TSTP Solution File: SWW474^1 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SWW474^1 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:22:54 EDT 2024
% Result : Theorem 20.64s 6.24s
% Output : Refutation 22.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 297
% Syntax : Number of formulae : 596 ( 177 unt; 0 typ; 0 def)
% Number of atoms : 2576 ( 618 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 3916 ( 182 ~; 72 |; 116 &;2942 @)
% ( 0 <=>; 604 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 1350 (1350 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 62 usr; 5 con; 0-3 aty)
% Number of variables : 1479 ( 173 ^1292 !; 14 ?;1479 :)
% Comments :
%------------------------------------------------------------------------------
thf(com_type,type,
com: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(hoare_1262092251_state_type,type,
hoare_1262092251_state: $tType ).
thf(option_com_type,type,
option_com: $tType ).
thf(wt_type,type,
wt: com > $o ).
thf(wT_bodies_type,type,
wT_bodies: $o ).
thf(body_type,type,
body: pname > option_com ).
thf(body_1_type,type,
body_1: pname > com ).
thf(finite1066544169me_o_o_type,type,
finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
thf(finite1303896758te_o_o_type,type,
finite1303896758te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > $o ).
thf(finite297249702name_o_type,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(finite1423311111tate_o_type,type,
finite1423311111tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(finite_finite_pname_type,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(finite1178804552_state_type,type,
finite1178804552_state: ( hoare_1262092251_state > $o ) > $o ).
thf(hoare_Mirabelle_MGT_type,type,
hoare_Mirabelle_MGT: com > hoare_1262092251_state ).
thf(hoare_930741239_state_type,type,
hoare_930741239_state: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(hoare_1821564147gleton_type,type,
hoare_1821564147gleton: $o ).
thf(dom_pname_o_com_type,type,
dom_pname_o_com: ( ( pname > $o ) > option_com ) > ( pname > $o ) > $o ).
thf(dom_Ho1489634536_o_com_type,type,
dom_Ho1489634536_o_com: ( ( hoare_1262092251_state > $o ) > option_com ) > ( hoare_1262092251_state > $o ) > $o ).
thf(dom_pname_com_type,type,
dom_pname_com: ( pname > option_com ) > pname > $o ).
thf(some_com_type,type,
some_com: com > option_com ).
thf(the_com_type,type,
the_com: option_com > com ).
thf(bot_bot_pname_o_o_type,type,
bot_bot_pname_o_o: ( pname > $o ) > $o ).
thf(bot_bo1962689075te_o_o_type,type,
bot_bo1962689075te_o_o: ( hoare_1262092251_state > $o ) > $o ).
thf(bot_bot_pname_o_type,type,
bot_bot_pname_o: pname > $o ).
thf(bot_bo113204042tate_o_type,type,
bot_bo113204042tate_o: hoare_1262092251_state > $o ).
thf(ord_le1205211808me_o_o_type,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(ord_le2012720639te_o_o_type,type,
ord_le2012720639te_o_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(ord_less_eq_pname_o_type,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(ord_le870406270tate_o_type,type,
ord_le870406270tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(collect_pname_o_o_type,type,
collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(collec341954548te_o_o_type,type,
collec341954548te_o_o: ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(collect_pname_o_type,type,
collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(collec313158217tate_o_type,type,
collec313158217tate_o: ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(collect_pname_type,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(collec1121927558_state_type,type,
collec1121927558_state: ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
thf(image_471733107_pname_type,type,
image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
thf(image_1036078444_state_type,type,
image_1036078444_state: ( ( ( pname > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( pname > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
thf(image_893364936_pname_type,type,
image_893364936_pname: ( ( ( hoare_1262092251_state > $o ) > $o ) > pname ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > pname > $o ).
thf(image_165349207_state_type,type,
image_165349207_state: ( ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state ) > ( ( ( hoare_1262092251_state > $o ) > $o ) > $o ) > hoare_1262092251_state > $o ).
thf(image_pname_o_pname_type,type,
image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
thf(image_1476171975_state_type,type,
image_1476171975_state: ( ( pname > $o ) > hoare_1262092251_state ) > ( ( pname > $o ) > $o ) > hoare_1262092251_state > $o ).
thf(image_1820530197_pname_type,type,
image_1820530197_pname: ( ( hoare_1262092251_state > $o ) > pname ) > ( ( hoare_1262092251_state > $o ) > $o ) > pname > $o ).
thf(image_234589002_state_type,type,
image_234589002_state: ( ( hoare_1262092251_state > $o ) > hoare_1262092251_state ) > ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state > $o ).
thf(image_pname_pname_o_type,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(image_518521461tate_o_type,type,
image_518521461tate_o: ( pname > hoare_1262092251_state > $o ) > ( pname > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(image_pname_pname_type,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(image_669833818_state_type,type,
image_669833818_state: ( pname > hoare_1262092251_state ) > ( pname > $o ) > hoare_1262092251_state > $o ).
thf(image_1320925383name_o_type,type,
image_1320925383name_o: ( hoare_1262092251_state > pname > $o ) > ( hoare_1262092251_state > $o ) > ( pname > $o ) > $o ).
thf(image_1403668518tate_o_type,type,
image_1403668518tate_o: ( hoare_1262092251_state > hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(image_202231862_pname_type,type,
image_202231862_pname: ( hoare_1262092251_state > pname ) > ( hoare_1262092251_state > $o ) > pname > $o ).
thf(insert_pname_o_type,type,
insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
thf(insert1042460334tate_o_type,type,
insert1042460334tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(insert_pname_type,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(insert81609953_state_type,type,
insert81609953_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > hoare_1262092251_state > $o ).
thf(fequal_pname_o_type,type,
fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(fequal1529404211tate_o_type,type,
fequal1529404211tate_o: ( hoare_1262092251_state > $o ) > ( hoare_1262092251_state > $o ) > $o ).
thf(fequal_pname_type,type,
fequal_pname: pname > pname > $o ).
thf(fequal1925511196_state_type,type,
fequal1925511196_state: hoare_1262092251_state > hoare_1262092251_state > $o ).
thf(member_pname_o_type,type,
member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(member907417095tate_o_type,type,
member907417095tate_o: ( hoare_1262092251_state > $o ) > ( ( hoare_1262092251_state > $o ) > $o ) > $o ).
thf(member_pname_type,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(member5164104_state_type,type,
member5164104_state: hoare_1262092251_state > ( hoare_1262092251_state > $o ) > $o ).
thf(fa_type,type,
fa: hoare_1262092251_state > $o ).
thf(pn_type,type,
pn: pname ).
thf(y_type,type,
y: com ).
thf(69,axiom,
! [A: ( pname > $o ) > $o] :
( ( ? [B: pname > $o] : ( member_pname_o @ B @ A ) )
= ( A != bot_bot_pname_o_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_ex__in__conv) ).
thf(479,plain,
! [A: ( pname > $o ) > $o] :
( ( ? [B: pname > $o] : ( member_pname_o @ B @ A ) )
= ( A != bot_bot_pname_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(198,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( member907417095tate_o @ A @ ( insert1042460334tate_o @ B @ C ) )
=> ( ( A != B )
=> ( member907417095tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_insertE) ).
thf(941,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( member907417095tate_o @ A @ ( insert1042460334tate_o @ B @ C ) )
=> ( ( A != B )
=> ( member907417095tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(262,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ord_le870406270tate_o @ B @ ( insert81609953_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_subset__insertI2) ).
thf(1179,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ord_le870406270tate_o @ B @ ( insert81609953_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(87,axiom,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( B = bot_bot_pname_o_o )
=> ~ ( member_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_equals0D) ).
thf(555,plain,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( B = bot_bot_pname_o_o )
=> ~ ( member_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(297,axiom,
! [A: pname > hoare_1262092251_state,B: pname > $o] :
( ( ( image_669833818_state @ A @ B )
= bot_bo113204042tate_o )
= ( B = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_image__is__empty) ).
thf(1295,plain,
! [A: pname > hoare_1262092251_state,B: pname > $o] :
( ( ( image_669833818_state @ A @ B )
= bot_bo113204042tate_o )
= ( B = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(27,axiom,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ ( insert_pname_o @ A @ B ) )
= ( finite297249702name_o @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__insert) ).
thf(365,plain,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ ( insert_pname_o @ A @ B ) )
= ( finite297249702name_o @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(266,axiom,
! [A: com] :
( hoare_1821564147gleton
=> ( wT_bodies
=> ( ( wt @ A )
=> ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo113204042tate_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_MGF) ).
thf(1190,plain,
! [A: com] :
( hoare_1821564147gleton
=> ( wT_bodies
=> ( ( wt @ A )
=> ( hoare_930741239_state @ bot_bo113204042tate_o @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo113204042tate_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(258,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ B @ C )
=> ( ( ord_le870406270tate_o @ A @ C )
=> ( hoare_930741239_state @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_weaken) ).
thf(1168,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ B @ C )
=> ( ( ord_le870406270tate_o @ A @ C )
=> ( hoare_930741239_state @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(151,axiom,
! [A: pname,B: pname > $o,C: ( pname > $o ) > $o] :
( ( member_pname_o @ B @ C )
=> ( ( image_pname_o_pname
@ ^ [D: pname > $o] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_image__constant) ).
thf(760,plain,
! [A: pname,B: pname > $o,C: ( pname > $o ) > $o] :
( ( member_pname_o @ B @ C )
=> ( ( image_pname_o_pname
@ ^ [D: pname > $o] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(189,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ( A != B )
| ( fequal1925511196_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com) ).
thf(909,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ( A != B )
| ( fequal1925511196_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(110,axiom,
! [A: hoare_1262092251_state > $o,B: ( pname > $o ) > hoare_1262092251_state,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_1476171975_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__surj) ).
thf(628,plain,
! [A: hoare_1262092251_state > $o,B: ( pname > $o ) > hoare_1262092251_state,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_1476171975_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(232,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state] :
( ( hoare_930741239_state @ B @ ( insert81609953_state @ C @ bot_bo113204042tate_o ) )
=> ( ( hoare_930741239_state @ B @ A )
=> ( hoare_930741239_state @ B @ ( insert81609953_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).
thf(1083,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state] :
( ( hoare_930741239_state @ B @ ( insert81609953_state @ C @ bot_bo113204042tate_o ) )
=> ( ( hoare_930741239_state @ B @ A )
=> ( hoare_930741239_state @ B @ ( insert81609953_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(206,axiom,
! [A: pname > $o] :
( ( collect_pname_o @ ( fequal_pname_o @ A ) )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_singleton__conv2) ).
thf(962,plain,
! [A: pname > $o] :
( ( collect_pname_o @ ( fequal_pname_o @ A ) )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(65,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_206_set__eq__subset) ).
thf(468,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)],[65]) ).
thf(269,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ ( insert81609953_state @ A @ B ) )
= ( insert81609953_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_insert__absorb2) ).
thf(1200,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ ( insert81609953_state @ A @ B ) )
= ( insert81609953_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(215,axiom,
! [A: hoare_1262092251_state,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_669833818_state
@ ^ [C: pname] : A
@ B )
= bot_bo113204042tate_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_669833818_state
@ ^ [C: pname] : A
@ B )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_image__constant__conv) ).
thf(1005,plain,
! [A: hoare_1262092251_state,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_669833818_state
@ ^ [C: pname] : A
@ B )
= bot_bo113204042tate_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_669833818_state
@ ^ [C: pname] : A
@ B )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(60,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_8_finite__Collect__subsets) ).
thf(449,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)],[60]) ).
thf(119,axiom,
! [A: pname > $o] :
~ ( member_pname_o @ A @ bot_bot_pname_o_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_emptyE) ).
thf(655,plain,
! [A: pname > $o] :
~ ( member_pname_o @ A @ bot_bot_pname_o_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(77,axiom,
! [A: ( ( hoare_1262092251_state > $o ) > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ C )
=> ( ( ord_le2012720639te_o_o @ C @ B )
=> ( ( A @ bot_bo1962689075te_o_o )
=> ( ! [D: hoare_1262092251_state > $o,E: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ E )
=> ( ( member907417095tate_o @ D @ B )
=> ( ~ ( member907417095tate_o @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert1042460334tate_o @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_finite__subset__induct) ).
thf(511,plain,
! [A: ( ( hoare_1262092251_state > $o ) > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ C )
=> ( ( ord_le2012720639te_o_o @ C @ B )
=> ( ( A @ bot_bo1962689075te_o_o )
=> ( ! [D: hoare_1262092251_state > $o,E: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ E )
=> ( ( member907417095tate_o @ D @ B )
=> ( ~ ( member907417095tate_o @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert1042460334tate_o @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(34,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_49_finite__Collect__conjI) ).
thf(384,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)],[34]) ).
thf(249,axiom,
! [A: hoare_1262092251_state,B: pname > $o,C: ( pname > $o ) > $o] :
( ( member_pname_o @ B @ C )
=> ( ( image_1476171975_state
@ ^ [D: pname > $o] : A
@ C )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_image__constant) ).
thf(1137,plain,
! [A: hoare_1262092251_state,B: pname > $o,C: ( pname > $o ) > $o] :
( ( member_pname_o @ B @ C )
=> ( ( image_1476171975_state
@ ^ [D: pname > $o] : A
@ C )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(278,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ~ ( member5164104_state @ B @ C )
=> ( ~ ( member5164104_state @ B @ A )
=> ( ( ( insert81609953_state @ B @ C )
= ( insert81609953_state @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_insert__ident) ).
thf(1233,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ~ ( member5164104_state @ B @ C )
=> ( ~ ( member5164104_state @ B @ A )
=> ( ( ( insert81609953_state @ B @ C )
= ( insert81609953_state @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(164,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A = B )
=> ( ord_le870406270tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_equalityD2) ).
thf(814,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A = B )
=> ( ord_le870406270tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(190,axiom,
! [A: ( pname > $o ) > $o,B: hoare_1262092251_state,C: ( pname > $o ) > hoare_1262092251_state,D: pname > $o] :
( ( B
= ( C @ D ) )
=> ( ( member_pname_o @ D @ A )
=> ( member5164104_state @ B @ ( image_1476171975_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_image__eqI) ).
thf(913,plain,
! [A: ( pname > $o ) > $o,B: hoare_1262092251_state,C: ( pname > $o ) > hoare_1262092251_state,D: pname > $o] :
( ( B
= ( C @ D ) )
=> ( ( member_pname_o @ D @ A )
=> ( member5164104_state @ B @ ( image_1476171975_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(80,axiom,
! [A: ( pname > $o ) > $o] :
( ( ! [B: pname > $o] :
~ ( member_pname_o @ B @ A ) )
= ( A = bot_bot_pname_o_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_all__not__in__conv) ).
thf(538,plain,
! [A: ( pname > $o ) > $o] :
( ( ! [B: pname > $o] :
~ ( member_pname_o @ B @ A ) )
= ( A = bot_bot_pname_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(284,axiom,
! [A: hoare_1262092251_state] :
( ( collec1121927558_state @ ( fequal1925511196_state @ A ) )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_singleton__conv2) ).
thf(1260,plain,
! [A: hoare_1262092251_state] :
( ( collec1121927558_state @ ( fequal1925511196_state @ A ) )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(129,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ A @ B )
=> ( ( ord_le870406270tate_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_equalityI) ).
thf(698,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ A @ B )
=> ( ( ord_le870406270tate_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(274,axiom,
( hoare_930741239_state
@ ( image_669833818_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(1222,plain,
( hoare_930741239_state
@ ( image_669833818_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(196,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) ).
thf(930,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)],[196]) ).
thf(268,axiom,
! [A: pname > $o,B: hoare_1262092251_state,C: pname > hoare_1262092251_state,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member5164104_state @ B @ ( image_669833818_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_image__eqI) ).
thf(1196,plain,
! [A: pname > $o,B: hoare_1262092251_state,C: pname > hoare_1262092251_state,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member5164104_state @ B @ ( image_669833818_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(245,axiom,
finite_finite_pname @ ( dom_pname_com @ body ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_finite__dom__body) ).
thf(1127,plain,
finite_finite_pname @ ( dom_pname_com @ body ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(159,axiom,
! [A: pname > pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( image_pname_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
thf(782,plain,
! [A: pname > pname,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( image_pname_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(133,axiom,
! [A: pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( member_pname_o @ A @ ( insert_pname_o @ B @ C ) )
=> ( ( A != B )
=> ( member_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_insertE) ).
thf(709,plain,
! [A: pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( member_pname_o @ A @ ( insert_pname_o @ B @ C ) )
=> ( ( A != B )
=> ( member_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(183,axiom,
! [A: pname] :
( ( collect_pname
@ ^ [B: pname] : ( B = A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_singleton__conv) ).
thf(885,plain,
! [A: pname] :
( ( collect_pname
@ ^ [B: pname] : ( B = A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(55,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_246_rev__finite__subset) ).
thf(436,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)],[55]) ).
thf(237,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ B )
= ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C = A )
| ( member5164104_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_insert__compr) ).
thf(1095,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ B )
= ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C = A )
| ( member5164104_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(41,axiom,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ ( insert1042460334tate_o @ A @ B ) )
= ( finite1423311111tate_o @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite__insert) ).
thf(404,plain,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ ( insert1042460334tate_o @ A @ B ) )
= ( finite1423311111tate_o @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(224,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state] :
( ( ord_le870406270tate_o @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
=> ( ( A = bot_bo113204042tate_o )
| ( A
= ( insert81609953_state @ B @ bot_bo113204042tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_subset__singletonD) ).
thf(1055,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state] :
( ( ord_le870406270tate_o @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
=> ( ( A = bot_bo113204042tate_o )
| ( A
= ( insert81609953_state @ B @ bot_bo113204042tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(92,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_244_finite__subset) ).
thf(570,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)],[92]) ).
thf(298,axiom,
! [A: hoare_1262092251_state > $o,B: pname > hoare_1262092251_state,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_669833818_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite__surj) ).
thf(1298,plain,
! [A: hoare_1262092251_state > $o,B: pname > hoare_1262092251_state,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_669833818_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(136,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_172_insert__ident) ).
thf(719,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)],[136]) ).
thf(30,axiom,
! [A: pname > $o] :
( ( ( collect_pname @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Collect__empty__eq) ).
thf(372,plain,
! [A: pname > $o] :
( ( ( collect_pname @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(74,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_196_set__mp) ).
thf(504,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)],[74]) ).
thf(291,axiom,
! [A: pname > hoare_1262092251_state,B: pname,C: pname > $o] :
( ( image_669833818_state @ A @ ( insert_pname @ B @ C ) )
= ( insert81609953_state @ ( A @ B ) @ ( image_669833818_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_image__insert) ).
thf(1279,plain,
! [A: pname > hoare_1262092251_state,B: pname,C: pname > $o] :
( ( image_669833818_state @ A @ ( insert_pname @ B @ C ) )
= ( insert81609953_state @ ( A @ B ) @ ( image_669833818_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(107,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_176_insert__iff) ).
thf(619,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)],[107]) ).
thf(169,axiom,
! [A: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_subset__refl) ).
thf(838,plain,
! [A: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(191,axiom,
! [A: hoare_1262092251_state > $o] :
~ ( member907417095tate_o @ A @ bot_bo1962689075te_o_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_emptyE) ).
thf(917,plain,
! [A: hoare_1262092251_state > $o] :
~ ( member907417095tate_o @ A @ bot_bo1962689075te_o_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(148,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state
@ ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1178804552_state @ ( collec1121927558_state @ A ) )
& ( finite1178804552_state @ ( collec1121927558_state @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_finite__Collect__disjI) ).
thf(751,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state
@ ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1178804552_state @ ( collec1121927558_state @ A ) )
& ( finite1178804552_state @ ( collec1121927558_state @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(188,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > $o] :
( ( ( A @ B )
=> ( ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C = B )
& ( A @ C ) ) )
= ( insert1042460334tate_o @ B @ bot_bo1962689075te_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo1962689075te_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_Collect__conv__if) ).
thf(902,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > $o] :
( ( ( A @ B )
=> ( ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C = B )
& ( A @ C ) ) )
= ( insert1042460334tate_o @ B @ bot_bo1962689075te_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo1962689075te_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(88,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_227_singleton__iff) ).
thf(559,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)],[88]) ).
thf(48,axiom,
! [A: pname > $o,B: pname > $o] :
( ~ ( fequal_pname_o @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T) ).
thf(421,plain,
! [A: pname > $o,B: pname > $o] :
( ~ ( fequal_pname_o @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(216,axiom,
! [A: hoare_1262092251_state,B: pname > hoare_1262092251_state,C: pname > $o] :
( ( member5164104_state @ A @ ( image_669833818_state @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_imageE) ).
thf(1013,plain,
! [A: hoare_1262092251_state,B: pname > hoare_1262092251_state,C: pname > $o] :
( ( member5164104_state @ A @ ( image_669833818_state @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(182,axiom,
! [A: ( pname > $o ) > option_com,B: pname > $o,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( ( insert_pname_o @ B @ ( dom_pname_o_com @ A ) )
= ( dom_pname_o_com @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_insert__dom) ).
thf(881,plain,
! [A: ( pname > $o ) > option_com,B: pname > $o,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( ( insert_pname_o @ B @ ( dom_pname_o_com @ A ) )
= ( dom_pname_o_com @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(46,axiom,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( insert1042460334tate_o @ A @ ( collec313158217tate_o @ B ) )
= ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_insert__Collect) ).
thf(416,plain,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( insert1042460334tate_o @ A @ ( collec313158217tate_o @ B ) )
= ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(72,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_equalityD2) ).
thf(492,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(98,axiom,
! [A: pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( ~ ( member_pname_o @ B @ C )
=> ( B = A ) )
=> ( member_pname_o @ B @ ( insert_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_insertCI) ).
thf(591,plain,
! [A: pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( ~ ( member_pname_o @ B @ C )
=> ( B = A ) )
=> ( member_pname_o @ B @ ( insert_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(58,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_93_finite__surj) ).
thf(443,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)],[58]) ).
thf(254,axiom,
! [A: com,B: hoare_1262092251_state > $o] :
( hoare_1821564147gleton
=> ( ! [C: pname] :
( ( member_pname @ C @ ( dom_pname_com @ body ) )
=> ( hoare_930741239_state @ B @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ C ) ) @ bot_bo113204042tate_o ) ) )
=> ( ( wt @ A )
=> ( hoare_930741239_state @ B @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo113204042tate_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_MGF__lemma1) ).
thf(1151,plain,
! [A: com,B: hoare_1262092251_state > $o] :
( hoare_1821564147gleton
=> ( ! [C: pname] :
( ( member_pname @ C @ ( dom_pname_com @ body ) )
=> ( hoare_930741239_state @ B @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ C ) ) @ bot_bo113204042tate_o ) ) )
=> ( ( wt @ A )
=> ( hoare_930741239_state @ B @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo113204042tate_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(21,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ord_le2012720639te_o_o @ A @ B )
=> ( ( ord_le2012720639te_o_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_equalityI) ).
thf(348,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ord_le2012720639te_o_o @ A @ B )
=> ( ( ord_le2012720639te_o_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(223,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_77_insert__dom) ).
thf(1051,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)],[223]) ).
thf(219,axiom,
! [A: hoare_1262092251_state > $o] : ( hoare_930741239_state @ A @ bot_bo113204042tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
thf(1040,plain,
! [A: hoare_1262092251_state > $o] : ( hoare_930741239_state @ A @ bot_bo113204042tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(242,axiom,
! [A: pname > $o,B: hoare_1262092251_state > $o] :
( ( ( B = bot_bo113204042tate_o )
=> ( ( image_1320925383name_o
@ ^ [C: hoare_1262092251_state] : A
@ B )
= bot_bot_pname_o_o ) )
& ( ( B != bot_bo113204042tate_o )
=> ( ( image_1320925383name_o
@ ^ [C: hoare_1262092251_state] : A
@ B )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_image__constant__conv) ).
thf(1109,plain,
! [A: pname > $o,B: hoare_1262092251_state > $o] :
( ( ( B = bot_bo113204042tate_o )
=> ( ( image_1320925383name_o
@ ^ [C: hoare_1262092251_state] : A
@ B )
= bot_bot_pname_o_o ) )
& ( ( B != bot_bo113204042tate_o )
=> ( ( image_1320925383name_o
@ ^ [C: hoare_1262092251_state] : A
@ B )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(9,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( collec313158217tate_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Collect__def) ).
thf(321,plain,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( collec313158217tate_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(153,axiom,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( insert_pname_o @ A @ B )
= ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C = A )
| ( member_pname_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_insert__compr) ).
thf(766,plain,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( insert_pname_o @ A @ B )
= ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C = A )
| ( member_pname_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(141,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_empty__subsetI) ).
thf(734,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(244,axiom,
! [A: hoare_1262092251_state,B: ( pname > $o ) > $o] :
( ( ( B = bot_bot_pname_o_o )
=> ( ( image_1476171975_state
@ ^ [C: pname > $o] : A
@ B )
= bot_bo113204042tate_o ) )
& ( ( B != bot_bot_pname_o_o )
=> ( ( image_1476171975_state
@ ^ [C: pname > $o] : A
@ B )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_image__constant__conv) ).
thf(1119,plain,
! [A: hoare_1262092251_state,B: ( pname > $o ) > $o] :
( ( ( B = bot_bot_pname_o_o )
=> ( ( image_1476171975_state
@ ^ [C: pname > $o] : A
@ B )
= bot_bo113204042tate_o ) )
& ( ( B != bot_bot_pname_o_o )
=> ( ( image_1476171975_state
@ ^ [C: pname > $o] : A
@ B )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(44,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ B )
=> ( ( ord_le2012720639te_o_o @ A @ B )
=> ( finite1423311111tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_rev__finite__subset) ).
thf(411,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ B )
=> ( ( ord_le2012720639te_o_o @ A @ B )
=> ( finite1423311111tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(51,axiom,
! [A: ( hoare_1262092251_state > $o ) > pname,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ B )
=> ( finite_finite_pname @ ( image_1820530197_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(428,plain,
! [A: ( hoare_1262092251_state > $o ) > pname,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ B )
=> ( finite_finite_pname @ ( image_1820530197_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(229,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( member5164104_state @ B @ ( insert81609953_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_insertI2) ).
thf(1074,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( member5164104_state @ B @ ( insert81609953_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(192,axiom,
! [A: hoare_1262092251_state > pname > $o,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( finite297249702name_o @ ( image_1320925383name_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_finite__imageI) ).
thf(920,plain,
! [A: hoare_1262092251_state > pname > $o,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( finite297249702name_o @ ( image_1320925383name_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(125,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_237_subset__empty) ).
thf(678,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)],[125]) ).
thf(194,axiom,
! [A: hoare_1262092251_state > $o,B: ( ( pname > $o ) > $o ) > hoare_1262092251_state,C: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_1036078444_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__surj) ).
thf(925,plain,
! [A: hoare_1262092251_state > $o,B: ( ( pname > $o ) > $o ) > hoare_1262092251_state,C: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_1036078444_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(33,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_215_finite__Collect__disjI) ).
thf(381,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)],[33]) ).
thf(227,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( B = bot_bo113204042tate_o )
=> ~ ( member5164104_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_equals0D) ).
thf(1067,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( B = bot_bo113204042tate_o )
=> ~ ( member5164104_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(222,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( bot_bo113204042tate_o
!= ( insert81609953_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_empty__not__insert) ).
thf(1047,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( bot_bo113204042tate_o
!= ( insert81609953_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(256,axiom,
! [A: hoare_1262092251_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_669833818_state
@ ^ [D: pname] : A
@ C )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_image__constant) ).
thf(1163,plain,
! [A: hoare_1262092251_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_669833818_state
@ ^ [D: pname] : A
@ C )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(289,axiom,
! [A: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ bot_bo113204042tate_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_empty__subsetI) ).
thf(1274,plain,
! [A: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ bot_bo113204042tate_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(166,axiom,
! [A: pname,B: ( pname > $o ) > $o] :
( ( ( B = bot_bot_pname_o_o )
=> ( ( image_pname_o_pname
@ ^ [C: pname > $o] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bot_pname_o_o )
=> ( ( image_pname_o_pname
@ ^ [C: pname > $o] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_image__constant__conv) ).
thf(825,plain,
! [A: pname,B: ( pname > $o ) > $o] :
( ( ( B = bot_bot_pname_o_o )
=> ( ( image_pname_o_pname
@ ^ [C: pname > $o] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bot_pname_o_o )
=> ( ( image_pname_o_pname
@ ^ [C: pname > $o] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(158,axiom,
! [A: pname,B: pname > $o] :
( bot_bot_pname_o
!= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_empty__not__insert) ).
thf(778,plain,
! [A: pname,B: pname > $o] :
( bot_bot_pname_o
!= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(220,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state] :
( ( insert81609953_state @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_insert__code) ).
thf(1042,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state] :
( ( insert81609953_state @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(282,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ~ ( member5164104_state @ B @ C )
=> ( ( ord_le870406270tate_o @ C @ ( insert81609953_state @ B @ A ) )
= ( ord_le870406270tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_subset__insert) ).
thf(1255,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ~ ( member5164104_state @ B @ C )
=> ( ( ord_le870406270tate_o @ C @ ( insert81609953_state @ B @ A ) )
= ( ord_le870406270tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(177,axiom,
( bot_bot_pname_o_o
= ( collect_pname_o
@ ^ [A: pname > $o] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_empty__def) ).
thf(862,plain,
( bot_bot_pname_o_o
= ( collect_pname_o
@ ^ [A: pname > $o] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(260,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state,D: hoare_1262092251_state] :
( ( ( insert81609953_state @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
= ( insert81609953_state @ C @ ( insert81609953_state @ D @ bot_bo113204042tate_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_doubleton__eq__iff) ).
thf(1174,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state,D: hoare_1262092251_state] :
( ( ( insert81609953_state @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
= ( insert81609953_state @ C @ ( insert81609953_state @ D @ bot_bo113204042tate_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(273,axiom,
! [A: pname > hoare_1262092251_state,B: pname > $o,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_le870406270tate_o @ C @ ( image_669833818_state @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_669833818_state @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_finite__subset__image) ).
thf(1217,plain,
! [A: pname > hoare_1262092251_state,B: pname > $o,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_le870406270tate_o @ C @ ( image_669833818_state @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_669833818_state @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(37,axiom,
! [A: ( pname > $o ) > $o] :
( ( bot_bot_pname_o_o
= ( collect_pname_o @ A ) )
= ( ! [B: pname > $o] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_empty__Collect__eq) ).
thf(392,plain,
! [A: ( pname > $o ) > $o] :
( ( bot_bot_pname_o_o
= ( collect_pname_o @ A ) )
= ( ! [B: pname > $o] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(49,axiom,
! [A: pname > $o,B: ( hoare_1262092251_state > $o ) > pname,C: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_1820530197_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_finite__surj) ).
thf(424,plain,
! [A: pname > $o,B: ( hoare_1262092251_state > $o ) > pname,C: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_1820530197_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(139,axiom,
! [A: pname > $o,B: ( ( hoare_1262092251_state > $o ) > $o ) > pname,C: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( finite1303896758te_o_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_893364936_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_finite__surj) ).
thf(729,plain,
! [A: pname > $o,B: ( ( hoare_1262092251_state > $o ) > $o ) > pname,C: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( finite1303896758te_o_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_893364936_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(204,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_258_subset__insertI2) ).
thf(957,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)],[204]) ).
thf(275,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ( ( insert81609953_state @ A @ bot_bo113204042tate_o )
= ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_singleton__inject) ).
thf(1223,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ( ( insert81609953_state @ A @ bot_bo113204042tate_o )
= ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(42,axiom,
! [A: ( ( pname > $o ) > $o ) > pname,B: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ B )
=> ( finite_finite_pname @ ( image_471733107_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(407,plain,
! [A: ( ( pname > $o ) > $o ) > pname,B: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ B )
=> ( finite_finite_pname @ ( image_471733107_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(111,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_225_doubleton__eq__iff) ).
thf(630,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)],[111]) ).
thf(25,axiom,
! [A: ( ( pname > $o ) > $o ) > hoare_1262092251_state,B: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ B )
=> ( finite1178804552_state @ ( image_1036078444_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(361,plain,
! [A: ( ( pname > $o ) > $o ) > hoare_1262092251_state,B: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ B )
=> ( finite1178804552_state @ ( image_1036078444_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(109,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_emptyE) ).
thf(625,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(121,axiom,
! [A: ( hoare_1262092251_state > $o ) > option_com,B: hoare_1262092251_state > $o,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( ( insert1042460334tate_o @ B @ ( dom_Ho1489634536_o_com @ A ) )
= ( dom_Ho1489634536_o_com @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_insert__dom) ).
thf(665,plain,
! [A: ( hoare_1262092251_state > $o ) > option_com,B: hoare_1262092251_state > $o,C: com] :
( ( ( A @ B )
= ( some_com @ C ) )
=> ( ( insert1042460334tate_o @ B @ ( dom_Ho1489634536_o_com @ A ) )
= ( dom_Ho1489634536_o_com @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(271,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ A @ ( insert81609953_state @ B @ C ) )
= ( ( A = B )
| ( member5164104_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_insert__iff) ).
thf(1210,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ A @ ( insert81609953_state @ B @ C ) )
= ( ( A = B )
| ( member5164104_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(150,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_233_finite__insert) ).
thf(757,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)],[150]) ).
thf(10,axiom,
! [A: pname > $o,B: ( pname > $o ) > $o,C: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ B @ C )
=> ( ( member_pname_o @ A @ B )
=> ( member_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_subsetD) ).
thf(324,plain,
! [A: pname > $o,B: ( pname > $o ) > $o,C: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ B @ C )
=> ( ( member_pname_o @ A @ B )
=> ( member_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(241,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( member907417095tate_o @ B @ C )
=> ( ( image_234589002_state
@ ^ [D: hoare_1262092251_state > $o] : A
@ C )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_image__constant) ).
thf(1106,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( member907417095tate_o @ B @ C )
=> ( ( image_234589002_state
@ ^ [D: hoare_1262092251_state > $o] : A
@ C )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(172,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_119_equalityI) ).
thf(847,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)],[172]) ).
thf(90,axiom,
wT_bodies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(566,plain,
wT_bodies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(85,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_170_insertI2) ).
thf(551,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)],[85]) ).
thf(246,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ B )
= ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C = A )
| ( member5164104_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_insert__compr__raw) ).
thf(1128,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ B )
= ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C = A )
| ( member5164104_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(217,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_le870406270tate_o @ C @ B )
=> ( ( A @ bot_bo113204042tate_o )
=> ( ! [D: hoare_1262092251_state,E: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ E )
=> ( ( member5164104_state @ D @ B )
=> ( ~ ( member5164104_state @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert81609953_state @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_finite__subset__induct) ).
thf(1017,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_le870406270tate_o @ C @ B )
=> ( ( A @ bot_bo113204042tate_o )
=> ( ! [D: hoare_1262092251_state,E: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ E )
=> ( ( member5164104_state @ D @ B )
=> ( ~ ( member5164104_state @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert81609953_state @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(105,axiom,
! [A: hoare_1262092251_state > $o,B: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,C: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( finite1303896758te_o_o @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_165349207_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__surj) ).
thf(615,plain,
! [A: hoare_1262092251_state > $o,B: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,C: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( finite1303896758te_o_o @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_165349207_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(103,axiom,
! [A: pname > $o,B: hoare_1262092251_state > pname,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_202231862_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_finite__surj) ).
thf(610,plain,
! [A: pname > $o,B: hoare_1262092251_state > pname,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_202231862_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(174,axiom,
finite1178804552_state @ fa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(857,plain,
finite1178804552_state @ fa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(144,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_248_rev__finite__subset) ).
thf(742,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)],[144]) ).
thf(95,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > $o] :
( ( ( A @ B )
=> ( ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( B = C )
& ( A @ C ) ) )
= ( insert1042460334tate_o @ B @ bot_bo1962689075te_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo1962689075te_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_Collect__conv__if2) ).
thf(578,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > $o] :
( ( ( A @ B )
=> ( ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( B = C )
& ( A @ C ) ) )
= ( insert1042460334tate_o @ B @ bot_bo1962689075te_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo1962689075te_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(181,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A = B )
=> ~ ( ( ord_le870406270tate_o @ A @ B )
=> ~ ( ord_le870406270tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_equalityE) ).
thf(874,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A = B )
=> ~ ( ( ord_le870406270tate_o @ A @ B )
=> ~ ( ord_le870406270tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(251,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ord_le870406270tate_o @ ( insert81609953_state @ A @ B ) @ ( insert81609953_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_insert__mono) ).
thf(1143,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ord_le870406270tate_o @ ( insert81609953_state @ A @ B ) @ ( insert81609953_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(66,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_subset__refl) ).
thf(471,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(17,axiom,
! [A: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ A )
=> ( finite1423311111tate_o
@ ( collec313158217tate_o
@ ^ [B: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).
thf(339,plain,
! [A: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ A )
=> ( finite1423311111tate_o
@ ( collec313158217tate_o
@ ^ [B: hoare_1262092251_state > $o] : ( ord_le870406270tate_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(122,axiom,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_ex__in__conv) ).
thf(669,plain,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(115,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_250_insert__mono) ).
thf(642,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)],[115]) ).
thf(208,axiom,
! [A: hoare_1262092251_state > hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( finite1423311111tate_o @ ( image_1403668518tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_finite__imageI) ).
thf(970,plain,
! [A: hoare_1262092251_state > hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( finite1423311111tate_o @ ( image_1403668518tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(255,axiom,
! [A: hoare_1262092251_state,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ( B = bot_bo1962689075te_o_o )
=> ( ( image_234589002_state
@ ^ [C: hoare_1262092251_state > $o] : A
@ B )
= bot_bo113204042tate_o ) )
& ( ( B != bot_bo1962689075te_o_o )
=> ( ( image_234589002_state
@ ^ [C: hoare_1262092251_state > $o] : A
@ B )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_image__constant__conv) ).
thf(1155,plain,
! [A: hoare_1262092251_state,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ( B = bot_bo1962689075te_o_o )
=> ( ( image_234589002_state
@ ^ [C: hoare_1262092251_state > $o] : A
@ B )
= bot_bo113204042tate_o ) )
& ( ( B != bot_bo1962689075te_o_o )
=> ( ( image_234589002_state
@ ^ [C: hoare_1262092251_state > $o] : A
@ B )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(132,axiom,
! [A: pname] :
( ( collect_pname @ ( fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_singleton__conv2) ).
thf(706,plain,
! [A: pname] :
( ( collect_pname @ ( fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(295,axiom,
( ( body @ pn )
= ( some_com @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(1292,plain,
( ( body @ pn )
= ( some_com @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(197,axiom,
! [A: pname,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_pname_pname
@ ^ [C: pname] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_pname_pname
@ ^ [C: pname] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_image__constant__conv) ).
thf(933,plain,
! [A: pname,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_pname_pname
@ ^ [C: pname] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_pname_pname
@ ^ [C: pname] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(127,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: pname,C: ( hoare_1262092251_state > $o ) > pname,D: hoare_1262092251_state > $o] :
( ( B
= ( C @ D ) )
=> ( ( member907417095tate_o @ D @ A )
=> ( member_pname @ B @ ( image_1820530197_pname @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_image__eqI) ).
thf(686,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: pname,C: ( hoare_1262092251_state > $o ) > pname,D: hoare_1262092251_state > $o] :
( ( B
= ( C @ D ) )
=> ( ( member907417095tate_o @ D @ A )
=> ( member_pname @ B @ ( image_1820530197_pname @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(68,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_260_subset__insert) ).
thf(476,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)],[68]) ).
thf(108,axiom,
! [A: pname > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( ( image_1320925383name_o
@ ^ [D: hoare_1262092251_state] : A
@ C )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_image__constant) ).
thf(622,plain,
! [A: pname > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( ( image_1320925383name_o
@ ^ [D: hoare_1262092251_state] : A
@ C )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(130,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ A @ B )
=> ( ( finite1178804552_state @ B )
=> ( finite1178804552_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_finite__subset) ).
thf(701,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ A @ B )
=> ( ( finite1178804552_state @ B )
=> ( finite1178804552_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(286,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ B @ C )
=> ( ( hoare_930741239_state @ A @ B )
=> ( hoare_930741239_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cut) ).
thf(1266,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ B @ C )
=> ( ( hoare_930741239_state @ A @ B )
=> ( hoare_930741239_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(247,axiom,
! [A: hoare_1262092251_state > $o] :
( ( bot_bo113204042tate_o
= ( collec1121927558_state @ A ) )
= ( ! [B: hoare_1262092251_state] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_empty__Collect__eq) ).
thf(1131,plain,
! [A: hoare_1262092251_state > $o] :
( ( bot_bo113204042tate_o
= ( collec1121927558_state @ A ) )
= ( ! [B: hoare_1262092251_state] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(63,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_271_Collect__conv__if) ).
thf(457,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)],[63]) ).
thf(117,axiom,
! [A: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ B )
=> ( finite1178804552_state @ ( image_234589002_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(647,plain,
! [A: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ B )
=> ( finite1178804552_state @ ( image_234589002_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(285,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( member5164104_state @ A @ B )
=> ( ( insert81609953_state @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_insert__absorb) ).
thf(1263,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( member5164104_state @ A @ B )
=> ( ( insert81609953_state @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(212,axiom,
! [A: hoare_1262092251_state] :
~ ( member5164104_state @ A @ bot_bo113204042tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_empty__iff) ).
thf(997,plain,
! [A: hoare_1262092251_state] :
~ ( member5164104_state @ A @ bot_bo113204042tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(19,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o
@ ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1423311111tate_o @ ( collec313158217tate_o @ A ) )
& ( finite1423311111tate_o @ ( collec313158217tate_o @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_finite__Collect__disjI) ).
thf(343,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o
@ ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1423311111tate_o @ ( collec313158217tate_o @ A ) )
& ( finite1423311111tate_o @ ( collec313158217tate_o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(112,axiom,
( bot_bot_pname_o
= ( collect_pname
@ ^ [A: pname] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_empty__def) ).
thf(633,plain,
( bot_bot_pname_o
= ( collect_pname
@ ^ [A: pname] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(76,axiom,
! [A: hoare_1262092251_state > $o] :
( ( collec313158217tate_o @ ( fequal1529404211tate_o @ A ) )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_singleton__conv2) ).
thf(508,plain,
! [A: hoare_1262092251_state > $o] :
( ( collec313158217tate_o @ ( fequal1529404211tate_o @ A ) )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(81,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ( member5164104_state @ A @ B )
=> ( member5164104_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_set__mp) ).
thf(541,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ( member5164104_state @ A @ B )
=> ( member5164104_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(259,axiom,
! [A: pname] :
( ( wt @ ( body_1 @ A ) )
=> ~ ! [B: com] :
( ( body @ A )
!= ( some_com @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_WTs__elim__cases_I7_J) ).
thf(1170,plain,
! [A: pname] :
( ( wt @ ( body_1 @ A ) )
=> ~ ! [B: com] :
( ( body @ A )
!= ( some_com @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(39,axiom,
! [A: pname > $o] :
( ( bot_bot_pname_o
= ( collect_pname @ A ) )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_empty__Collect__eq) ).
thf(398,plain,
! [A: pname > $o] :
( ( bot_bot_pname_o
= ( collect_pname @ A ) )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(228,axiom,
! [A: hoare_1262092251_state > $o,B: pname > hoare_1262092251_state,C: pname > $o] :
( ( ord_le870406270tate_o @ A @ ( image_669833818_state @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_669833818_state @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_subset__image__iff) ).
thf(1071,plain,
! [A: hoare_1262092251_state > $o,B: pname > hoare_1262092251_state,C: pname > $o] :
( ( ord_le870406270tate_o @ A @ ( image_669833818_state @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_669833818_state @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(265,axiom,
! [A: hoare_1262092251_state > $o] :
( ( ? [B: hoare_1262092251_state] : ( member5164104_state @ B @ A ) )
= ( A != bot_bo113204042tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_ex__in__conv) ).
thf(1187,plain,
! [A: hoare_1262092251_state > $o] :
( ( ? [B: hoare_1262092251_state] : ( member5164104_state @ B @ A ) )
= ( A != bot_bo113204042tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(156,axiom,
! [A: hoare_1262092251_state > $o] :
~ ( member907417095tate_o @ A @ bot_bo1962689075te_o_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_empty__iff) ).
thf(773,plain,
! [A: hoare_1262092251_state > $o] :
~ ( member907417095tate_o @ A @ bot_bo1962689075te_o_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(184,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( ( ord_le870406270tate_o @ C @ A )
=> ( member5164104_state @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_set__rev__mp) ).
thf(888,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( ( ord_le870406270tate_o @ C @ A )
=> ( member5164104_state @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(207,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( ~ ( member907417095tate_o @ B @ C )
=> ( B = A ) )
=> ( member907417095tate_o @ B @ ( insert1042460334tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_insertCI) ).
thf(965,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( ~ ( member907417095tate_o @ B @ C )
=> ( B = A ) )
=> ( member907417095tate_o @ B @ ( insert1042460334tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(52,axiom,
! [A: ( pname > $o ) > $o] :
( ( finite297249702name_o @ A )
=> ( finite1066544169me_o_o
@ ( collect_pname_o_o
@ ^ [B: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__Collect__subsets) ).
thf(430,plain,
! [A: ( pname > $o ) > $o] :
( ( finite297249702name_o @ A )
=> ( finite1066544169me_o_o
@ ( collect_pname_o_o
@ ^ [B: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(146,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( ? [B: hoare_1262092251_state > $o] : ( member907417095tate_o @ B @ A ) )
= ( A != bot_bo1962689075te_o_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_ex__in__conv) ).
thf(745,plain,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( ? [B: hoare_1262092251_state > $o] : ( member907417095tate_o @ B @ A ) )
= ( A != bot_bo1962689075te_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(31,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_182_insert__Collect) ).
thf(375,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)],[31]) ).
thf(89,axiom,
! [A: hoare_1262092251_state > $o,B: pname > $o,C: hoare_1262092251_state > pname > $o,D: hoare_1262092251_state] :
( ( B
= ( C @ D ) )
=> ( ( member5164104_state @ D @ A )
=> ( member_pname_o @ B @ ( image_1320925383name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_image__eqI) ).
thf(562,plain,
! [A: hoare_1262092251_state > $o,B: pname > $o,C: hoare_1262092251_state > pname > $o,D: hoare_1262092251_state] :
( ( B
= ( C @ D ) )
=> ( ( member5164104_state @ D @ A )
=> ( member_pname_o @ B @ ( image_1320925383name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(171,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_equalityD1) ).
thf(843,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(45,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ( finite1423311111tate_o @ ( collec313158217tate_o @ B ) )
| ( finite1423311111tate_o @ ( collec313158217tate_o @ A ) ) )
=> ( finite1423311111tate_o
@ ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_finite__Collect__conjI) ).
thf(413,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ( finite1423311111tate_o @ ( collec313158217tate_o @ B ) )
| ( finite1423311111tate_o @ ( collec313158217tate_o @ A ) ) )
=> ( finite1423311111tate_o
@ ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(276,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ ( insert81609953_state @ A @ B ) @ C )
= ( ( member5164104_state @ A @ C )
& ( ord_le870406270tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_insert__subset) ).
thf(1226,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ ( insert81609953_state @ A @ B ) @ C )
= ( ( member5164104_state @ A @ C )
& ( ord_le870406270tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(83,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_insert__absorb) ).
thf(545,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(59,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A != B )
| ( fequal_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T) ).
thf(445,plain,
! [A: pname > $o,B: pname > $o] :
( ( A != B )
| ( fequal_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(93,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_pname_pname_o
@ ^ [D: pname] : A
@ C )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_image__constant) ).
thf(572,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_pname_pname_o
@ ^ [D: pname] : A
@ C )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(7,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(313,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)],[7]) ).
thf(288,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ ( collec1121927558_state @ B ) )
= ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_insert__Collect) ).
thf(1271,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ ( collec1121927558_state @ B ) )
= ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(225,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state] :
( ( ( A @ B )
=> ( ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( B = C )
& ( A @ C ) ) )
= ( insert81609953_state @ B @ bot_bo113204042tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo113204042tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_Collect__conv__if2) ).
thf(1058,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state] :
( ( ( A @ B )
=> ( ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( B = C )
& ( A @ C ) ) )
= ( insert81609953_state @ B @ bot_bo113204042tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo113204042tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(236,axiom,
! [A: hoare_1262092251_state > $o] :
( ( ! [B: hoare_1262092251_state] :
~ ( member5164104_state @ B @ A ) )
= ( A = bot_bo113204042tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_all__not__in__conv) ).
thf(1092,plain,
! [A: hoare_1262092251_state > $o] :
( ( ! [B: hoare_1262092251_state] :
~ ( member5164104_state @ B @ A ) )
= ( A = bot_bo113204042tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(15,axiom,
finite1423311111tate_o @ bot_bo1962689075te_o_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite_OemptyI) ).
thf(335,plain,
finite1423311111tate_o @ bot_bo1962689075te_o_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(235,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( finite1178804552_state @ ( insert81609953_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_finite_OinsertI) ).
thf(1090,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( finite1178804552_state @ ( insert81609953_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(283,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ A @ B )
=> ( hoare_930741239_state @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_asm) ).
thf(1258,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ A @ B )
=> ( hoare_930741239_state @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(200,axiom,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( B = bot_bo1962689075te_o_o )
=> ~ ( member907417095tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_equals0D) ).
thf(947,plain,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( B = bot_bo1962689075te_o_o )
=> ~ ( member907417095tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(123,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_180_insert__absorb2) ).
thf(672,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)],[123]) ).
thf(101,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > hoare_1262092251_state > $o,D: hoare_1262092251_state] :
( ( B
= ( C @ D ) )
=> ( ( member5164104_state @ D @ A )
=> ( member907417095tate_o @ B @ ( image_1403668518tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_image__eqI) ).
thf(604,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > hoare_1262092251_state > $o,D: hoare_1262092251_state] :
( ( B
= ( C @ D ) )
=> ( ( member5164104_state @ D @ A )
=> ( member907417095tate_o @ B @ ( image_1403668518tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(187,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_38_finite_OinsertI) ).
thf(900,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)],[187]) ).
thf(126,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_111_insertCI) ).
thf(681,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)],[126]) ).
thf(292,axiom,
! [A: hoare_1262092251_state,B: pname > hoare_1262092251_state,C: pname > $o] :
( ( member5164104_state @ A @ ( image_669833818_state @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_image__iff) ).
thf(1282,plain,
! [A: hoare_1262092251_state,B: pname > hoare_1262092251_state,C: pname > $o] :
( ( member5164104_state @ A @ ( image_669833818_state @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(47,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: pname > hoare_1262092251_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le2012720639te_o_o @ A @ ( image_518521461tate_o @ B @ C ) )
=> ( finite1423311111tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__surj) ).
thf(419,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: pname > hoare_1262092251_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le2012720639te_o_o @ A @ ( image_518521461tate_o @ B @ C ) )
=> ( finite1423311111tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(142,axiom,
! [A: hoare_1262092251_state > $o] :
( ( collec1121927558_state @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Collect__def) ).
thf(736,plain,
! [A: hoare_1262092251_state > $o] :
( ( collec1121927558_state @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(54,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ bot_bo1962689075te_o_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_empty__subsetI) ).
thf(434,plain,
! [A: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ bot_bo1962689075te_o_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(4,axiom,
! [A: ( ( pname > $o ) > $o ) > $o,B: ( ( pname > $o ) > $o ) > $o] :
( ( ( finite1066544169me_o_o @ ( collect_pname_o_o @ B ) )
| ( finite1066544169me_o_o @ ( collect_pname_o_o @ A ) ) )
=> ( finite1066544169me_o_o
@ ( collect_pname_o_o
@ ^ [C: ( pname > $o ) > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_finite__Collect__conjI) ).
thf(303,plain,
! [A: ( ( pname > $o ) > $o ) > $o,B: ( ( pname > $o ) > $o ) > $o] :
( ( ( finite1066544169me_o_o @ ( collect_pname_o_o @ B ) )
| ( finite1066544169me_o_o @ ( collect_pname_o_o @ A ) ) )
=> ( finite1066544169me_o_o
@ ( collect_pname_o_o
@ ^ [C: ( pname > $o ) > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(160,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_198_set__rev__mp) ).
thf(784,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)],[160]) ).
thf(243,axiom,
! [A: pname > hoare_1262092251_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member5164104_state @ ( A @ B ) @ ( image_669833818_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_imageI) ).
thf(1117,plain,
! [A: pname > hoare_1262092251_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member5164104_state @ ( A @ B ) @ ( image_669833818_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(61,axiom,
! [A: pname,B: hoare_1262092251_state > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( member907417095tate_o @ B @ C )
=> ( ( image_1820530197_pname
@ ^ [D: hoare_1262092251_state > $o] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_image__constant) ).
thf(451,plain,
! [A: pname,B: hoare_1262092251_state > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( member907417095tate_o @ B @ C )
=> ( ( image_1820530197_pname
@ ^ [D: hoare_1262092251_state > $o] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(91,axiom,
! [A: pname > $o] :
( ( collect_pname_o
@ ^ [B: pname > $o] : ( B = A ) )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_singleton__conv) ).
thf(567,plain,
! [A: pname > $o] :
( ( collect_pname_o
@ ^ [B: pname > $o] : ( B = A ) )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(185,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_192_equalityE) ).
thf(890,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)],[185]) ).
thf(175,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_123_subsetD) ).
thf(858,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)],[175]) ).
thf(138,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_262_insert__subset) ).
thf(726,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)],[138]) ).
thf(154,axiom,
! [A: pname > $o,B: ( ( pname > $o ) > $o ) > pname,C: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_471733107_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_finite__surj) ).
thf(769,plain,
! [A: pname > $o,B: ( ( pname > $o ) > $o ) > pname,C: ( ( pname > $o ) > $o ) > $o] :
( ( finite1066544169me_o_o @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_471733107_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(261,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ B @ C )
=> ( ( ord_le870406270tate_o @ B @ A )
=> ( hoare_930741239_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_thin) ).
thf(1177,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ B @ C )
=> ( ( ord_le870406270tate_o @ B @ A )
=> ( hoare_930741239_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(13,axiom,
! [A: ( ( hoare_1262092251_state > $o ) > $o ) > pname,B: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( finite1303896758te_o_o @ B )
=> ( finite_finite_pname @ ( image_893364936_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(330,plain,
! [A: ( ( hoare_1262092251_state > $o ) > $o ) > pname,B: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( finite1303896758te_o_o @ B )
=> ( finite_finite_pname @ ( image_893364936_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(163,axiom,
! [A: pname,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( ( image_202231862_pname
@ ^ [D: hoare_1262092251_state] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_image__constant) ).
thf(811,plain,
! [A: pname,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( ( image_202231862_pname
@ ^ [D: hoare_1262092251_state] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(35,axiom,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ A @ B )
=> ( ( ord_le1205211808me_o_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_equalityI) ).
thf(387,plain,
! [A: ( pname > $o ) > $o,B: ( pname > $o ) > $o] :
( ( ord_le1205211808me_o_o @ A @ B )
=> ( ( ord_le1205211808me_o_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(205,axiom,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( insert1042460334tate_o @ A @ B )
= ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C = A )
| ( member907417095tate_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_insert__compr) ).
thf(959,plain,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( insert1042460334tate_o @ A @ B )
= ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C = A )
| ( member907417095tate_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(272,axiom,
! [A: hoare_1262092251_state,B: pname > hoare_1262092251_state,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member5164104_state @ A @ ( image_669833818_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_rev__image__eqI) ).
thf(1213,plain,
! [A: hoare_1262092251_state,B: pname > hoare_1262092251_state,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member5164104_state @ A @ ( image_669833818_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(179,axiom,
! [A: hoare_1262092251_state > $o] :
( ( collec313158217tate_o
@ ^ [B: hoare_1262092251_state > $o] : ( B = A ) )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_singleton__conv) ).
thf(868,plain,
! [A: hoare_1262092251_state > $o] :
( ( collec313158217tate_o
@ ^ [B: hoare_1262092251_state > $o] : ( B = A ) )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(102,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_91_finite__surj) ).
thf(608,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)],[102]) ).
thf(5,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(306,plain,
! [A: pname,B: pname] :
( ~ ( fequal_pname @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(213,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ ( insert81609953_state @ A @ B ) )
= ( finite1178804552_state @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite__insert) ).
thf(1000,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ ( insert81609953_state @ A @ B ) )
= ( finite1178804552_state @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(1,conjecture,
( hoare_930741239_state
@ ( image_669833818_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7) ).
thf(2,negated_conjecture,
~ ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(299,plain,
~ ( hoare_930741239_state
@ ( image_669833818_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo113204042tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(240,axiom,
! [A: pname,B: com] :
( wT_bodies
=> ( ( ( body @ A )
= ( some_com @ B ) )
=> ( wt @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_WT__bodiesD) ).
thf(1102,plain,
! [A: pname,B: com] :
( wT_bodies
=> ( ( ( body @ A )
= ( some_com @ B ) )
=> ( wt @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(56,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_213_finite__Collect__disjI) ).
thf(438,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)],[56]) ).
thf(118,axiom,
! [A: hoare_1262092251_state > pname,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( finite_finite_pname @ ( image_202231862_pname @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_finite__imageI) ).
thf(653,plain,
! [A: hoare_1262092251_state > pname,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( finite_finite_pname @ ( image_202231862_pname @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(193,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_mem__def) ).
thf(922,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(120,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_275_Collect__conv__if2) ).
thf(658,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)],[120]) ).
thf(137,axiom,
! [A: ( pname > $o ) > $o,B: pname,C: ( pname > $o ) > pname,D: pname > $o] :
( ( B
= ( C @ D ) )
=> ( ( member_pname_o @ D @ A )
=> ( member_pname @ B @ ( image_pname_o_pname @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_image__eqI) ).
thf(722,plain,
! [A: ( pname > $o ) > $o,B: pname,C: ( pname > $o ) > pname,D: pname > $o] :
( ( B
= ( C @ D ) )
=> ( ( member_pname_o @ D @ A )
=> ( member_pname @ B @ ( image_pname_o_pname @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(270,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state] :
( ( ( A @ B )
=> ( ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C = B )
& ( A @ C ) ) )
= ( insert81609953_state @ B @ bot_bo113204042tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo113204042tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_Collect__conv__if) ).
thf(1203,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state] :
( ( ( A @ B )
=> ( ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C = B )
& ( A @ C ) ) )
= ( insert81609953_state @ B @ bot_bo113204042tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo113204042tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(199,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_217_insert__compr__raw) ).
thf(944,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)],[199]) ).
thf(84,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_221_singleton__inject) ).
thf(548,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)],[84]) ).
thf(195,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_174_insert__code) ).
thf(927,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)],[195]) ).
thf(248,axiom,
! [A: pname,B: pname] :
( ( ( body_1 @ A )
= ( body_1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_com_Osimps_I6_J) ).
thf(1134,plain,
! [A: pname,B: pname] :
( ( ( body_1 @ A )
= ( body_1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(231,axiom,
( bot_bo113204042tate_o
= ( collec1121927558_state
@ ^ [A: hoare_1262092251_state] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_empty__def) ).
thf(1081,plain,
( bot_bo113204042tate_o
= ( collec1121927558_state
@ ^ [A: hoare_1262092251_state] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(106,axiom,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_subset__insertI) ).
thf(617,plain,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(252,axiom,
! [A: hoare_1262092251_state] :
~ ( member5164104_state @ A @ bot_bo113204042tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_emptyE) ).
thf(1145,plain,
! [A: hoare_1262092251_state] :
~ ( member5164104_state @ A @ bot_bo113204042tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(149,axiom,
! [A: pname > $o] :
~ ( member_pname_o @ A @ bot_bot_pname_o_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_empty__iff) ).
thf(754,plain,
! [A: pname > $o] :
~ ( member_pname_o @ A @ bot_bot_pname_o_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(86,axiom,
( bot_bo1962689075te_o_o
= ( collec313158217tate_o
@ ^ [A: hoare_1262092251_state > $o] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_empty__def) ).
thf(553,plain,
( bot_bo1962689075te_o_o
= ( collec313158217tate_o
@ ^ [A: hoare_1262092251_state > $o] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(263,axiom,
! [A: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ A @ bot_bo113204042tate_o )
= ( A = bot_bo113204042tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_subset__empty) ).
thf(1181,plain,
! [A: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ A @ bot_bo113204042tate_o )
= ( A = bot_bo113204042tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(168,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ( ord_le870406270tate_o @ C @ A )
=> ( ord_le870406270tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subset__trans) ).
thf(836,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ( ord_le870406270tate_o @ C @ A )
=> ( ord_le870406270tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(67,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_102_subset__singletonD) ).
thf(473,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)],[67]) ).
thf(230,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( ~ ( member5164104_state @ B @ C )
=> ( B = A ) )
=> ( member5164104_state @ B @ ( insert81609953_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_insertCI) ).
thf(1076,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( ~ ( member5164104_state @ B @ C )
=> ( B = A ) )
=> ( member5164104_state @ B @ ( insert81609953_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(71,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_le2012720639te_o_o @ A @ ( image_1403668518tate_o @ B @ C ) )
=> ( finite1423311111tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_finite__surj) ).
thf(490,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_le2012720639te_o_o @ A @ ( image_1403668518tate_o @ B @ C ) )
=> ( finite1423311111tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(124,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( ord_le1205211808me_o_o @ A @ ( insert_pname_o @ B @ bot_bot_pname_o_o ) )
=> ( ( A = bot_bot_pname_o_o )
| ( A
= ( insert_pname_o @ B @ bot_bot_pname_o_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_subset__singletonD) ).
thf(675,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( ord_le1205211808me_o_o @ A @ ( insert_pname_o @ B @ bot_bot_pname_o_o ) )
=> ( ( A = bot_bot_pname_o_o )
| ( A
= ( insert_pname_o @ B @ bot_bot_pname_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(50,axiom,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite297249702name_o @ ( insert_pname_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_finite_OinsertI) ).
thf(426,plain,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite297249702name_o @ ( insert_pname_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(257,axiom,
! [A: pname,B: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ B ) @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) ) @ bot_bo113204042tate_o ) )
=> ( hoare_930741239_state @ B @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ bot_bo113204042tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MGT__BodyN) ).
thf(1166,plain,
! [A: pname,B: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ B ) @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) ) @ bot_bo113204042tate_o ) )
=> ( hoare_930741239_state @ B @ ( insert81609953_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ bot_bo113204042tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(157,axiom,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insertI1) ).
thf(776,plain,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(128,axiom,
! [A: hoare_1262092251_state > $o,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_518521461tate_o
@ ^ [C: pname] : A
@ B )
= bot_bo1962689075te_o_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_518521461tate_o
@ ^ [C: pname] : A
@ B )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_image__constant__conv) ).
thf(690,plain,
! [A: hoare_1262092251_state > $o,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_518521461tate_o
@ ^ [C: pname] : A
@ B )
= bot_bo1962689075te_o_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_518521461tate_o
@ ^ [C: pname] : A
@ B )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(12,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ~ ( fequal1529404211tate_o @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It) ).
thf(327,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ~ ( fequal1529404211tate_o @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(143,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > $o] :
( ( ord_le2012720639te_o_o @ A @ ( insert1042460334tate_o @ B @ bot_bo1962689075te_o_o ) )
=> ( ( A = bot_bo1962689075te_o_o )
| ( A
= ( insert1042460334tate_o @ B @ bot_bo1962689075te_o_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_subset__singletonD) ).
thf(739,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state > $o] :
( ( ord_le2012720639te_o_o @ A @ ( insert1042460334tate_o @ B @ bot_bo1962689075te_o_o ) )
=> ( ( A = bot_bo1962689075te_o_o )
| ( A
= ( insert1042460334tate_o @ B @ bot_bo1962689075te_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(43,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_242_finite__subset) ).
thf(409,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)],[43]) ).
thf(238,axiom,
! [A: pname > hoare_1262092251_state,B: pname > $o] :
( ( bot_bo113204042tate_o
= ( image_669833818_state @ A @ B ) )
= ( B = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_empty__is__image) ).
thf(1098,plain,
! [A: pname > hoare_1262092251_state,B: pname > $o] :
( ( bot_bo113204042tate_o
= ( image_669833818_state @ A @ B ) )
= ( B = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(210,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ( member5164104_state @ A @ B )
=> ( member5164104_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_in__mono) ).
thf(993,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ( member5164104_state @ A @ B )
=> ( member5164104_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(134,axiom,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_equals0D) ).
thf(712,plain,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(214,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] : ( member5164104_state @ A @ ( insert81609953_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_insertI1) ).
thf(1003,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] : ( member5164104_state @ A @ ( insert81609953_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(202,axiom,
finite_finite_pname @ bot_bot_pname_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_finite_OemptyI) ).
thf(954,plain,
finite_finite_pname @ bot_bot_pname_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(281,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ A @ ( insert81609953_state @ B @ C ) )
=> ( ( hoare_930741239_state @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
& ( hoare_930741239_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_derivs__insertD) ).
thf(1252,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( hoare_930741239_state @ A @ ( insert81609953_state @ B @ C ) )
=> ( ( hoare_930741239_state @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
& ( hoare_930741239_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(57,axiom,
! [A: pname > hoare_1262092251_state > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1423311111tate_o @ ( image_518521461tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite__imageI) ).
thf(441,plain,
! [A: pname > hoare_1262092251_state > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1423311111tate_o @ ( image_518521461tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(170,axiom,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_all__not__in__conv) ).
thf(840,plain,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(233,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ ( insert81609953_state @ B @ C ) )
= ( insert81609953_state @ B @ ( insert81609953_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_insert__commute) ).
thf(1085,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ ( insert81609953_state @ B @ C ) )
= ( insert81609953_state @ B @ ( insert81609953_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(201,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_115_insertE) ).
thf(951,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)],[201]) ).
thf(293,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ A @ ( insert81609953_state @ B @ C ) )
=> ( ( A != B )
=> ( member5164104_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_insertE) ).
thf(1285,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ A @ ( insert81609953_state @ B @ C ) )
=> ( ( A != B )
=> ( member5164104_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(218,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state] : ( ord_le870406270tate_o @ A @ ( insert81609953_state @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_subset__insertI) ).
thf(1038,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state] : ( ord_le870406270tate_o @ A @ ( insert81609953_state @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(96,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( ( image_1403668518tate_o
@ ^ [D: hoare_1262092251_state] : A
@ C )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_image__constant) ).
thf(585,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state,C: hoare_1262092251_state > $o] :
( ( member5164104_state @ B @ C )
=> ( ( image_1403668518tate_o
@ ^ [D: hoare_1262092251_state] : A
@ C )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(29,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ord_le2012720639te_o_o @ A @ B )
=> ( ( finite1423311111tate_o @ B )
=> ( finite1423311111tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_finite__subset) ).
thf(370,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ord_le2012720639te_o_o @ A @ B )
=> ( ( finite1423311111tate_o @ B )
=> ( finite1423311111tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(145,axiom,
hoare_1821564147gleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(744,plain,
hoare_1821564147gleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(16,axiom,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Collect__def) ).
thf(336,plain,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(131,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_empty__iff) ).
thf(703,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(100,axiom,
! [A: pname > $o,B: pname,C: pname > pname,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_pname @ B @ ( image_pname_pname @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_image__eqI) ).
thf(600,plain,
! [A: pname > $o,B: pname,C: pname > pname,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_pname @ B @ ( image_pname_pname @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(178,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A = B )
=> ( ord_le870406270tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_equalityD1) ).
thf(864,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A = B )
=> ( ord_le870406270tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(250,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ( member5164104_state @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_singletonE) ).
thf(1140,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ( member5164104_state @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(104,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( ! [B: hoare_1262092251_state > $o] :
~ ( member907417095tate_o @ B @ A ) )
= ( A = bot_bo1962689075te_o_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_all__not__in__conv) ).
thf(612,plain,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( ! [B: hoare_1262092251_state > $o] :
~ ( member907417095tate_o @ B @ A ) )
= ( A = bot_bo1962689075te_o_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(26,axiom,
! [A: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,B: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( finite1303896758te_o_o @ B )
=> ( finite1178804552_state @ ( image_165349207_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(363,plain,
! [A: ( ( hoare_1262092251_state > $o ) > $o ) > hoare_1262092251_state,B: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( finite1303896758te_o_o @ B )
=> ( finite1178804552_state @ ( image_165349207_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(70,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_pname_pname_o
@ ^ [C: pname] : A
@ B )
= bot_bot_pname_o_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_pname_pname_o
@ ^ [C: pname] : A
@ B )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_image__constant__conv) ).
thf(482,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_pname_pname_o
@ ^ [C: pname] : A
@ B )
= bot_bot_pname_o_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_pname_pname_o
@ ^ [C: pname] : A
@ B )
= ( insert_pname_o @ A @ bot_bot_pname_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(28,axiom,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( ord_le2012720639te_o_o @ B @ C )
=> ( ( member907417095tate_o @ A @ B )
=> ( member907417095tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_subsetD) ).
thf(368,plain,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o,C: ( hoare_1262092251_state > $o ) > $o] :
( ( ord_le2012720639te_o_o @ B @ C )
=> ( ( member907417095tate_o @ A @ B )
=> ( member907417095tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(155,axiom,
! [A: ( pname > $o ) > $o,B: hoare_1262092251_state > pname > $o,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_1320925383name_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite__surj) ).
thf(771,plain,
! [A: ( pname > $o ) > $o,B: hoare_1262092251_state > pname > $o,C: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_1320925383name_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(290,axiom,
! [A: hoare_1262092251_state] :
( ( collec1121927558_state
@ ^ [B: hoare_1262092251_state] : ( B = A ) )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_singleton__conv) ).
thf(1276,plain,
! [A: hoare_1262092251_state] :
( ( collec1121927558_state
@ ^ [B: hoare_1262092251_state] : ( B = A ) )
= ( insert81609953_state @ A @ bot_bo113204042tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(97,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ~ ( fequal1925511196_state @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com) ).
thf(588,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ~ ( fequal1925511196_state @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(8,axiom,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ B )
=> ( finite1423311111tate_o @ ( insert1042460334tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_finite_OinsertI) ).
thf(319,plain,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ B )
=> ( finite1423311111tate_o @ ( insert1042460334tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(147,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_178_insert__commute) ).
thf(748,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)],[147]) ).
thf(239,axiom,
finite1178804552_state @ bot_bo113204042tate_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_finite_OemptyI) ).
thf(1101,plain,
finite1178804552_state @ bot_bo113204042tate_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(22,axiom,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( insert_pname_o @ A @ ( collect_pname_o @ B ) )
= ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_insert__Collect) ).
thf(351,plain,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( insert_pname_o @ A @ ( collect_pname_o @ B ) )
= ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(36,axiom,
! [A: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ bot_bot_pname_o_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_empty__subsetI) ).
thf(390,plain,
! [A: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ bot_bot_pname_o_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(40,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( bot_bo1962689075te_o_o
= ( collec313158217tate_o @ A ) )
= ( ! [B: hoare_1262092251_state > $o] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_empty__Collect__eq) ).
thf(401,plain,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( bot_bo1962689075te_o_o
= ( collec313158217tate_o @ A ) )
= ( ! [B: hoare_1262092251_state > $o] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(280,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ( B = bot_bo113204042tate_o )
=> ( ( image_1403668518tate_o
@ ^ [C: hoare_1262092251_state] : A
@ B )
= bot_bo1962689075te_o_o ) )
& ( ( B != bot_bo113204042tate_o )
=> ( ( image_1403668518tate_o
@ ^ [C: hoare_1262092251_state] : A
@ B )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_image__constant__conv) ).
thf(1244,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ( B = bot_bo113204042tate_o )
=> ( ( image_1403668518tate_o
@ ^ [C: hoare_1262092251_state] : A
@ B )
= bot_bo1962689075te_o_o ) )
& ( ( B != bot_bo113204042tate_o )
=> ( ( image_1403668518tate_o
@ ^ [C: hoare_1262092251_state] : A
@ B )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(211,axiom,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,C: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_234589002_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite__surj) ).
thf(995,plain,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,C: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ C )
=> ( ( ord_le870406270tate_o @ A @ ( image_234589002_state @ B @ C ) )
=> ( finite1178804552_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(140,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( member5164104_state @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_mem__def) ).
thf(731,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( member5164104_state @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(161,axiom,
! [A: hoare_1262092251_state > $o,B: pname,C: hoare_1262092251_state > pname,D: hoare_1262092251_state] :
( ( B
= ( C @ D ) )
=> ( ( member5164104_state @ D @ A )
=> ( member_pname @ B @ ( image_202231862_pname @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_image__eqI) ).
thf(786,plain,
! [A: hoare_1262092251_state > $o,B: pname,C: hoare_1262092251_state > pname,D: hoare_1262092251_state] :
( ( B
= ( C @ D ) )
=> ( ( member5164104_state @ D @ A )
=> ( member_pname @ B @ ( image_202231862_pname @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(32,axiom,
! [A: ( pname > $o ) > $o] :
( ( ( collect_pname_o @ A )
= bot_bot_pname_o_o )
= ( ! [B: pname > $o] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Collect__empty__eq) ).
thf(378,plain,
! [A: ( pname > $o ) > $o] :
( ( ( collect_pname_o @ A )
= bot_bot_pname_o_o )
= ( ! [B: pname > $o] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(296,axiom,
( ord_le870406270tate_o @ fa
@ ( image_669833818_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) )
@ ( dom_pname_com @ body ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(1294,plain,
( ord_le870406270tate_o @ fa
@ ( image_669833818_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) )
@ ( dom_pname_com @ body ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(267,axiom,
! [A: hoare_1262092251_state > $o] :
( ( ( collec1121927558_state @ A )
= bot_bo113204042tate_o )
= ( ! [B: hoare_1262092251_state] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Collect__empty__eq) ).
thf(1193,plain,
! [A: hoare_1262092251_state > $o] :
( ( ( collec1121927558_state @ A )
= bot_bo113204042tate_o )
= ( ! [B: hoare_1262092251_state] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(152,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_72_image__constant) ).
thf(763,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)],[152]) ).
thf(20,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ A )
=> ( finite1303896758te_o_o
@ ( collec341954548te_o_o
@ ^ [B: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__subsets) ).
thf(346,plain,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( finite1423311111tate_o @ A )
=> ( finite1303896758te_o_o
@ ( collec341954548te_o_o
@ ^ [B: ( hoare_1262092251_state > $o ) > $o] : ( ord_le2012720639te_o_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(79,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_194_subset__trans) ).
thf(536,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)],[79]) ).
thf(221,axiom,
! [A: pname > hoare_1262092251_state,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1178804552_state @ ( image_669833818_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(1045,plain,
! [A: pname > hoare_1262092251_state,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1178804552_state @ ( image_669833818_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(135,axiom,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( insert1042460334tate_o @ A @ B )
= ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C = A )
| ( member907417095tate_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_insert__compr__raw) ).
thf(716,plain,
! [A: hoare_1262092251_state > $o,B: ( hoare_1262092251_state > $o ) > $o] :
( ( insert1042460334tate_o @ A @ B )
= ( collec313158217tate_o
@ ^ [C: hoare_1262092251_state > $o] :
( ( C = A )
| ( member907417095tate_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(3,axiom,
! [A: ( ( hoare_1262092251_state > $o ) > $o ) > $o,B: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( ( finite1303896758te_o_o @ ( collec341954548te_o_o @ B ) )
| ( finite1303896758te_o_o @ ( collec341954548te_o_o @ A ) ) )
=> ( finite1303896758te_o_o
@ ( collec341954548te_o_o
@ ^ [C: ( hoare_1262092251_state > $o ) > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite__Collect__conjI) ).
thf(300,plain,
! [A: ( ( hoare_1262092251_state > $o ) > $o ) > $o,B: ( ( hoare_1262092251_state > $o ) > $o ) > $o] :
( ( ( finite1303896758te_o_o @ ( collec341954548te_o_o @ B ) )
| ( finite1303896758te_o_o @ ( collec341954548te_o_o @ A ) ) )
=> ( finite1303896758te_o_o
@ ( collec341954548te_o_o
@ ^ [C: ( hoare_1262092251_state > $o ) > $o] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(53,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_84_finite__surj) ).
thf(432,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)],[53]) ).
thf(167,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_223_singletonE) ).
thf(833,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)],[167]) ).
thf(277,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ B )
!= bot_bo113204042tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insert__not__empty) ).
thf(1229,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o] :
( ( insert81609953_state @ A @ B )
!= bot_bo113204042tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(165,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( ( A @ B )
=> ( ( collect_pname_o
@ ^ [C: pname > $o] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_pname_o @ B @ bot_bot_pname_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname_o
@ ^ [C: pname > $o] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_pname_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_Collect__conv__if2) ).
thf(818,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( ( A @ B )
=> ( ( collect_pname_o
@ ^ [C: pname > $o] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_pname_o @ B @ bot_bot_pname_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname_o
@ ^ [C: pname > $o] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_pname_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(253,axiom,
! [A: pname > hoare_1262092251_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert81609953_state @ ( A @ B ) @ ( image_669833818_state @ A @ C ) )
= ( image_669833818_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_insert__image) ).
thf(1148,plain,
! [A: pname > hoare_1262092251_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert81609953_state @ ( A @ B ) @ ( image_669833818_state @ A @ C ) )
= ( image_669833818_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(162,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_290_finite__subset__induct) ).
thf(790,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)],[162]) ).
thf(11,axiom,
finite297249702name_o @ bot_bot_pname_o_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_finite_OemptyI) ).
thf(326,plain,
finite297249702name_o @ bot_bot_pname_o_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,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_26_finite__imageI) ).
thf(341,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)],[18]) ).
thf(75,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( ( ord_le870406270tate_o @ A @ B )
=> ( finite1178804552_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_rev__finite__subset) ).
thf(506,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( finite1178804552_state @ B )
=> ( ( ord_le870406270tate_o @ A @ B )
=> ( finite1178804552_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(24,axiom,
! [A: ( pname > $o ) > $o] :
( ( collect_pname_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Collect__def) ).
thf(358,plain,
! [A: ( pname > $o ) > $o] :
( ( collect_pname_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(186,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_295_subsetI) ).
thf(897,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)],[186]) ).
thf(294,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_270_domI) ).
thf(1288,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)],[294]) ).
thf(113,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state,C: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,D: hoare_1262092251_state > $o] :
( ( B
= ( C @ D ) )
=> ( ( member907417095tate_o @ D @ A )
=> ( member5164104_state @ B @ ( image_234589002_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_image__eqI) ).
thf(635,plain,
! [A: ( hoare_1262092251_state > $o ) > $o,B: hoare_1262092251_state,C: ( hoare_1262092251_state > $o ) > hoare_1262092251_state,D: hoare_1262092251_state > $o] :
( ( B
= ( C @ D ) )
=> ( ( member907417095tate_o @ D @ A )
=> ( member5164104_state @ B @ ( image_234589002_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(203,axiom,
! [A: ( pname > $o ) > hoare_1262092251_state,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite1178804552_state @ ( image_1476171975_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(955,plain,
! [A: ( pname > $o ) > hoare_1262092251_state,B: ( pname > $o ) > $o] :
( ( finite297249702name_o @ B )
=> ( finite1178804552_state @ ( image_1476171975_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(78,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_insert__not__empty) ).
thf(532,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(226,axiom,
! [A: pname > hoare_1262092251_state,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_le870406270tate_o @ ( image_669833818_state @ A @ B ) @ ( image_669833818_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_image__mono) ).
thf(1065,plain,
! [A: pname > hoare_1262092251_state,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_le870406270tate_o @ ( image_669833818_state @ A @ B ) @ ( image_669833818_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(38,axiom,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( ( collec313158217tate_o @ A )
= bot_bo1962689075te_o_o )
= ( ! [B: hoare_1262092251_state > $o] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Collect__empty__eq) ).
thf(395,plain,
! [A: ( hoare_1262092251_state > $o ) > $o] :
( ( ( collec313158217tate_o @ A )
= bot_bo1962689075te_o_o )
= ( ! [B: hoare_1262092251_state > $o] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(279,axiom,
! [A: pname,B: hoare_1262092251_state > $o] :
( ( ( B = bot_bo113204042tate_o )
=> ( ( image_202231862_pname
@ ^ [C: hoare_1262092251_state] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bo113204042tate_o )
=> ( ( image_202231862_pname
@ ^ [C: hoare_1262092251_state] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_image__constant__conv) ).
thf(1236,plain,
! [A: pname,B: hoare_1262092251_state > $o] :
( ( ( B = bot_bo113204042tate_o )
=> ( ( image_202231862_pname
@ ^ [C: hoare_1262092251_state] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bo113204042tate_o )
=> ( ( image_202231862_pname
@ ^ [C: hoare_1262092251_state] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(64,axiom,
! [A: pname > $o,B: hoare_1262092251_state > $o,C: pname > hoare_1262092251_state > $o,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member907417095tate_o @ B @ ( image_518521461tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_image__eqI) ).
thf(464,plain,
! [A: pname > $o,B: hoare_1262092251_state > $o,C: pname > hoare_1262092251_state > $o,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member907417095tate_o @ B @ ( image_518521461tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(14,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_54_finite__Collect__conjI) ).
thf(332,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)],[14]) ).
thf(176,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_200_in__mono) ).
thf(860,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)],[176]) ).
thf(99,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > $o,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_pname_o @ B @ ( image_pname_pname_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_image__eqI) ).
thf(596,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > $o,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member_pname_o @ B @ ( image_pname_pname_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(116,axiom,
! [A: hoare_1262092251_state > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_518521461tate_o
@ ^ [D: pname] : A
@ C )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_image__constant) ).
thf(644,plain,
! [A: hoare_1262092251_state > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_518521461tate_o
@ ^ [D: pname] : A
@ C )
= ( insert1042460334tate_o @ A @ bot_bo1962689075te_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(173,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( ( A @ B )
=> ( ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_pname_o @ B @ bot_bot_pname_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_pname_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_Collect__conv__if) ).
thf(850,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( ( A @ B )
=> ( ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_pname_o @ B @ bot_bot_pname_o_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_pname_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(180,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ( finite1178804552_state @ ( collec1121927558_state @ B ) )
| ( finite1178804552_state @ ( collec1121927558_state @ A ) ) )
=> ( finite1178804552_state
@ ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite__Collect__conjI) ).
thf(871,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( ( finite1178804552_state @ ( collec1121927558_state @ B ) )
| ( finite1178804552_state @ ( collec1121927558_state @ A ) ) )
=> ( finite1178804552_state
@ ( collec1121927558_state
@ ^ [C: hoare_1262092251_state] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(287,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ( member5164104_state @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_singleton__iff) ).
thf(1268,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state] :
( ( member5164104_state @ A @ ( insert81609953_state @ B @ bot_bo113204042tate_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(94,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ! [C: hoare_1262092251_state] :
( ( member5164104_state @ C @ B )
=> ( member5164104_state @ C @ A ) )
=> ( ord_le870406270tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_subsetI) ).
thf(575,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ! [C: hoare_1262092251_state] :
( ( member5164104_state @ C @ B )
=> ( member5164104_state @ C @ A ) )
=> ( ord_le870406270tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(23,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(354,plain,
! [A: pname,B: pname] :
( ( A != B )
| ( fequal_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(264,axiom,
! [A: pname > hoare_1262092251_state] :
( ( image_669833818_state @ A @ bot_bot_pname_o )
= bot_bo113204042tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_image__empty) ).
thf(1184,plain,
! [A: pname > hoare_1262092251_state] :
( ( image_669833818_state @ A @ bot_bot_pname_o )
= bot_bo113204042tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(6,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A != B )
| ( fequal1529404211tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It) ).
thf(309,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A != B )
| ( fequal1529404211tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(82,axiom,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ( member5164104_state @ A @ B )
=> ( member5164104_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_subsetD) ).
thf(543,plain,
! [A: hoare_1262092251_state,B: hoare_1262092251_state > $o,C: hoare_1262092251_state > $o] :
( ( ord_le870406270tate_o @ B @ C )
=> ( ( member5164104_state @ A @ B )
=> ( member5164104_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(114,axiom,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A = B )
= ( ( ord_le870406270tate_o @ A @ B )
& ( ord_le870406270tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_set__eq__subset) ).
thf(639,plain,
! [A: hoare_1262092251_state > $o,B: hoare_1262092251_state > $o] :
( ( A = B )
= ( ( ord_le870406270tate_o @ A @ B )
& ( ord_le870406270tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(234,axiom,
~ ( member5164104_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(1088,plain,
~ ( member5164104_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(209,axiom,
! [A: ( ( pname > $o ) > $o ) > $o,B: ( pname > $o ) > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ B )
=> ( ( A @ bot_bot_pname_o_o )
=> ( ! [D: pname > $o,E: ( pname > $o ) > $o] :
( ( finite297249702name_o @ E )
=> ( ( member_pname_o @ D @ B )
=> ( ~ ( member_pname_o @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_pname_o @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_finite__subset__induct) ).
thf(972,plain,
! [A: ( ( pname > $o ) > $o ) > $o,B: ( pname > $o ) > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ B )
=> ( ( A @ bot_bot_pname_o_o )
=> ( ! [D: pname > $o,E: ( pname > $o ) > $o] :
( ( finite297249702name_o @ E )
=> ( ( member_pname_o @ D @ B )
=> ( ~ ( member_pname_o @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert_pname_o @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(73,axiom,
! [A: pname,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ( B = bot_bo1962689075te_o_o )
=> ( ( image_1820530197_pname
@ ^ [C: hoare_1262092251_state > $o] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bo1962689075te_o_o )
=> ( ( image_1820530197_pname
@ ^ [C: hoare_1262092251_state > $o] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_image__constant__conv) ).
thf(496,plain,
! [A: pname,B: ( hoare_1262092251_state > $o ) > $o] :
( ( ( B = bot_bo1962689075te_o_o )
=> ( ( image_1820530197_pname
@ ^ [C: hoare_1262092251_state > $o] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bo1962689075te_o_o )
=> ( ( image_1820530197_pname
@ ^ [C: hoare_1262092251_state > $o] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(62,axiom,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( insert_pname_o @ A @ B )
= ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C = A )
| ( member_pname_o @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_insert__compr__raw) ).
thf(454,plain,
! [A: pname > $o,B: ( pname > $o ) > $o] :
( ( insert_pname_o @ A @ B )
= ( collect_pname_o
@ ^ [C: pname > $o] :
( ( C = A )
| ( member_pname_o @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1336,plain,
$false,
inference(e,[status(thm)],[479,941,1179,555,1295,365,1190,1168,760,909,628,1083,962,468,1200,1005,449,655,511,384,1137,1233,814,913,538,1260,698,1222,930,1196,1127,782,709,885,436,1095,404,1055,570,1298,719,372,504,1279,619,838,917,751,902,559,421,1013,881,416,492,591,443,1151,348,1051,1040,1109,321,766,734,1119,411,428,1074,920,678,925,381,1067,1047,1163,1274,825,778,1042,1255,862,1174,1217,392,424,729,957,1223,407,630,361,625,665,1210,757,324,1106,847,566,551,1128,1017,615,610,857,742,578,874,1143,471,339,669,642,970,1155,706,1292,933,686,476,622,701,1266,1131,457,647,1263,997,343,633,508,541,1170,398,1071,1187,773,888,965,430,745,375,562,843,413,1226,545,445,572,313,1271,1058,1092,335,1090,1258,947,672,604,900,681,1282,419,736,434,303,784,1117,451,567,890,858,726,769,1177,330,811,387,959,1213,868,608,306,1000,299,1102,438,653,922,658,722,1203,944,548,927,1134,1081,617,1145,754,553,1181,836,473,1076,490,675,426,1166,776,690,327,739,409,1098,993,712,1003,954,1252,441,840,1085,951,1285,1038,585,370,744,336,703,600,864,1140,612,363,482,368,771,1276,588,319,748,1101,351,390,401,1244,995,731,786,378,1294,1193,763,346,536,1045,716,300,432,833,1229,818,1148,790,326,341,506,358,897,1288,635,955,532,1065,395,1236,464,332,860,596,644,850,871,1268,575,354,1184,309,543,639,1088,972,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW474^1 : TPTP v8.2.0. Released v5.3.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jun 19 09:43:40 EDT 2024
% 0.11/0.33 % CPUTime :
% 1.12/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.28/1.40 % [INFO] Parsing done (382ms).
% 2.28/1.42 % [INFO] Running in sequential loop mode.
% 3.47/1.79 % [INFO] eprover registered as external prover.
% 3.47/1.80 % [INFO] Scanning for conjecture ...
% 3.75/1.96 % [INFO] Found a conjecture (or negated_conjecture) and 315 axioms. Running axiom selection ...
% 4.30/2.12 % [INFO] Axiom selection finished. Selected 296 axioms (removed 19 axioms).
% 4.98/2.38 % [INFO] Problem is higher-order (TPTP THF).
% 4.98/2.41 % [INFO] Type checking passed.
% 4.98/2.41 % [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 ...
% 20.64/6.24 % External prover 'e' found a proof!
% 20.64/6.24 % [INFO] Killing All external provers ...
% 20.64/6.24 % Time passed: 5724ms (effective reasoning time: 4816ms)
% 20.64/6.24 % 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)>
% 20.64/6.24 % Axioms used in derivation (296): fact_173_insert__ident, fact_56_image__constant__conv, fact_184_insert__Collect, fact_296_subsetI, fact_262_insert__subset, fact_231_empty__not__insert, fact_8_finite__Collect__subsets, fact_135_equals0D, fact_238_subset__empty, fact_234_finite__insert, fact_93_finite__surj, fact_224_singletonE, fact_104_emptyE, fact_293_finite__subset__induct, fact_174_insert__code, fact_243_finite__subset, fact_154_empty__Collect__eq, fact_15_finite__imageI, fact_244_finite__subset, fact_260_subset__insert, fact_110_insertCI, help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T, fact_185_insert__Collect, fact_186_insert__compr, fact_124_image__eqI, fact_167_empty__def, fact_91_finite__surj, fact_275_Collect__conv__if2, fact_49_finite__Collect__conjI, fact_29_finite__imageI, fact_106_emptyE, fact_1_asm, fact_155_ex__in__conv, fact_206_set__eq__subset, fact_64_image__constant__conv, fact_25_finite__imageI, fact_32_finite__imageI, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com, fact_188_insert__compr, fact_137_equals0D, fact_277_Collect__conv__if2, fact_142_Collect__empty__eq, fact_274_Collect__conv__if, fact_43_finite_OemptyI, fact_255_Collect__def, conj_3, fact_148_empty__iff, fact_157_ex__in__conv, fact_132_image__eqI, fact_3_thin, fact_281_singleton__conv, fact_249_rev__finite__subset, fact_105_emptyE, fact_67_image__constant, fact_143_Collect__empty__eq, fact_209_subset__refl, fact_103_MGF, fact_168_insert__absorb, fact_0_empty, fact_153_empty__Collect__eq, fact_216_finite__Collect__disjI, fact_146_empty__iff, fact_284_singleton__conv2, fact_152_empty__Collect__eq, fact_264_subset__insertI, fact_204_equalityD1, fact_287_MGF__lemma1, fact_229_insert__not__empty, fact_268_image__mono, fact_195_subset__trans, fact_26_finite__imageI, fact_99_subset__singletonD, fact_240_image__empty, fact_283_singleton__conv2, fact_96_finite__surj, fact_292_finite__subset__induct, fact_159_all__not__in__conv, fact_272_Collect__conv__if, fact_191_insertI1, fact_212_image__iff, fact_233_finite__insert, fact_265_subset__insertI, fact_61_image__constant__conv, fact_130_image__eqI, fact_75_image__constant, fact_76_image__constant, fact_181_insert__absorb2, fact_269_subset__image__iff, fact_237_subset__empty, fact_171_insertI2, fact_179_insert__commute, fact_134_image__eqI, fact_128_image__eqI, fact_172_insert__ident, fact_219_insert__compr__raw, fact_123_subsetD, fact_222_singleton__inject, fact_111_insertCI, fact_248_rev__finite__subset, fact_280_singleton__conv, fact_83_finite__surj, fact_162_all__not__in__conv, fact_35_empty__subsetI, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_41_finite_OinsertI, fact_92_finite__surj, fact_252_mem__def, fact_176_insert__iff, fact_114_insertE, fact_259_subset__insertI2, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com, fact_286_singleton__conv2, fact_246_rev__finite__subset, fact_253_mem__def, help_fequal_1_1_fequal_000tc__Com__Opname_T, fact_57_image__constant__conv, fact_256_Collect__def, fact_9_finite__Collect__subsets, fact_102_subset__singletonD, fact_245_finite__subset, conj_2, fact_250_insert__mono, fact_161_all__not__in__conv, fact_276_Collect__conv__if2, fact_86_finite__surj, fact_20_finite__imageI, fact_119_equalityI, fact_194_subset__trans, fact_145_empty__iff, fact_88_finite__surj, fact_271_Collect__conv__if, fact_169_insert__absorb, fact_66_image__constant, help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T, fact_203_equalityD2, fact_68_image__constant, fact_207_set__eq__subset, fact_109_insertCI, fact_44_finite_OemptyI, fact_131_image__eqI, fact_201_in__mono, fact_273_Collect__conv__if, fact_112_insertE, fact_70_image__constant, fact_97_finite__surj, fact_79_insert__dom, fact_100_subset__singletonD, fact_291_finite__subset__induct, fact_164_empty__def, fact_278_Collect__conv__if2, fact_84_finite__surj, fact_220_insert__compr__raw, fact_214_finite__Collect__disjI, fact_202_equalityD2, fact_217_insert__compr__raw, fact_125_image__eqI, fact_21_finite__imageI, fact_136_equals0D, fact_133_image__eqI, help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It, fact_87_finite__surj, fact_5_hoare__derivs_Oinsert, fact_282_singleton__conv, fact_108_insertCI, fact_215_finite__Collect__disjI, fact_213_finite__Collect__disjI, fact_285_singleton__conv2, fact_6_derivs__insertD, fact_211_imageI, fact_298_finite__dom__body, fact_279_singleton__conv, fact_74_image__constant, fact_200_in__mono, fact_170_insertI2, fact_138_equals0D, fact_299_com_Osimps_I6_J, fact_254_Collect__def, fact_117_equalityI, fact_187_insert__compr, fact_263_insert__subset, fact_16_finite__imageI, fact_225_doubleton__eq__iff, fact_190_insertI1, fact_48_finite_OemptyI, fact_52_finite__Collect__conjI, fact_126_image__eqI, fact_251_insert__mono, fact_158_ex__in__conv, fact_218_insert__compr__raw, fact_258_subset__insertI2, fact_107_emptyE, fact_22_finite__imageI, fact_51_finite__Collect__conjI, fact_13_finite__Collect__subsets, fact_227_singleton__iff, fact_193_equalityE, fact_47_finite_OemptyI, fact_221_singleton__inject, fact_247_rev__finite__subset, fact_85_finite__surj, fact_62_image__constant__conv, fact_261_subset__insert, fact_294_WTs__elim__cases_I7_J, fact_223_singletonE, help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It, fact_198_set__rev__mp, fact_141_Collect__empty__eq, fact_267_image__insert, fact_73_image__constant, fact_101_subset__singletonD, fact_72_image__constant, conj_6, fact_182_insert__Collect, conj_1, fact_82_finite__surj, fact_205_equalityD1, fact_156_ex__in__conv, fact_78_insert__dom, fact_232_empty__not__insert, fact_65_image__constant__conv, fact_199_set__rev__mp, fact_266_insert__image, fact_230_insert__not__empty, fact_122_subsetD, fact_63_image__constant__conv, fact_98_finite__surj, fact_297_finite__subset__image, fact_81_finite__surj, fact_189_insert__compr, fact_50_finite__Collect__conjI, fact_295_subsetI, fact_196_set__mp, fact_288_WT__bodiesD, fact_270_domI, fact_34_empty__subsetI, fact_55_image__constant__conv, fact_113_insertE, fact_165_empty__def, fact_2_weaken, fact_116_equalityI, fact_197_set__mp, fact_226_doubleton__eq__iff, fact_147_empty__iff, fact_241_empty__is__image, fact_69_image__constant, conj_4, fact_210_rev__image__eqI, fact_115_insertE, fact_30_finite__imageI, fact_4_cut, fact_127_image__eqI, fact_192_equalityE, fact_289_imageE, fact_290_finite__subset__induct, fact_175_insert__code, fact_80_finite__surj, fact_31_finite__imageI, fact_129_image__eqI, fact_19_finite__imageI, fact_12_finite__Collect__subsets, fact_71_image__constant, fact_18_finite__imageI, fact_7_MGT__BodyN, fact_239_image__is__empty, conj_5, fact_118_equalityI, fact_53_finite__Collect__conjI, fact_121_subsetD, conj_0, fact_59_image__constant__conv, fact_36_empty__subsetI, fact_120_subsetD, fact_180_insert__absorb2, fact_17_finite__imageI, fact_60_image__constant__conv, fact_235_finite__insert, fact_58_image__constant__conv, fact_54_finite__Collect__conjI, fact_242_finite__subset, fact_236_finite__insert, fact_37_finite_OinsertI, fact_160_all__not__in__conv, fact_183_insert__Collect, fact_178_insert__commute, fact_42_finite_OinsertI, fact_166_empty__def, fact_144_Collect__empty__eq, fact_14_finite__imageI, fact_177_insert__iff, fact_208_subset__refl, fact_33_empty__subsetI, fact_77_insert__dom, fact_38_finite_OinsertI, fact_151_empty__Collect__eq, fact_228_singleton__iff, fact_257_Collect__def
% 20.64/6.24 % No. of inferences in proof: 596
% 20.64/6.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5724 ms resp. 4816 ms w/o parsing
% 22.02/6.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.02/6.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------