A: pname] :
( ( collect_pname
@ ^ [B: pname] : ( B = A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_singleton__conv) ).
thf(2684,plain,
! [A: pname] :
( ( collect_pname
@ ^ [B: pname] : ( B = A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(428,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( B @ C )
=> ( semila1122118281tate_o @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_sup1I1) ).
thf(2256,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( B @ C )
=> ( semila1122118281tate_o @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(524,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( semila1673364395name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_Int__insert__left__if0) ).
thf(2564,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( semila1673364395name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(728,axiom,
! [A: hoare_1708887482_state] :
( ( bot_bo19817387tate_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_bot__apply) ).
thf(3292,plain,
! [A: hoare_1708887482_state] :
( ( bot_bo19817387tate_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(623,axiom,
! [A: com] :
( ( bot_bot_com_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_bot__fun__def) ).
thf(2899,plain,
! [A: com] :
( ( bot_bot_com_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(225,axiom,
! [A: pname > hoare_1708887482_state,B: hoare_1708887482_state,C: pname,D: pname > $o] :
( ( ( member_pname @ C @ D )
=> ( ( image_1116629049_state @ ( fun_up1986763201_state @ A @ C @ B ) @ D )
= ( insert528405184_state @ B @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ D @ ( insert_pname @ C @ bot_bot_pname_o ) ) ) ) ) )
& ( ~ ( member_pname @ C @ D )
=> ( ( image_1116629049_state @ ( fun_up1986763201_state @ A @ C @ B ) @ D )
= ( image_1116629049_state @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_fun__upd__image) ).
thf(1551,plain,
! [A: pname > hoare_1708887482_state,B: hoare_1708887482_state,C: pname,D: pname > $o] :
( ( ( member_pname @ C @ D )
=> ( ( image_1116629049_state @ ( fun_up1986763201_state @ A @ C @ B ) @ D )
= ( insert528405184_state @ B @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ D @ ( insert_pname @ C @ bot_bot_pname_o ) ) ) ) ) )
& ( ~ ( member_pname @ C @ D )
=> ( ( image_1116629049_state @ ( fun_up1986763201_state @ A @ C @ B ) @ D )
= ( image_1116629049_state @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(282,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( semila1780557381name_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_UnI1) ).
thf(1748,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( semila1780557381name_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(754,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
=> ~ ! [C: hoare_1708887482_state > $o] :
( ( B
= ( insert528405184_state @ A @ C ) )
=> ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_Set_Oset__insert) ).
thf(3391,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
=> ~ ! [C: hoare_1708887482_state > $o] :
( ( B
= ( insert528405184_state @ A @ C ) )
=> ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(366,axiom,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_predicate1I) ).
thf(2060,plain,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(392,axiom,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
= ( ( A = bot_bot_pname_o )
| ? [B: pname > $o,C: pname] :
( ( A
= ( insert_pname @ C @ B ) )
& ( finite_finite_pname @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_finite_Osimps) ).
thf(2143,plain,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
= ( ( A = bot_bot_pname_o )
| ? [B: pname > $o,C: pname] :
( ( A
= ( insert_pname @ C @ B ) )
& ( finite_finite_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(511,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_sup__least) ).
thf(2518,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(602,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_inf__sup__ord_I4_J) ).
thf(2821,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ ( semila1122118281tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(571,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( finite1625599783_state @ B )
| ( finite1625599783_state @ A ) )
=> ( finite1625599783_state @ ( semila129691299tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_finite__Int) ).
thf(2720,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( finite1625599783_state @ B )
| ( finite1625599783_state @ A ) )
=> ( finite1625599783_state @ ( semila129691299tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(218,axiom,
! [A: pname > $o,B: pname > $o] :
( ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila1673364395name_o @ ( collect_pname @ A ) @ ( collect_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_Collect__conj__eq) ).
thf(1531,plain,
! [A: pname > $o,B: pname > $o] :
( ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila1673364395name_o @ ( collect_pname @ A ) @ ( collect_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(525,axiom,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
=> ( finite297249702name_o
@ ( collect_pname_o
@ ^ [B: pname > $o] : ( ord_less_eq_pname_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__Collect__subsets) ).
thf(2567,plain,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
=> ( finite297249702name_o
@ ( collect_pname_o
@ ^ [B: pname > $o] : ( ord_less_eq_pname_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(312,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_inf__le2) ).
thf(1845,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(569,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_Un__absorb2) ).
thf(2715,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(213,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ C ) @ ( semila1673364395name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_Int__Un__distrib2) ).
thf(1516,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ C ) @ ( semila1673364395name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(617,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_order__antisym__conv) ).
thf(2863,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(648,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_sup__inf__absorb) ).
thf(2977,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila129691299tate_o @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(242,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le777019615tate_o @ C @ ( image_1116629049_state @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_1116629049_state @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_finite__subset__image) ).
thf(1611,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le777019615tate_o @ C @ ( image_1116629049_state @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_1116629049_state @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(465,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_sup__idem) ).
thf(2375,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(673,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
=> ( ( insert528405184_state @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_insert__absorb) ).
thf(3082,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
=> ( ( insert528405184_state @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(406,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila1122118281tate_o @ B @ C ) )
=> ( ~ ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_UnE) ).
thf(2192,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila1122118281tate_o @ B @ C ) )
=> ( ~ ( member451959335_state @ A @ B )
=> ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(240,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( ( some_H1974565227_state @ A )
= ( some_H1974565227_state @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_option_Oinject) ).
thf(1605,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( ( some_H1974565227_state @ A )
= ( some_H1974565227_state @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(716,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
=> ? [C: hoare_1708887482_state > $o] :
( ( B
= ( insert528405184_state @ A @ C ) )
& ~ ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_750_mk__disjoint__insert) ).
thf(3260,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
=> ? [C: hoare_1708887482_state > $o] :
( ( B
= ( insert528405184_state @ A @ C ) )
& ~ ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(37,axiom,
! [A: pname > $o,B: pname > pname,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ! [E: pname,F: pname] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_pname_pname @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_721_folding__one__idem_Ohom__commute) ).
thf(954,plain,
! [A: pname > $o,B: pname > pname,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ! [E: pname,F: pname] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_pname_pname @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(128,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_Un__Int__distrib) ).
thf(1252,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(284,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_in__mono) ).
thf(1753,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(476,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( semila1673364395name_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_Int__insert__left__if1) ).
thf(2407,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( semila1673364395name_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(133,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_le__supI2) ).
thf(1267,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(826,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ B @ C )
=> ( ~ ( member451959335_state @ B @ A )
=> ( ( ( insert528405184_state @ B @ C )
= ( insert528405184_state @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_insert__ident) ).
thf(3608,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ B @ C )
=> ( ~ ( member451959335_state @ B @ A )
=> ( ( ( insert528405184_state @ B @ C )
= ( insert528405184_state @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(120,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( semila129691299tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_Int__insert__right__if0) ).
thf(1230,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( semila129691299tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(613,axiom,
! [A: state,B: state] :
( ( evalc @ skip @ A @ B )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_evalc__elim__cases_I1_J) ).
thf(2850,plain,
! [A: state,B: state] :
( ( evalc @ skip @ A @ B )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(202,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_order__eq__refl) ).
thf(1484,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(579,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ( finite1625599783_state @ A )
=> ( ( A != bot_bo19817387tate_o )
=> ( ( ( semila129691299tate_o @ B @ A )
= bot_bo19817387tate_o )
=> ( ( D @ ( semila1122118281tate_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_folding__one_Ounion__disjoint) ).
thf(2747,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ( finite1625599783_state @ A )
=> ( ( A != bot_bo19817387tate_o )
=> ( ( ( semila129691299tate_o @ B @ A )
= bot_bo19817387tate_o )
=> ( ( D @ ( semila1122118281tate_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(526,axiom,
! [A: pname > com,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_com @ ( A @ B ) @ ( image_pname_com @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_imageI) ).
thf(2569,plain,
! [A: pname > com,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_com @ ( A @ B ) @ ( image_pname_com @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(773,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( insert528405184_state @ A @ B ) @ C )
= ( insert528405184_state @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_Un__insert__left) ).
thf(3448,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( insert528405184_state @ A @ B ) @ C )
= ( insert528405184_state @ A @ ( semila1122118281tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(376,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_order__antisym) ).
thf(2092,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(304,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_le__supI) ).
thf(1813,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ C )
=> ( ord_le777019615tate_o @ ( semila1122118281tate_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(107,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_Un__absorb1) ).
thf(1188,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(415,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila129691299tate_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_Int__absorb2) ).
thf(2219,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( semila129691299tate_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(329,axiom,
! [A: pname > $o,B: com,C: pname > com,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_com @ B @ ( image_pname_com @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_image__eqI) ).
thf(1901,plain,
! [A: pname > $o,B: com,C: pname > com,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_com @ B @ ( image_pname_com @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(256,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_sup__assoc) ).
thf(1658,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(831,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ bot_bo19817387tate_o )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_inf__bot__right) ).
thf(3623,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ A @ bot_bo19817387tate_o )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(116,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > option1624383643_state] :
( ( member451959335_state @ A @ ( dom_Ho1703271284_state @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( B @ A )
= ( some_H1974565227_state @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_domD) ).
thf(1218,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > option1624383643_state] :
( ( member451959335_state @ A @ ( dom_Ho1703271284_state @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( B @ A )
= ( some_H1974565227_state @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(345,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_Un__left__commute) ).
thf(1987,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(271,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ C ) @ ( semila1673364395name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_inf__sup__distrib2) ).
thf(1716,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ C ) @ ( semila1673364395name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(3035,plain,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ bot_bo19817387tate_o @ A )
= bot_bo19817387tate_o ),
inference(cnf,[status(esa)],[3034]) ).
thf(3036,plain,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ bot_bo19817387tate_o @ A )
= bot_bo19817387tate_o ),
inference(lifteq,[status(thm)],[3035]) ).
thf(4549,plain,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o
@ ^ [B: hoare_1708887482_state] : bot_bot_o
@ A )
= ( ^ [B: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[3036,3234]) ).
thf(839,plain,
! [B: pname,A: pname] :
( ~ ( fequal_pname @ A @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[838]) ).
thf(840,plain,
! [B: pname,A: pname] :
( ( A = B )
| ~ ( fequal_pname @ A @ B ) ),
inference(lifteq,[status(thm)],[839]) ).
thf(295,axiom,
! [A: pname > $o,B: hoare_1708887482_state > pname,C: hoare_1708887482_state > $o] :
( ( ord_less_eq_pname_o @ A @ ( image_1509414295_pname @ B @ C ) )
= ( ? [D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ C )
& ( A
= ( image_1509414295_pname @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_subset__image__iff) ).
thf(1785,plain,
! [A: pname > $o,B: hoare_1708887482_state > pname,C: hoare_1708887482_state > $o] :
( ( ord_less_eq_pname_o @ A @ ( image_1509414295_pname @ B @ C ) )
= ( ? [D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ D @ C )
& ( A
= ( image_1509414295_pname @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(287,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_inf__sup__ord_I3_J) ).
thf(1763,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(564,axiom,
! [A: pname,B: pname > $o] :
( ~ ( member_pname @ A @ B )
=> ( ( minus_minus_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ bot_bot_pname_o ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1033_Diff__insert__absorb) ).
thf(2701,plain,
! [A: pname,B: pname > $o] :
( ~ ( member_pname @ A @ B )
=> ( ( minus_minus_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ bot_bot_pname_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(520,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_sup_Ocommute) ).
thf(2545,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(735,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( hoare_90032982_state @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_asm) ).
thf(3329,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( hoare_90032982_state @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(360,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_UnI2) ).
thf(2044,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(222,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_Int__absorb2) ).
thf(1543,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(328,axiom,
! [A: option_com] :
( ( ( set_com @ A )
= bot_bot_com_o )
= ( A = none_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_set__empty__eq) ).
thf(1898,plain,
! [A: option_com] :
( ( ( set_com @ A )
= bot_bot_com_o )
= ( A = none_com ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(519,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1625599783_state @ ( image_1116629049_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(2543,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1625599783_state @ ( image_1116629049_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(117,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] : ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ ( image_1116629049_state @ A @ B ) @ ( image_1116629049_state @ A @ C ) ) @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_image__diff__subset) ).
thf(1221,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] : ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ ( image_1116629049_state @ A @ B ) @ ( image_1116629049_state @ A @ C ) ) @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(340,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ~ ( member451959335_state @ B @ A )
=> ( member451959335_state @ B @ ( minus_2056855718tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_811_DiffI) ).
thf(1972,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ~ ( member451959335_state @ B @ A )
=> ( member451959335_state @ B @ ( minus_2056855718tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(208,axiom,
! [A: state,B: state] :
( ( A != B )
| ( fequal_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Ostate_T) ).
thf(1504,plain,
! [A: state,B: state] :
( ( A != B )
| ( fequal_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(76,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_897_inf__absorb1) ).
thf(1094,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(636,axiom,
! [A: pname > $o,B: ( hoare_1708887482_state > $o ) > pname,C: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_2051418740_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_finite__surj) ).
thf(2939,plain,
! [A: pname > $o,B: ( hoare_1708887482_state > $o ) > pname,C: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_2051418740_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(875,plain,
! [C: pname > $o,B: pname > $o,A: pname > $o] :
( ( minus_minus_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ C ) @ ( minus_minus_pname_o @ B @ C ) ) ),
inference(cnf,[status(esa)],[874]) ).
thf(876,plain,
! [C: pname > $o,B: pname > $o,A: pname > $o] :
( ( semila1780557381name_o @ ( minus_minus_pname_o @ A @ C ) @ ( minus_minus_pname_o @ B @ C ) )
= ( minus_minus_pname_o @ ( semila1780557381name_o @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[875]) ).
thf(243,axiom,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_inf__bot__left) ).
thf(1617,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(175,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ C )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ C ) @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_Un__Int__distrib2) ).
thf(1404,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ C )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ C ) @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(161,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1780557381name_o @ A @ B )
= bot_bot_pname_o )
= ( ( A = bot_bot_pname_o )
& ( B = bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_sup__eq__bot__iff) ).
thf(1358,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1780557381name_o @ A @ B )
= bot_bot_pname_o )
= ( ( A = bot_bot_pname_o )
& ( B = bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(653,axiom,
! [A: pname,B: pname] :
( ( ( some_pname @ A )
= ( some_pname @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_option_Oinject) ).
thf(2992,plain,
! [A: pname,B: pname] :
( ( ( some_pname @ A )
= ( some_pname @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(343,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ! [D: pname] :
( ( member_pname @ D @ ( semila1780557381name_o @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: pname] :
( ( member_pname @ D @ B )
=> ( A @ D ) )
& ! [D: pname] :
( ( member_pname @ D @ C )
=> ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_ball__Un) ).
thf(1981,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ! [D: pname] :
( ( member_pname @ D @ ( semila1780557381name_o @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: pname] :
( ( member_pname @ D @ B )
=> ( A @ D ) )
& ! [D: pname] :
( ( member_pname @ D @ C )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(3499,plain,
( ( set_Ho525251890_state @ none_H1106584047_state )
= bot_bo19817387tate_o ),
inference(lifteq,[status(thm)],[3498]) ).
thf(4143,plain,
( ( set_Ho525251890_state @ none_H1106584047_state )
= ( ^ [A: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[3499,3234]) ).
thf(13,axiom,
! [A: com > $o] :
( ( ( collect_com @ A )
= bot_bot_com_o )
= ( ! [B: com] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Collect__empty__eq) ).
thf(871,plain,
! [A: com > $o] :
( ( ( collect_com @ A )
= bot_bot_com_o )
= ( ! [B: com] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(872,plain,
! [A: com > $o] :
( ( ( collect_com @ A )
= bot_bot_com_o )
= ( ! [B: com] :
~ ( A @ B ) ) ),
inference(cnf,[status(esa)],[871]) ).
thf(873,plain,
! [A: com > $o] :
( ( ( collect_com @ A )
= bot_bot_com_o )
= ( ! [B: com] :
~ ( A @ B ) ) ),
inference(lifteq,[status(thm)],[872]) ).
thf(4538,plain,
! [A: com > $o] :
( ( ( collect_com @ A )
= ( ^ [B: com] : bot_bot_o ) )
= ( ! [B: com] :
~ ( A @ B ) ) ),
inference(rewrite,[status(thm)],[873,1863]) ).
thf(260,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( member_pname @ B @ A )
=> ( member_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_804_IntI) ).
thf(1670,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( member_pname @ B @ A )
=> ( member_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(299,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( B = A ) )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_insertCI) ).
thf(1797,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( B = A ) )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(795,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( semila1122118281tate_o @ A @ B )
= bot_bo19817387tate_o )
= ( ( A = bot_bo19817387tate_o )
& ( B = bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_sup__eq__bot__iff) ).
thf(3520,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( semila1122118281tate_o @ A @ B )
= bot_bo19817387tate_o )
= ( ( A = bot_bo19817387tate_o )
& ( B = bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(746,axiom,
! [A: pname > hoare_1708887482_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert528405184_state @ ( A @ B ) @ ( image_1116629049_state @ A @ C ) )
= ( image_1116629049_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_insert__image) ).
thf(3366,plain,
! [A: pname > hoare_1708887482_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert528405184_state @ ( A @ B ) @ ( image_1116629049_state @ A @ C ) )
= ( image_1116629049_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(336,axiom,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_Int__empty__left) ).
thf(1940,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(4289,plain,
( ~ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1708887482_state] : bot_bot_o
@ sk146 )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[4288]) ).
thf(817,axiom,
! [A: hoare_1708887482_state > $o,B: pname > state > state > $o,C: pname > state > state > $o,D: pname > $o] :
( ( hoare_90032982_state
@ ( semila1122118281tate_o @ A
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) )
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( the_com @ ( body @ E ) ) @ ( C @ E ) )
@ D ) )
=> ( hoare_90032982_state @ A
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_hoare__derivs_OBody) ).
thf(3584,plain,
! [A: hoare_1708887482_state > $o,B: pname > state > state > $o,C: pname > state > state > $o,D: pname > $o] :
( ( hoare_90032982_state
@ ( semila1122118281tate_o @ A
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) )
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( the_com @ ( body @ E ) ) @ ( C @ E ) )
@ D ) )
=> ( hoare_90032982_state @ A
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(809,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ A @ B )
=> ( ( minus_2056855718tate_o @ ( insert528405184_state @ A @ B ) @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1034_Diff__insert__absorb) ).
thf(3565,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ~ ( member451959335_state @ A @ B )
=> ( ( minus_2056855718tate_o @ ( insert528405184_state @ A @ B ) @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(676,axiom,
! [A: pname > hoare_1708887482_state,B: pname > hoare_1708887482_state,C: pname > $o,D: pname > $o] :
( ( C = D )
=> ( ! [E: pname] :
( ( member_pname @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( image_1116629049_state @ A @ C )
= ( image_1116629049_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_image__cong) ).
thf(3092,plain,
! [A: pname > hoare_1708887482_state,B: pname > hoare_1708887482_state,C: pname > $o,D: pname > $o] :
( ( C = D )
=> ( ! [E: pname] :
( ( member_pname @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( image_1116629049_state @ A @ C )
= ( image_1116629049_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(31,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) )
= ( minus_minus_pname_o @ ( minus_minus_pname_o @ A @ C ) @ ( insert_pname @ B @ bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_Diff__insert) ).
thf(931,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( minus_minus_pname_o @ A @ ( insert_pname @ B @ C ) )
= ( minus_minus_pname_o @ ( minus_minus_pname_o @ A @ C ) @ ( insert_pname @ B @ bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(605,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite1625599783_state @ ( image_1116629049_state @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_pigeonhole__infinite) ).
thf(2828,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite1625599783_state @ ( image_1116629049_state @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(457,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_rev__predicate1D) ).
thf(2347,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(414,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ ( collect_pname @ B ) )
| ( finite_finite_pname @ ( collect_pname @ A ) ) )
=> ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_finite__Collect__conjI) ).
thf(2215,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ ( collect_pname @ B ) )
| ( finite_finite_pname @ ( collect_pname @ A ) ) )
=> ( finite_finite_pname
@ ( collect_pname
@ ^ [C: pname] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(369,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ ( collect_pname @ C ) ) )
= ( ( member_pname @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_Int__Collect) ).
thf(2071,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ ( collect_pname @ C ) ) )
= ( ( member_pname @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(725,axiom,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ A )
= bot_bo19817387tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_Diff__cancel) ).
thf(3284,plain,
! [A: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ A )
= bot_bo19817387tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(584,axiom,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_subset__refl) ).
thf(2760,plain,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(756,axiom,
! [A: pname,B: state,C: state] :
( ( evalc @ ( body_1 @ A ) @ B @ C )
=> ( evalc @ ( the_com @ ( body @ A ) ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_evalc__elim__cases_I6_J) ).
thf(3400,plain,
! [A: pname,B: state,C: state] :
( ( evalc @ ( body_1 @ A ) @ B @ C )
=> ( evalc @ ( the_com @ ( body @ A ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(631,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( A != B )
| ( fequal224822779_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com) ).
thf(2924,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state] :
( ( A != B )
| ( fequal224822779_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(4138,plain,
! [A: hoare_1708887482_state > $o] :
( hoare_90032982_state @ A
@ ^ [B: hoare_1708887482_state] : bot_bot_o ),
inference(rewrite,[status(thm)],[3136,3234]) ).
thf(460,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,C: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ B @ C )
=> ( ( B @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_folding__one__idem_Oidem) ).
thf(2352,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,C: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ B @ C )
=> ( ( B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(73,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_sup_Oleft__commute) ).
thf(1084,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila1122118281tate_o @ B @ ( semila1122118281tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(96,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( insert528405184_state @ B @ ( semila129691299tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_Int__insert__left__if1) ).
thf(1157,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( insert528405184_state @ B @ ( semila129691299tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(149,axiom,
! [A: pname > $o] :
( ! [B: pname] :
~ ( member_pname @ B @ A )
=> ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_equals0I) ).
thf(1321,plain,
! [A: pname > $o] :
( ! [B: pname] :
~ ( member_pname @ B @ A )
=> ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(804,axiom,
! [A: pname,B: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ B ) @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MGT__BodyN) ).
thf(3548,plain,
! [A: pname,B: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ B ) @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(407,axiom,
! [A: hoare_1708887482_state,B: pname > hoare_1708887482_state,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member451959335_state @ A @ ( image_1116629049_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_rev__image__eqI) ).
thf(2194,plain,
! [A: hoare_1708887482_state,B: pname > hoare_1708887482_state,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member451959335_state @ A @ ( image_1116629049_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(20,axiom,
! [A: pname > pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_pname_pname_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_finite__subset__image) ).
thf(891,plain,
! [A: pname > pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_pname_pname_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(412,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ! [D: pname > $o,E: pname > $o,F: pname > $o] :
( ( semila1673364395name_o @ D @ ( semila1780557381name_o @ E @ F ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ D @ E ) @ ( semila1673364395name_o @ D @ F ) ) )
=> ( ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_distrib__imp1) ).
thf(2209,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ! [D: pname > $o,E: pname > $o,F: pname > $o] :
( ( semila1673364395name_o @ D @ ( semila1780557381name_o @ E @ F ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ D @ E ) @ ( semila1673364395name_o @ D @ F ) ) )
=> ( ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(578,axiom,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_com_Osimps_I12_J) ).
thf(2743,plain,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(655,axiom,
! [A: hoare_1708887482_state,B: option1624383643_state] :
( ( member451959335_state @ A @ ( set_Ho525251890_state @ B ) )
= ( B
= ( some_H1974565227_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_elem__set) ).
thf(2997,plain,
! [A: hoare_1708887482_state,B: option1624383643_state] :
( ( member451959335_state @ A @ ( set_Ho525251890_state @ B ) )
= ( B
= ( some_H1974565227_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(188,axiom,
! [A: state] : ( evalc @ skip @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_766_evalc_OSkip) ).
thf(1448,plain,
! [A: state] : ( evalc @ skip @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(740,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] : ( member451959335_state @ A @ ( insert528405184_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_insertI1) ).
thf(3346,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] : ( member451959335_state @ A @ ( insert528405184_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(731,axiom,
! [A: hoare_1708887482_state > $o,B: state > state > $o] : ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ B @ skip @ B ) @ bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_hoare__derivs_OSkip) ).
thf(3320,plain,
! [A: hoare_1708887482_state > $o,B: state > state > $o] : ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ B @ skip @ B ) @ bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(54,axiom,
! [A: pname > hoare_1708887482_state > $o,B: pname > $o,C: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ C )
=> ( ( ord_le1728773982te_o_o @ C @ ( image_425134806tate_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_425134806tate_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_finite__subset__image) ).
thf(1010,plain,
! [A: pname > hoare_1708887482_state > $o,B: pname > $o,C: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ C )
=> ( ( ord_le1728773982te_o_o @ C @ ( image_425134806tate_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_425134806tate_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(232,axiom,
! [A: hoare_1708887482_state > hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( ord_le777019615tate_o @ ( image_757158439_state @ A @ B ) @ B )
=> ( ( inj_on632008595_state @ A @ B )
=> ( ( image_757158439_state @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_endo__inj__surj) ).
thf(1575,plain,
! [A: hoare_1708887482_state > hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( ord_le777019615tate_o @ ( image_757158439_state @ A @ B ) @ B )
=> ( ( inj_on632008595_state @ A @ B )
=> ( ( image_757158439_state @ A @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(844,plain,
! [C: pname > $o,B: pname > $o,A: pname > pname] :
( ~ ( finite_finite_pname @ C )
| ~ ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
| ( finite_finite_pname @ ( sk1 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[842]) ).
thf(190,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila129691299tate_o @ ( minus_2056855718tate_o @ A @ B ) @ ( minus_2056855718tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_Diff__Un) ).
thf(1453,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( minus_2056855718tate_o @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( semila129691299tate_o @ ( minus_2056855718tate_o @ A @ B ) @ ( minus_2056855718tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(594,axiom,
! [A: pname > $o,B: pname > $o,C: ( pname > $o ) > pname > $o,D: pname > $o] :
( ( B
= ( C @ D ) )
=> ( ( ord_less_eq_pname_o @ A @ D )
=> ( ! [E: pname > $o,F: pname > $o] :
( ( ord_less_eq_pname_o @ F @ E )
=> ( ord_less_eq_pname_o @ ( C @ F ) @ ( C @ E ) ) )
=> ( ord_less_eq_pname_o @ ( C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_xt1_I15_J) ).
thf(2792,plain,
! [A: pname > $o,B: pname > $o,C: ( pname > $o ) > pname > $o,D: pname > $o] :
( ( B
= ( C @ D ) )
=> ( ( ord_less_eq_pname_o @ A @ D )
=> ( ! [E: pname > $o,F: pname > $o] :
( ( ord_less_eq_pname_o @ F @ E )
=> ( ord_less_eq_pname_o @ ( C @ F ) @ ( C @ E ) ) )
=> ( ord_less_eq_pname_o @ ( C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(302,axiom,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_subset__empty) ).
thf(1807,plain,
! [A: pname > $o] :
( ( ord_less_eq_pname_o @ A @ bot_bot_pname_o )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(566,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_sup__left__idem) ).
thf(2707,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(209,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( collect_pname @ B ) )
= ( collect_pname
@ ^ [C: pname] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_insert__Collect) ).
thf(1508,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( collect_pname @ B ) )
= ( collect_pname
@ ^ [C: pname] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(598,axiom,
! [A: com] :
~ ( member_com @ A @ bot_bot_com_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_emptyE) ).
thf(2811,plain,
! [A: com] :
~ ( member_com @ A @ bot_bot_com_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(281,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( ord_le777019615tate_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_order__antisym__conv) ).
thf(1745,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
=> ( ( ord_le777019615tate_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1936,plain,
! [A: hoare_1708887482_state > pname] :
( ( image_1509414295_pname @ A @ bot_bo19817387tate_o )
= bot_bot_pname_o ),
inference(cnf,[status(esa)],[1935]) ).
thf(1937,plain,
! [A: hoare_1708887482_state > pname] :
( ( image_1509414295_pname @ A @ bot_bo19817387tate_o )
= bot_bot_pname_o ),
inference(lifteq,[status(thm)],[1936]) ).
thf(4495,plain,
! [A: hoare_1708887482_state > pname] :
( ( image_1509414295_pname @ A
@ ^ [B: hoare_1708887482_state] : bot_bot_o )
= ( ^ [B: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1937,3234,2398]) ).
thf(736,axiom,
! [A: hoare_1708887482_state > $o,B: pname > state > state > $o,C: pname > state > state > $o,D: pname > $o] :
( ( hoare_496444244_state
@ ( semila1122118281tate_o @ A
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) )
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( the_com @ ( body @ E ) ) @ ( C @ E ) )
@ D ) )
=> ( hoare_496444244_state @ A
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_Body__sound__lemma) ).
thf(3331,plain,
! [A: hoare_1708887482_state > $o,B: pname > state > state > $o,C: pname > state > state > $o,D: pname > $o] :
( ( hoare_496444244_state
@ ( semila1122118281tate_o @ A
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) )
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( the_com @ ( body @ E ) ) @ ( C @ E ) )
@ D ) )
=> ( hoare_496444244_state @ A
@ ( image_1116629049_state
@ ^ [E: pname] : ( hoare_858012674_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(674,axiom,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ bot_bo19817387tate_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_Un__empty__right) ).
thf(3085,plain,
! [A: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ bot_bo19817387tate_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(137,axiom,
! [A: hoare_1708887482_state > hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ~ ( finite1625599783_state @ B )
=> ( ( finite1625599783_state @ ( image_757158439_state @ A @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
& ~ ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_pigeonhole__infinite) ).
thf(1276,plain,
! [A: hoare_1708887482_state > hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ~ ( finite1625599783_state @ B )
=> ( ( finite1625599783_state @ ( image_757158439_state @ A @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
& ~ ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(237,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ! [E: pname] :
( ( member_pname @ E @ C )
=> ( ( B @ E )
=> ( A @ E ) ) )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ ( collect_pname @ B ) ) @ ( semila1673364395name_o @ D @ ( collect_pname @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1072_Int__Collect__mono) ).
thf(1590,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ! [E: pname] :
( ( member_pname @ E @ C )
=> ( ( B @ E )
=> ( A @ E ) ) )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ ( collect_pname @ B ) ) @ ( semila1673364395name_o @ D @ ( collect_pname @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(652,axiom,
! [A: state > $o,B: com,C: com,D: com] :
( ( while @ A @ B )
!= ( semi @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_com_Osimps_I47_J) ).
thf(2988,plain,
! [A: state > $o,B: com,C: com,D: com] :
( ( while @ A @ B )
!= ( semi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(169,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ~ ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_IntE) ).
thf(1385,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ~ ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(615,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_Un__left__absorb) ).
thf(2855,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(250,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ C )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ C ) @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_sup__inf__distrib2) ).
thf(1639,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ C )
= ( semila1673364395name_o @ ( semila1780557381name_o @ A @ C ) @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(614,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_Un__upper1) ).
thf(2853,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(440,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( ( ord_le777019615tate_o @ A @ B )
& ( ord_le777019615tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_le__inf__iff) ).
thf(2290,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ ( semila129691299tate_o @ B @ C ) )
= ( ( ord_le777019615tate_o @ A @ B )
& ( ord_le777019615tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(426,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A @ B ) @ B )
= ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_Un__Diff__cancel2) ).
thf(2251,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A @ B ) @ B )
= ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(747,axiom,
! [A: hoare_1708887482_state > $o,B: state > state > $o,C: com,D: state > state > $o,E: $o] :
( ( E
=> ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ B @ C @ D ) @ bot_bo19817387tate_o ) ) )
=> ( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [F: state,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_constant) ).
thf(3369,plain,
! [A: hoare_1708887482_state > $o,B: state > state > $o,C: com,D: state > state > $o,E: $o] :
( ( E
=> ( hoare_90032982_state @ A @ ( insert528405184_state @ ( hoare_858012674_state @ B @ C @ D ) @ bot_bo19817387tate_o ) ) )
=> ( hoare_90032982_state @ A
@ ( insert528405184_state
@ ( hoare_858012674_state
@ ^ [F: state,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(603,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) @ ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_distrib__inf__le) ).
thf(2823,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) @ ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(539,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ A ) @ ( semila1673364395name_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_inf__mono) ).
thf(2608,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ A ) @ ( semila1673364395name_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(713,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( A @ B )
=> ( ! [C: hoare_1708887482_state,D: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ D )
=> ( ( member451959335_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_2056855718tate_o @ D @ ( insert528405184_state @ C @ bot_bo19817387tate_o ) ) ) ) ) )
=> ( A @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_finite__empty__induct) ).
thf(3235,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( A @ B )
=> ( ! [C: hoare_1708887482_state,D: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ D )
=> ( ( member451959335_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_2056855718tate_o @ D @ ( insert528405184_state @ C @ bot_bo19817387tate_o ) ) ) ) ) )
=> ( A @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(484,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_inf__le1) ).
thf(2431,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(657,axiom,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_insertI2) ).
thf(3003,plain,
! [A: pname,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( insert_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(479,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_inf__sup__distrib1) ).
thf(2416,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(638,axiom,
! [A: pname > $o,B: pname] :
( ( ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_pname @ B @ bot_bot_pname_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_Collect__conv__if) ).
thf(2944,plain,
! [A: pname > $o,B: pname] :
( ( ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_pname @ B @ bot_bot_pname_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname
@ ^ [C: pname] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(266,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_Int__absorb1) ).
thf(1689,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(473,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( member_pname @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_set__rev__mp) ).
thf(2399,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( member_pname @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(3879,plain,
( ( dom_pname_com
@ ^ [A: pname] : none_com )
= ( ^ [A: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[3345,2398]) ).
thf(408,axiom,
! [A: pname > $o,B: pname > $o,C: pname > hoare_1708887482_state,D: pname > $o] :
( ( inj_on1553129421_state @ C @ D )
=> ( ( ord_less_eq_pname_o @ B @ D )
=> ( ( ord_less_eq_pname_o @ A @ D )
=> ( ( image_1116629049_state @ C @ ( semila1673364395name_o @ B @ A ) )
= ( semila129691299tate_o @ ( image_1116629049_state @ C @ B ) @ ( image_1116629049_state @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_inj__on__image__Int) ).
thf(2198,plain,
! [A: pname > $o,B: pname > $o,C: pname > hoare_1708887482_state,D: pname > $o] :
( ( inj_on1553129421_state @ C @ D )
=> ( ( ord_less_eq_pname_o @ B @ D )
=> ( ( ord_less_eq_pname_o @ A @ D )
=> ( ( image_1116629049_state @ C @ ( semila1673364395name_o @ B @ A ) )
= ( semila129691299tate_o @ ( image_1116629049_state @ C @ B ) @ ( image_1116629049_state @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(403,axiom,
! [A: pname > $o] :
( ( bot_bot_pname_o
= ( collect_pname @ A ) )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_empty__Collect__eq) ).
thf(2183,plain,
! [A: pname > $o] :
( ( bot_bot_pname_o
= ( collect_pname @ A ) )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(257,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ C ) @ ( semila129691299tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_inf__sup__distrib2) ).
thf(1661,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ C ) @ ( semila129691299tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(624,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( ( member451959335_state @ A @ B )
| ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_Un__iff) ).
thf(2902,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila1122118281tate_o @ B @ C ) )
= ( ( member451959335_state @ A @ B )
| ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(377,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( member451959335_state @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_set__rev__mp) ).
thf(2095,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ B @ C )
=> ( ( ord_le777019615tate_o @ C @ A )
=> ( member451959335_state @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(449,axiom,
! [A: hoare_1708887482_state > option_pname,B: hoare_1708887482_state,C: pname] :
( ( ( A @ B )
= ( some_pname @ C ) )
=> ( member451959335_state @ B @ ( dom_Ho1805192458_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_domI) ).
thf(2315,plain,
! [A: hoare_1708887482_state > option_pname,B: hoare_1708887482_state,C: pname] :
( ( ( A @ B )
= ( some_pname @ C ) )
=> ( member451959335_state @ B @ ( dom_Ho1805192458_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(186,axiom,
! [A: pname > $o,B: pname > option_com,C: pname > option_com] :
( ( dom_pname_com
@ ^ [D: pname] : ( if_option_com @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ B ) @ ( collect_pname @ A ) )
@ ( semila1673364395name_o @ ( dom_pname_com @ C )
@ ( collect_pname
@ ^ [D: pname] :
~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_dom__if) ).
thf(1442,plain,
! [A: pname > $o,B: pname > option_com,C: pname > option_com] :
( ( dom_pname_com
@ ^ [D: pname] : ( if_option_com @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ B ) @ ( collect_pname @ A ) )
@ ( semila1673364395name_o @ ( dom_pname_com @ C )
@ ( collect_pname
@ ^ [D: pname] :
~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(348,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( minus_2056855718tate_o @ B @ C ) )
= ( ( member451959335_state @ A @ B )
& ~ ( member451959335_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_Diff__iff) ).
thf(1994,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( minus_2056855718tate_o @ B @ C ) )
= ( ( member451959335_state @ A @ B )
& ~ ( member451959335_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(589,axiom,
wt @ skip,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_WT_OSkip) ).
thf(2779,plain,
wt @ skip,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(481,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_distrib__sup__le) ).
thf(2421,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(4182,plain,
( ~ ( top_to832624271tate_o @ sk147 )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[4155]) ).
thf(498,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_mem__def) ).
thf(2475,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(592,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_le__supI2) ).
thf(2786,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(718,axiom,
! [A: pname > option_com,B: pname,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( member_pname @ B @ ( dom_pname_com @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_domI) ).
thf(3267,plain,
! [A: pname > option_com,B: pname,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( member_pname @ B @ ( dom_pname_com @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(141,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ C ) @ ( semila129691299tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_Int__Un__distrib2) ).
thf(1294,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ C )
= ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ C ) @ ( semila129691299tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(185,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_inf__sup__ord_I4_J) ).
thf(1440,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(798,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ ( insert528405184_state @ B @ C ) )
= ( insert528405184_state @ B @ ( insert528405184_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_insert__commute) ).
thf(3529,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ ( insert528405184_state @ B @ C ) )
= ( insert528405184_state @ B @ ( insert528405184_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(109,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_subset__refl) ).
thf(1193,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(326,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] :
( ( inj_on1553129421_state @ A @ ( semila1780557381name_o @ B @ C ) )
= ( ( inj_on1553129421_state @ A @ B )
& ( inj_on1553129421_state @ A @ C )
& ( ( semila129691299tate_o @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ B @ C ) ) @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ C @ B ) ) )
= bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_inj__on__Un) ).
thf(1893,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: pname > $o] :
( ( inj_on1553129421_state @ A @ ( semila1780557381name_o @ B @ C ) )
= ( ( inj_on1553129421_state @ A @ B )
& ( inj_on1553129421_state @ A @ C )
& ( ( semila129691299tate_o @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ B @ C ) ) @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ C @ B ) ) )
= bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(359,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( semila1673364395name_o @ A @ C ) ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( semila1673364395name_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_Int__insert__left) ).
thf(2036,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( semila1673364395name_o @ A @ C ) ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( semila1673364395name_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(4039,plain,
( ( top_top_com_o @ sk144 )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[4037]) ).
thf(251,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_Un__Diff__Int) ).
thf(1642,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A @ B ) @ ( semila129691299tate_o @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(211,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_inf__le1) ).
thf(1512,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(138,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( insert528405184_state @ B @ ( semila129691299tate_o @ A @ C ) ) ) )
& ( ~ ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( semila129691299tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_Int__insert__left) ).
thf(1280,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( insert528405184_state @ B @ ( semila129691299tate_o @ A @ C ) ) ) )
& ( ~ ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ ( insert528405184_state @ B @ A ) @ C )
= ( semila129691299tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(233,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o
@ ^ [C: hoare_1708887482_state] : ( member451959335_state @ C @ A )
@ ^ [C: hoare_1708887482_state] : ( member451959335_state @ C @ B ) )
= ( ord_le777019615tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_pred__subset__eq) ).
thf(1578,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o
@ ^ [C: hoare_1708887482_state] : ( member451959335_state @ C @ A )
@ ^ [C: hoare_1708887482_state] : ( member451959335_state @ C @ B ) )
= ( ord_le777019615tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(420,axiom,
! [A: pname > pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(2233,plain,
! [A: pname > pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(172,axiom,
! [A: pname > pname,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( image_pname_pname @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_pigeonhole__infinite) ).
thf(1395,plain,
! [A: pname > pname,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( image_pname_pname @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(677,axiom,
! [A: state > state > $o,B: hoare_1708887482_state > $o,C: com,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ? [G: state > state > $o,H: state > state > $o] :
( ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ G @ C @ H ) @ bot_bo19817387tate_o ) )
& ! [I: state] :
( ! [J: state] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ D @ C @ A ) @ bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_conseq) ).
thf(3100,plain,
! [A: state > state > $o,B: hoare_1708887482_state > $o,C: com,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ? [G: state > state > $o,H: state > state > $o] :
( ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ G @ C @ H ) @ bot_bo19817387tate_o ) )
& ! [I: state] :
( ! [J: state] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_858012674_state @ D @ C @ A ) @ bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(575,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ C @ A ) @ ( semila129691299tate_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_Int__mono) ).
thf(2736,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ C @ A ) @ ( semila129691299tate_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(697,axiom,
finite662762081tate_o @ insert528405184_state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_comp__fun__idem__insert) ).
thf(3164,plain,
finite662762081tate_o @ insert528405184_state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(429,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_sup__left__commute) ).
thf(2258,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(633,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ B @ C ) ) @ ( semila1673364395name_o @ C @ A ) )
= ( semila1673364395name_o @ ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ B @ C ) ) @ ( semila1780557381name_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_Un__Int__crazy) ).
thf(2930,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ B @ C ) ) @ ( semila1673364395name_o @ C @ A ) )
= ( semila1673364395name_o @ ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ B @ C ) ) @ ( semila1780557381name_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(385,axiom,
! [A: pname > $o,B: pname] :
( ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( ( A = bot_bot_pname_o )
| ( A
= ( insert_pname @ B @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_subset__singletonD) ).
thf(2123,plain,
! [A: pname > $o,B: pname] :
( ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
=> ( ( A = bot_bot_pname_o )
| ( A
= ( insert_pname @ B @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(50,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1673364395name_o @ A @ B )
= bot_bot_pname_o )
=> ( ( minus_minus_pname_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_Diff__triv) ).
thf(999,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1673364395name_o @ A @ B )
= bot_bot_pname_o )
=> ( ( minus_minus_pname_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(439,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
| ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_Un__def) ).
thf(2287,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
| ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(469,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Un__left__absorb) ).
thf(2385,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ A @ B ) )
= ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(263,axiom,
! [A: hoare_1708887482_state > pname > $o,B: hoare_1708887482_state > $o] :
( ~ ( finite1625599783_state @ B )
=> ( ( finite297249702name_o @ ( image_1552895654name_o @ A @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
& ~ ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_pigeonhole__infinite) ).
thf(1678,plain,
! [A: hoare_1708887482_state > pname > $o,B: hoare_1708887482_state > $o] :
( ~ ( finite1625599783_state @ B )
=> ( ( finite297249702name_o @ ( image_1552895654name_o @ A @ B ) )
=> ? [C: hoare_1708887482_state] :
( ( member451959335_state @ C @ B )
& ~ ( finite1625599783_state
@ ( collec1568722789_state
@ ^ [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(516,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_order__antisym) ).
thf(2534,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(36,axiom,
! [A: pname,B: pname] :
( ( A != B )
| ( fequal_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(950,plain,
! [A: pname,B: pname] :
( ( A != B )
| ( fequal_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(77,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ! [C: hoare_1708887482_state] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le777019615tate_o @ ( collec1568722789_state @ B ) @ ( collec1568722789_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_Collect__mono) ).
thf(1097,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ! [C: hoare_1708887482_state] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le777019615tate_o @ ( collec1568722789_state @ B ) @ ( collec1568722789_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(748,axiom,
! [A: com,B: hoare_1708887482_state > $o] :
( hoare_1160767572gleton
=> ( ! [C: pname] :
( ( member_pname @ C @ ( dom_pname_com @ body ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ C ) ) @ bot_bo19817387tate_o ) ) )
=> ( ( wt @ A )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo19817387tate_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_MGF__lemma1) ).
thf(3373,plain,
! [A: com,B: hoare_1708887482_state > $o] :
( hoare_1160767572gleton
=> ( ! [C: pname] :
( ( member_pname @ C @ ( dom_pname_com @ body ) )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ C ) ) @ bot_bo19817387tate_o ) ) )
=> ( ( wt @ A )
=> ( hoare_90032982_state @ B @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo19817387tate_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(167,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_inf__sup__aci_I8_J) ).
thf(1380,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(544,axiom,
! [A: ( hoare_1708887482_state > $o ) > pname,B: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ B )
=> ( finite_finite_pname @ ( image_2051418740_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(2636,plain,
! [A: ( hoare_1708887482_state > $o ) > pname,B: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o @ B )
=> ( finite_finite_pname @ ( image_2051418740_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(4146,plain,
( finite1625599783_state
@ ^ [A: hoare_1708887482_state] : bot_bot_o ),
inference(rewrite,[status(thm)],[3576,3234]) ).
thf(595,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
= ( ( ord_le777019615tate_o @ A @ B )
& ( ord_le777019615tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_order__eq__iff) ).
thf(2800,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
= ( ( ord_le777019615tate_o @ A @ B )
& ( ord_le777019615tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(205,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_folding__one__idem_Oinsert__idem) ).
thf(1495,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(808,axiom,
! [A: state > state > $o,B: state > state > $o,C: hoare_1708887482_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ D @ E @ F ) @ bot_bo19817387tate_o ) )
=> ( ! [G: state,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: state] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ B @ E @ A ) @ bot_bo19817387tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_conseq12) ).
thf(3560,plain,
! [A: state > state > $o,B: state > state > $o,C: hoare_1708887482_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ D @ E @ F ) @ bot_bo19817387tate_o ) )
=> ( ! [G: state,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: state] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ B @ E @ A ) @ bot_bo19817387tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(404,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
= ( ( semila1122118281tate_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_subset__Un__eq) ).
thf(2186,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ B )
= ( ( semila1122118281tate_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(565,axiom,
! [A: pname,B: pname,C: pname,D: pname] :
( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
= ( insert_pname @ C @ ( insert_pname @ D @ bot_bot_pname_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_doubleton__eq__iff) ).
thf(2704,plain,
! [A: pname,B: pname,C: pname,D: pname] :
( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bot_pname_o ) )
= ( insert_pname @ C @ ( insert_pname @ D @ bot_bot_pname_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(703,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ ( collec1568722789_state @ B ) )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_insert__Collect) ).
thf(3196,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o] :
( ( insert528405184_state @ A @ ( collec1568722789_state @ B ) )
= ( collec1568722789_state
@ ^ [C: hoare_1708887482_state] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(197,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( finite1625599783_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_rev__finite__subset) ).
thf(1473,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( finite1625599783_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(764,axiom,
! [A: pname > $o,B: hoare_1708887482_state > $o] :
( ( B != bot_bo19817387tate_o )
=> ( ( ? [C: hoare_1708887482_state > pname] :
( ( inj_on1945914667_pname @ C @ B )
& ( ord_less_eq_pname_o @ ( image_1509414295_pname @ C @ B ) @ A ) ) )
= ( ? [C: pname > hoare_1708887482_state] :
( ( image_1116629049_state @ C @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_inj__on__iff__surj) ).
thf(3424,plain,
! [A: pname > $o,B: hoare_1708887482_state > $o] :
( ( B != bot_bo19817387tate_o )
=> ( ( ? [C: hoare_1708887482_state > pname] :
( ( inj_on1945914667_pname @ C @ B )
& ( ord_less_eq_pname_o @ ( image_1509414295_pname @ C @ B ) @ A ) ) )
= ( ? [C: pname > hoare_1708887482_state] :
( ( image_1116629049_state @ C @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(4157,plain,
( ( top_to832624271tate_o @ sk145 )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[4145]) ).
thf(154,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ A )
=> ( finite_finite_pname @ ( semila1780557381name_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_finite__UnI) ).
thf(1335,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ A )
=> ( finite_finite_pname @ ( semila1780557381name_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(102,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ ( collec1568722789_state @ C ) ) )
= ( ( member451959335_state @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_859_Int__Collect) ).
thf(1172,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( member451959335_state @ A @ ( semila129691299tate_o @ B @ ( collec1568722789_state @ C ) ) )
= ( ( member451959335_state @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(21,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ( finite297249702name_o @ ( collect_pname_o @ B ) )
| ( finite297249702name_o @ ( collect_pname_o @ A ) ) )
=> ( finite297249702name_o
@ ( collect_pname_o
@ ^ [C: pname > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_finite__Collect__conjI) ).
thf(897,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ( finite297249702name_o @ ( collect_pname_o @ B ) )
| ( finite297249702name_o @ ( collect_pname_o @ A ) ) )
=> ( finite297249702name_o
@ ( collect_pname_o
@ ^ [C: pname > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(60,axiom,
! [A: ( pname > $o ) > $o,B: hoare_1708887482_state > pname > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_1552895654name_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite__surj) ).
thf(1033,plain,
! [A: ( pname > $o ) > $o,B: hoare_1708887482_state > pname > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_1552895654name_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(642,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( ord_le777019615tate_o @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_Int__greatest) ).
thf(2961,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ B @ A )
=> ( ord_le777019615tate_o @ B @ ( semila129691299tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(139,axiom,
! [A: com > $o] :
( ( ? [B: com] : ( member_com @ B @ A ) )
= ( A != bot_bot_com_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ex__in__conv) ).
thf(1288,plain,
! [A: com > $o] :
( ( ? [B: com] : ( member_com @ B @ A ) )
= ( A != bot_bot_com_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(111,axiom,
! [A: hoare_1708887482_state] :
~ ! [B: state > state > $o,C: com,D: state > state > $o] :
( A
!= ( hoare_858012674_state @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_triple_Oexhaust) ).
thf(1197,plain,
! [A: hoare_1708887482_state] :
~ ! [B: state > state > $o,C: com,D: state > state > $o] :
( A
!= ( hoare_858012674_state @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(627,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ B @ ( semila1122118281tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_le__supI1) ).
thf(2913,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ord_le777019615tate_o @ B @ ( semila1122118281tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(475,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( member451959335_state @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_folding__one__idem_Oin__idem) ).
thf(2404,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( member451959335_state @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(733,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,C: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ B @ C )
=> ( ( C @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_folding__one_Osingleton) ).
thf(3323,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,C: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ B @ C )
=> ( ( C @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(354,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_sup_Oleft__commute) ).
thf(2021,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(158,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( insert528405184_state @ B @ ( semila129691299tate_o @ C @ A ) ) ) )
& ( ~ ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( semila129691299tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_Int__insert__right) ).
thf(1346,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( insert528405184_state @ B @ ( semila129691299tate_o @ C @ A ) ) ) )
& ( ~ ( member451959335_state @ B @ C )
=> ( ( semila129691299tate_o @ C @ ( insert528405184_state @ B @ A ) )
= ( semila129691299tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(280,axiom,
! [A: option1624383643_state] :
( ( A != none_H1106584047_state )
= ( ? [B: hoare_1708887482_state] :
( A
= ( some_H1974565227_state @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_not__None__eq) ).
thf(1742,plain,
! [A: option1624383643_state] :
( ( A != none_H1106584047_state )
= ( ? [B: hoare_1708887482_state] :
( A
= ( some_H1974565227_state @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(30,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1036_insert__Diff__single) ).
thf(928,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(423,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ! [E: hoare_1708887482_state] :
( ( member451959335_state @ E @ C )
=> ( ( B @ E )
=> ( A @ E ) ) )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ C @ ( collec1568722789_state @ B ) ) @ ( semila129691299tate_o @ D @ ( collec1568722789_state @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_Int__Collect__mono) ).
thf(2241,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ C @ D )
=> ( ! [E: hoare_1708887482_state] :
( ( member451959335_state @ E @ C )
=> ( ( B @ E )
=> ( A @ E ) ) )
=> ( ord_le777019615tate_o @ ( semila129691299tate_o @ C @ ( collec1568722789_state @ B ) ) @ ( semila129691299tate_o @ D @ ( collec1568722789_state @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(644,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ B @ C ) ) @ ( semila129691299tate_o @ C @ A ) )
= ( semila129691299tate_o @ ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ B @ C ) ) @ ( semila1122118281tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_Un__Int__crazy) ).
thf(2966,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ A @ B ) @ ( semila129691299tate_o @ B @ C ) ) @ ( semila129691299tate_o @ C @ A ) )
= ( semila129691299tate_o @ ( semila129691299tate_o @ ( semila1122118281tate_o @ A @ B ) @ ( semila1122118281tate_o @ B @ C ) ) @ ( semila1122118281tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(56,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ( ord_le1728773982te_o_o @ A @ B )
=> ( ( finite1329924456tate_o @ B )
=> ( finite1329924456tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_finite__subset) ).
thf(1019,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ( ord_le1728773982te_o_o @ A @ B )
=> ( ( finite1329924456tate_o @ B )
=> ( finite1329924456tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(3886,plain,
! [A: pname] :
~ ( member_pname @ A
@ ^ [B: pname] : bot_bot_o ),
inference(rewrite,[status(thm)],[1258,2398]) ).
thf(682,axiom,
! [A: hoare_1708887482_state] :
( ( the_el864710747_state @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_the__elem__eq) ).
thf(3113,plain,
! [A: hoare_1708887482_state] :
( ( the_el864710747_state @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(464,axiom,
! [A: com,B: com > $o] :
( ( member_com @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_mem__def) ).
thf(2372,plain,
! [A: com,B: com > $o] :
( ( member_com @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(738,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_folding__one__idem_Oinsert__idem) ).
thf(3341,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1347568576_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( B != bot_bo19817387tate_o )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(574,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ~ ! [C: pname > $o] :
( ( B
= ( insert_pname @ A @ C ) )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_Set_Oset__insert) ).
thf(2731,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ~ ! [C: pname > $o] :
( ( B
= ( insert_pname @ A @ C ) )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(687,axiom,
! [A: pname > hoare_1708887482_state,B: pname,C: pname > $o] :
( ( image_1116629049_state @ A @ ( insert_pname @ B @ C ) )
= ( insert528405184_state @ ( A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_image__insert) ).
thf(3128,plain,
! [A: pname > hoare_1708887482_state,B: pname,C: pname > $o] :
( ( image_1116629049_state @ A @ ( insert_pname @ B @ C ) )
= ( insert528405184_state @ ( A @ B ) @ ( image_1116629049_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(307,axiom,
! [A: state > $o,B: com] :
( skip
!= ( while @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_com_Osimps_I16_J) ).
thf(1829,plain,
! [A: state > $o,B: com] :
( skip
!= ( while @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(342,axiom,
! [A: pname > hoare_1708887482_state,B: hoare_1708887482_state > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member451959335_state @ ( A @ D ) @ B ) )
=> ( ord_le777019615tate_o @ ( image_1116629049_state @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_image__subsetI) ).
thf(1977,plain,
! [A: pname > hoare_1708887482_state,B: hoare_1708887482_state > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member451959335_state @ ( A @ D ) @ B ) )
=> ( ord_le777019615tate_o @ ( image_1116629049_state @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(671,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le777019615tate_o @ C @ B )
=> ( ( A @ bot_bo19817387tate_o )
=> ( ! [D: hoare_1708887482_state,E: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ E )
=> ( ( member451959335_state @ D @ B )
=> ( ~ ( member451959335_state @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert528405184_state @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_finite__subset__induct) ).
thf(3057,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ C )
=> ( ( ord_le777019615tate_o @ C @ B )
=> ( ( A @ bot_bo19817387tate_o )
=> ( ! [D: hoare_1708887482_state,E: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ E )
=> ( ( member451959335_state @ D @ B )
=> ( ~ ( member451959335_state @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert528405184_state @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(596,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( image_1509414295_pname @ A @ ( insert528405184_state @ B @ C ) )
= ( insert_pname @ ( A @ B ) @ ( image_1509414295_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_image__insert) ).
thf(2803,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state,C: hoare_1708887482_state > $o] :
( ( image_1509414295_pname @ A @ ( insert528405184_state @ B @ C ) )
= ( insert_pname @ ( A @ B ) @ ( image_1509414295_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(859,plain,
! [C: ( pname > $o ) > $o,B: hoare_1708887482_state > $o,A: hoare_1708887482_state > pname > $o] :
( ~ ( finite297249702name_o @ C )
| ~ ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) )
| ( C
= ( image_1552895654name_o @ A @ ( sk2 @ C @ B @ A ) ) ) ),
inference(cnfConj,[status(thm)],[856]) ).
thf(860,plain,
! [C: ( pname > $o ) > $o,B: hoare_1708887482_state > $o,A: hoare_1708887482_state > pname > $o] :
( ( C
= ( image_1552895654name_o @ A @ ( sk2 @ C @ B @ A ) ) )
| ~ ( finite297249702name_o @ C )
| ~ ( ord_le1205211808me_o_o @ C @ ( image_1552895654name_o @ A @ B ) ) ),
inference(lifteq,[status(thm)],[859]) ).
thf(612,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_xt1_I5_J) ).
thf(2847,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(811,axiom,
! [A: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ bot_bo19817387tate_o )
= ( A = bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_bot__unique) ).
thf(3570,plain,
! [A: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ A @ bot_bo19817387tate_o )
= ( A = bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(825,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( insert528405184_state @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_insert__code) ).
thf(3605,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state] :
( ( insert528405184_state @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(760,axiom,
! [A: hoare_1708887482_state] :
( ( collec1568722789_state
@ ^ [B: hoare_1708887482_state] : ( B = A ) )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_singleton__conv) ).
thf(3411,plain,
! [A: hoare_1708887482_state] :
( ( collec1568722789_state
@ ^ [B: hoare_1708887482_state] : ( B = A ) )
= ( insert528405184_state @ A @ bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(501,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( finite1625599783_state @ ( minus_2056855718tate_o @ A @ B ) )
= ( finite1625599783_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_finite__Diff2) ).
thf(2485,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( finite1625599783_state @ B )
=> ( ( finite1625599783_state @ ( minus_2056855718tate_o @ A @ B ) )
= ( finite1625599783_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(220,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( ( ord_less_eq_pname_o @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_le__sup__iff) ).
thf(1537,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( ( ord_less_eq_pname_o @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(2032,plain,
! [A: com > hoare_1708887482_state] :
( ( image_934102463_state @ A @ bot_bot_com_o )
= bot_bo19817387tate_o ),
inference(cnf,[status(esa)],[2031]) ).
thf(2033,plain,
! [A: com > hoare_1708887482_state] :
( ( image_934102463_state @ A @ bot_bot_com_o )
= bot_bo19817387tate_o ),
inference(lifteq,[status(thm)],[2032]) ).
thf(4506,plain,
! [A: com > hoare_1708887482_state] :
( ( image_934102463_state @ A
@ ^ [B: com] : bot_bot_o )
= ( ^ [B: hoare_1708887482_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[2033,3234,1863]) ).
thf(24,axiom,
! [A: pname,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite89670078_pname @ B @ C )
=> ( ( B @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_folding__one__idem_Oidem) ).
thf(908,plain,
! [A: pname,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite89670078_pname @ B @ C )
=> ( ( B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(785,axiom,
! [A: pname,B: com] :
( wT_bodies
=> ( ( ( body @ A )
= ( some_com @ B ) )
=> ( wt @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_WT__bodiesD) ).
thf(3489,plain,
! [A: pname,B: com] :
( wT_bodies
=> ( ( ( body @ A )
= ( some_com @ B ) )
=> ( wt @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(48,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ( ( finite1329924456tate_o @ ( collec219771562tate_o @ B ) )
| ( finite1329924456tate_o @ ( collec219771562tate_o @ A ) ) )
=> ( finite1329924456tate_o
@ ( collec219771562tate_o
@ ^ [C: hoare_1708887482_state > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_finite__Collect__conjI) ).
thf(992,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ( ( finite1329924456tate_o @ ( collec219771562tate_o @ B ) )
| ( finite1329924456tate_o @ ( collec219771562tate_o @ A ) ) )
=> ( finite1329924456tate_o
@ ( collec219771562tate_o
@ ^ [C: hoare_1708887482_state > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(331,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
=> ~ ( ( ord_le777019615tate_o @ A @ B )
=> ~ ( ord_le777019615tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_equalityE) ).
thf(1923,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( A = B )
=> ~ ( ( ord_le777019615tate_o @ A @ B )
=> ~ ( ord_le777019615tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1618,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(cnf,[status(esa)],[1617]) ).
thf(1619,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(lifteq,[status(thm)],[1618]) ).
thf(4410,plain,
! [A: pname > $o] :
( ( semila1673364395name_o
@ ^ [B: pname] : bot_bot_o
@ A )
= ( ^ [B: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1619,2398]) ).
thf(559,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_Int__Un__distrib) ).
thf(2687,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(321,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_insert__compr) ).
thf(1880,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( C = A )
| ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(184,axiom,
! [A: pname > option_com,B: pname,C: option_com] :
( ( ( C = none_com )
=> ( ( dom_pname_com @ ( fun_up879233478on_com @ A @ B @ C ) )
= ( minus_minus_pname_o @ ( dom_pname_com @ A ) @ ( insert_pname @ B @ bot_bot_pname_o ) ) ) )
& ( ( C != none_com )
=> ( ( dom_pname_com @ ( fun_up879233478on_com @ A @ B @ C ) )
= ( insert_pname @ B @ ( dom_pname_com @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_dom__fun__upd) ).
thf(1431,plain,
! [A: pname > option_com,B: pname,C: option_com] :
( ( ( C = none_com )
=> ( ( dom_pname_com @ ( fun_up879233478on_com @ A @ B @ C ) )
= ( minus_minus_pname_o @ ( dom_pname_com @ A ) @ ( insert_pname @ B @ bot_bot_pname_o ) ) ) )
& ( ( C != none_com )
=> ( ( dom_pname_com @ ( fun_up879233478on_com @ A @ B @ C ) )
= ( insert_pname @ B @ ( dom_pname_com @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(173,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( D @ ( semila1780557381name_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_folding__one__idem_Ounion__idem) ).
thf(1399,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( D @ ( semila1780557381name_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(433,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_inf__greatest) ).
thf(2270,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(554,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_xt1_I6_J) ).
thf(2672,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( ord_le777019615tate_o @ A @ B )
=> ( ord_le777019615tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(777,axiom,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( ( ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= bot_bo19817387tate_o )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= A ) )
& ( ( ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
!= bot_bo19817387tate_o )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( C @ A @ ( D @ ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_788_folding__one_Oinsert__remove) ).
thf(3461,plain,
! [A: hoare_1708887482_state,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,D: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
( ( finite1615457021_state @ C @ D )
=> ( ( finite1625599783_state @ B )
=> ( ( ( ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
= bot_bo19817387tate_o )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= A ) )
& ( ( ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) )
!= bot_bo19817387tate_o )
=> ( ( D @ ( insert528405184_state @ A @ B ) )
= ( C @ A @ ( D @ ( minus_2056855718tate_o @ B @ ( insert528405184_state @ A @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(832,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( semila1122118281tate_o @ A @ B )
= bot_bo19817387tate_o )
= ( ( A = bot_bo19817387tate_o )
& ( B = bot_bo19817387tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_Un__empty) ).
thf(3626,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( ( semila1122118281tate_o @ A @ B )
= bot_bo19817387tate_o )
= ( ( A = bot_bo19817387tate_o )
& ( B = bot_bo19817387tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(486,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_pname_o @ A @ C )
=> ~ ( ord_less_eq_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_le__supE) ).
thf(2436,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_pname_o @ A @ C )
=> ~ ( ord_less_eq_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(767,axiom,
! [A: ( pname > $o ) > state > state > $o,B: ( pname > $o ) > state > state > $o,C: hoare_1708887482_state > $o,D: ( pname > $o ) > state > state > $o,E: ( pname > $o ) > com,F: ( pname > $o ) > state > state > $o,G: ( pname > $o ) > $o] :
( ( finite297249702name_o @ G )
=> ( ! [H: pname > $o] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) ) @ bot_bo19817387tate_o ) ) )
=> ( ( hoare_90032982_state @ C
@ ( image_1922967206_state
@ ^ [H: pname > $o] : ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) )
@ G ) )
=> ( hoare_90032982_state @ C
@ ( image_1922967206_state
@ ^ [H: pname > $o] : ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) )
@ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_finite__pointwise) ).
thf(3432,plain,
! [A: ( pname > $o ) > state > state > $o,B: ( pname > $o ) > state > state > $o,C: hoare_1708887482_state > $o,D: ( pname > $o ) > state > state > $o,E: ( pname > $o ) > com,F: ( pname > $o ) > state > state > $o,G: ( pname > $o ) > $o] :
( ( finite297249702name_o @ G )
=> ( ! [H: pname > $o] :
( ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) ) @ bot_bo19817387tate_o ) )
=> ( hoare_90032982_state @ C @ ( insert528405184_state @ ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) ) @ bot_bo19817387tate_o ) ) )
=> ( ( hoare_90032982_state @ C
@ ( image_1922967206_state
@ ^ [H: pname > $o] : ( hoare_858012674_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) )
@ G ) )
=> ( hoare_90032982_state @ C
@ ( image_1922967206_state
@ ^ [H: pname > $o] : ( hoare_858012674_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) )
@ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(542,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_finite__induct) ).
thf(2615,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(459,axiom,
finite1625599783_state @ fa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2351,plain,
finite1625599783_state @ fa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(806,axiom,
! [A: pname] :
( ( body_1 @ A )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_com_Osimps_I19_J) ).
thf(3553,plain,
! [A: pname] :
( ( body_1 @ A )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(649,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_sup__ge2) ).
thf(2980,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(659,axiom,
! [A: pname,B: pname > $o,C: pname] :
( ( insert_pname @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_insert__code) ).
thf(3013,plain,
! [A: pname,B: pname > $o,C: pname] :
( ( insert_pname @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(797,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( ( image_1116629049_state @ A @ B )
= bot_bo19817387tate_o )
= ( B = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_image__is__empty) ).
thf(3526,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o] :
( ( ( image_1116629049_state @ A @ B )
= bot_bo19817387tate_o )
= ( B = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(152,axiom,
wT_bodies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(1331,plain,
wT_bodies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(780,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ B @ C )
=> ( ( hoare_90032982_state @ A @ B )
=> ( hoare_90032982_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cut) ).
thf(3474,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( hoare_90032982_state @ B @ C )
=> ( ( hoare_90032982_state @ A @ B )
=> ( hoare_90032982_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(28,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o
@ ( collec219771562tate_o
@ ^ [C: hoare_1708887482_state > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1329924456tate_o @ ( collec219771562tate_o @ A ) )
& ( finite1329924456tate_o @ ( collec219771562tate_o @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_finite__Collect__disjI) ).
thf(923,plain,
! [A: ( hoare_1708887482_state > $o ) > $o,B: ( hoare_1708887482_state > $o ) > $o] :
( ( finite1329924456tate_o
@ ( collec219771562tate_o
@ ^ [C: hoare_1708887482_state > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1329924456tate_o @ ( collec219771562tate_o @ A ) )
& ( finite1329924456tate_o @ ( collec219771562tate_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(411,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_Un__insert__right) ).
thf(2206,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(106,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( B = A )
=> ( ord_le777019615tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_xt1_I4_J) ).
thf(1184,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ B @ C )
=> ( ( B = A )
=> ( ord_le777019615tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(370,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_sup__left__idem) ).
thf(2074,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( semila1122118281tate_o @ A @ B ) )
= ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(560,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( minus_2056855718tate_o @ B @ A ) )
= ( semila1122118281tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_Un__Diff__cancel) ).
thf(2690,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] :
( ( semila1122118281tate_o @ A @ ( minus_2056855718tate_o @ B @ A ) )
= ( semila1122118281tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(193,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_inf__sup__ord_I1_J) ).
thf(1463,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ ( semila129691299tate_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(228,axiom,
! [A: state,B: com,C: state,D: state > $o,E: state] :
( ( D @ E )
=> ( ( evalc @ B @ E @ C )
=> ( ( evalc @ ( while @ D @ B ) @ C @ A )
=> ( evalc @ ( while @ D @ B ) @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_evalc_OWhileTrue) ).
thf(1565,plain,
! [A: state,B: com,C: state,D: state > $o,E: state] :
( ( D @ E )
=> ( ( evalc @ B @ E @ C )
=> ( ( evalc @ ( while @ D @ B ) @ C @ A )
=> ( evalc @ ( while @ D @ B ) @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(618,axiom,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ? [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ ( semila1122118281tate_o @ B @ C ) )
& ( A @ D ) ) )
= ( ? [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( A @ D ) )
| ? [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ C )
& ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_bex__Un) ).
thf(2866,plain,
! [A: hoare_1708887482_state > $o,B: hoare_1708887482_state > $o,C: hoare_1708887482_state > $o] :
( ( ? [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ ( semila1122118281tate_o @ B @ C ) )
& ( A @ D ) ) )
= ( ? [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ B )
& ( A @ D ) )
| ? [D: hoare_1708887482_state] :
( ( member451959335_state @ D @ C )
& ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(606,axiom,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_bot__fun__def) ).
thf(2832,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(422,axiom,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o] :
( ( ( image_1509414295_pname @ A @ B )
= bot_bot_pname_o )
= ( B = bot_bo19817387tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_image__is__empty) ).
thf(2238,plain,
! [A: hoare_1708887482_state > pname,B: hoare_1708887482_state > $o] :
( ( ( image_1509414295_pname @ A @ B )
= bot_bot_pname_o )
= ( B = bot_bo19817387tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(62,axiom,
! [A: ( pname > $o ) > $o,B: pname > pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_pname_pname_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_finite__surj) ).
thf(1037,plain,
! [A: ( pname > $o ) > $o,B: pname > pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_pname_pname_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(17,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ B ) @ C )
= ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_Diff__subset__conv) ).
thf(882,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A @ B ) @ C )
= ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(551,axiom,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: hoare_1708887482_state > pname,D: hoare_1708887482_state > $o] :
? [E: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ E @ D )
& ! [F: hoare_1708887482_state] :
( ( member451959335_state @ F @ E )
=> ~ ( member451959335_state @ F @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ B @ ( image_1509414295_pname @ C @ E ) ) ) ) )
& ? [F: hoare_1708887482_state > pname] :
( ! [G: hoare_1708887482_state] :
( ( member451959335_state @ G @ E )
=> ( ( F @ G )
= ( C @ G ) ) )
& ! [G: hoare_1708887482_state] :
( ( member451959335_state @ G @ ( minus_2056855718tate_o @ D @ E ) )
=> ( ( member_pname @ ( F @ G ) @ ( minus_minus_pname_o @ B @ ( image_1509414295_pname @ C @ E ) ) )
& ( G
= ( A @ ( F @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_Cantor__Bernstein__aux) ).
thf(2655,plain,
! [A: pname > hoare_1708887482_state,B: pname > $o,C: hoare_1708887482_state > pname,D: hoare_1708887482_state > $o] :
? [E: hoare_1708887482_state > $o] :
( ( ord_le777019615tate_o @ E @ D )
& ! [F: hoare_1708887482_state] :
( ( member451959335_state @ F @ E )
=> ~ ( member451959335_state @ F @ ( image_1116629049_state @ A @ ( minus_minus_pname_o @ B @ ( image_1509414295_pname @ C @ E ) ) ) ) )
& ? [F: hoare_1708887482_state > pname] :
( ! [G: hoare_1708887482_state] :
( ( member451959335_state @ G @ E )
=> ( ( F @ G )
= ( C @ G ) ) )
& ! [G: hoare_1708887482_state] :
( ( member451959335_state @ G @ ( minus_2056855718tate_o @ D @ E ) )
=> ( ( member_pname @ ( F @ G ) @ ( minus_minus_pname_o @ B @ ( image_1509414295_pname @ C @ E ) ) )
& ( G
= ( A @ ( F @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(179,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_xt1_I6_J) ).
thf(1417,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(317,axiom,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_order__refl) ).
thf(1870,plain,
! [A: hoare_1708887482_state > $o] : ( ord_le777019615tate_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(42,axiom,
! [A: ( hoare_1708887482_state > $o ) > $o] :
( ( collec219771562tate_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Collect__def) ).
thf(972,plain,
! [A: ( hoare_1708887482_state > $o ) > $o] :
( ( collec219771562tate_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(5278,plain,
$false,
inference(e,[status(thm)],[3021,1337,1411,3883,1633,1559,1729,2463,2559,3172,2612,1024,1168,2306,2131,2031,1237,846,4183,2921,4290,3979,1840,3581,2427,2480,1179,2331,1950,1549,2077,1750,1005,3317,2231,2381,3498,1692,4037,2512,1522,2644,2776,3417,2527,3040,3153,1569,2248,2837,1142,1269,1793,3402,1041,861,1608,1655,3429,3135,1999,1233,4564,2168,3253,2580,2844,3577,3276,1078,1788,4575,1310,2740,2918,1867,3175,2448,2933,1872,2712,3414,1342,1354,2146,3629,3545,841,1935,1645,2173,3878,2531,2972,2046,2491,2548,1782,885,3088,3140,1475,2067,2825,2819,4156,1803,3880,1482,3597,3688,2869,1628,3442,2603,3029,2814,3495,2501,1511,1313,2488,1992,2698,3131,3116,2667,4151,2339,3689,3617,2444,1264,3653,838,3125,1826,934,1191,2466,2126,1132,3043,2571,2356,1147,2049,1479,1572,3216,3470,1931,2024,1773,1815,2388,1847,1087,1514,870,1890,2520,4141,3602,3557,4400,2222,3322,1664,3199,1450,2451,1051,1946,1465,3887,2027,1373,3724,3295,2782,1109,2469,1682,1136,3438,4147,1864,1383,2254,2540,2034,1581,2335,2017,905,2367,1377,2281,1215,1072,2137,4038,2392,3389,981,1896,877,3421,866,1886,2002,4536,2103,2750,1943,1201,3588,849,2718,2205,1696,2982,2762,3378,1863,1651,3229,1206,2574,4531,2164,2118,1470,2641,942,3591,3169,3265,2296,3054,2083,1736,2496,1768,2905,3550,2773,1047,3037,1163,1274,2589,2264,1723,2601,1021,1519,1255,1123,1502,2969,2937,2606,4160,1883,957,1223,2150,1370,2396,3682,3271,3980,2670,2433,879,3137,3578,1888,1687,1624,2179,3144,1291,1740,3445,1106,3282,2958,1423,1938,847,2758,852,2332,4155,3535,1836,1027,2327,2213,1195,1407,2313,1128,1392,2228,1402,1534,1328,1121,869,1755,2638,989,3105,3467,2300,874,2840,2115,1762,2515,2100,1259,3122,2577,3381,1111,1227,1498,1587,2509,1672,1540,3518,2724,1719,2858,2537,2268,3440,3018,857,1567,2460,1160,3326,1361,3922,3000,1182,2455,2080,1584,3032,2349,3723,3573,3407,2561,3210,901,2419,1075,1414,2053,1842,1810,1791,1016,2085,2472,2649,1039,4530,1419,837,1114,3486,1456,2598,3222,1984,1002,1874,1429,3333,4152,2272,1525,1776,1263,3611,1150,1249,1297,2681,3541,3354,2153,1668,1974,3109,3005,2140,2756,3162,1759,3476,4148,2788,2203,3225,1779,3279,921,1170,4036,3508,4572,3147,3454,4288,1241,2057,1054,2963,1035,2915,2440,2189,2995,2423,888,926,2909,1648,965,2413,2275,2585,3257,3289,2602,1631,2121,2235,2677,2176,1698,1103,3079,2941,1301,1595,3523,3111,3274,3686,4017,2524,3396,1833,1007,3234,1389,843,4159,1620,2674,2806,3458,2398,3404,1124,3213,3536,1154,975,3387,4268,2727,2225,3504,2695,1488,2134,3599,1428,4537,3118,2738,3208,1332,2055,4060,2457,4273,947,3568,2319,1675,3532,2293,3051,1271,2308,1635,1733,3594,1239,1997,2753,3436,3619,3579,1765,1090,2311,3631,2478,2383,2493,1117,2097,3106,1144,1771,3500,1122,3384,1307,3287,3515,996,2284,1933,1492,1603,2955,2246,2378,2896,3586,2871,4509,863,1175,1877,2610,858,2111,2780,3165,848,3451,2874,915,3483,2278,2928,2974,2710,2129,2343,2261,1731,3034,2410,1325,3614,1460,2647,3150,2842,912,2401,2835,2086,3687,986,3016,2592,1477,2303,1562,3539,2770,983,959,2171,1044,1245,1445,1528,2064,2369,2633,3363,1726,1364,3512,3178,3348,2156,3876,1694,2693,2984,4158,1805,2816,2952,1166,1203,1467,2652,1905,4529,2503,1081,1340,3278,968,2582,2005,3881,1304,3427,3576,944,1990,2684,2202,2256,2564,3292,2899,836,1551,1748,3391,3112,2060,2143,2518,2821,2720,1531,2567,1845,855,2715,1516,2863,2977,1611,2375,3082,2192,1605,3260,954,1252,1753,2407,1267,3608,1230,2850,1484,2747,2569,3448,2092,1813,1188,4145,2219,1901,1658,3623,1218,1987,1716,3344,4549,840,1785,1317,1763,2701,2545,3329,2044,1543,1898,3493,2543,1221,1972,864,1504,1094,2939,876,1617,1404,1358,2992,1981,4143,4538,1427,1670,1797,3520,3366,1940,4289,3584,3565,3092,931,2828,3874,2347,2215,2071,3284,2760,3400,2924,4138,2352,1084,1157,1321,3548,2194,891,2209,2743,2997,1448,3346,3320,1010,1575,844,1453,2792,1807,2707,1508,1101,2811,1745,4495,3331,3085,1276,1590,2988,1385,2855,1639,2853,2290,2251,3369,2823,2608,3235,2431,3003,1244,4527,2416,2944,1689,2399,3879,2198,2183,3351,1661,2902,2095,2315,1442,1994,2779,2421,4182,1861,2475,2786,3267,1294,1440,2330,3529,1193,1893,2036,4039,1642,1512,1280,1578,2233,3892,1546,1395,3100,2736,867,3164,2258,2930,2123,999,2287,2385,1678,2534,3232,950,1097,835,3373,1380,2636,4146,2800,2201,1495,3560,2186,2704,3196,1473,3424,4157,1335,1172,897,3479,1410,1033,2961,1288,1197,2913,2404,3323,2021,1346,1742,928,2241,1261,2966,1019,3886,3113,871,1120,2372,3341,3362,2731,3128,1829,1977,3057,2803,860,2847,3570,3605,3411,2485,1537,1357,4506,908,3489,992,1923,4410,2687,1880,1431,1399,2270,2672,3461,3626,2436,3432,2615,2351,3553,2980,3013,3526,1331,3474,923,2206,1184,2074,2690,1463,1565,2866,2832,2238,1037,882,2655,1417,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW474^3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.21 % Computer : n003.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:07:58 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.65/0.52 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.35/0.91 % [INFO] Parsing done (390ms).
% 2.35/0.92 % [INFO] Running in sequential loop mode.
% 3.74/1.32 % [INFO] eprover registered as external prover.
% 3.74/1.33 % [INFO] Scanning for conjecture ...
% 4.24/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 1224 axioms. Running axiom selection ...
% 5.41/1.86 % [INFO] Axiom selection finished. Selected 832 axioms (removed 392 axioms).
% 7.12/2.32 % [INFO] Problem is higher-order (TPTP THF).
% 7.12/2.36 % [INFO] Type checking passed.
% 7.12/2.36 % [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 ...
% 145.50/46.12 % External prover 'e' found a proof!
% 145.50/46.12 % [INFO] Killing All external provers ...
% 145.50/46.13 % Time passed: 45822ms (effective reasoning time: 45202ms)
% 145.50/46.13 % 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)>
% 145.50/46.13 % Axioms used in derivation (832): fact_804_IntI, fact_1073_Int__Collect__mono, fact_347_pigeonhole__infinite, fact_1051_Diff__partition, fact_1077_distrib__imp2, fact_1060_diff__single__insert, fact_412_Un__absorb, fact_227_finite__subset, fact_463_insert__is__Un, fact_1088_fun__upd__image, fact_344_pigeonhole__infinite, fact_1056_Un__Int__assoc__eq, fact_945_Diff__empty, fact_290_singleton__conv, fact_57_finite__surj, fact_1114_not__Some__eq, fact_957_insert__Diff__if, fact_863_Collect__conj__eq, fact_897_inf__absorb1, fact_1197_UNIV__I, fact_952_finite__Diff2, fact_792_folding__one_Oremove, fact_396_Un__assoc, fact_544_rev__predicate1D, fact_145_insertI1, fact_149_subset__trans, fact_729_folding__one_Oinsert, fact_202_insert__not__empty, fact_172_rev__image__eqI, fact_810_DiffI, fact_1118_dom__def, fact_1021_Int__Un__distrib, fact_824_Diff__disjoint, fact_1095_inj__on__Un, fact_1155_union__fold__insert, fact_401_Un__left__commute, fact_853_set__diff__eq, fact_697_com_Osimps_I12_J, fact_954_insert__Diff1, fact_374_the_Osimps, fact_535_sup1E, fact_346_pigeonhole__infinite, fact_744_Collect__mono, fact_679_folding__one__idem_Osubset__idem, fact_353_domD, fact_1184_option_Oexhaust, fact_423_Un__empty__left, fact_266_image__mono, fact_178_image__iff, fact_734_folding__one_Osingleton, fact_883_inf__le2, fact_1008_Int__absorb2, fact_622_sup__ge1, fact_873_inf__sup__ord_I1_J, fact_100_empty__Collect__eq, fact_936_inf__sup__distrib2, fact_366_order__refl, fact_15_finite__imageI, fact_663_sup__bot__right, fact_66_MGF, fact_101_empty__Collect__eq, fact_471_order__trans, fact_393_bex__Un, fact_891_le__infI1, fact_1112_not__Some__eq, fact_554_pred__subset__eq, fact_432_finite__Un, fact_906_inf__greatest, fact_252_insert__subset, fact_400_Un__left__commute, fact_248_subset__insert, fact_632_le__sup__iff, fact_315_finite__subset__image, fact_75_insertE, fact_217_image__is__empty, fact_755_equals0I, fact_970_Diff__mono, fact_656_le__supE, fact_743_Collect__mono, fact_575_sup_Oidem, fact_573_elem__set, fact_1174_inj__on__insert, fact_870_Un__Diff__Int, fact_583_sup_Ocommute, fact_260_insert__image, fact_808_DiffE, fact_480_ord__le__eq__trans, fact_226_finite__subset, fact_448_subset__Un__eq, fact_479_xt1_I4_J, fact_1170_folding__one__idem_Oeq__fold__idem_H, fact_939_sup__inf__distrib2, fact_799_conseq, fact_1093_comp__fun__idem__sup, fact_32_finite_OemptyI, fact_379_UnCI, fact_1025_distrib__inf__le, fact_1042_Diff__insert, fact_452_Un__upper1, fact_531_Body__sound__lemma, fact_420_Un__empty__right, fact_1_asm, fact_268_subset__image__iff, fact_710_WT_OSemi, fact_390_UnI1, fact_673_folding__one__idem_Ounion__idem, fact_711_com_Osimps_I18_J, fact_120_insert__ident, fact_275_domI, fact_880_inf__sup__ord_I2_J, help_fequal_1_1_fequal_000tc__Com__Ostate_T, fact_72_insertCI, fact_626_sup__ge2, fact_360_image__subsetI, fact_1020_Un__Int__distrib, fact_198_singleton__iff, fact_932_sup__inf__distrib1, fact_738_folding__one_Oclosed, fact_498_option_Oinject, fact_280_Collect__conv__if, fact_1106_option_Osimps_I2_J, fact_394_bex__Un, conj_3, fact_849_Int__def, fact_210_finite__insert, fact_301_imageE, fact_124_insert__code, fact_327_finite__induct, fact_525_bot__fun__def, fact_404_Un__commute, fact_131_insert__absorb2, fact_640_le__supI2, fact_659_sup__bot__left, fact_246_subset__insertI2, fact_1064_subset__insert__iff, fact_96_empty__iff, fact_522_bot__apply, fact_969_double__diff, fact_3_thin, fact_444_Un__absorb2, fact_968_double__diff, fact_1049_image__diff__subset, fact_460_insert__def, fact_923_inf__sup__absorb, fact_662_sup__bot__left, fact_130_insert__commute, fact_456_insert__def, fact_607_sup__left__commute, fact_343_pigeonhole__infinite, fact_365_image__subsetI, fact_488_ord__eq__le__trans, fact_996_Int__insert__left, fact_788_folding__one_Oinsert__remove, fact_947_empty__Diff, fact_787_folding__one_Oinsert__remove, fact_470_xt1_I5_J, fact_1138_Option_Oset_Osimps_I1_J, fact_1159_dom__minus, fact_1031_insert__Diff, fact_0_empty, fact_371_nonempty__iff, fact_689_finite__ne__induct, fact_192_singletonE, fact_232_rev__finite__subset, fact_605_sup__left__commute, fact_1109_option_Osimps_I3_J, fact_1006_Int__absorb1, fact_230_rev__finite__subset, fact_595_inf__sup__aci_I8_J, fact_971_Diff__mono, fact_909_inf__mono, fact_491_order__antisym__conv, fact_186_insert__compr__raw, fact_778_folding__one_Ounion__inter, fact_1040_Diff__insert2, fact_238_mem__def, fact_181_finite__Collect__disjI, fact_538_sup1CI, fact_993_insert__inter__insert, fact_59_finite__surj, fact_196_doubleton__eq__iff, fact_668_ospec, fact_771_evalc__elim__cases_I4_J, fact_274_domI, fact_328_finite__induct, fact_764_evalc_OBody, fact_637_le__supI1, fact_756_equals0I, fact_56_finite__surj, fact_556_sup__Un__eq, fact_1005_Int__absorb1, fact_146_insertI1, fact_215_image__is__empty, fact_691_LoopF, fact_910_inf__mono, fact_340_pigeonhole__infinite, fact_1103_inj__Some, fact_704_com_Osimps_I5_J, fact_38_image__constant__conv, fact_425_Un__empty__left, fact_871_Un__Diff__Int, fact_322_finite__subset__image, fact_190_singleton__inject, fact_1019_Un__Int__distrib, fact_51_insert__dom, fact_760_xt1_I15_J, fact_638_le__supI2, fact_572_elem__set, fact_1017_Int__Un__distrib2, fact_653_sup__mono, fact_523_bot__apply, fact_895_le__infI2, fact_1143_set__empty__eq, fact_1072_Int__Collect__mono, fact_802_IntE, fact_320_finite__subset__image, fact_450_Un__upper2, fact_1015_Un__Int__distrib2, fact_534_MGF__complete, fact_23_empty__subsetI, fact_350_domD, fact_944_Diff__empty, fact_1198_rangeI, fact_122_insert__code, fact_537_sup1CI, fact_961_disjoint__iff__not__equal, fact_1161_Sup__fin_Oidem, fact_13_finite__imageI, fact_1141_set__empty__eq, fact_948_empty__Diff, fact_990_Int__insert__right__if0, fact_737_folding__one_Oclosed, fact_143_insert__compr, fact_602_inf__sup__aci_I7_J, fact_770_com__det, fact_269_subset__image__iff, fact_214_image__is__empty, fact_115_insert__absorb, fact_255_subset__insertI, fact_158_in__mono, fact_382_UnE, fact_973_Diff__subset, fact_54_finite__surj, fact_1001_Int__mono, fact_1014_Un__Int__crazy, fact_319_finite__subset__image, fact_345_pigeonhole__infinite, fact_693_WTs__elim__cases_I6_J, fact_180_finite__Collect__disjI, fact_613_inf__sup__aci_I6_J, fact_244_subset__insertI2, fact_1111_option_Osimps_I3_J, fact_142_insert__compr, fact_1027_distrib__sup__le, fact_747_predicate1I, fact_106_all__not__in__conv, fact_977_Un__Diff__cancel2, fact_441_Un__mono, fact_88_equals0D, fact_11_finite__Collect__subsets, fact_87_equals0D, fact_1137_dom__empty, fact_272_domI, fact_291_singleton__conv2, fact_499_option_Oinject, fact_239_mem__def, fact_308_WTs__elim__cases_I7_J, fact_1153_inj__on__image__set__diff, fact_40_image__constant__conv, fact_1104_inj__Some, fact_848_Int__def, fact_920_inf__bot__left, fact_74_insertE, fact_858_Int__Collect, fact_620_sup__ge1, fact_658_le__supE, fact_728_folding__one_Oinsert, fact_267_image__mono, fact_913_le__infE, fact_179_finite__Collect__disjI, fact_854_set__diff__eq, fact_55_finite__surj, fact_765_evalc__elim__cases_I1_J, fact_546_predicate1D, fact_886_le__iff__inf, fact_223_empty__is__image, fact_815_finite__Int, fact_649_le__supI, fact_834_IntD2, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_105_all__not__in__conv, fact_61_finite__surj, fact_706_com_Osimps_I58_J, fact_126_insert__iff, fact_646_sup__absorb1, fact_793_folding__one_Oremove, fact_921_inf__bot__left, fact_845_Diff__iff, fact_589_sup__commute, fact_364_image__subsetI, fact_933_sup__inf__distrib1, fact_373_the_Osimps, fact_194_doubleton__eq__iff, fact_1043_Diff__insert, fact_629_le__iff__sup, fact_955_insert__Diff1, fact_643_sup__absorb2, fact_211_subset__empty, fact_128_insert__commute, fact_1108_option_Osimps_I2_J, fact_60_finite__surj, fact_355_domD, fact_929_inf__sup__distrib1, fact_434_Un__insert__left, fact_746_predicate1I, fact_199_singleton__iff, fact_53_finite__surj, fact_521_bot__apply, fact_1102_image__eq__fold__image, fact_323_finite__dom__body, fact_171_rev__image__eqI, fact_690_finite__ne__induct, fact_745_Collect__mono, fact_93_Collect__empty__eq, fact_44_image__constant, help_fequal_1_1_fequal_000tc__Com__Opname_T, fact_92_Collect__empty__eq, fact_757_MGT__alternD, fact_587_sup__commute, fact_165_set__eq__subset, fact_114_insert__absorb, fact_767_evalc_OSemi, fact_203_empty__not__insert, conj_2, fact_21_empty__subsetI, fact_601_sup_Oleft__commute, fact_611_inf__sup__aci_I6_J, fact_759_xt1_I15_J, fact_542_bot__empty__eq, fact_805_IntI, fact_439_Un__insert__right, fact_243_Collect__def, fact_721_folding__one__idem_Ohom__commute, fact_1078_distrib__imp2, fact_1175_dom__fun__upd, fact_1022_Int__Un__distrib, fact_732_triple_Oexhaust, fact_261_insert__image, fact_889_le__inf__iff, fact_20_finite__imageI, fact_312_finite__subset__image, fact_942_Diff__cancel, fact_715_folding__one__idem_Oin__idem, fact_298_imageE, fact_85_image__eqI, fact_220_image__empty, fact_222_empty__is__image, fact_1091_comp__fun__idem__insert, fact_577_sup_Oidem, fact_1002_Int__mono, fact_71_insertCI, fact_1055_Un__Int__assoc__eq, fact_339_pigeonhole__infinite, fact_650_sup__least, fact_840_DiffD1, fact_713_WT_OSkip, fact_869_Diff__Un, fact_249_subset__insert, fact_592_sup_Oleft__idem, fact_295_singleton__conv2, fact_50_insert__dom, fact_548_sup1I2, fact_821_inf__Int__eq, fact_1058_dom__if, fact_80_subsetD, fact_437_Un__insert__right, fact_67_emptyE, fact_310_subsetI, fact_453_Un__upper1, fact_1162_Sup__fin_Oidem, fact_362_image__subsetI, fact_501_constant, fact_1087_comp__fun__idem__remove, fact_1147_endo__inj__surj, fact_473_order__trans, fact_410_Un__def, fact_316_finite__subset__image, fact_1195_UNIV__I, fact_258_insert__image, fact_698_com_Osimps_I16_J, fact_52_finite__surj, fact_754_equals0I, fact_348_com_Osimps_I6_J, fact_991_Int__insert__right__if0, fact_299_imageE, fact_221_image__empty, fact_76_equalityI, fact_801_IntE, fact_12_finite__imageI, 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% 145.50/46.13 % No. of inferences in proof: 1867
% 145.50/46.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 45822 ms resp. 45202 ms w/o parsing
% 135.19/46.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 135.19/46.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------