%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW474^2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:15 AM UTC 2026
% Result : Theorem 58.81s 14.02s
% Output : Refutation 61.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 605
% Syntax : Number of formulae : 1253 ( 496 unt; 0 typ; 2 def)
% Number of atoms : 5440 (1152 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 10063 ( 390 ~; 82 |; 208 &;8117 @)
% ( 0 <=>;1266 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 2594 (2594 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 74 usr; 11 con; 0-3 aty)
% Number of variables : 3403 ( 219 ^;3104 !; 78 ?;3403 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(com_type,type,
com: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(state_type,type,
state: $tType ).
thf(hoare_1167836817_state_type,type,
hoare_1167836817_state: $tType ).
thf(option_com_type,type,
option_com: $tType ).
thf(option_pname_type,type,
option_pname: $tType ).
thf(option1574264306_state_type,type,
option1574264306_state: $tType ).
thf(wt_decl,type,
wt: com > $o ).
thf(wT_bodies_decl,type,
wT_bodies: $o ).
thf(body_decl,type,
body: pname > option_com ).
thf(body_1_decl,type,
body_1: pname > com ).
thf(skip_decl,type,
skip: com ).
thf(semi_decl,type,
semi: com > com > com ).
thf(while_decl,type,
while: ( state > $o ) > com > com ).
thf(finite297249702name_o_decl,type,
finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
thf(finite1380128977tate_o_decl,type,
finite1380128977tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: ( pname > $o ) > $o ).
thf(finite1084549118_state_decl,type,
finite1084549118_state: ( hoare_1167836817_state > $o ) > $o ).
thf(finite1282449217_pname_decl,type,
finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(finite1074406356_state_decl,type,
finite1074406356_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
thf(finite89670078_pname_decl,type,
finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
thf(finite806517911_state_decl,type,
finite806517911_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o ).
thf(minus_minus_pname_o_decl,type,
minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(minus_2107060239tate_o_decl,type,
minus_2107060239tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(the_pname_decl,type,
the_pname: ( pname > $o ) > pname ).
thf(the_Ho310147232_state_decl,type,
the_Ho310147232_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(hoare_Mirabelle_MGT_decl,type,
hoare_Mirabelle_MGT: com > hoare_1167836817_state ).
thf(hoare_123228589_state_decl,type,
hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(hoare_529639851_state_decl,type,
hoare_529639851_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(hoare_1201148605gleton_decl,type,
hoare_1201148605gleton: $o ).
thf(hoare_908217195_state_decl,type,
hoare_908217195_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1167836817_state ).
thf(if_Hoa833675553_state_decl,type,
if_Hoa833675553_state: $o > hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ).
thf(if_option_com_decl,type,
if_option_com: $o > option_com > option_com > option_com ).
thf(semila1673364395name_o_decl,type,
semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(semila179895820tate_o_decl,type,
semila179895820tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(semila1780557381name_o_decl,type,
semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
thf(semila1172322802tate_o_decl,type,
semila1172322802tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(semila10642723_sup_o_decl,type,
semila10642723_sup_o: $o > $o > $o ).
thf(dom_pname_com_decl,type,
dom_pname_com: ( pname > option_com ) > pname > $o ).
thf(evalc_decl,type,
evalc: com > state > state > $o ).
thf(some_com_decl,type,
some_com: com > option_com ).
thf(some_pname_decl,type,
some_pname: pname > option_pname ).
thf(some_H1433514562_state_decl,type,
some_H1433514562_state: hoare_1167836817_state > option1574264306_state ).
thf(set_com_decl,type,
set_com: option_com > com > $o ).
thf(set_pname_decl,type,
set_pname: option_pname > pname > $o ).
thf(set_Ho2131684873_state_decl,type,
set_Ho2131684873_state: option1574264306_state > hoare_1167836817_state > $o ).
thf(the_com_decl,type,
the_com: option_com > com ).
thf(bot_bot_com_o_decl,type,
bot_bot_com_o: com > $o ).
thf(bot_bot_pname_o_decl,type,
bot_bot_pname_o: pname > $o ).
thf(bot_bo70021908tate_o_decl,type,
bot_bo70021908tate_o: hoare_1167836817_state > $o ).
thf(bot_bot_o_decl,type,
bot_bot_o: $o ).
thf(ord_le1205211808me_o_o_decl,type,
ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
thf(ord_le741939125te_o_o_decl,type,
ord_le741939125te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o ).
thf(ord_less_eq_pname_o_decl,type,
ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
thf(ord_le827224136tate_o_decl,type,
ord_le827224136tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(collect_pname_decl,type,
collect_pname: ( pname > $o ) > pname > $o ).
thf(collec1027672124_state_decl,type,
collec1027672124_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(image_pname_pname_o_decl,type,
image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
thf(image_475339327tate_o_decl,type,
image_475339327tate_o: ( pname > hoare_1167836817_state > $o ) > ( pname > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(image_pname_pname_decl,type,
image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
thf(image_575578384_state_decl,type,
image_575578384_state: ( pname > hoare_1167836817_state ) > ( pname > $o ) > hoare_1167836817_state > $o ).
thf(image_2066861949name_o_decl,type,
image_2066861949name_o: ( hoare_1167836817_state > pname > $o ) > ( hoare_1167836817_state > $o ) > ( pname > $o ) > $o ).
thf(image_1745649338tate_o_decl,type,
image_1745649338tate_o: ( hoare_1167836817_state > hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o ).
thf(image_8178176_pname_decl,type,
image_8178176_pname: ( hoare_1167836817_state > pname ) > ( hoare_1167836817_state > $o ) > pname > $o ).
thf(image_31595733_state_decl,type,
image_31595733_state: ( hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(insert_com_decl,type,
insert_com: com > ( com > $o ) > com > $o ).
thf(insert_pname_decl,type,
insert_pname: pname > ( pname > $o ) > pname > $o ).
thf(insert2134838167_state_decl,type,
insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ).
thf(the_elem_pname_decl,type,
the_elem_pname: ( pname > $o ) > pname ).
thf(the_el323660082_state_decl,type,
the_el323660082_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state ).
thf(fequal_pname_decl,type,
fequal_pname: pname > pname > $o ).
thf(fequal_state_decl,type,
fequal_state: state > state > $o ).
thf(fequal1831255762_state_decl,type,
fequal1831255762_state: hoare_1167836817_state > hoare_1167836817_state > $o ).
thf(member_pname_decl,type,
member_pname: pname > ( pname > $o ) > $o ).
thf(member2058392318_state_decl,type,
member2058392318_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > $o ).
thf(fa_decl,type,
fa: hoare_1167836817_state > $o ).
thf(pn_decl,type,
pn: pname ).
thf(y_decl,type,
y: com ).
thf(sk90_decl,type,
sk90: state ).
thf(sk91_decl,type,
sk91: state ).
thf(sk93_decl,type,
sk93: hoare_1167836817_state ).
thf(sk90_def,definition,
( sk90
= ( @+[A: state] :
? [B: state] : ( A != B ) ) ) ).
thf(sk91_def,definition,
( sk91
= ( @+[A: state] : ( sk90 != A ) ) ) ).
thf(492,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite1084549118_state @ ( insert2134838167_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).
thf(2163,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite1084549118_state @ ( insert2134838167_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(328,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_UnI2) ).
thf(1665,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(348,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( A != bot_bot_pname_o )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_folding__one__idem_Osubset__idem) ).
thf(1718,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( A != bot_bot_pname_o )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(134,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_sup__idem) ).
thf(1024,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(537,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ bot_bo70021908tate_o )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_inf__bot__right) ).
thf(2341,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ bot_bo70021908tate_o )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(450,axiom,
! [A: com] :
( ( hoare_Mirabelle_MGT @ A )
= ( hoare_908217195_state @ fequal_state @ A @ ( evalc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_MGT__def) ).
thf(2031,plain,
! [A: com] :
( ( hoare_Mirabelle_MGT @ A )
= ( hoare_908217195_state @ fequal_state @ A @ ( evalc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(365,axiom,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_predicate1I) ).
thf(1767,plain,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(352,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_173_insert__mono) ).
thf(1729,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)],[352]) ).
thf(136,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ A ) @ ( semila1673364395name_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_Int__mono) ).
thf(1031,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ A ) @ ( semila1673364395name_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(410,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_com_Osimps_I3_J) ).
thf(1899,plain,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(597,axiom,
! [A: pname > $o,B: pname > hoare_1167836817_state,C: pname > hoare_1167836817_state,D: pname > $o] :
( ( image_575578384_state
@ ^ [E: pname] : ( if_Hoa833675553_state @ ( A @ E ) @ ( B @ E ) @ ( C @ E ) )
@ D )
= ( semila1172322802tate_o @ ( image_575578384_state @ B @ ( semila1673364395name_o @ D @ ( collect_pname @ A ) ) )
@ ( image_575578384_state @ C
@ ( semila1673364395name_o @ D
@ ( collect_pname
@ ^ [E: pname] :
~ ( A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_if__image__distrib) ).
thf(2544,plain,
! [A: pname > $o,B: pname > hoare_1167836817_state,C: pname > hoare_1167836817_state,D: pname > $o] :
( ( image_575578384_state
@ ^ [E: pname] : ( if_Hoa833675553_state @ ( A @ E ) @ ( B @ E ) @ ( C @ E ) )
@ D )
= ( semila1172322802tate_o @ ( image_575578384_state @ B @ ( semila1673364395name_o @ D @ ( collect_pname @ A ) ) )
@ ( image_575578384_state @ C
@ ( semila1673364395name_o @ D
@ ( collect_pname
@ ^ [E: pname] :
~ ( A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(157,axiom,
! [A: state > state > $o,B: com,C: state > state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( ( hoare_908217195_state @ A @ B @ C )
= ( hoare_908217195_state @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_triple_Oinject) ).
thf(1110,plain,
! [A: state > state > $o,B: com,C: state > state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( ( hoare_908217195_state @ A @ B @ C )
= ( hoare_908217195_state @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(515,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ B @ C )
=> ( ( C @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_folding__one_Osingleton) ).
thf(2250,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ B @ C )
=> ( ( C @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(138,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila1172322802tate_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_Un__absorb1) ).
thf(1036,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila1172322802tate_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(559,axiom,
! [A: hoare_1167836817_state > $o] : ( hoare_123228589_state @ A @ bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
thf(2417,plain,
! [A: hoare_1167836817_state > $o] : ( hoare_123228589_state @ A @ bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(2418,plain,
! [A: hoare_1167836817_state > $o] : ( hoare_123228589_state @ A @ bot_bo70021908tate_o ),
inference(cnf,[status(esa)],[2417]) ).
thf(493,axiom,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_bot__apply) ).
thf(2165,plain,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(2166,plain,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[2165]) ).
thf(2167,plain,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[2166]) ).
thf(2626,plain,
! [A: hoare_1167836817_state > $o] :
( hoare_123228589_state @ A
@ ^ [B: hoare_1167836817_state] : bot_bot_o ),
inference(rewrite,[status(thm)],[2418,2167]) ).
thf(1,conjecture,
( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7) ).
thf(2,negated_conjecture,
~ ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(605,plain,
~ ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(2602,plain,
~ ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1167836817_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[605,2167]) ).
thf(2627,plain,
! [A: hoare_1167836817_state > $o] :
( ~ $true
| ( ( hoare_123228589_state @ A
@ ^ [B: hoare_1167836817_state] : bot_bot_o )
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [B: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ B ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [B: hoare_1167836817_state] : bot_bot_o ) ) ) ),
inference(paramod_ordered,[status(thm)],[2626,2602]) ).
thf(2628,plain,
! [A: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ A
@ ^ [B: hoare_1167836817_state] : bot_bot_o )
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [B: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ B ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [B: hoare_1167836817_state] : bot_bot_o ) ) ),
inference(simp,[status(thm)],[2627]) ).
thf(2629,plain,
! [A: hoare_1167836817_state > $o] :
( ( A
!= ( image_575578384_state
@ ^ [B: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ B ) )
@ ( dom_pname_com @ body ) ) )
| ( ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [B: hoare_1167836817_state] : bot_bot_o )
!= ( ^ [B: hoare_1167836817_state] : bot_bot_o ) ) ),
inference(simp,[status(thm)],[2628]) ).
thf(2630,plain,
( ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1167836817_state] : bot_bot_o )
!= ( ^ [A: hoare_1167836817_state] : bot_bot_o ) ),
inference(simp,[status(thm)],[2629]) ).
thf(303,axiom,
finite1084549118_state @ fa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(1586,plain,
finite1084549118_state @ fa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(278,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( finite1084549118_state @ ( collec1027672124_state @ B ) )
| ( finite1084549118_state @ ( collec1027672124_state @ A ) ) )
=> ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_finite__Collect__conjI) ).
thf(1501,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( finite1084549118_state @ ( collec1027672124_state @ B ) )
| ( finite1084549118_state @ ( collec1027672124_state @ A ) ) )
=> ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(568,axiom,
! [A: hoare_1167836817_state,B: pname > hoare_1167836817_state,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2058392318_state @ A @ ( image_575578384_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_rev__image__eqI) ).
thf(2452,plain,
! [A: hoare_1167836817_state,B: pname > hoare_1167836817_state,C: pname,D: pname > $o] :
( ( member_pname @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member2058392318_state @ A @ ( image_575578384_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(557,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ A @ B )
=> ( hoare_529639851_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_hoare__sound) ).
thf(2412,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ A @ B )
=> ( hoare_529639851_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(76,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila179895820tate_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_Int__absorb1) ).
thf(846,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila179895820tate_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(222,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_172_rev__finite__subset) ).
thf(1315,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)],[222]) ).
thf(171,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_empty__subsetI) ).
thf(1150,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1151,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(cnf,[status(esa)],[1150]) ).
thf(81,axiom,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_bot__apply) ).
thf(859,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(860,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[859]) ).
thf(861,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[860]) ).
thf(2595,plain,
! [A: pname > $o] :
( ord_less_eq_pname_o
@ ^ [B: pname] : bot_bot_o
@ A ),
inference(rewrite,[status(thm)],[1151,861]) ).
thf(580,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ( D @ ( semila1172322802tate_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_folding__one__idem_Ounion__idem) ).
thf(2499,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ( D @ ( semila1172322802tate_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(113,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ B )
| ( finite_finite_pname @ A ) )
=> ( finite_finite_pname @ ( semila1673364395name_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_finite__Int) ).
thf(962,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( finite_finite_pname @ B )
| ( finite_finite_pname @ A ) )
=> ( finite_finite_pname @ ( semila1673364395name_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(561,axiom,
! [A: hoare_1167836817_state] :
( ( the_el323660082_state @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_the__elem__eq) ).
thf(2427,plain,
! [A: hoare_1167836817_state] :
( ( the_el323660082_state @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(575,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
=> ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_le__bot) ).
thf(2480,plain,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
=> ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(419,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ B @ C ) ) @ ( semila179895820tate_o @ C @ A ) )
= ( semila179895820tate_o @ ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ B @ C ) ) @ ( semila1172322802tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_Un__Int__crazy) ).
thf(1924,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ B @ C ) ) @ ( semila179895820tate_o @ C @ A ) )
= ( semila179895820tate_o @ ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ B @ C ) ) @ ( semila1172322802tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(308,axiom,
! [A: pname > $o,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ! [D: pname,E: pname] : ( member_pname @ ( B @ D @ E ) @ ( insert_pname @ D @ ( insert_pname @ E @ bot_bot_pname_o ) ) )
=> ( member_pname @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_folding__one_Oclosed) ).
thf(1596,plain,
! [A: pname > $o,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ! [D: pname,E: pname] : ( member_pname @ ( B @ D @ E ) @ ( insert_pname @ D @ ( insert_pname @ E @ bot_bot_pname_o ) ) )
=> ( member_pname @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(41,axiom,
! [A: pname,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( image_8178176_pname
@ ^ [D: hoare_1167836817_state] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_image__constant) ).
thf(730,plain,
! [A: pname,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( image_8178176_pname
@ ^ [D: hoare_1167836817_state] : A
@ C )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(146,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
= ( ( semila1172322802tate_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_subset__Un__eq) ).
thf(1068,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
= ( ( semila1172322802tate_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(547,axiom,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: pname,D: state > state > $o] :
( ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ ( the_com @ ( body @ C ) ) @ D ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ ( body_1 @ C ) @ D ) @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_weak__Body) ).
thf(2381,plain,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: pname,D: state > state > $o] :
( ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ ( the_com @ ( body @ C ) ) @ D ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ ( body_1 @ C ) @ D ) @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(259,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_subset__refl) ).
thf(1443,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(46,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila179895820tate_o
@ ^ [D: hoare_1167836817_state] : ( member2058392318_state @ D @ A )
@ ^ [D: hoare_1167836817_state] : ( member2058392318_state @ D @ B )
@ C )
= ( member2058392318_state @ C @ ( semila179895820tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_inf__Int__eq) ).
thf(741,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila179895820tate_o
@ ^ [D: hoare_1167836817_state] : ( member2058392318_state @ D @ A )
@ ^ [D: hoare_1167836817_state] : ( member2058392318_state @ D @ B )
@ C )
= ( member2058392318_state @ C @ ( semila179895820tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(191,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( semila1780557381name_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_UnI1) ).
thf(1205,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member_pname @ B @ ( semila1780557381name_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(477,axiom,
! [A: hoare_1167836817_state > $o,B: pname > state > state > $o,C: pname > state > state > $o,D: pname > $o] :
( ( hoare_529639851_state
@ ( semila1172322802tate_o @ A
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) )
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( the_com @ ( body @ E ) ) @ ( C @ E ) )
@ D ) )
=> ( hoare_529639851_state @ A
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_Body__sound__lemma) ).
thf(2114,plain,
! [A: hoare_1167836817_state > $o,B: pname > state > state > $o,C: pname > state > state > $o,D: pname > $o] :
( ( hoare_529639851_state
@ ( semila1172322802tate_o @ A
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) )
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( the_com @ ( body @ E ) ) @ ( C @ E ) )
@ D ) )
=> ( hoare_529639851_state @ A
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(88,axiom,
! [A: pname > $o,B: pname > $o,C: ( pname > $o ) > pname > $o,D: pname > $o] :
( ( B
= ( C @ D ) )
=> ( ( ord_less_eq_pname_o @ A @ D )
=> ( ! [E: pname > $o,F: pname > $o] :
( ( ord_less_eq_pname_o @ F @ E )
=> ( ord_less_eq_pname_o @ ( C @ F ) @ ( C @ E ) ) )
=> ( ord_less_eq_pname_o @ ( C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_xt1_I15_J) ).
thf(878,plain,
! [A: pname > $o,B: pname > $o,C: ( pname > $o ) > pname > $o,D: pname > $o] :
( ( B
= ( C @ D ) )
=> ( ( ord_less_eq_pname_o @ A @ D )
=> ( ! [E: pname > $o,F: pname > $o] :
( ( ord_less_eq_pname_o @ F @ E )
=> ( ord_less_eq_pname_o @ ( C @ F ) @ ( C @ E ) ) )
=> ( ord_less_eq_pname_o @ ( C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(7,axiom,
! [A: ( pname > $o ) > $o,B: hoare_1167836817_state > pname > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_2066861949name_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_finite__surj) ).
thf(614,plain,
! [A: ( pname > $o ) > $o,B: hoare_1167836817_state > pname > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le1205211808me_o_o @ A @ ( image_2066861949name_o @ B @ C ) )
=> ( finite297249702name_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(273,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( ord_le827224136tate_o @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_Int__greatest) ).
thf(1486,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( ord_le827224136tate_o @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(189,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_25_finite_OinsertI) ).
thf(1200,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)],[189]) ).
thf(464,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > hoare_1167836817_state,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ! [E: hoare_1167836817_state,F: hoare_1167836817_state] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_31595733_state @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_folding__one__idem_Ohom__commute) ).
thf(2077,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > hoare_1167836817_state,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ! [E: hoare_1167836817_state,F: hoare_1167836817_state] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_31595733_state @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(123,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ A )
| ( member2058392318_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Un__def) ).
thf(994,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ A )
| ( member2058392318_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(590,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( collec1027672124_state @ B ) )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_insert__Collect) ).
thf(2527,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( collec1027672124_state @ B ) )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(524,axiom,
! [A: pname > state > state > $o,B: pname > state > state > $o,C: hoare_1167836817_state > $o,D: pname > state > state > $o,E: pname > com,F: pname > state > state > $o,G: pname > $o] :
( ( finite_finite_pname @ G )
=> ( ! [H: pname] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) ) @ bot_bo70021908tate_o ) ) )
=> ( ( hoare_123228589_state @ C
@ ( image_575578384_state
@ ^ [H: pname] : ( hoare_908217195_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) )
@ G ) )
=> ( hoare_123228589_state @ C
@ ( image_575578384_state
@ ^ [H: pname] : ( hoare_908217195_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) )
@ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_finite__pointwise) ).
thf(2282,plain,
! [A: pname > state > state > $o,B: pname > state > state > $o,C: hoare_1167836817_state > $o,D: pname > state > state > $o,E: pname > com,F: pname > state > state > $o,G: pname > $o] :
( ( finite_finite_pname @ G )
=> ( ! [H: pname] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) ) @ bot_bo70021908tate_o ) ) )
=> ( ( hoare_123228589_state @ C
@ ( image_575578384_state
@ ^ [H: pname] : ( hoare_908217195_state @ ( D @ H ) @ ( E @ H ) @ ( F @ H ) )
@ G ) )
=> ( hoare_123228589_state @ C
@ ( image_575578384_state
@ ^ [H: pname] : ( hoare_908217195_state @ ( A @ H ) @ ( E @ H ) @ ( B @ H ) )
@ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(305,axiom,
( hoare_1201148605gleton
= ( ? [A: state,B: state] : ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_state__not__singleton__def) ).
thf(1591,plain,
( hoare_1201148605gleton
= ( ? [A: state,B: state] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(150,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( ( ord_less_eq_pname_o @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_le__sup__iff) ).
thf(1078,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
= ( ( ord_less_eq_pname_o @ A @ C )
& ( ord_less_eq_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(167,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( B = C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( ord_le827224136tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_xt1_I3_J) ).
thf(1137,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( B = C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( ord_le827224136tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(220,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( finite1084549118_state @ A )
=> ( finite1084549118_state @ ( semila1172322802tate_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_finite__UnI) ).
thf(1310,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( finite1084549118_state @ A )
=> ( finite1084549118_state @ ( semila1172322802tate_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(354,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_inf__sup__ord_I2_J) ).
thf(1735,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(176,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila179895820tate_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_Int__absorb2) ).
thf(1164,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila179895820tate_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(71,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_220_finite__subset__induct) ).
thf(814,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)],[71]) ).
thf(494,axiom,
! [A: pname > hoare_1167836817_state,B: pname > $o,C: pname > $o] : ( ord_le827224136tate_o @ ( image_575578384_state @ A @ ( semila1673364395name_o @ B @ C ) ) @ ( semila179895820tate_o @ ( image_575578384_state @ A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_image__Int__subset) ).
thf(2168,plain,
! [A: pname > hoare_1167836817_state,B: pname > $o,C: pname > $o] : ( ord_le827224136tate_o @ ( image_575578384_state @ A @ ( semila1673364395name_o @ B @ C ) ) @ ( semila179895820tate_o @ ( image_575578384_state @ A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(97,axiom,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_Int__empty__left) ).
thf(913,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(102,axiom,
! [A: state,B: state] :
( ( A != B )
| ( fequal_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Ostate_T) ).
thf(930,plain,
! [A: state,B: state] :
( ( A != B )
| ( fequal_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(398,axiom,
! [A: pname > $o,B: pname > $o] :
( ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila1780557381name_o @ ( collect_pname @ A ) @ ( collect_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_Collect__disj__eq) ).
thf(1867,plain,
! [A: pname > $o,B: pname > $o] :
( ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila1780557381name_o @ ( collect_pname @ A ) @ ( collect_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(500,axiom,
! [A: hoare_1167836817_state > $o,B: pname > state > state > $o,C: pname > state > state > $o,D: pname > $o] :
( ( hoare_123228589_state
@ ( semila1172322802tate_o @ A
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) )
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( the_com @ ( body @ E ) ) @ ( C @ E ) )
@ D ) )
=> ( hoare_123228589_state @ A
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_hoare__derivs_OBody) ).
thf(2184,plain,
! [A: hoare_1167836817_state > $o,B: pname > state > state > $o,C: pname > state > state > $o,D: pname > $o] :
( ( hoare_123228589_state
@ ( semila1172322802tate_o @ A
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) )
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( the_com @ ( body @ E ) ) @ ( C @ E ) )
@ D ) )
=> ( hoare_123228589_state @ A
@ ( image_575578384_state
@ ^ [E: pname] : ( hoare_908217195_state @ ( B @ E ) @ ( body_1 @ E ) @ ( C @ E ) )
@ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(563,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( A != bot_bo70021908tate_o )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_folding__one__idem_Osubset__idem) ).
thf(2434,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( A != bot_bo70021908tate_o )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(400,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_155_finite__insert) ).
thf(1872,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)],[400]) ).
thf(188,axiom,
! [A: pname,B: hoare_1167836817_state > pname,C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( member2058392318_state @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_pname @ A @ ( image_8178176_pname @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_rev__image__eqI) ).
thf(1196,plain,
! [A: pname,B: hoare_1167836817_state > pname,C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( member2058392318_state @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member_pname @ A @ ( image_8178176_pname @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(387,axiom,
! [A: com] :
( ( set_com @ ( some_com @ A ) )
= ( insert_com @ A @ bot_bot_com_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_Option_Oset_Osimps_I2_J) ).
thf(1835,plain,
! [A: com] :
( ( set_com @ ( some_com @ A ) )
= ( insert_com @ A @ bot_bot_com_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(125,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) @ ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_distrib__inf__le) ).
thf(1001,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ ( semila1673364395name_o @ A @ C ) ) @ ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(423,axiom,
! [A: com] :
( ( the_com @ ( some_com @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_the_Osimps) ).
thf(1935,plain,
! [A: com] :
( ( the_com @ ( some_com @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(232,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ C ) )
=> ~ ( ( member2058392318_state @ A @ B )
=> ~ ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_IntE) ).
thf(1359,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ C ) )
=> ~ ( ( member2058392318_state @ A @ B )
=> ~ ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(242,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( member2058392318_state @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_folding__one__idem_Oin__idem) ).
thf(1386,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( member2058392318_state @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(466,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ bot_bo70021908tate_o )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_Int__empty__right) ).
thf(2082,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ bot_bo70021908tate_o )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(412,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ A )
=> ( finite_finite_pname @ ( semila1780557381name_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_finite__UnI) ).
thf(1904,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ A )
=> ( finite_finite_pname @ ( semila1780557381name_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(272,axiom,
! [A: com,B: com] :
( ( wt @ ( semi @ A @ B ) )
=> ~ ( ( wt @ A )
=> ~ ( wt @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_WTs__elim__cases_I4_J) ).
thf(1482,plain,
! [A: com,B: com] :
( ( wt @ ( semi @ A @ B ) )
=> ~ ( ( wt @ A )
=> ~ ( wt @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(406,axiom,
! [A: pname > $o] :
( ( A != bot_bot_pname_o )
= ( ? [B: pname,C: pname > $o] :
( ( A
= ( insert_pname @ B @ C ) )
& ~ ( member_pname @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_nonempty__iff) ).
thf(1887,plain,
! [A: pname > $o] :
( ( A != bot_bot_pname_o )
= ( ? [B: pname,C: pname > $o] :
( ( A
= ( insert_pname @ B @ C ) )
& ~ ( member_pname @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(18,axiom,
! [A: pname,B: option_pname] :
( ( member_pname @ A @ ( set_pname @ B ) )
= ( B
= ( some_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_elem__set) ).
thf(651,plain,
! [A: pname,B: option_pname] :
( ( member_pname @ A @ ( set_pname @ B ) )
= ( B
= ( some_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(357,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ C )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ C ) @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_sup__inf__distrib2) ).
thf(1746,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ C )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ C ) @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(92,axiom,
! [A: pname,B: pname > $o] :
( bot_bot_pname_o
!= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_empty__not__insert) ).
thf(898,plain,
! [A: pname,B: pname > $o] :
( bot_bot_pname_o
!= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(163,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( ord_le827224136tate_o @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_inf__greatest) ).
thf(1127,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( ord_le827224136tate_o @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(578,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ! [B: hoare_1167836817_state] :
~ ( member2058392318_state @ B @ A ) )
= ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_all__not__in__conv) ).
thf(2491,plain,
! [A: hoare_1167836817_state > $o] :
( ( ! [B: hoare_1167836817_state] :
~ ( member2058392318_state @ B @ A ) )
= ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(198,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( semila1780557381name_o @ ( insert_pname @ A @ bot_bot_pname_o ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_insert__is__Un) ).
thf(1243,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( semila1780557381name_o @ ( insert_pname @ A @ bot_bot_pname_o ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(323,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_Un__assoc) ).
thf(1650,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(418,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1780557381name_o
@ ^ [D: pname] : ( member_pname @ D @ A )
@ ^ [D: pname] : ( member_pname @ D @ B )
@ C )
= ( member_pname @ C @ ( semila1780557381name_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_sup__Un__eq) ).
thf(1921,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1780557381name_o
@ ^ [D: pname] : ( member_pname @ D @ A )
@ ^ [D: pname] : ( member_pname @ D @ B )
@ C )
= ( member_pname @ C @ ( semila1780557381name_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(350,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ A ) @ ( semila1673364395name_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_inf__mono) ).
thf(1724,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ A ) @ ( semila1673364395name_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(270,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( A != B )
| ( fequal1831255762_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com) ).
thf(1475,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( A != B )
| ( fequal1831255762_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(552,axiom,
finite1084549118_state @ bot_bo70021908tate_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_finite_OemptyI) ).
thf(2400,plain,
finite1084549118_state @ bot_bo70021908tate_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(461,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ bot_bo70021908tate_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_Un__empty__right) ).
thf(2067,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ bot_bo70021908tate_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(318,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ! [C: hoare_1167836817_state] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le827224136tate_o @ ( collec1027672124_state @ B ) @ ( collec1027672124_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_Collect__mono) ).
thf(1628,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ! [C: hoare_1167836817_state] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le827224136tate_o @ ( collec1027672124_state @ B ) @ ( collec1027672124_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(251,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_sup__absorb1) ).
thf(1409,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(2603,plain,
( finite1084549118_state
@ ^ [A: hoare_1167836817_state] : bot_bot_o ),
inference(rewrite,[status(thm)],[2400,2167]) ).
thf(216,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ! [D: hoare_1167836817_state > $o,E: hoare_1167836817_state > $o,F: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ D @ ( semila179895820tate_o @ E @ F ) )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ D @ E ) @ ( semila1172322802tate_o @ D @ F ) ) )
=> ( ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_distrib__imp2) ).
thf(1298,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ! [D: hoare_1167836817_state > $o,E: hoare_1167836817_state > $o,F: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ D @ ( semila179895820tate_o @ E @ F ) )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ D @ E ) @ ( semila1172322802tate_o @ D @ F ) ) )
=> ( ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(61,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1780557381name_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_le__iff__sup) ).
thf(785,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1780557381name_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(225,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( semila1172322802tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_inf__sup__aci_I5_J) ).
thf(1323,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( semila1172322802tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(67,axiom,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_insertI1) ).
thf(802,plain,
! [A: pname,B: pname > $o] : ( member_pname @ A @ ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(263,axiom,
! [A: pname > pname,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( image_pname_pname @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_pigeonhole__infinite) ).
thf(1455,plain,
! [A: pname > pname,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ ( image_pname_pname @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(372,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_34_finite__Collect__conjI) ).
thf(1792,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)],[372]) ).
thf(256,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ ( collect_pname @ C ) ) )
= ( ( member_pname @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_Int__Collect) ).
thf(1430,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ ( collect_pname @ C ) ) )
= ( ( member_pname @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(281,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
= ( ( ord_le827224136tate_o @ A @ B )
& ( ord_le827224136tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_le__inf__iff) ).
thf(1511,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
= ( ( ord_le827224136tate_o @ A @ B )
& ( ord_le827224136tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(49,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) )
= ( insert_pname @ A @ ( semila1673364395name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_insert__inter__insert) ).
thf(751,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( semila1673364395name_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ C ) )
= ( insert_pname @ A @ ( semila1673364395name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(103,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ bot_bot_pname_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_Un__empty__left) ).
thf(934,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ bot_bot_pname_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(186,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= ( semila1172322802tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_sup_Oleft__idem) ).
thf(1191,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= ( semila1172322802tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(108,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ ( semila1172322802tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_UnI1) ).
thf(949,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ ( semila1172322802tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(541,axiom,
! [A: pname] :
( ( body_1 @ A )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_com_Osimps_I19_J) ).
thf(2353,plain,
! [A: pname] :
( ( body_1 @ A )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(2354,plain,
~ ? [A: pname] :
( ( body_1 @ A )
= skip ),
inference(miniscope,[status(thm)],[2353]) ).
thf(2355,plain,
! [A: pname] :
( ( body_1 @ A )
!= skip ),
inference(cnf,[status(esa)],[2354]) ).
thf(2356,plain,
! [A: pname] :
( ( body_1 @ A )
!= skip ),
inference(lifteq,[status(thm)],[2355]) ).
thf(291,axiom,
! [A: pname > $o,B: hoare_1167836817_state > pname,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_8178176_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_finite__surj) ).
thf(1545,plain,
! [A: pname > $o,B: hoare_1167836817_state > pname,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_less_eq_pname_o @ A @ ( image_8178176_pname @ B @ C ) )
=> ( finite_finite_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(93,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_58_insertE) ).
thf(902,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)],[93]) ).
thf(282,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_order__refl) ).
thf(1514,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(587,axiom,
! [A: hoare_1167836817_state > $o,B: com] :
( ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ B ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [C: state,D: state] :
! [E: state] :
( ( evalc @ B @ D @ E )
=> ( C = E ) )
@ B
@ fequal_state )
@ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_MGT__alternI) ).
thf(2520,plain,
! [A: hoare_1167836817_state > $o,B: com] :
( ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ B ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [C: state,D: state] :
! [E: state] :
( ( evalc @ B @ D @ E )
=> ( C = E ) )
@ B
@ fequal_state )
@ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(401,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_insert__Diff) ).
thf(1875,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(550,axiom,
! [A: hoare_1167836817_state > $o,B: com,C: state > state > $o,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [G: state,H: state] : ( H = F )
@ B
@ ^ [G: state] : ( C @ E ) )
@ bot_bo70021908tate_o ) ) )
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ B @ C ) @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_escape) ).
thf(2388,plain,
! [A: hoare_1167836817_state > $o,B: com,C: state > state > $o,D: state > state > $o] :
( ! [E: state,F: state] :
( ( D @ E @ F )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [G: state,H: state] : ( H = F )
@ B
@ ^ [G: state] : ( C @ E ) )
@ bot_bo70021908tate_o ) ) )
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ B @ C ) @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(343,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_98_insert__absorb2) ).
thf(1704,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)],[343]) ).
thf(407,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate) ).
thf(1890,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(271,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( semila1673364395name_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_Int__insert__left__if1) ).
thf(1479,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( semila1673364395name_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(312,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_Int__greatest) ).
thf(1609,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(115,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_inf__le2) ).
thf(969,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(3,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le741939125te_o_o @ A @ ( image_1745649338tate_o @ B @ C ) )
=> ( finite1380128977tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_finite__surj) ).
thf(606,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le741939125te_o_o @ A @ ( image_1745649338tate_o @ B @ C ) )
=> ( finite1380128977tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(228,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ C ) @ ( semila179895820tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_inf__sup__distrib2) ).
thf(1347,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ C ) @ ( semila179895820tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(300,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( insert_pname @ A @ B ) @ C )
= ( insert_pname @ A @ ( semila1780557381name_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_Un__insert__left) ).
thf(1572,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( semila1780557381name_o @ ( insert_pname @ A @ B ) @ C )
= ( insert_pname @ A @ ( semila1780557381name_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(100,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_340_order__trans) ).
thf(924,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)],[100]) ).
thf(469,axiom,
( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(2091,plain,
( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(2613,plain,
( ~ $true
| ( ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1167836817_state] : bot_bot_o ) )
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ) ) ),
inference(paramod_ordered,[status(thm)],[2091,2602]) ).
thf(2614,plain,
( ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1167836817_state] : bot_bot_o ) )
!= ( hoare_123228589_state
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
@ fa ) ),
inference(simp,[status(thm)],[2613]) ).
thf(2615,plain,
( ( ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) )
!= ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ A ) )
@ ( dom_pname_com @ body ) ) )
| ( ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1167836817_state] : bot_bot_o )
!= fa ) ),
inference(simp,[status(thm)],[2614]) ).
thf(2616,plain,
( ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1167836817_state] : bot_bot_o )
!= fa ),
inference(simp,[status(thm)],[2615]) ).
thf(217,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ A )
=> ( member2058392318_state @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_set__rev__mp) ).
thf(1302,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ A )
=> ( member2058392318_state @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(237,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_xt1_I6_J) ).
thf(1373,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(319,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ ( semila1172322802tate_o @ B @ C ) )
& ( A @ D ) ) )
= ( ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( A @ D ) )
| ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
& ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_bex__Un) ).
thf(1632,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ ( semila1172322802tate_o @ B @ C ) )
& ( A @ D ) ) )
= ( ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( A @ D ) )
| ? [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
& ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(511,axiom,
! [A: pname > hoare_1167836817_state,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1084549118_state @ ( image_575578384_state @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(2236,plain,
! [A: pname > hoare_1167836817_state,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1084549118_state @ ( image_575578384_state @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(397,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1673364395name_o @ A @ B )
= bot_bot_pname_o )
= ( ! [C: pname] :
( ( member_pname @ C @ A )
=> ! [D: pname] :
( ( member_pname @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_disjoint__iff__not__equal) ).
thf(1864,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1673364395name_o @ A @ B )
= bot_bot_pname_o )
= ( ! [C: pname] :
( ( member_pname @ C @ A )
=> ! [D: pname] :
( ( member_pname @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(104,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1780557381name_o @ B @ C ) )
= ( ( member_pname @ A @ B )
| ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_Un__iff) ).
thf(937,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1780557381name_o @ B @ C ) )
= ( ( member_pname @ A @ B )
| ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(451,axiom,
! [A: hoare_1167836817_state > $o] :
( ! [B: hoare_1167836817_state] :
~ ( member2058392318_state @ B @ A )
=> ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_equals0I) ).
thf(2034,plain,
! [A: hoare_1167836817_state > $o] :
( ! [B: hoare_1167836817_state] :
~ ( member2058392318_state @ B @ A )
=> ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(114,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ C )
= ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) )
= ( ord_le827224136tate_o @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_Un__Int__assoc__eq) ).
thf(966,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ C )
= ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) )
= ( ord_le827224136tate_o @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(210,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila1172322802tate_o @ A @ B @ C )
= ( semila10642723_sup_o @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_sup__fun__def) ).
thf(1283,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila1172322802tate_o @ A @ B @ C )
= ( semila10642723_sup_o @ ( A @ C ) @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(94,axiom,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_8178176_pname @ A @ C ) )
= ( image_8178176_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_insert__image) ).
thf(905,plain,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( insert_pname @ ( A @ B ) @ ( image_8178176_pname @ A @ C ) )
= ( image_8178176_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(569,axiom,
! [A: pname > hoare_1167836817_state,B: hoare_1167836817_state > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member2058392318_state @ ( A @ D ) @ B ) )
=> ( ord_le827224136tate_o @ ( image_575578384_state @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_image__subsetI) ).
thf(2456,plain,
! [A: pname > hoare_1167836817_state,B: hoare_1167836817_state > $o,C: pname > $o] :
( ! [D: pname] :
( ( member_pname @ D @ C )
=> ( member2058392318_state @ ( A @ D ) @ B ) )
=> ( ord_le827224136tate_o @ ( image_575578384_state @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(447,axiom,
! [A: pname,B: com] :
( wT_bodies
=> ( ( ( body @ A )
= ( some_com @ B ) )
=> ( wt @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_WT__bodiesD) ).
thf(2007,plain,
! [A: pname,B: com] :
( wT_bodies
=> ( ( ( body @ A )
= ( some_com @ B ) )
=> ( wt @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(498,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ B @ C )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ! [D: hoare_1167836817_state,E: hoare_1167836817_state] : ( member2058392318_state @ ( B @ D @ E ) @ ( insert2134838167_state @ D @ ( insert2134838167_state @ E @ bot_bo70021908tate_o ) ) )
=> ( member2058392318_state @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_folding__one_Oclosed) ).
thf(2178,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ B @ C )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ! [D: hoare_1167836817_state,E: hoare_1167836817_state] : ( member2058392318_state @ ( B @ D @ E ) @ ( insert2134838167_state @ D @ ( insert2134838167_state @ E @ bot_bo70021908tate_o ) ) )
=> ( member2058392318_state @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(507,axiom,
! [A: pname > $o,B: hoare_1167836817_state,C: pname > hoare_1167836817_state,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member2058392318_state @ B @ ( image_575578384_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_image__eqI) ).
thf(2222,plain,
! [A: pname > $o,B: hoare_1167836817_state,C: pname > hoare_1167836817_state,D: pname] :
( ( B
= ( C @ D ) )
=> ( ( member_pname @ D @ A )
=> ( member2058392318_state @ B @ ( image_575578384_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(384,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_inf__le1) ).
thf(1828,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(439,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) )
= ( insert2134838167_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_insert__Diff__single) ).
thf(1978,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) )
= ( insert2134838167_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(55,axiom,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_Int__empty__right) ).
thf(766,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(178,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_363_bot__unique) ).
thf(1169,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)],[178]) ).
thf(564,axiom,
! [A: pname > hoare_1167836817_state,B: pname > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le827224136tate_o @ C @ ( image_575578384_state @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_575578384_state @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__subset__image) ).
thf(2437,plain,
! [A: pname > hoare_1167836817_state,B: pname > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le827224136tate_o @ C @ ( image_575578384_state @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_575578384_state @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(576,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
= ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_bot__unique) ).
thf(2483,plain,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
= ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(160,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ C @ A ) @ ( semila1172322802tate_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_sup__mono) ).
thf(1119,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ C @ A ) @ ( semila1172322802tate_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(245,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_51_subset__singletonD) ).
thf(1394,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)],[245]) ).
thf(484,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ~ ( member2058392318_state @ B @ C )
=> ( B = A ) )
=> ( member2058392318_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_insertCI) ).
thf(2137,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ~ ( member2058392318_state @ B @ C )
=> ( B = A ) )
=> ( member2058392318_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(21,axiom,
! [A: pname > $o,B: pname > pname,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ! [E: pname,F: pname] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_pname_pname @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_folding__one__idem_Ohom__commute) ).
thf(660,plain,
! [A: pname > $o,B: pname > pname,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ! [E: pname,F: pname] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_pname_pname @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(445,axiom,
( ( body @ pn )
= ( some_com @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(2002,plain,
( ( body @ pn )
= ( some_com @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(257,axiom,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_subset__insertI) ).
thf(1433,plain,
! [A: pname > $o,B: pname] : ( ord_less_eq_pname_o @ A @ ( insert_pname @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(551,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( semila179895820tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_Int__insert__right) ).
thf(2392,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( semila179895820tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(591,axiom,
! [A: pname > hoare_1167836817_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member2058392318_state @ ( A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_imageI) ).
thf(2530,plain,
! [A: pname > hoare_1167836817_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( member2058392318_state @ ( A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(589,axiom,
! [A: com,B: com,C: pname] :
( ( semi @ A @ B )
!= ( body_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_com_Osimps_I48_J) ).
thf(2523,plain,
! [A: com,B: com,C: pname] :
( ( semi @ A @ B )
!= ( body_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(373,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_le__supI) ).
thf(1796,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(121,axiom,
! [A: pname] :
( ( collect_pname @ ( fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_singleton__conv2) ).
thf(988,plain,
! [A: pname] :
( ( collect_pname @ ( fequal_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(525,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ( ( insert2134838167_state @ A @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_insert__Diff) ).
thf(2286,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ( ( insert2134838167_state @ A @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(474,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ( ( insert2134838167_state @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_insert__absorb) ).
thf(2103,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ( ( insert2134838167_state @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(249,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_sup__ge2) ).
thf(1405,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(155,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_Un__left__commute) ).
thf(1104,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(340,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( semila1780557381name_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_le__supI1) ).
thf(1697,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( semila1780557381name_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(77,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( ( ord_le827224136tate_o @ A @ C )
& ( ord_le827224136tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_le__sup__iff) ).
thf(849,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( ( ord_le827224136tate_o @ A @ C )
& ( ord_le827224136tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(438,axiom,
! [A: hoare_1167836817_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_575578384_state
@ ^ [D: pname] : A
@ C )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_image__constant) ).
thf(1975,plain,
! [A: hoare_1167836817_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( image_575578384_state
@ ^ [D: pname] : A
@ C )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(297,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ C )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ C ) @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_Un__Int__distrib2) ).
thf(1564,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ C )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ C ) @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(448,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( A @ bot_bo70021908tate_o )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ~ ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert2134838167_state @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_finite__induct) ).
thf(2011,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( A @ bot_bo70021908tate_o )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ~ ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert2134838167_state @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(99,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_ord__eq__le__trans) ).
thf(920,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ C @ A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(27,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_equalityD1) ).
thf(678,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(338,axiom,
! [A: state,B: state] :
( ~ ( fequal_state @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Ostate_T) ).
thf(1691,plain,
! [A: state,B: state] :
( ~ ( fequal_state @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(53,axiom,
! [A: pname] :
( ( collect_pname
@ ^ [B: pname] : ( B = A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_singleton__conv) ).
thf(761,plain,
! [A: pname] :
( ( collect_pname
@ ^ [B: pname] : ( B = A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(479,axiom,
! [A: pname,B: hoare_1167836817_state > $o] :
( ( ( B = bot_bo70021908tate_o )
=> ( ( image_8178176_pname
@ ^ [C: hoare_1167836817_state] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bo70021908tate_o )
=> ( ( image_8178176_pname
@ ^ [C: hoare_1167836817_state] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_image__constant__conv) ).
thf(2118,plain,
! [A: pname,B: hoare_1167836817_state > $o] :
( ( ( B = bot_bo70021908tate_o )
=> ( ( image_8178176_pname
@ ^ [C: hoare_1167836817_state] : A
@ B )
= bot_bot_pname_o ) )
& ( ( B != bot_bo70021908tate_o )
=> ( ( image_8178176_pname
@ ^ [C: hoare_1167836817_state] : A
@ B )
= ( insert_pname @ A @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(455,axiom,
! [A: state > $o,B: com,C: pname] :
( ( while @ A @ B )
!= ( body_1 @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_com_Osimps_I58_J) ).
thf(2047,plain,
! [A: state > $o,B: com,C: pname] :
( ( while @ A @ B )
!= ( body_1 @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(416,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_145_doubleton__eq__iff) ).
thf(1915,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)],[416]) ).
thf(65,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_le__infI2) ).
thf(798,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(148,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_inf__sup__ord_I2_J) ).
thf(1074,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(310,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_60_equalityI) ).
thf(1604,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)],[310]) ).
thf(207,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_Int__lower2) ).
thf(1274,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(556,axiom,
! [A: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ A )
= ( ( A = bot_bo70021908tate_o )
| ? [B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( A
= ( insert2134838167_state @ C @ B ) )
& ( finite1084549118_state @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_finite_Osimps) ).
thf(2409,plain,
! [A: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ A )
= ( ( A = bot_bo70021908tate_o )
| ? [B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( A
= ( insert2134838167_state @ C @ B ) )
& ( finite1084549118_state @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(96,axiom,
! [A: com,B: com] :
( ( ( some_com @ A )
= ( some_com @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_option_Oinject) ).
thf(910,plain,
! [A: com,B: com] :
( ( ( some_com @ A )
= ( some_com @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(133,axiom,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_all__not__in__conv) ).
thf(1021,plain,
! [A: pname > $o] :
( ( ! [B: pname] :
~ ( member_pname @ B @ A ) )
= ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(284,axiom,
finite_finite_pname @ bot_bot_pname_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_finite_OemptyI) ).
thf(1519,plain,
finite_finite_pname @ bot_bot_pname_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(202,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ bot_bot_pname_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_Un__empty__right) ).
thf(1255,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ bot_bot_pname_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(558,axiom,
! [A: pname > hoare_1167836817_state,B: pname > $o] :
( ( ( image_575578384_state @ A @ B )
= bot_bo70021908tate_o )
= ( B = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_image__is__empty) ).
thf(2414,plain,
! [A: pname > hoare_1167836817_state,B: pname > $o] :
( ( ( image_575578384_state @ A @ B )
= bot_bo70021908tate_o )
= ( B = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(404,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite1084549118_state @ ( minus_2107060239tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_finite__Diff) ).
thf(1883,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite1084549118_state @ ( minus_2107060239tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(111,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_le__infI2) ).
thf(957,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(91,axiom,
! [A: hoare_1167836817_state] :
~ ! [B: state > state > $o,C: com,D: state > state > $o] :
( A
!= ( hoare_908217195_state @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_triple_Oexhaust) ).
thf(894,plain,
! [A: hoare_1167836817_state] :
~ ! [B: state > state > $o,C: com,D: state > state > $o] :
( A
!= ( hoare_908217195_state @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(140,axiom,
! [A: state > $o,B: com,C: state,D: state] :
( ( evalc @ ( while @ A @ B ) @ C @ D )
=> ( ( ( D = C )
=> ( A @ C ) )
=> ~ ( ( A @ C )
=> ! [E: state] :
( ( evalc @ B @ C @ E )
=> ~ ( evalc @ ( while @ A @ B ) @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_evalc__WHILE__case) ).
thf(1042,plain,
! [A: state > $o,B: com,C: state,D: state] :
( ( evalc @ ( while @ A @ B ) @ C @ D )
=> ( ( ( D = C )
=> ( A @ C ) )
=> ~ ( ( A @ C )
=> ! [E: state] :
( ( evalc @ B @ C @ E )
=> ~ ( evalc @ ( while @ A @ B ) @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(596,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ bot_bo70021908tate_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_sup__bot__left) ).
thf(2541,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ bot_bo70021908tate_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(162,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
=> ~ ( ( ord_le827224136tate_o @ A @ B )
=> ~ ( ord_le827224136tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_le__infE) ).
thf(1123,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
=> ~ ( ( ord_le827224136tate_o @ A @ B )
=> ~ ( ord_le827224136tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(82,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_185_insert__subset) ).
thf(862,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)],[82]) ).
thf(299,axiom,
! [A: state] : ( evalc @ skip @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_evalc_OSkip) ).
thf(1570,plain,
! [A: state] : ( evalc @ skip @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(333,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1084549118_state @ ( collec1027672124_state @ A ) )
& ( finite1084549118_state @ ( collec1027672124_state @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_finite__Collect__disjI) ).
thf(1676,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1084549118_state @ ( collec1027672124_state @ A ) )
& ( finite1084549118_state @ ( collec1027672124_state @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(482,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ B @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_subset__insertI2) ).
thf(2133,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ B @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(195,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ! [C: pname] : ( A @ ( insert_pname @ C @ bot_bot_pname_o ) )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( D != bot_bot_pname_o )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_finite__ne__induct) ).
thf(1217,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ! [C: pname] : ( A @ ( insert_pname @ C @ bot_bot_pname_o ) )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ( D != bot_bot_pname_o )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(486,axiom,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( image_8178176_pname @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert_pname @ ( A @ B ) @ ( image_8178176_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_image__insert) ).
thf(2147,plain,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( image_8178176_pname @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert_pname @ ( A @ B ) @ ( image_8178176_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(383,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
=> ( ord_le827224136tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_equalityD1) ).
thf(1824,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
=> ( ord_le827224136tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(62,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_sup__inf__absorb) ).
thf(788,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(487,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ bot_bo70021908tate_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_Un__empty__left) ).
thf(2150,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ bot_bo70021908tate_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(254,axiom,
! [A: pname > pname > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_pigeonhole__infinite) ).
thf(1423,plain,
! [A: pname > pname > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(98,axiom,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_com_Osimps_I13_J) ).
thf(916,plain,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(424,axiom,
! [A: state > $o,B: com] :
( ( wt @ ( while @ A @ B ) )
=> ( wt @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_WTs__elim__cases_I6_J) ).
thf(1938,plain,
! [A: state > $o,B: com] :
( ( wt @ ( while @ A @ B ) )
=> ( wt @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(234,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ A )
=> ( ord_le827224136tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_order__trans) ).
thf(1365,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ A )
=> ( ord_le827224136tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(435,axiom,
~ ( member2058392318_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(1968,plain,
~ ( member2058392318_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(181,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_88_insertI2) ).
thf(1178,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)],[181]) ).
thf(429,axiom,
! [A: pname > hoare_1167836817_state > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite1380128977tate_o @ ( image_475339327tate_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_pigeonhole__infinite) ).
thf(1951,plain,
! [A: pname > hoare_1167836817_state > $o,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite1380128977tate_o @ ( image_475339327tate_o @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(337,axiom,
! [A: pname > $o] :
( ! [B: pname] :
~ ( member_pname @ B @ A )
=> ( A = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_equals0I) ).
thf(1687,plain,
! [A: pname > $o] :
( ! [B: pname] :
~ ( member_pname @ B @ A )
=> ( A = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(381,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( semila1172322802tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_sup_Ocommute) ).
thf(1819,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( semila1172322802tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(174,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_118_in__mono) ).
thf(1159,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)],[174]) ).
thf(499,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert2134838167_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_insert__commute) ).
thf(2181,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert2134838167_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(51,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_116_set__rev__mp) ).
thf(757,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)],[51]) ).
thf(244,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ B @ ( semila1172322802tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_le__supI1) ).
thf(1392,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ B @ ( semila1172322802tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(213,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_181_subset__insertI2) ).
thf(1291,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)],[213]) ).
thf(74,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( if_Hoa833675553_state @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate) ).
thf(842,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( if_Hoa833675553_state @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(117,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ! [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
=> ( member2058392318_state @ C @ A ) )
=> ( ord_le827224136tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_subsetI) ).
thf(974,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ! [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
=> ( member2058392318_state @ C @ A ) )
=> ( ord_le827224136tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(129,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila1172322802tate_o @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_sup1E) ).
thf(1012,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila1172322802tate_o @ A @ B @ C )
=> ( ~ ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(12,axiom,
! [A: pname > hoare_1167836817_state > $o,B: pname > $o,C: ( hoare_1167836817_state > $o ) > $o] :
( ( finite1380128977tate_o @ C )
=> ( ( ord_le741939125te_o_o @ C @ ( image_475339327tate_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_475339327tate_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_finite__subset__image) ).
thf(625,plain,
! [A: pname > hoare_1167836817_state > $o,B: pname > $o,C: ( hoare_1167836817_state > $o ) > $o] :
( ( finite1380128977tate_o @ C )
=> ( ( ord_le741939125te_o_o @ C @ ( image_475339327tate_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_475339327tate_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(574,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila179895820tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ! [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ A )
=> ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_disjoint__iff__not__equal) ).
thf(2477,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila179895820tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ! [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ A )
=> ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(78,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_inf__absorb1) ).
thf(852,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(534,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( hoare_123228589_state @ A @ B )
=> ( hoare_123228589_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cut) ).
thf(2332,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( hoare_123228589_state @ A @ B )
=> ( hoare_123228589_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(215,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_rev__predicate1D) ).
thf(1296,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(23,axiom,
! [A: hoare_1167836817_state > pname > $o,B: hoare_1167836817_state > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_2066861949name_o @ A @ B ) )
=> ? [D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ D @ B )
& ( finite1084549118_state @ D )
& ( C
= ( image_2066861949name_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_finite__subset__image) ).
thf(665,plain,
! [A: hoare_1167836817_state > pname > $o,B: hoare_1167836817_state > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_2066861949name_o @ A @ B ) )
=> ? [D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ D @ B )
& ( finite1084549118_state @ D )
& ( C
= ( image_2066861949name_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(193,axiom,
! [A: pname] :
( ( set_pname @ ( some_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Option_Oset_Osimps_I2_J) ).
thf(1210,plain,
! [A: pname] :
( ( set_pname @ ( some_pname @ A ) )
= ( insert_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(325,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ C ) @ ( semila179895820tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_Int__Un__distrib2) ).
thf(1656,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ C ) @ ( semila179895820tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(135,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_order__eq__refl) ).
thf(1027,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(532,axiom,
! [A: pname,B: state,C: state] :
( ( evalc @ ( the_com @ ( body @ A ) ) @ B @ C )
=> ( evalc @ ( body_1 @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_evalc_OBody) ).
thf(2327,plain,
! [A: pname,B: state,C: state] :
( ( evalc @ ( the_com @ ( body @ A ) ) @ B @ C )
=> ( evalc @ ( body_1 @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(28,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_Int__lower1) ).
thf(682,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(250,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_sup__least) ).
thf(1407,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(598,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ bot_bo70021908tate_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_sup__bot__right) ).
thf(2547,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ bot_bo70021908tate_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(538,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( insert2134838167_state @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_insert__code) ).
thf(2344,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( insert2134838167_state @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(229,axiom,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_bot__least) ).
thf(1350,plain,
! [A: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(490,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( semila1172322802tate_o
@ ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] : ( C = A ) )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_insert__def) ).
thf(2157,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( semila1172322802tate_o
@ ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] : ( C = A ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(392,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ C @ A ) @ ( semila1780557381name_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_Un__mono) ).
thf(1851,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ C @ A ) @ ( semila1780557381name_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(131,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ A @ C ) ) @ ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_distrib__inf__le) ).
thf(1017,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ A @ C ) ) @ ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(376,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_le__supI) ).
thf(1804,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(144,axiom,
! [A: com,B: com] :
( ( wt @ B )
=> ( ( wt @ A )
=> ( wt @ ( semi @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_WT_OSemi) ).
thf(1064,plain,
! [A: com,B: com] :
( ( wt @ B )
=> ( ( wt @ A )
=> ( wt @ ( semi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(436,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( ord_le827224136tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_subset__insert) ).
thf(1970,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( ord_le827224136tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(331,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_Un__least) ).
thf(1672,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(594,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] : ( member2058392318_state @ A @ ( insert2134838167_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_insertI1) ).
thf(2537,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] : ( member2058392318_state @ A @ ( insert2134838167_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(85,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_Int__absorb1) ).
thf(869,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(5,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_165_finite__subset) ).
thf(610,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)],[5]) ).
thf(60,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ~ ( member2058392318_state @ B @ A )
=> ( member2058392318_state @ B @ ( minus_2107060239tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_DiffI) ).
thf(783,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ~ ( member2058392318_state @ B @ A )
=> ( member2058392318_state @ B @ ( minus_2107060239tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(32,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1673364395name_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_le__iff__inf) ).
thf(697,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1673364395name_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(152,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_110_equalityE) ).
thf(1089,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)],[152]) ).
thf(363,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_distrib__sup__le) ).
thf(1762,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] : ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ ( semila1673364395name_o @ B @ C ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ A @ B ) @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(585,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( hoare_123228589_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_thin) ).
thf(2515,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( hoare_123228589_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(238,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_emptyE) ).
thf(1375,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(161,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_inf__sup__ord_I1_J) ).
thf(1121,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(394,axiom,
! [A: option_com,B: option_com] :
( ( if_option_com @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) ).
thf(1856,plain,
! [A: option_com,B: option_com] :
( ( if_option_com @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(39,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_sup__left__commute) ).
thf(725,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(119,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ? [C: pname > $o] :
( ( B
= ( insert_pname @ A @ C ) )
& ~ ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_mk__disjoint__insert) ).
thf(980,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ? [C: pname > $o] :
( ( B
= ( insert_pname @ A @ C ) )
& ~ ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(304,axiom,
! [A: com,B: com,C: state > $o,D: com] :
( ( semi @ A @ B )
!= ( while @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_com_Osimps_I46_J) ).
thf(1587,plain,
! [A: com,B: com,C: state > $o,D: com] :
( ( semi @ A @ B )
!= ( while @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(289,axiom,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( image_8178176_pname @ A @ B ) @ ( image_8178176_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_image__mono) ).
thf(1540,plain,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( image_8178176_pname @ A @ B ) @ ( image_8178176_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(127,axiom,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member_pname @ ( A @ B ) @ ( image_8178176_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_imageI) ).
thf(1006,plain,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member_pname @ ( A @ B ) @ ( image_8178176_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(402,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_45_finite__surj) ).
thf(1878,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)],[402]) ).
thf(2631,plain,
( ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y )
@ ^ [A: hoare_1167836817_state] : bot_bot_o
@ sk93 )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[2630]) ).
thf(80,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_UnI2) ).
thf(857,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(246,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o
@ ^ [C: hoare_1167836817_state] : ( member2058392318_state @ C @ A )
@ ^ [C: hoare_1167836817_state] : ( member2058392318_state @ C @ B ) )
= ( ord_le827224136tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_pred__subset__eq) ).
thf(1397,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o
@ ^ [C: hoare_1167836817_state] : ( member2058392318_state @ C @ A )
@ ^ [C: hoare_1167836817_state] : ( member2058392318_state @ C @ B ) )
= ( ord_le827224136tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(298,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_sup_Oleft__commute) ).
thf(1567,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(570,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = B )
& ( A @ C ) ) )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Collect__conv__if) ).
thf(2460,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = B )
& ( A @ C ) ) )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(602,axiom,
! [A: pname,B: pname] :
( ( ( body_1 @ A )
= ( body_1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_com_Osimps_I6_J) ).
thf(2561,plain,
! [A: pname,B: pname] :
( ( ( body_1 @ A )
= ( body_1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(183,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_sup__ge1) ).
thf(1182,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(265,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_Int__lower2) ).
thf(1461,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(465,axiom,
! [A: pname,B: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ B ) @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MGT__BodyN) ).
thf(2080,plain,
! [A: pname,B: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ B ) @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ A ) ) @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(389,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_sup_Oassoc) ).
thf(1842,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(496,axiom,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o] :
( ( ( image_8178176_pname @ A @ B )
= bot_bot_pname_o )
= ( B = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_image__is__empty) ).
thf(2172,plain,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o] :
( ( ( image_8178176_pname @ A @ B )
= bot_bot_pname_o )
= ( B = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(452,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ~ ( member2058392318_state @ A @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_folding__one_Oinsert) ).
thf(2038,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ~ ( member2058392318_state @ A @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(139,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( insert_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_Int__insert__right__if1) ).
thf(1039,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( insert_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(426,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_order__antisym__conv) ).
thf(1942,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(326,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_342_order__antisym) ).
thf(1659,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)],[326]) ).
thf(30,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_inf__sup__aci_I6_J) ).
thf(686,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(560,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B = C )
& ( A @ C ) ) )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_Collect__conv__if2) ).
thf(2419,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B = C )
& ( A @ C ) ) )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(192,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_mem__def) ).
thf(1207,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(467,axiom,
! [A: pname > hoare_1167836817_state,B: pname > $o,C: pname > $o] :
( ( image_575578384_state @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1172322802tate_o @ ( image_575578384_state @ A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_image__Un) ).
thf(2085,plain,
! [A: pname > hoare_1167836817_state,B: pname > $o,C: pname > $o] :
( ( image_575578384_state @ A @ ( semila1780557381name_o @ B @ C ) )
= ( semila1172322802tate_o @ ( image_575578384_state @ A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(11,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(622,plain,
! [A: pname,B: pname] :
( ~ ( fequal_pname @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(124,axiom,
! [A: state > $o,B: com,C: com,D: com] :
( ( while @ A @ B )
!= ( semi @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_com_Osimps_I47_J) ).
thf(997,plain,
! [A: state > $o,B: com,C: com,D: com] :
( ( while @ A @ B )
!= ( semi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(120,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_Un__insert__right) ).
thf(985,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( semila1780557381name_o @ A @ ( insert_pname @ B @ C ) )
= ( insert_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(488,axiom,
! [A: hoare_1167836817_state > $o] :
( ( the_el323660082_state @ A )
= ( the_Ho310147232_state
@ ^ [B: hoare_1167836817_state] :
( A
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_the__elem__def) ).
thf(2153,plain,
! [A: hoare_1167836817_state > $o] :
( ( the_el323660082_state @ A )
= ( the_Ho310147232_state
@ ^ [B: hoare_1167836817_state] :
( A
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(422,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila1172322802tate_o @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_sup__absorb1) ).
thf(1932,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila1172322802tate_o @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(582,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_insert__mono) ).
thf(2505,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(428,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_le__infE) ).
thf(1947,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
=> ~ ( ( ord_less_eq_pname_o @ A @ B )
=> ~ ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(441,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_Int__insert__left__if1) ).
thf(1984,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(59,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_xt1_I4_J) ).
thf(779,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(200,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
= ( ( semila179895820tate_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_le__iff__inf) ).
thf(1249,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
= ( ( semila179895820tate_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(165,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila179895820tate_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_inf__absorb1) ).
thf(1131,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila179895820tate_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(19,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( member_pname @ B @ ( minus_minus_pname_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_DiffI) ).
thf(654,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ~ ( member_pname @ B @ A )
=> ( member_pname @ B @ ( minus_minus_pname_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(309,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ! [E: hoare_1167836817_state] :
( ( member2058392318_state @ E @ C )
=> ( ( B @ E )
=> ( A @ E ) ) )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ C @ ( collec1027672124_state @ B ) ) @ ( semila179895820tate_o @ D @ ( collec1027672124_state @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_Int__Collect__mono) ).
thf(1599,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ! [E: hoare_1167836817_state] :
( ( member2058392318_state @ E @ C )
=> ( ( B @ E )
=> ( A @ E ) ) )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ C @ ( collec1027672124_state @ B ) ) @ ( semila179895820tate_o @ D @ ( collec1027672124_state @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(199,axiom,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_ex__in__conv) ).
thf(1246,plain,
! [A: pname > $o] :
( ( ? [B: pname] : ( member_pname @ B @ A ) )
= ( A != bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(362,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_356_order__eq__iff) ).
thf(1759,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)],[362]) ).
thf(190,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= ( semila1172322802tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_inf__sup__aci_I8_J) ).
thf(1202,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= ( semila1172322802tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(197,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_inf__sup__ord_I4_J) ).
thf(1241,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(14,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: ( hoare_1167836817_state > $o ) > $o] :
( ( finite1380128977tate_o @ C )
=> ( ( ord_le741939125te_o_o @ C @ ( image_1745649338tate_o @ A @ B ) )
=> ? [D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ D @ B )
& ( finite1084549118_state @ D )
& ( C
= ( image_1745649338tate_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_finite__subset__image) ).
thf(633,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: ( hoare_1167836817_state > $o ) > $o] :
( ( finite1380128977tate_o @ C )
=> ( ( ord_le741939125te_o_o @ C @ ( image_1745649338tate_o @ A @ B ) )
=> ? [D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ D @ B )
& ( finite1084549118_state @ D )
& ( C
= ( image_1745649338tate_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(458,axiom,
! [A: hoare_1167836817_state] :
( ( set_Ho2131684873_state @ ( some_H1433514562_state @ A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_Option_Oset_Osimps_I2_J) ).
thf(2057,plain,
! [A: hoare_1167836817_state] :
( ( set_Ho2131684873_state @ ( some_H1433514562_state @ A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(211,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_insert__absorb) ).
thf(1286,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ( ( insert_pname @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(177,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_Un__upper2) ).
thf(1167,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(57,axiom,
! [A: pname,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( C @ ( insert_pname @ A @ bot_bot_pname_o ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_folding__one_Osingleton) ).
thf(773,plain,
! [A: pname,B: pname > pname > pname,C: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ B @ C )
=> ( ( C @ ( insert_pname @ A @ bot_bot_pname_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(37,axiom,
! [A: hoare_1167836817_state > pname,B: pname > $o,C: hoare_1167836817_state > $o] :
( ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_8178176_pname @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_image__subsetI) ).
thf(718,plain,
! [A: hoare_1167836817_state > pname,B: pname > $o,C: hoare_1167836817_state > $o] :
( ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
=> ( member_pname @ ( A @ D ) @ B ) )
=> ( ord_less_eq_pname_o @ ( image_8178176_pname @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(101,axiom,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o] :
( ~ ( finite1084549118_state @ B )
=> ( ( finite_finite_pname @ ( image_8178176_pname @ A @ B ) )
=> ? [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
& ~ ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_pigeonhole__infinite) ).
thf(926,plain,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o] :
( ~ ( finite1084549118_state @ B )
=> ( ( finite_finite_pname @ ( image_8178176_pname @ A @ B ) )
=> ? [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
& ~ ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(267,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_Un__upper2) ).
thf(1466,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(147,axiom,
! [A: state,B: state] :
( ( evalc @ skip @ A @ B )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_evalc__elim__cases_I1_J) ).
thf(1071,plain,
! [A: state,B: state] :
( ( evalc @ skip @ A @ B )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(413,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( semila1673364395name_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_Int__insert__right__if0) ).
thf(1906,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( semila1673364395name_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(360,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_folding__one_Oinsert) ).
thf(1754,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ~ ( member_pname @ A @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(516,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( bot_bo70021908tate_o
!= ( insert2134838167_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_empty__not__insert) ).
thf(2253,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( bot_bo70021908tate_o
!= ( insert2134838167_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(386,axiom,
( bot_bot_pname_o
= ( collect_pname
@ ^ [A: pname] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_empty__def) ).
thf(1833,plain,
( bot_bot_pname_o
= ( collect_pname
@ ^ [A: pname] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(1834,plain,
( ( collect_pname
@ ^ [A: pname] : $false )
= bot_bot_pname_o ),
inference(lifteq,[status(thm)],[1833]) ).
thf(2585,plain,
( ( collect_pname
@ ^ [A: pname] : $false )
= ( ^ [A: pname] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1834,861]) ).
thf(420,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_folding__one__idem_Oin__idem) ).
thf(1927,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(31,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( B
= ( C @ D ) )
=> ( ( ord_le827224136tate_o @ A @ D )
=> ( ! [E: hoare_1167836817_state > $o,F: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ F @ E )
=> ( ord_le827224136tate_o @ ( C @ F ) @ ( C @ E ) ) )
=> ( ord_le827224136tate_o @ ( C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_xt1_I15_J) ).
thf(689,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( B
= ( C @ D ) )
=> ( ( ord_le827224136tate_o @ A @ D )
=> ( ! [E: hoare_1167836817_state > $o,F: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ F @ E )
=> ( ord_le827224136tate_o @ ( C @ F ) @ ( C @ E ) ) )
=> ( ord_le827224136tate_o @ ( C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(42,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ C ) )
=> ( member2058392318_state @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_IntD2) ).
thf(733,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ C ) )
=> ( member2058392318_state @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(518,axiom,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_bot__least) ).
thf(2260,plain,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(9,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: ( hoare_1167836817_state > $o ) > $o] :
( ( ord_le741939125te_o_o @ A @ B )
=> ( ( finite1380128977tate_o @ B )
=> ( finite1380128977tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_finite__subset) ).
thf(618,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: ( hoare_1167836817_state > $o ) > $o] :
( ( ord_le741939125te_o_o @ A @ B )
=> ( ( finite1380128977tate_o @ B )
=> ( finite1380128977tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(364,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_inf__sup__aci_I7_J) ).
thf(1764,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(432,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ C ) )
= ( insert2134838167_state @ A @ ( semila179895820tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_insert__inter__insert) ).
thf(1959,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ C ) )
= ( insert2134838167_state @ A @ ( semila179895820tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(601,axiom,
! [A: hoare_1167836817_state,B: pname > hoare_1167836817_state,C: pname > $o] :
( ( member2058392318_state @ A @ ( image_575578384_state @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_imageE) ).
thf(2556,plain,
! [A: hoare_1167836817_state,B: pname > hoare_1167836817_state,C: pname > $o] :
( ( member2058392318_state @ A @ ( image_575578384_state @ B @ C ) )
=> ~ ! [D: pname] :
( ( A
= ( B @ D ) )
=> ~ ( member_pname @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(502,axiom,
! [A: pname > hoare_1167836817_state,B: pname > $o] :
( ( bot_bo70021908tate_o
= ( image_575578384_state @ A @ B ) )
= ( B = bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_empty__is__image) ).
thf(2188,plain,
! [A: pname > hoare_1167836817_state,B: pname > $o] :
( ( bot_bo70021908tate_o
= ( image_575578384_state @ A @ B ) )
= ( B = bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(359,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_62_subsetD) ).
thf(1752,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)],[359]) ).
thf(604,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] : ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_subset__insertI) ).
thf(2568,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] : ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(248,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_xt1_I6_J) ).
thf(1403,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(434,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_singleton__iff) ).
thf(1965,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(285,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
=> ~ ( ( ord_le827224136tate_o @ A @ B )
=> ~ ( ord_le827224136tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_equalityE) ).
thf(1520,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
=> ~ ( ( ord_le827224136tate_o @ A @ B )
=> ~ ( ord_le827224136tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(274,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( minus_2107060239tate_o @ B @ C ) )
=> ~ ( ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_DiffE) ).
thf(1488,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( minus_2107060239tate_o @ B @ C ) )
=> ~ ( ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(369,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_Int__lower1) ).
thf(1784,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(243,axiom,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_bot__fun__def) ).
thf(1389,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(87,axiom,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_inf__bot__right) ).
thf(875,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ A @ bot_bot_pname_o )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(35,axiom,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ~ ! [C: pname > $o] :
( ( B
= ( insert_pname @ A @ C ) )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_Set_Oset__insert) ).
thf(711,plain,
! [A: pname,B: pname > $o] :
( ( member_pname @ A @ B )
=> ~ ! [C: pname > $o] :
( ( B
= ( insert_pname @ A @ C ) )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(506,axiom,
! [A: hoare_1167836817_state > $o,B: pname > hoare_1167836817_state,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le827224136tate_o @ A @ ( image_575578384_state @ B @ C ) )
=> ( finite1084549118_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite__surj) ).
thf(2220,plain,
! [A: hoare_1167836817_state > $o,B: pname > hoare_1167836817_state,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le827224136tate_o @ A @ ( image_575578384_state @ B @ C ) )
=> ( finite1084549118_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(449,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insertI2) ).
thf(2029,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ ( insert2134838167_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(344,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( B = C )
=> ( ( ord_le827224136tate_o @ C @ A )
=> ( ord_le827224136tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_ord__eq__le__trans) ).
thf(1707,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( B = C )
=> ( ( ord_le827224136tate_o @ C @ A )
=> ( ord_le827224136tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(221,axiom,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_inf__bot__left) ).
thf(1312,plain,
! [A: pname > $o] :
( ( semila1673364395name_o @ bot_bot_pname_o @ A )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(611,plain,
! [B: ( pname > $o ) > $o,A: ( pname > $o ) > $o] :
( ~ ( ord_le1205211808me_o_o @ A @ B )
| ~ ( finite297249702name_o @ B )
| ( finite297249702name_o @ A ) ),
inference(cnf,[status(esa)],[610]) ).
thf(320,axiom,
! [A: pname > $o] :
( ( ( collect_pname @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Collect__empty__eq) ).
thf(1635,plain,
! [A: pname > $o] :
( ( ( collect_pname @ A )
= bot_bot_pname_o )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(196,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_sup__ge2) ).
thf(1239,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(68,axiom,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_less_eq_pname_o @ ( collect_pname @ B ) @ ( collect_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_Collect__mono) ).
thf(804,plain,
! [A: pname > $o,B: pname > $o] :
( ! [C: pname] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_less_eq_pname_o @ ( collect_pname @ B ) @ ( collect_pname @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(203,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_pname_o @ A @ C )
=> ~ ( ord_less_eq_pname_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_le__supE) ).
thf(1258,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_pname_o @ A @ C )
=> ~ ( ord_less_eq_pname_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(573,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ C ) )
= ( ( A = B )
| ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_insert__iff) ).
thf(2474,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ C ) )
= ( ( A = B )
| ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(321,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( insert_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_Int__insert__right) ).
thf(1638,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( insert_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ C @ ( insert_pname @ B @ A ) )
= ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(231,axiom,
! [A: pname > $o,B: pname > $o] :
( ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila1673364395name_o @ ( collect_pname @ A ) @ ( collect_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_Collect__conj__eq) ).
thf(1356,plain,
! [A: pname > $o,B: pname > $o] :
( ( collect_pname
@ ^ [C: pname] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila1673364395name_o @ ( collect_pname @ A ) @ ( collect_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(370,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
= ( ( semila1172322802tate_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_le__iff__sup) ).
thf(1786,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
= ( ( semila1172322802tate_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(330,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_sup__inf__distrib1) ).
thf(1669,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(206,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ~ ( fequal1831255762_state @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com) ).
thf(1271,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ~ ( fequal1831255762_state @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(236,axiom,
! [A: state > $o,B: com] :
( ( wt @ B )
=> ( wt @ ( while @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_While) ).
thf(1371,plain,
! [A: state > $o,B: com] :
( ( wt @ B )
=> ( wt @ ( while @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(142,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila1172322802tate_o
@ ^ [D: hoare_1167836817_state] : ( member2058392318_state @ D @ A )
@ ^ [D: hoare_1167836817_state] : ( member2058392318_state @ D @ B )
@ C )
= ( member2058392318_state @ C @ ( semila1172322802tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_sup__Un__eq) ).
thf(1058,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila1172322802tate_o
@ ^ [D: hoare_1167836817_state] : ( member2058392318_state @ D @ A )
@ ^ [D: hoare_1167836817_state] : ( member2058392318_state @ D @ B )
@ C )
= ( member2058392318_state @ C @ ( semila1172322802tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(156,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1780557381name_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_subset__Un__eq) ).
thf(1107,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
= ( ( semila1780557381name_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(187,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ C @ A ) @ ( semila179895820tate_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_Int__mono) ).
thf(1194,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ C @ A ) @ ( semila179895820tate_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(393,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( if_Hoa833675553_state @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate) ).
thf(1853,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( if_Hoa833675553_state @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(548,axiom,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_bot__fun__def) ).
thf(2383,plain,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(409,axiom,
! [A: pname,B: hoare_1167836817_state > pname,C: hoare_1167836817_state > $o] :
( ( member_pname @ A @ ( image_8178176_pname @ B @ C ) )
=> ~ ! [D: hoare_1167836817_state] :
( ( A
= ( B @ D ) )
=> ~ ( member2058392318_state @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_imageE) ).
thf(1894,plain,
! [A: pname,B: hoare_1167836817_state > pname,C: hoare_1167836817_state > $o] :
( ( member_pname @ A @ ( image_8178176_pname @ B @ C ) )
=> ~ ! [D: hoare_1167836817_state] :
( ( A
= ( B @ D ) )
=> ~ ( member2058392318_state @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(377,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_order__antisym) ).
thf(1806,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(517,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
= ( A = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_subset__empty) ).
thf(2257,plain,
! [A: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ bot_bo70021908tate_o )
= ( A = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(275,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ~ ( finite1084549118_state @ B )
=> ( ( finite1084549118_state @ ( image_31595733_state @ A @ B ) )
=> ? [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
& ~ ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_pigeonhole__infinite) ).
thf(1492,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ~ ( finite1084549118_state @ B )
=> ( ( finite1084549118_state @ ( image_31595733_state @ A @ B ) )
=> ? [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
& ~ ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(290,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( semila1172322802tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_sup__commute) ).
thf(1542,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( semila1172322802tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(478,axiom,
! [A: pname,B: hoare_1167836817_state > $o,C: pname > state > state > $o,D: pname > state > state > $o,E: pname > $o] :
( ( hoare_123228589_state
@ ( semila1172322802tate_o @ B
@ ( image_575578384_state
@ ^ [F: pname] : ( hoare_908217195_state @ ( C @ F ) @ ( body_1 @ F ) @ ( D @ F ) )
@ E ) )
@ ( image_575578384_state
@ ^ [F: pname] : ( hoare_908217195_state @ ( C @ F ) @ ( the_com @ ( body @ F ) ) @ ( D @ F ) )
@ E ) )
=> ( ( member_pname @ A @ E )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ ( C @ A ) @ ( body_1 @ A ) @ ( D @ A ) ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_Body1) ).
thf(2116,plain,
! [A: pname,B: hoare_1167836817_state > $o,C: pname > state > state > $o,D: pname > state > state > $o,E: pname > $o] :
( ( hoare_123228589_state
@ ( semila1172322802tate_o @ B
@ ( image_575578384_state
@ ^ [F: pname] : ( hoare_908217195_state @ ( C @ F ) @ ( body_1 @ F ) @ ( D @ F ) )
@ E ) )
@ ( image_575578384_state
@ ^ [F: pname] : ( hoare_908217195_state @ ( C @ F ) @ ( the_com @ ( body @ F ) ) @ ( D @ F ) )
@ E ) )
=> ( ( member_pname @ A @ E )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ ( C @ A ) @ ( body_1 @ A ) @ ( D @ A ) ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(8,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_169_rev__finite__subset) ).
thf(616,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)],[8]) ).
thf(584,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ~ ! [C: hoare_1167836817_state > $o] :
( ( B
= ( insert2134838167_state @ A @ C ) )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_Set_Oset__insert) ).
thf(2510,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ~ ! [C: hoare_1167836817_state > $o] :
( ( B
= ( insert2134838167_state @ A @ C ) )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(54,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_subsetD) ).
thf(764,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(543,axiom,
! [A: pname > hoare_1167836817_state,B: pname > hoare_1167836817_state,C: pname > $o,D: pname > $o] :
( ( C = D )
=> ( ! [E: pname] :
( ( member_pname @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( image_575578384_state @ A @ C )
= ( image_575578384_state @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_image__cong) ).
thf(2361,plain,
! [A: pname > hoare_1167836817_state,B: pname > hoare_1167836817_state,C: pname > $o,D: pname > $o] :
( ( C = D )
=> ( ! [E: pname] :
( ( member_pname @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( image_575578384_state @ A @ C )
= ( image_575578384_state @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(527,axiom,
! [A: pname] :
( ( wt @ ( body_1 @ A ) )
=> ~ ! [B: com] :
( ( body @ A )
!= ( some_com @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_WTs__elim__cases_I7_J) ).
thf(2311,plain,
! [A: pname] :
( ( wt @ ( body_1 @ A ) )
=> ~ ! [B: com] :
( ( body @ A )
!= ( some_com @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(366,axiom,
! [A: state > $o,B: com] :
( ( while @ A @ B )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_com_Osimps_I17_J) ).
thf(1771,plain,
! [A: state > $o,B: com] :
( ( while @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(44,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_Un__least) ).
thf(737,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(17,axiom,
! [A: hoare_1167836817_state > pname > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite297249702name_o @ ( image_2066861949name_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(649,plain,
! [A: hoare_1167836817_state > pname > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite297249702name_o @ ( image_2066861949name_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(375,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_sup__assoc) ).
thf(1801,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
= ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(1969,plain,
~ ( member2058392318_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ),
inference(polarity_switch,[status(thm)],[1968]) ).
thf(219,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila1172322802tate_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_sup__absorb2) ).
thf(1307,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila1172322802tate_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(70,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1780557381name_o @ A @ B )
= bot_bot_pname_o )
= ( ( A = bot_bot_pname_o )
& ( B = bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_sup__eq__bot__iff) ).
thf(811,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1780557381name_o @ A @ B )
= bot_bot_pname_o )
= ( ( A = bot_bot_pname_o )
& ( B = bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(13,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( minus_minus_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_finite__Diff) ).
thf(631,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite_finite_pname @ ( minus_minus_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(481,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_197_domI) ).
thf(2129,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)],[481]) ).
thf(444,axiom,
! [A: hoare_1167836817_state,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_575578384_state
@ ^ [C: pname] : A
@ B )
= bot_bo70021908tate_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_575578384_state
@ ^ [C: pname] : A
@ B )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_image__constant__conv) ).
thf(1993,plain,
! [A: hoare_1167836817_state,B: pname > $o] :
( ( ( B = bot_bot_pname_o )
=> ( ( image_575578384_state
@ ^ [C: pname] : A
@ B )
= bot_bo70021908tate_o ) )
& ( ( B != bot_bot_pname_o )
=> ( ( image_575578384_state
@ ^ [C: pname] : A
@ B )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(353,axiom,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_equalityD2) ).
thf(1731,plain,
! [A: pname > $o,B: pname > $o] :
( ( A = B )
=> ( ord_less_eq_pname_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(414,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_183_subset__insert) ).
thf(1909,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)],[414]) ).
thf(566,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ? [B: hoare_1167836817_state] : ( member2058392318_state @ B @ A ) )
= ( A != bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_ex__in__conv) ).
thf(2446,plain,
! [A: hoare_1167836817_state > $o] :
( ( ? [B: hoare_1167836817_state] : ( member2058392318_state @ B @ A ) )
= ( A != bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(396,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ A )
=> ( ord_le827224136tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_subset__trans) ).
thf(1862,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ C @ A )
=> ( ord_le827224136tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(33,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( semila1673364395name_o @ A @ C ) ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( semila1673364395name_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_Int__insert__left) ).
thf(700,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( insert_pname @ B @ ( semila1673364395name_o @ A @ C ) ) ) )
& ( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( semila1673364395name_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(388,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ~ ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_IntE) ).
thf(1838,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ~ ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(227,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
= ( ( ord_le827224136tate_o @ A @ B )
& ( ord_le827224136tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_order__eq__iff) ).
thf(1344,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
= ( ( ord_le827224136tate_o @ A @ B )
& ( ord_le827224136tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(106,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_94_insert__iff) ).
thf(943,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)],[106]) ).
thf(240,axiom,
! [A: com,B: com,C: state,D: state] :
( ( evalc @ ( semi @ A @ B ) @ C @ D )
=> ~ ! [E: state] :
( ( evalc @ A @ C @ E )
=> ~ ( evalc @ B @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_evalc__elim__cases_I4_J) ).
thf(1381,plain,
! [A: com,B: com,C: state,D: state] :
( ( evalc @ ( semi @ A @ B ) @ C @ D )
=> ~ ! [E: state] :
( ( evalc @ A @ C @ E )
=> ~ ( evalc @ B @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(90,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_xt1_I3_J) ).
thf(890,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( B = C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(329,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_inf__sup__ord_I3_J) ).
thf(1667,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(4,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_43_finite__surj) ).
thf(608,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)],[4]) ).
thf(609,plain,
! [C: pname > $o,B: pname > pname > $o,A: ( pname > $o ) > $o] :
( ~ ( finite_finite_pname @ C )
| ~ ( ord_le1205211808me_o_o @ A @ ( image_pname_pname_o @ B @ C ) )
| ( finite297249702name_o @ A ) ),
inference(cnf,[status(esa)],[608]) ).
thf(476,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( ( insert2134838167_state @ A @ bot_bo70021908tate_o )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_singleton__inject) ).
thf(2111,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( ( insert2134838167_state @ A @ bot_bo70021908tate_o )
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(295,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_folding__one_Oinsert__remove) ).
thf(1556,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(56,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( ~ ( B @ C )
=> ( A @ C ) )
=> ( semila1172322802tate_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_sup1CI) ).
thf(769,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( ~ ( B @ C )
=> ( A @ C ) )
=> ( semila1172322802tate_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(526,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ! [C: hoare_1167836817_state] : ( A @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ( D != bot_bo70021908tate_o )
=> ( ~ ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert2134838167_state @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_finite__ne__induct) ).
thf(2289,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ! [C: hoare_1167836817_state] : ( A @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
=> ( ! [C: hoare_1167836817_state,D: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ D )
=> ( ( D != bot_bo70021908tate_o )
=> ( ~ ( member2058392318_state @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert2134838167_state @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(214,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ ( semila1172322802tate_o @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
=> ( A @ D ) )
& ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
=> ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_ball__Un) ).
thf(1293,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ ( semila1172322802tate_o @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
=> ( A @ D ) )
& ! [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ C )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(600,axiom,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= ( member2058392318_state @ A @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_bot__empty__eq) ).
thf(2553,plain,
! [A: hoare_1167836817_state] :
( ( bot_bo70021908tate_o @ A )
= ( member2058392318_state @ A @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(533,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = A )
| ( member2058392318_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_insert__compr) ).
thf(2329,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = A )
| ( member2058392318_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(143,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= ( semila1172322802tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_Un__left__absorb) ).
thf(1061,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= ( semila1172322802tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(540,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( insert2134838167_state @ A @ B ) )
= ( insert2134838167_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_insert__absorb2) ).
thf(2350,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ ( insert2134838167_state @ A @ B ) )
= ( insert2134838167_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(112,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_Un__absorb) ).
thf(959,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(194,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( finite1084549118_state @ B )
| ( finite1084549118_state @ A ) )
=> ( finite1084549118_state @ ( semila179895820tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_finite__Int) ).
thf(1213,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( finite1084549118_state @ B )
| ( finite1084549118_state @ A ) )
=> ( finite1084549118_state @ ( semila179895820tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(544,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = A )
| ( member2058392318_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_insert__compr__raw) ).
thf(2369,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( C = A )
| ( member2058392318_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(158,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila179895820tate_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_inf__absorb2) ).
thf(1113,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila179895820tate_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(351,axiom,
! [A: state,B: com,C: state,D: state] :
( ( evalc @ B @ C @ D )
=> ( ( evalc @ B @ C @ A )
=> ( A = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_com__det) ).
thf(1726,plain,
! [A: state,B: com,C: state,D: state] :
( ( evalc @ B @ C @ D )
=> ( ( evalc @ B @ C @ A )
=> ( A = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(276,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( insert_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_insert__Diff__single) ).
thf(1496,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) )
= ( insert_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(489,axiom,
finite_finite_pname @ ( dom_pname_com @ body ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite__dom__body) ).
thf(2156,plain,
finite_finite_pname @ ( dom_pname_com @ body ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(339,axiom,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Collect__def) ).
thf(1694,plain,
! [A: pname > $o] :
( ( collect_pname @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(437,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( hoare_123228589_state @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_weaken) ).
thf(1973,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ B @ C )
=> ( ( ord_le827224136tate_o @ A @ C )
=> ( hoare_123228589_state @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(296,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( ord_le827224136tate_o @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_le__infI) ).
thf(1562,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( ord_le827224136tate_o @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(341,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_inf__sup__distrib1) ).
thf(1699,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(553,axiom,
! [A: pname > hoare_1167836817_state] :
( ( image_575578384_state @ A @ bot_bot_pname_o )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_image__empty) ).
thf(2401,plain,
! [A: pname > hoare_1167836817_state] :
( ( image_575578384_state @ A @ bot_bot_pname_o )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(307,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_168_finite__subset) ).
thf(1594,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)],[307]) ).
thf(456,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ( A = bot_bo70021908tate_o )
& ( B = bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_Un__empty) ).
thf(2051,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ( A = bot_bo70021908tate_o )
& ( B = bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(599,axiom,
! [A: hoare_1167836817_state > $o] :
( ( ( collec1027672124_state @ A )
= bot_bo70021908tate_o )
= ( ! [B: hoare_1167836817_state] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Collect__empty__eq) ).
thf(2550,plain,
! [A: hoare_1167836817_state > $o] :
( ( ( collec1027672124_state @ A )
= bot_bo70021908tate_o )
= ( ! [B: hoare_1167836817_state] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(145,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_inf__sup__ord_I4_J) ).
thf(1066,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(260,axiom,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_com_Osimps_I12_J) ).
thf(1445,plain,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(286,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( ord_le827224136tate_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_order__antisym__conv) ).
thf(1528,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( ord_le827224136tate_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(180,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( B @ C )
=> ( semila1172322802tate_o @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_sup1I1) ).
thf(1176,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( B @ C )
=> ( semila1172322802tate_o @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(367,axiom,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite__subset__image) ).
thf(1775,plain,
! [A: pname > pname,B: pname > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_pname_pname @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(513,axiom,
! [A: pname > hoare_1167836817_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert2134838167_state @ ( A @ B ) @ ( image_575578384_state @ A @ C ) )
= ( image_575578384_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insert__image) ).
thf(2244,plain,
! [A: pname > hoare_1167836817_state,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( insert2134838167_state @ ( A @ B ) @ ( image_575578384_state @ A @ C ) )
= ( image_575578384_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(258,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_198_Collect__conv__if) ).
thf(1435,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)],[258]) ).
thf(593,axiom,
! [A: pname,B: state,C: state] :
( ( evalc @ ( body_1 @ A ) @ B @ C )
=> ( evalc @ ( the_com @ ( body @ A ) ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_evalc__elim__cases_I6_J) ).
thf(2535,plain,
! [A: pname,B: state,C: state] :
( ( evalc @ ( body_1 @ A ) @ B @ C )
=> ( evalc @ ( the_com @ ( body @ A ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(473,axiom,
! [A: hoare_1167836817_state > $o,B: pname > $o] :
( ( hoare_123228589_state
@ ( semila1172322802tate_o @ A
@ ( image_575578384_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ C ) )
@ B ) )
@ ( image_575578384_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ C ) ) )
@ B ) )
=> ( ( finite_finite_pname @ B )
=> ( hoare_123228589_state @ A
@ ( image_575578384_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ C ) )
@ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_MGT__Body) ).
thf(2101,plain,
! [A: hoare_1167836817_state > $o,B: pname > $o] :
( ( hoare_123228589_state
@ ( semila1172322802tate_o @ A
@ ( image_575578384_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ C ) )
@ B ) )
@ ( image_575578384_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ C ) ) )
@ B ) )
=> ( ( finite_finite_pname @ B )
=> ( hoare_123228589_state @ A
@ ( image_575578384_state
@ ^ [C: pname] : ( hoare_Mirabelle_MGT @ ( body_1 @ C ) )
@ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(149,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1780557381name_o @ B @ C ) )
=> ( ~ ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_UnE) ).
thf(1076,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1780557381name_o @ B @ C ) )
=> ( ~ ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(378,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( C = A )
=> ( ord_le827224136tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_ord__le__eq__trans) ).
thf(1809,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( C = A )
=> ( ord_le827224136tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(327,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_inf__sup__absorb) ).
thf(1662,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(218,axiom,
! [A: pname > $o] :
( ( the_elem_pname @ A )
= ( the_pname
@ ^ [B: pname] :
( A
= ( insert_pname @ B @ bot_bot_pname_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_the__elem__def) ).
thf(1304,plain,
! [A: pname > $o] :
( ( the_elem_pname @ A )
= ( the_pname
@ ^ [B: pname] :
( A
= ( insert_pname @ B @ bot_bot_pname_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(336,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ A )
=> ( ( ( semila1673364395name_o @ B @ A )
!= bot_bot_pname_o )
=> ( ( C @ ( D @ ( semila1780557381name_o @ B @ A ) ) @ ( D @ ( semila1673364395name_o @ B @ A ) ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_folding__one_Ounion__inter) ).
thf(1684,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( finite_finite_pname @ A )
=> ( ( ( semila1673364395name_o @ B @ A )
!= bot_bot_pname_o )
=> ( ( C @ ( D @ ( semila1780557381name_o @ B @ A ) ) @ ( D @ ( semila1673364395name_o @ B @ A ) ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(166,axiom,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
= ( ( A = bot_bot_pname_o )
| ? [B: pname > $o,C: pname] :
( ( A
= ( insert_pname @ C @ B ) )
& ( finite_finite_pname @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_finite_Osimps) ).
thf(1134,plain,
! [A: pname > $o] :
( ( finite_finite_pname @ A )
= ( ( A = bot_bot_pname_o )
| ? [B: pname > $o,C: pname] :
( ( A
= ( insert_pname @ C @ B ) )
& ( finite_finite_pname @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(567,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( insert2134838167_state @ A @ B ) @ C )
= ( ( member2058392318_state @ A @ C )
& ( ord_le827224136tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_insert__subset) ).
thf(2449,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( insert2134838167_state @ A @ B ) @ C )
= ( ( member2058392318_state @ A @ C )
& ( ord_le827224136tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(151,axiom,
! [A: ( pname > $o ) > pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ( A @ C )
= B )
=> ( ! [E: pname > $o,F: pname > $o] :
( ( ord_less_eq_pname_o @ F @ E )
=> ( ord_less_eq_pname_o @ ( A @ F ) @ ( A @ E ) ) )
=> ( ord_less_eq_pname_o @ B @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_xt1_I16_J) ).
thf(1081,plain,
! [A: ( pname > $o ) > pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ( A @ C )
= B )
=> ( ! [E: pname > $o,F: pname > $o] :
( ( ord_less_eq_pname_o @ F @ E )
=> ( ord_less_eq_pname_o @ ( A @ F ) @ ( A @ E ) ) )
=> ( ord_less_eq_pname_o @ B @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(443,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ( ( semila179895820tate_o @ B @ A )
= bot_bo70021908tate_o )
=> ( ( D @ ( semila1172322802tate_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_folding__one_Ounion__disjoint) ).
thf(1990,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( finite1084549118_state @ A )
=> ( ( A != bot_bo70021908tate_o )
=> ( ( ( semila179895820tate_o @ B @ A )
= bot_bo70021908tate_o )
=> ( ( D @ ( semila1172322802tate_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(269,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_136_finite__Collect__disjI) ).
thf(1472,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)],[269]) ).
thf(50,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_inf__absorb2) ).
thf(754,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(72,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila179895820tate_o @ ( collec1027672124_state @ A ) @ ( collec1027672124_state @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_Collect__conj__eq) ).
thf(836,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( A @ C )
& ( B @ C ) ) )
= ( semila179895820tate_o @ ( collec1027672124_state @ A ) @ ( collec1027672124_state @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1592,plain,
( hoare_1201148605gleton
= ( ? [A: state,B: state] : ( A != B ) ) ),
inference(lifteq,[status(thm)],[1591]) ).
thf(287,axiom,
hoare_1201148605gleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1531,plain,
hoare_1201148605gleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(2580,plain,
? [A: state,B: state] : ( A != B ),
inference(rewrite,[status(thm)],[1592,1531]) ).
thf(2581,plain,
sk90 != sk91,
inference(cnf,[status(esa)],[2580]) ).
thf(2582,plain,
sk91 != sk90,
inference(lifteq,[status(thm)],[2581]) ).
thf(457,axiom,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o] :
( ( bot_bot_pname_o
= ( image_8178176_pname @ A @ B ) )
= ( B = bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_empty__is__image) ).
thf(2054,plain,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o] :
( ( bot_bot_pname_o
= ( image_8178176_pname @ A @ B ) )
= ( B = bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(38,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_96_insert__commute) ).
thf(722,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)],[38]) ).
thf(26,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( D @ ( semila1780557381name_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_folding__one__idem_Ounion__idem) ).
thf(675,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( D @ ( semila1780557381name_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(302,axiom,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_empty__iff) ).
thf(1583,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(64,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( semila1780557381name_o
@ ( collect_pname
@ ^ [C: pname] : ( C = A ) )
@ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_insert__def) ).
thf(795,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
= ( semila1780557381name_o
@ ( collect_pname
@ ^ [C: pname] : ( C = A ) )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(529,axiom,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: com,D: state > state > $o,E: $o] :
( ( E
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ C @ D ) @ bot_bo70021908tate_o ) ) )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [F: state,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_constant) ).
thf(2318,plain,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: com,D: state > state > $o,E: $o] :
( ( E
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ C @ D ) @ bot_bo70021908tate_o ) ) )
=> ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [F: state,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(22,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite1380128977tate_o @ ( image_1745649338tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(663,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( finite1380128977tate_o @ ( image_1745649338tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(572,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( ( A = bot_bo70021908tate_o )
| ( A
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_subset__singletonD) ).
thf(2471,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state] :
( ( ord_le827224136tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( ( A = bot_bo70021908tate_o )
| ( A
= ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(169,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( semila1172322802tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Un__commute) ).
thf(1145,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ B )
= ( semila1172322802tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(603,axiom,
! [A: pname,B: state > $o,C: com] :
( ( body_1 @ A )
!= ( while @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_com_Osimps_I59_J) ).
thf(2564,plain,
! [A: pname,B: state > $o,C: com] :
( ( body_1 @ A )
!= ( while @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(390,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ! [D: hoare_1167836817_state > $o,E: hoare_1167836817_state > $o,F: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ D @ ( semila1172322802tate_o @ E @ F ) )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ D @ E ) @ ( semila179895820tate_o @ D @ F ) ) )
=> ( ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_distrib__imp1) ).
thf(1845,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ! [D: hoare_1167836817_state > $o,E: hoare_1167836817_state > $o,F: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ D @ ( semila1172322802tate_o @ E @ F ) )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ D @ E ) @ ( semila179895820tate_o @ D @ F ) ) )
=> ( ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(374,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1673364395name_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
& ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_Int__def) ).
thf(1798,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1673364395name_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
& ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(126,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_90_insert__ident) ).
thf(1003,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)],[126]) ).
thf(79,axiom,
! [A: com,B: state,C: com,D: state,E: state] :
( ( evalc @ C @ D @ E )
=> ( ( evalc @ A @ E @ B )
=> ( evalc @ ( semi @ C @ A ) @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_evalc_OSemi) ).
thf(855,plain,
! [A: com,B: state,C: com,D: state,E: state] :
( ( evalc @ C @ D @ E )
=> ( ( evalc @ A @ E @ B )
=> ( evalc @ ( semi @ C @ A ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(283,axiom,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1673364395name_o
@ ^ [D: pname] : ( member_pname @ D @ A )
@ ^ [D: pname] : ( member_pname @ D @ B )
@ C )
= ( member_pname @ C @ ( semila1673364395name_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_inf__Int__eq) ).
thf(1516,plain,
! [A: pname > $o,B: pname > $o,C: pname] :
( ( semila1673364395name_o
@ ^ [D: pname] : ( member_pname @ D @ A )
@ ^ [D: pname] : ( member_pname @ D @ B )
@ C )
= ( member_pname @ C @ ( semila1673364395name_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(86,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_sup_Oidem) ).
thf(872,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(116,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_361_le__bot) ).
thf(971,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)],[116]) ).
thf(485,axiom,
! [A: pname > hoare_1167836817_state,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite1084549118_state @ ( image_575578384_state @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_pigeonhole__infinite) ).
thf(2143,plain,
! [A: pname > hoare_1167836817_state,B: pname > $o] :
( ~ ( finite_finite_pname @ B )
=> ( ( finite1084549118_state @ ( image_575578384_state @ A @ B ) )
=> ? [C: pname] :
( ( member_pname @ C @ B )
& ~ ( finite_finite_pname
@ ( collect_pname
@ ^ [D: pname] :
( ( member_pname @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(45,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B @ A )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_predicate1D) ).
thf(739,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( B @ A )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(497,axiom,
! [A: hoare_1167836817_state > $o] :
( ( bot_bo70021908tate_o
= ( collec1027672124_state @ A ) )
= ( ! [B: hoare_1167836817_state] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_empty__Collect__eq) ).
thf(2175,plain,
! [A: hoare_1167836817_state > $o] :
( ( bot_bo70021908tate_o
= ( collec1027672124_state @ A ) )
= ( ! [B: hoare_1167836817_state] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(549,axiom,
! [A: hoare_1167836817_state > $o,B: state > state > $o] : ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ skip @ B ) @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_hoare__derivs_OSkip) ).
thf(2386,plain,
! [A: hoare_1167836817_state > $o,B: state > state > $o] : ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ skip @ B ) @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(491,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_folding__one__idem_Oinsert__idem) ).
thf(2160,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite806517911_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( B != bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(292,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_143_singletonE) ).
thf(1547,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)],[292]) ).
thf(58,axiom,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( ( semila1673364395name_o @ B @ A )
= bot_bot_pname_o )
=> ( ( D @ ( semila1780557381name_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_folding__one_Ounion__disjoint) ).
thf(776,plain,
! [A: pname > $o,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( finite_finite_pname @ A )
=> ( ( A != bot_bot_pname_o )
=> ( ( ( semila1673364395name_o @ B @ A )
= bot_bot_pname_o )
=> ( ( D @ ( semila1780557381name_o @ B @ A ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(313,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_Int__Un__distrib) ).
thf(1611,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( semila1172322802tate_o @ ( semila179895820tate_o @ A @ B ) @ ( semila179895820tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(546,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= A ) )
& ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
!= bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_folding__one_Oinsert__remove) ).
thf(2375,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= A ) )
& ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
!= bot_bo70021908tate_o )
=> ( ( D @ ( insert2134838167_state @ A @ B ) )
= ( C @ A @ ( D @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(173,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_Un__Int__distrib) ).
thf(1156,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ B @ C ) )
= ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(459,axiom,
! [A: hoare_1167836817_state] :
~ ( member2058392318_state @ A @ bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_emptyE) ).
thf(2060,plain,
! [A: hoare_1167836817_state] :
~ ( member2058392318_state @ A @ bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(356,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_equalityI) ).
thf(1743,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(247,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_104_insert__compr) ).
thf(1400,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)],[247]) ).
thf(110,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ C ) )
=> ( member2058392318_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_IntD1) ).
thf(954,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ C ) )
=> ( member2058392318_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(201,axiom,
! [A: option_com,B: option_com] :
( ( if_option_com @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) ).
thf(1252,plain,
! [A: option_com,B: option_com] :
( ( if_option_com @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(63,axiom,
! [A: hoare_1167836817_state > pname > $o,B: hoare_1167836817_state > $o] :
( ~ ( finite1084549118_state @ B )
=> ( ( finite297249702name_o @ ( image_2066861949name_o @ A @ B ) )
=> ? [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
& ~ ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_pigeonhole__infinite) ).
thf(791,plain,
! [A: hoare_1167836817_state > pname > $o,B: hoare_1167836817_state > $o] :
( ~ ( finite1084549118_state @ B )
=> ( ( finite297249702name_o @ ( image_2066861949name_o @ A @ B ) )
=> ? [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
& ~ ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(185,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_xt1_I5_J) ).
thf(1188,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(204,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_56_insertCI) ).
thf(1262,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)],[204]) ).
thf(536,axiom,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ E ) @ bot_bo70021908tate_o ) )
=> ( ! [F: state,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ D @ E ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_conseq1) ).
thf(2337,plain,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ E ) @ bot_bo70021908tate_o ) )
=> ( ! [F: state,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ D @ E ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(522,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( semila1172322802tate_o @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_insert__is__Un) ).
thf(2276,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
= ( semila1172322802tate_o @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(530,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert2134838167_state @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_Un__insert__right) ).
thf(2322,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( insert2134838167_state @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(334,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_112_subset__trans) ).
thf(1679,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)],[334]) ).
thf(16,axiom,
! [A: pname > pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_pname_pname_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname_o @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_finite__subset__image) ).
thf(643,plain,
! [A: pname > pname > $o,B: pname > $o,C: ( pname > $o ) > $o] :
( ( finite297249702name_o @ C )
=> ( ( ord_le1205211808me_o_o @ C @ ( image_pname_pname_o @ A @ B ) )
=> ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ B )
& ( finite_finite_pname @ D )
& ( C
= ( image_pname_pname_o @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(571,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ~ ( member2058392318_state @ B @ A )
=> ( ( ( insert2134838167_state @ B @ C )
= ( insert2134838167_state @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_insert__ident) ).
thf(2468,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ~ ( member2058392318_state @ B @ A )
=> ( ( ( insert2134838167_state @ B @ C )
= ( insert2134838167_state @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(345,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ( member_pname @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_IntD2) ).
thf(1711,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ( member_pname @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(277,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila1172322802tate_o @ B @ C ) )
=> ( ~ ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_UnE) ).
thf(1499,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila1172322802tate_o @ B @ C ) )
=> ( ~ ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(25,axiom,
! [A: pname > pname > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite297249702name_o @ ( image_pname_pname_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(673,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)],[25]) ).
thf(470,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_Diff__insert2) ).
thf(2092,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ C ) )
= ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(442,axiom,
! [A: pname > $o,B: pname > option_com,C: pname > option_com] :
( ( dom_pname_com
@ ^ [D: pname] : ( if_option_com @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ B ) @ ( collect_pname @ A ) )
@ ( semila1673364395name_o @ ( dom_pname_com @ C )
@ ( collect_pname
@ ^ [D: pname] :
~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_dom__if) ).
thf(1987,plain,
! [A: pname > $o,B: pname > option_com,C: pname > option_com] :
( ( dom_pname_com
@ ^ [D: pname] : ( if_option_com @ ( A @ D ) @ ( B @ D ) @ ( C @ D ) ) )
= ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ B ) @ ( collect_pname @ A ) )
@ ( semila1673364395name_o @ ( dom_pname_com @ C )
@ ( collect_pname
@ ^ [D: pname] :
~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(347,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_le__supI2) ).
thf(1716,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(379,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_sup__absorb2) ).
thf(1813,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(262,axiom,
! [A: pname] :
( ( the_elem_pname @ ( insert_pname @ A @ bot_bot_pname_o ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_the__elem__eq) ).
thf(1452,plain,
! [A: pname] :
( ( the_elem_pname @ ( insert_pname @ A @ bot_bot_pname_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(223,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_124_set__eq__subset) ).
thf(1317,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)],[223]) ).
thf(385,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
= ( ( member_pname @ A @ B )
& ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_Int__iff) ).
thf(1830,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
= ( ( member_pname @ A @ B )
& ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(577,axiom,
! [A: state > state > $o,B: state > state > $o,C: hoare_1167836817_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ E @ F ) @ bot_bo70021908tate_o ) )
=> ( ! [G: state,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: state] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ E @ A ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_conseq12) ).
thf(2486,plain,
! [A: state > state > $o,B: state > state > $o,C: hoare_1167836817_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ E @ F ) @ bot_bo70021908tate_o ) )
=> ( ! [G: state,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: state] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ B @ E @ A ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(109,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_147_singleton__iff) ).
thf(951,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)],[109]) ).
thf(69,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ C )
= ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) ) )
= ( ord_less_eq_pname_o @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_Un__Int__assoc__eq) ).
thf(808,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A @ B ) @ C )
= ( semila1673364395name_o @ A @ ( semila1780557381name_o @ B @ C ) ) )
= ( ord_less_eq_pname_o @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(514,axiom,
! [A: pname > hoare_1167836817_state,B: pname,C: pname > $o] :
( ( image_575578384_state @ A @ ( insert_pname @ B @ C ) )
= ( insert2134838167_state @ ( A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_image__insert) ).
thf(2247,plain,
! [A: pname > hoare_1167836817_state,B: pname,C: pname > $o] :
( ( image_575578384_state @ A @ ( insert_pname @ B @ C ) )
= ( insert2134838167_state @ ( A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(47,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ! [C: hoare_1167836817_state] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le827224136tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_predicate1I) ).
thf(744,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ! [C: hoare_1167836817_state] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le827224136tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(391,axiom,
! [A: com,B: state > $o,C: state] :
( ~ ( B @ C )
=> ( evalc @ ( while @ B @ A ) @ C @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_evalc_OWhileFalse) ).
thf(1849,plain,
! [A: com,B: state > $o,C: state] :
( ~ ( B @ C )
=> ( evalc @ ( while @ B @ A ) @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(20,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(656,plain,
! [A: pname,B: pname] :
( ( A != B )
| ( fequal_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(342,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_inf__le2) ).
thf(1702,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(6,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: pname > hoare_1167836817_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le741939125te_o_o @ A @ ( image_475339327tate_o @ B @ C ) )
=> ( finite1380128977tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_finite__surj) ).
thf(612,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: pname > hoare_1167836817_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_le741939125te_o_o @ A @ ( image_475339327tate_o @ B @ C ) )
=> ( finite1380128977tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(613,plain,
! [C: pname > $o,B: pname > hoare_1167836817_state > $o,A: ( hoare_1167836817_state > $o ) > $o] :
( ~ ( finite_finite_pname @ C )
| ~ ( ord_le741939125te_o_o @ A @ ( image_475339327tate_o @ B @ C ) )
| ( finite1380128977tate_o @ A ) ),
inference(cnf,[status(esa)],[612]) ).
thf(118,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_inf__le1) ).
thf(978,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(128,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
=> ( ord_le827224136tate_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_equalityD2) ).
thf(1008,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
=> ( ord_le827224136tate_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(172,axiom,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_equals0D) ).
thf(1152,plain,
! [A: pname,B: pname > $o] :
( ( B = bot_bot_pname_o )
=> ~ ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1153,plain,
! [B: pname > $o,A: pname] :
( ( B != bot_bot_pname_o )
| ~ ( member_pname @ A @ B ) ),
inference(cnf,[status(esa)],[1152]) ).
thf(1154,plain,
! [B: pname > $o,A: pname] :
( ( B != bot_bot_pname_o )
| ~ ( member_pname @ A @ B ) ),
inference(lifteq,[status(thm)],[1153]) ).
thf(1155,plain,
! [A: pname] :
~ ( member_pname @ A @ bot_bot_pname_o ),
inference(simp,[status(thm)],[1154]) ).
thf(2584,plain,
! [A: pname] :
~ ( member_pname @ A
@ ^ [B: pname] : bot_bot_o ),
inference(rewrite,[status(thm)],[1155,861]) ).
thf(168,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_223_subsetI) ).
thf(1141,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)],[168]) ).
thf(440,axiom,
! [A: hoare_1167836817_state] :
~ ( member2058392318_state @ A @ bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_empty__iff) ).
thf(1981,plain,
! [A: hoare_1167836817_state] :
~ ( member2058392318_state @ A @ bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(523,axiom,
! [A: hoare_1167836817_state > $o,B: com] :
( hoare_1201148605gleton
=> ( ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [C: state,D: state] :
! [E: state] :
( ( evalc @ B @ D @ E )
=> ( C = E ) )
@ B
@ fequal_state )
@ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ B ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_MGT__alternD) ).
thf(2279,plain,
! [A: hoare_1167836817_state > $o,B: com] :
( hoare_1201148605gleton
=> ( ( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [C: state,D: state] :
! [E: state] :
( ( evalc @ B @ D @ E )
=> ( C = E ) )
@ B
@ fequal_state )
@ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ A @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ B ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(542,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_39_insert__dom) ).
thf(2357,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)],[542]) ).
thf(430,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_inf__sup__ord_I3_J) ).
thf(1955,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(358,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_157_subset__empty) ).
thf(1749,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)],[358]) ).
thf(255,axiom,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ ( semila1780557381name_o @ A @ B ) )
= ( ( finite_finite_pname @ A )
& ( finite_finite_pname @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_finite__Un) ).
thf(1427,plain,
! [A: pname > $o,B: pname > $o] :
( ( finite_finite_pname @ ( semila1780557381name_o @ A @ B ) )
= ( ( finite_finite_pname @ A )
& ( finite_finite_pname @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(122,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
= ( ( ord_le827224136tate_o @ A @ B )
& ( ord_le827224136tate_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_set__eq__subset) ).
thf(991,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
= ( ( ord_le827224136tate_o @ A @ B )
& ( ord_le827224136tate_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(315,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( member_pname @ B @ A ) )
=> ( member_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_UnCI) ).
thf(1617,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( ~ ( member_pname @ B @ C )
=> ( member_pname @ B @ A ) )
=> ( member_pname @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(425,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_Un__upper1) ).
thf(1940,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(75,axiom,
wT_bodies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(845,plain,
wT_bodies,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(468,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_inf__bot__left) ).
thf(2088,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(182,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_sup__least) ).
thf(1180,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ A @ C )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(294,axiom,
! [A: hoare_1167836817_state > $o] :
( ( collec1027672124_state @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Collect__def) ).
thf(1553,plain,
! [A: hoare_1167836817_state > $o] :
( ( collec1027672124_state @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(24,axiom,
! [A: pname > hoare_1167836817_state > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1380128977tate_o @ ( image_475339327tate_o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(671,plain,
! [A: pname > hoare_1167836817_state > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( finite1380128977tate_o @ ( image_475339327tate_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(504,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
!= bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_insert__not__empty) ).
thf(2194,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( insert2134838167_state @ A @ B )
!= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(368,axiom,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= ( member_pname @ A @ bot_bot_pname_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_bot__empty__eq) ).
thf(1781,plain,
! [A: pname] :
( ( bot_bot_pname_o @ A )
= ( member_pname @ A @ bot_bot_pname_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(301,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_202_Collect__conv__if2) ).
thf(1575,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)],[301]) ).
thf(417,axiom,
! [A: pname > $o,B: hoare_1167836817_state > pname,C: hoare_1167836817_state > $o] :
( ( ord_less_eq_pname_o @ A @ ( image_8178176_pname @ B @ C ) )
= ( ? [D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ D @ C )
& ( A
= ( image_8178176_pname @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subset__image__iff) ).
thf(1918,plain,
! [A: pname > $o,B: hoare_1167836817_state > pname,C: hoare_1167836817_state > $o] :
( ( ord_less_eq_pname_o @ A @ ( image_8178176_pname @ B @ C ) )
= ( ? [D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ D @ C )
& ( A
= ( image_8178176_pname @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(264,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( member_pname @ B @ A )
=> ( member_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_IntI) ).
thf(1459,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ( member_pname @ B @ C )
=> ( ( member_pname @ B @ A )
=> ( member_pname @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(454,axiom,
! [A: state > state > $o,B: pname,C: state > state > $o,D: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ ( body_1 @ B ) @ C ) @ D ) @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ ( the_com @ ( body @ B ) ) @ C ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ D @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ ( body_1 @ B ) @ C ) @ bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_BodyN) ).
thf(2045,plain,
! [A: state > state > $o,B: pname,C: state > state > $o,D: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ ( body_1 @ B ) @ C ) @ D ) @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ ( the_com @ ( body @ B ) ) @ C ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ D @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ ( body_1 @ B ) @ C ) @ bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(539,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state,D: hoare_1167836817_state] :
( ( ( insert2134838167_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= ( insert2134838167_state @ C @ ( insert2134838167_state @ D @ bot_bo70021908tate_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_doubleton__eq__iff) ).
thf(2347,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state,D: hoare_1167836817_state] :
( ( ( insert2134838167_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
= ( insert2134838167_state @ C @ ( insert2134838167_state @ D @ bot_bo70021908tate_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(252,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ! [E: pname] :
( ( member_pname @ E @ C )
=> ( ( B @ E )
=> ( A @ E ) ) )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ ( collect_pname @ B ) ) @ ( semila1673364395name_o @ D @ ( collect_pname @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_Int__Collect__mono) ).
thf(1412,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ! [E: pname] :
( ( member_pname @ E @ C )
=> ( ( B @ E )
=> ( A @ E ) ) )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ C @ ( collect_pname @ B ) ) @ ( semila1673364395name_o @ D @ ( collect_pname @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(501,axiom,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_empty__subsetI) ).
thf(2186,plain,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(2187,plain,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A ),
inference(cnf,[status(esa)],[2186]) ).
thf(2611,plain,
! [A: hoare_1167836817_state > $o] :
( ord_le827224136tate_o
@ ^ [B: hoare_1167836817_state] : bot_bot_o
@ A ),
inference(rewrite,[status(thm)],[2187,2167]) ).
thf(531,axiom,
! [A: pname > hoare_1167836817_state,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_le827224136tate_o @ ( image_575578384_state @ A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_image__mono) ).
thf(2325,plain,
! [A: pname > hoare_1167836817_state,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_le827224136tate_o @ ( image_575578384_state @ A @ B ) @ ( image_575578384_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(52,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_le__infI1) ).
thf(759,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ ( semila1673364395name_o @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(212,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_in__mono) ).
thf(1289,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(508,axiom,
! [A: pname,B: com,C: com] :
( ( body_1 @ A )
!= ( semi @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_com_Osimps_I49_J) ).
thf(2226,plain,
! [A: pname,B: com,C: com] :
( ( body_1 @ A )
!= ( semi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(208,axiom,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_insert__not__empty) ).
thf(1276,plain,
! [A: pname,B: pname > $o] :
( ( insert_pname @ A @ B )
!= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(226,axiom,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_finite__induct) ).
thf(1326,plain,
! [A: ( pname > $o ) > $o,B: pname > $o] :
( ( finite_finite_pname @ B )
=> ( ( A @ bot_bot_pname_o )
=> ( ! [C: pname,D: pname > $o] :
( ( finite_finite_pname @ D )
=> ( ~ ( member_pname @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert_pname @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(332,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_set__mp) ).
thf(1674,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( member2058392318_state @ A @ B )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(446,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( semila179895820tate_o @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_Int__insert__right__if0) ).
thf(2004,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( semila179895820tate_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(382,axiom,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_subset__refl) ).
thf(1822,plain,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(519,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ A @ C ) ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( semila179895820tate_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_Int__insert__left) ).
thf(2262,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ A @ C ) ) ) )
& ( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( semila179895820tate_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(322,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
=> ~ ( ( ord_le827224136tate_o @ A @ C )
=> ~ ( ord_le827224136tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_le__supE) ).
thf(1646,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A @ B ) @ C )
=> ~ ( ( ord_le827224136tate_o @ A @ C )
=> ~ ( ord_le827224136tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(565,axiom,
! [A: hoare_1167836817_state] :
( ( collec1027672124_state @ ( fequal1831255762_state @ A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_singleton__conv2) ).
thf(2443,plain,
! [A: hoare_1167836817_state] :
( ( collec1027672124_state @ ( fequal1831255762_state @ A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(241,axiom,
wt @ skip,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_WT_OSkip) ).
thf(1385,plain,
wt @ skip,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(349,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_Un__absorb2) ).
thf(1721,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(521,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ A @ B )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_Diff__insert__absorb) ).
thf(2273,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ A @ B )
=> ( ( minus_2107060239tate_o @ ( insert2134838167_state @ A @ B ) @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(472,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( insert2134838167_state @ A @ B ) @ C )
= ( insert2134838167_state @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_Un__insert__left) ).
thf(2098,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ ( insert2134838167_state @ A @ B ) @ C )
= ( insert2134838167_state @ A @ ( semila1172322802tate_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(48,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= ( semila1172322802tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_sup__left__idem) ).
thf(748,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila1172322802tate_o @ A @ ( semila1172322802tate_o @ A @ B ) )
= ( semila1172322802tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(483,axiom,
! [A: state > state > $o,B: state > state > $o,C: com] :
( ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C ) @ bot_bo70021908tate_o ) )
=> ( ( hoare_529639851_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ C @ B ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ C @ B ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_MGF__complete) ).
thf(2135,plain,
! [A: state > state > $o,B: state > state > $o,C: com] :
( ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C ) @ bot_bo70021908tate_o ) )
=> ( ( hoare_529639851_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ C @ B ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ A @ C @ B ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(555,axiom,
! [A: hoare_1167836817_state > $o] :
( ( A != bot_bo70021908tate_o )
= ( ? [B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( A
= ( insert2134838167_state @ B @ C ) )
& ~ ( member2058392318_state @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_nonempty__iff) ).
thf(2406,plain,
! [A: hoare_1167836817_state > $o] :
( ( A != bot_bo70021908tate_o )
= ( ? [B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( A
= ( insert2134838167_state @ B @ C ) )
& ~ ( member2058392318_state @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(592,axiom,
! [A: pname,B: pname > option_com] :
( ( member_pname @ A @ ( dom_pname_com @ B ) )
=> ? [C: com] :
( ( B @ A )
= ( some_com @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_domD) ).
thf(2532,plain,
! [A: pname,B: pname > option_com] :
( ( member_pname @ A @ ( dom_pname_com @ B ) )
=> ? [C: com] :
( ( B @ A )
= ( some_com @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(280,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ bot_bot_pname_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_sup__bot__right) ).
thf(1508,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ A @ bot_bot_pname_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(107,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ ( collec1027672124_state @ C ) ) )
= ( ( member2058392318_state @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_Int__Collect) ).
thf(946,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ ( collec1027672124_state @ C ) ) )
= ( ( member2058392318_state @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(154,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ A )
& ( member2058392318_state @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_Int__def) ).
thf(1101,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ A @ B )
= ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ A )
& ( member2058392318_state @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(453,axiom,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ E ) @ bot_bo70021908tate_o ) )
=> ( ! [F: state,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ A ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_conseq2) ).
thf(2041,plain,
! [A: state > state > $o,B: hoare_1167836817_state > $o,C: state > state > $o,D: com,E: state > state > $o] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ E ) @ bot_bo70021908tate_o ) )
=> ( ! [F: state,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_908217195_state @ C @ D @ A ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(505,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le827224136tate_o @ C @ B )
=> ( ( A @ bot_bo70021908tate_o )
=> ( ! [D: hoare_1167836817_state,E: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ E )
=> ( ( member2058392318_state @ D @ B )
=> ( ~ ( member2058392318_state @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert2134838167_state @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_finite__subset__induct) ).
thf(2198,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ C )
=> ( ( ord_le827224136tate_o @ C @ B )
=> ( ( A @ bot_bo70021908tate_o )
=> ( ! [D: hoare_1167836817_state,E: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ E )
=> ( ( member2058392318_state @ D @ B )
=> ( ~ ( member2058392318_state @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert2134838167_state @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(311,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_le__supI2) ).
thf(1607,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ord_less_eq_pname_o @ B @ ( semila1780557381name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(509,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ C ) )
=> ( ( A != B )
=> ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_insertE) ).
thf(2230,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ C ) )
=> ( ( A != B )
=> ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(528,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_singletonE) ).
thf(2315,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state] :
( ( member2058392318_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(579,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ? [C: hoare_1167836817_state > $o] :
( ( B
= ( insert2134838167_state @ A @ C ) )
& ~ ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_mk__disjoint__insert) ).
thf(2494,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
=> ? [C: hoare_1167836817_state > $o] :
( ( B
= ( insert2134838167_state @ A @ C ) )
& ~ ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(471,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_Int__insert__right__if1) ).
thf(2095,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ C @ ( insert2134838167_state @ B @ A ) )
= ( insert2134838167_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(29,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_inf__sup__ord_I1_J) ).
thf(684,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila179895820tate_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(36,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( finite1084549118_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_rev__finite__subset) ).
thf(716,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ B )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( finite1084549118_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(175,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_Un__absorb1) ).
thf(1161,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1780557381name_o @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(314,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ ( semila1172322802tate_o @ A @ B ) )
= ( ( finite1084549118_state @ A )
& ( finite1084549118_state @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_finite__Un) ).
thf(1614,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ ( semila1172322802tate_o @ A @ B ) )
= ( ( finite1084549118_state @ A )
& ( finite1084549118_state @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(66,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_le__infI) ).
thf(800,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(10,axiom,
! [A: ( hoare_1167836817_state > $o ) > $o,B: ( hoare_1167836817_state > $o ) > $o] :
( ( finite1380128977tate_o @ B )
=> ( ( ord_le741939125te_o_o @ A @ B )
=> ( finite1380128977tate_o @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_rev__finite__subset) ).
thf(620,plain,
! [A: ( hoare_1167836817_state > $o ) > $o,B: ( hoare_1167836817_state > $o ) > $o] :
( ( finite1380128977tate_o @ B )
=> ( ( ord_le741939125te_o_o @ A @ B )
=> ( finite1380128977tate_o @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(586,axiom,
! [A: hoare_1167836817_state,B: pname > hoare_1167836817_state,C: pname > $o] :
( ( member2058392318_state @ A @ ( image_575578384_state @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_image__iff) ).
thf(2517,plain,
! [A: hoare_1167836817_state,B: pname > hoare_1167836817_state,C: pname > $o] :
( ( member2058392318_state @ A @ ( image_575578384_state @ B @ C ) )
= ( ? [D: pname] :
( ( member_pname @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(209,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_folding__one__idem_Oinsert__idem) ).
thf(1280,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite89670078_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( B != bot_bot_pname_o )
=> ( ( D @ ( insert_pname @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(431,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( hoare_123228589_state @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_asm) ).
thf(1957,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( hoare_123228589_state @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(153,axiom,
! [A: hoare_1167836817_state > $o,B: pname,C: hoare_1167836817_state > pname,D: hoare_1167836817_state] :
( ( B
= ( C @ D ) )
=> ( ( member2058392318_state @ D @ A )
=> ( member_pname @ B @ ( image_8178176_pname @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_image__eqI) ).
thf(1097,plain,
! [A: hoare_1167836817_state > $o,B: pname,C: hoare_1167836817_state > pname,D: hoare_1167836817_state] :
( ( B
= ( C @ D ) )
=> ( ( member2058392318_state @ D @ A )
=> ( member_pname @ B @ ( image_8178176_pname @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(510,axiom,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_Int__empty__left) ).
thf(2233,plain,
! [A: hoare_1167836817_state > $o] :
( ( semila179895820tate_o @ bot_bo70021908tate_o @ A )
= bot_bo70021908tate_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(317,axiom,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
| ( member_pname @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_Un__def) ).
thf(1625,plain,
! [A: pname > $o,B: pname > $o] :
( ( semila1780557381name_o @ A @ B )
= ( collect_pname
@ ^ [C: pname] :
( ( member_pname @ C @ A )
| ( member_pname @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(588,axiom,
( ord_le827224136tate_o @ fa
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) )
@ ( dom_pname_com @ body ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(2522,plain,
( ord_le827224136tate_o @ fa
@ ( image_575578384_state
@ ^ [A: pname] : ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ A ) ) )
@ ( dom_pname_com @ body ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(170,axiom,
! [A: state,B: com,C: state,D: state > $o,E: state] :
( ( D @ E )
=> ( ( evalc @ B @ E @ C )
=> ( ( evalc @ ( while @ D @ B ) @ C @ A )
=> ( evalc @ ( while @ D @ B ) @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_evalc_OWhileTrue) ).
thf(1148,plain,
! [A: state,B: com,C: state,D: state > $o,E: state] :
( ( D @ E )
=> ( ( evalc @ B @ E @ C )
=> ( ( evalc @ ( while @ D @ B ) @ C @ A )
=> ( evalc @ ( while @ D @ B ) @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(83,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_inf__greatest) ).
thf(865,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( ord_less_eq_pname_o @ B @ ( semila1673364395name_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(43,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_114_set__mp) ).
thf(735,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)],[43]) ).
thf(159,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o
@ ^ [C: pname] : ( member_pname @ C @ A )
@ ^ [C: pname] : ( member_pname @ C @ B ) )
= ( ord_less_eq_pname_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_pred__subset__eq) ).
thf(1116,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o
@ ^ [C: pname] : ( member_pname @ C @ A )
@ ^ [C: pname] : ( member_pname @ C @ B ) )
= ( ord_less_eq_pname_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(2003,plain,
( ( some_com @ y )
= ( body @ pn ) ),
inference(lifteq,[status(thm)],[2002]) ).
thf(306,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T) ).
thf(1593,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(554,axiom,
( bot_bo70021908tate_o
= ( collec1027672124_state
@ ^ [A: hoare_1167836817_state] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_empty__def) ).
thf(2404,plain,
( bot_bo70021908tate_o
= ( collec1027672124_state
@ ^ [A: hoare_1167836817_state] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(2405,plain,
( ( collec1027672124_state
@ ^ [A: hoare_1167836817_state] : $false )
= bot_bo70021908tate_o ),
inference(lifteq,[status(thm)],[2404]) ).
thf(2604,plain,
( ( collec1027672124_state
@ ^ [A: hoare_1167836817_state] : $false )
= ( ^ [A: hoare_1167836817_state] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[2405,2167]) ).
thf(84,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ B @ C ) ) @ ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_distrib__sup__le) ).
thf(867,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A @ ( semila179895820tate_o @ B @ C ) ) @ ( semila179895820tate_o @ ( semila1172322802tate_o @ A @ B ) @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(361,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ C @ A ) @ ( semila1172322802tate_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_Un__mono) ).
thf(1757,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ ( semila1172322802tate_o @ C @ A ) @ ( semila1172322802tate_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(395,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ C ) )
= ( ( member2058392318_state @ A @ B )
& ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_Int__iff) ).
thf(1859,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila179895820tate_o @ B @ C ) )
= ( ( member2058392318_state @ A @ B )
& ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(233,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ C @ A ) @ ( semila1780557381name_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_sup__mono) ).
thf(1363,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o,D: pname > $o] :
( ( ord_less_eq_pname_o @ C @ D )
=> ( ( ord_less_eq_pname_o @ A @ B )
=> ( ord_less_eq_pname_o @ ( semila1780557381name_o @ C @ A ) @ ( semila1780557381name_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(380,axiom,
! [A: state > $o,B: com,C: state > $o,D: com] :
( ( ( while @ A @ B )
= ( while @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_com_Osimps_I5_J) ).
thf(1816,plain,
! [A: state > $o,B: com,C: state > $o,D: com] :
( ( ( while @ A @ B )
= ( while @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(535,axiom,
! [A: hoare_1167836817_state] :
( ( collec1027672124_state
@ ^ [B: hoare_1167836817_state] : ( B = A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_singleton__conv) ).
thf(2334,plain,
! [A: hoare_1167836817_state] :
( ( collec1027672124_state
@ ^ [B: hoare_1167836817_state] : ( B = A ) )
= ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(462,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( B = bot_bo70021908tate_o )
=> ~ ( member2058392318_state @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_equals0D) ).
thf(2070,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( B = bot_bo70021908tate_o )
=> ~ ( member2058392318_state @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(137,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_137_insert__compr__raw) ).
thf(1033,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)],[137]) ).
thf(408,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila1172322802tate_o @ ( collec1027672124_state @ A ) @ ( collec1027672124_state @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_Collect__disj__eq) ).
thf(1891,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( collec1027672124_state
@ ^ [C: hoare_1167836817_state] :
( ( A @ C )
| ( B @ C ) ) )
= ( semila1172322802tate_o @ ( collec1027672124_state @ A ) @ ( collec1027672124_state @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(460,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ A @ ( insert2134838167_state @ B @ C ) )
=> ( ( hoare_123228589_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
& ( hoare_123228589_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_derivs__insertD) ).
thf(2063,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( hoare_123228589_state @ A @ ( insert2134838167_state @ B @ C ) )
=> ( ( hoare_123228589_state @ A @ ( insert2134838167_state @ B @ bot_bo70021908tate_o ) )
& ( hoare_123228589_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(89,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_ord__le__eq__trans) ).
thf(886,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_pname_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(179,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( B = A )
=> ( ord_le827224136tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_xt1_I4_J) ).
thf(1172,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( B = A )
=> ( ord_le827224136tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(141,axiom,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_Un__upper1) ).
thf(1056,plain,
! [A: pname > $o,B: pname > $o] : ( ord_less_eq_pname_o @ A @ ( semila1780557381name_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(371,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila1172322802tate_o @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_Un__absorb2) ).
thf(1789,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( semila1172322802tate_o @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(40,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_rev__predicate1D) ).
thf(728,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( B @ C )
=> ( ( ord_le827224136tate_o @ B @ A )
=> ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(230,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
=> ( ord_le827224136tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_order__eq__refl) ).
thf(1352,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( A = B )
=> ( ord_le827224136tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(164,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( member2058392318_state @ B @ A )
=> ( member2058392318_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_IntI) ).
thf(1129,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ B @ C )
=> ( ( member2058392318_state @ B @ A )
=> ( member2058392318_state @ B @ ( semila179895820tate_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(288,axiom,
! [A: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ( A @ C )
= B )
=> ( ! [E: hoare_1167836817_state > $o,F: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ F @ E )
=> ( ord_le827224136tate_o @ ( A @ F ) @ ( A @ E ) ) )
=> ( ord_le827224136tate_o @ B @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_xt1_I16_J) ).
thf(1532,plain,
! [A: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ( A @ C )
= B )
=> ( ! [E: hoare_1167836817_state > $o,F: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ F @ E )
=> ( ord_le827224136tate_o @ ( A @ F ) @ ( A @ E ) ) )
=> ( ord_le827224136tate_o @ B @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(239,axiom,
! [A: hoare_1167836817_state,B: option1574264306_state] :
( ( member2058392318_state @ A @ ( set_Ho2131684873_state @ B ) )
= ( B
= ( some_H1433514562_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_elem__set) ).
thf(1378,plain,
! [A: hoare_1167836817_state,B: option1574264306_state] :
( ( member2058392318_state @ A @ ( set_Ho2131684873_state @ B ) )
= ( B
= ( some_H1433514562_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(132,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( finite1084549118_state @ B )
=> ( finite1084549118_state @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_finite__subset) ).
thf(1019,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ A @ B )
=> ( ( finite1084549118_state @ B )
=> ( finite1084549118_state @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(293,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_xt1_I5_J) ).
thf(1550,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( ord_less_eq_pname_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(2583,plain,
( finite_finite_pname
@ ^ [A: pname] : bot_bot_o ),
inference(rewrite,[status(thm)],[1519,861]) ).
thf(95,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ C @ A ) @ ( semila179895820tate_o @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_inf__mono) ).
thf(908,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ C @ D )
=> ( ( ord_le827224136tate_o @ A @ B )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ C @ A ) @ ( semila179895820tate_o @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(583,axiom,
! [A: hoare_1167836817_state > pname] :
( ( image_8178176_pname @ A @ bot_bo70021908tate_o )
= bot_bot_pname_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_image__empty) ).
thf(2507,plain,
! [A: hoare_1167836817_state > pname] :
( ( image_8178176_pname @ A @ bot_bo70021908tate_o )
= bot_bot_pname_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(403,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_92_insert__code) ).
thf(1880,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)],[403]) ).
thf(411,axiom,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_order__refl) ).
thf(1902,plain,
! [A: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(405,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( B @ C )
=> ( semila1172322802tate_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_sup1I2) ).
thf(1885,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( B @ C )
=> ( semila1172322802tate_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(545,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( finite1084549118_state @ A )
=> ( ( ( semila179895820tate_o @ B @ A )
!= bot_bo70021908tate_o )
=> ( ( C @ ( D @ ( semila1172322802tate_o @ B @ A ) ) @ ( D @ ( semila179895820tate_o @ B @ A ) ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_folding__one_Ounion__inter) ).
thf(2372,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( finite1084549118_state @ A )
=> ( ( ( semila179895820tate_o @ B @ A )
!= bot_bo70021908tate_o )
=> ( ( C @ ( D @ ( semila1172322802tate_o @ B @ A ) ) @ ( D @ ( semila179895820tate_o @ B @ A ) ) )
= ( C @ ( D @ B ) @ ( D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(607,plain,
! [C: hoare_1167836817_state > $o,B: hoare_1167836817_state > hoare_1167836817_state > $o,A: ( hoare_1167836817_state > $o ) > $o] :
( ~ ( finite1084549118_state @ C )
| ~ ( ord_le741939125te_o_o @ A @ ( image_1745649338tate_o @ B @ C ) )
| ( finite1380128977tate_o @ A ) ),
inference(cnf,[status(esa)],[606]) ).
thf(421,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_le__infI1) ).
thf(1930,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ord_le827224136tate_o @ ( semila179895820tate_o @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(73,axiom,
! [A: pname > $o] :
( ( semila1780557381name_o @ bot_bot_pname_o @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_sup__bot__left) ).
thf(839,plain,
! [A: pname > $o] :
( ( semila1780557381name_o @ bot_bot_pname_o @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(581,axiom,
! [A: hoare_1167836817_state > $o,B: pname > hoare_1167836817_state,C: pname > $o] :
( ( ord_le827224136tate_o @ A @ ( image_575578384_state @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_575578384_state @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_subset__image__iff) ).
thf(2502,plain,
! [A: hoare_1167836817_state > $o,B: pname > hoare_1167836817_state,C: pname > $o] :
( ( ord_le827224136tate_o @ A @ ( image_575578384_state @ B @ C ) )
= ( ? [D: pname > $o] :
( ( ord_less_eq_pname_o @ D @ C )
& ( A
= ( image_575578384_state @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(480,axiom,
! [A: com,B: state > state > $o,C: hoare_1167836817_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ E @ F ) @ bot_bo70021908tate_o ) )
=> ( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ F @ A @ B ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ ( semi @ E @ A ) @ B ) @ bot_bo70021908tate_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_Comp) ).
thf(2127,plain,
! [A: com,B: state > state > $o,C: hoare_1167836817_state > $o,D: state > state > $o,E: com,F: state > state > $o] :
( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ E @ F ) @ bot_bo70021908tate_o ) )
=> ( ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ F @ A @ B ) @ bot_bo70021908tate_o ) )
=> ( hoare_123228589_state @ C @ ( insert2134838167_state @ ( hoare_908217195_state @ D @ ( semi @ E @ A ) @ B ) @ bot_bo70021908tate_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(562,axiom,
! [A: pname] :
( skip
!= ( body_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_com_Osimps_I18_J) ).
thf(2430,plain,
! [A: pname] :
( skip
!= ( body_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(205,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_141_singleton__inject) ).
thf(1268,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)],[205]) ).
thf(595,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
=> ( ( hoare_123228589_state @ B @ A )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).
thf(2539,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( hoare_123228589_state @ B @ ( insert2134838167_state @ C @ bot_bo70021908tate_o ) )
=> ( ( hoare_123228589_state @ B @ A )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(346,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( ( member2058392318_state @ A @ B )
| ( member2058392318_state @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_Un__iff) ).
thf(1713,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ ( semila1172322802tate_o @ B @ C ) )
= ( ( member2058392318_state @ A @ B )
| ( member2058392318_state @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(279,axiom,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( semila1673364395name_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_Int__insert__left__if0) ).
thf(1505,plain,
! [A: pname > $o,B: pname,C: pname > $o] :
( ~ ( member_pname @ B @ C )
=> ( ( semila1673364395name_o @ ( insert_pname @ B @ A ) @ C )
= ( semila1673364395name_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(520,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ( A = bot_bo70021908tate_o )
& ( B = bot_bo70021908tate_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_sup__eq__bot__iff) ).
thf(2270,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ( ( semila1172322802tate_o @ A @ B )
= bot_bo70021908tate_o )
= ( ( A = bot_bo70021908tate_o )
& ( B = bot_bo70021908tate_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(316,axiom,
( hoare_1201148605gleton
=> ! [A: state] :
~ ! [B: state] : ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_single__stateE) ).
thf(1621,plain,
( hoare_1201148605gleton
=> ! [A: state] :
~ ! [B: state] : ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(224,axiom,
! [A: pname > $o] :
( ( bot_bot_pname_o
= ( collect_pname @ A ) )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_empty__Collect__eq) ).
thf(1320,plain,
! [A: pname > $o] :
( ( bot_bot_pname_o
= ( collect_pname @ A ) )
= ( ! [B: pname] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(433,axiom,
! [A: com] :
( hoare_1201148605gleton
=> ( wT_bodies
=> ( ( wt @ A )
=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo70021908tate_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_MGF) ).
thf(1962,plain,
! [A: com] :
( hoare_1201148605gleton
=> ( wT_bodies
=> ( ( wt @ A )
=> ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo70021908tate_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(427,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_sup__ge1) ).
thf(1945,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] : ( ord_le827224136tate_o @ A @ ( semila1172322802tate_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(355,axiom,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_8178176_pname @ A @ B ) )
=> ? [D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ D @ B )
& ( finite1084549118_state @ D )
& ( C
= ( image_8178176_pname @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_finite__subset__image) ).
thf(1737,plain,
! [A: hoare_1167836817_state > pname,B: hoare_1167836817_state > $o,C: pname > $o] :
( ( finite_finite_pname @ C )
=> ( ( ord_less_eq_pname_o @ C @ ( image_8178176_pname @ A @ B ) )
=> ? [D: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ D @ B )
& ( finite1084549118_state @ D )
& ( C
= ( image_8178176_pname @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(266,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_mem__def) ).
thf(1463,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( member2058392318_state @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(512,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( member2058392318_state @ A @ B )
=> ( ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= bot_bo70021908tate_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
!= bot_bo70021908tate_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_folding__one_Oremove) ).
thf(2238,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,D: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
( ( finite1074406356_state @ C @ D )
=> ( ( finite1084549118_state @ B )
=> ( ( member2058392318_state @ A @ B )
=> ( ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
= bot_bo70021908tate_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) )
!= bot_bo70021908tate_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_2107060239tate_o @ B @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(15,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_DiffE) ).
thf(639,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( minus_minus_pname_o @ B @ C ) )
=> ~ ( ( member_pname @ A @ B )
=> ( member_pname @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(495,axiom,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: state > $o,D: com] :
( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [E: state,F: state] :
( ( B @ E @ F )
& ~ ( C @ F ) )
@ ( while @ C @ D )
@ B )
@ bot_bo70021908tate_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_LoopF) ).
thf(2170,plain,
! [A: hoare_1167836817_state > $o,B: state > state > $o,C: state > $o,D: com] :
( hoare_123228589_state @ A
@ ( insert2134838167_state
@ ( hoare_908217195_state
@ ^ [E: state,F: state] :
( ( B @ E @ F )
& ~ ( C @ F ) )
@ ( while @ C @ D )
@ B )
@ bot_bo70021908tate_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(475,axiom,
! [A: com,B: hoare_1167836817_state > $o] :
( hoare_1201148605gleton
=> ( ! [C: pname] :
( ( member_pname @ C @ ( dom_pname_com @ body ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ C ) ) @ bot_bo70021908tate_o ) ) )
=> ( ( wt @ A )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo70021908tate_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_MGF__lemma1) ).
thf(2106,plain,
! [A: com,B: hoare_1167836817_state > $o] :
( hoare_1201148605gleton
=> ( ! [C: pname] :
( ( member_pname @ C @ ( dom_pname_com @ body ) )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ C ) ) @ bot_bo70021908tate_o ) ) )
=> ( ( wt @ A )
=> ( hoare_123228589_state @ B @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ A ) @ bot_bo70021908tate_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(268,axiom,
! [A: hoare_1167836817_state > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ~ ( finite1084549118_state @ B )
=> ( ( finite1380128977tate_o @ ( image_1745649338tate_o @ A @ B ) )
=> ? [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
& ~ ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_pigeonhole__infinite) ).
thf(1468,plain,
! [A: hoare_1167836817_state > hoare_1167836817_state > $o,B: hoare_1167836817_state > $o] :
( ~ ( finite1084549118_state @ B )
=> ( ( finite1380128977tate_o @ ( image_1745649338tate_o @ A @ B ) )
=> ? [C: hoare_1167836817_state] :
( ( member2058392318_state @ C @ B )
& ~ ( finite1084549118_state
@ ( collec1027672124_state
@ ^ [D: hoare_1167836817_state] :
( ( member2058392318_state @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(324,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_100_insert__Collect) ).
thf(1653,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)],[324]) ).
thf(235,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ~ ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ A ) )
=> ( member2058392318_state @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_UnCI) ).
thf(1367,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ( ~ ( member2058392318_state @ B @ C )
=> ( member2058392318_state @ B @ A ) )
=> ( member2058392318_state @ B @ ( semila1172322802tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(105,axiom,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_le__inf__iff) ).
thf(940,plain,
! [A: pname > $o,B: pname > $o,C: pname > $o] :
( ( ord_less_eq_pname_o @ A @ ( semila1673364395name_o @ B @ C ) )
= ( ( ord_less_eq_pname_o @ A @ B )
& ( ord_less_eq_pname_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(335,axiom,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ( member_pname @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_IntD1) ).
thf(1681,plain,
! [A: pname,B: pname > $o,C: pname > $o] :
( ( member_pname @ A @ ( semila1673364395name_o @ B @ C ) )
=> ( member_pname @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(184,axiom,
! [A: state > $o,B: com] :
( skip
!= ( while @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_com_Osimps_I16_J) ).
thf(1184,plain,
! [A: state > $o,B: com] :
( skip
!= ( while @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(463,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( semila179895820tate_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_Int__insert__left__if0) ).
thf(2074,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state,C: hoare_1167836817_state > $o] :
( ~ ( member2058392318_state @ B @ C )
=> ( ( semila179895820tate_o @ ( insert2134838167_state @ B @ A ) @ C )
= ( semila179895820tate_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(503,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ ( insert2134838167_state @ A @ B ) )
= ( finite1084549118_state @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_finite__insert) ).
thf(2191,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
( ( finite1084549118_state @ ( insert2134838167_state @ A @ B ) )
= ( finite1084549118_state @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(261,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1780557381name_o @ A @ B )
= bot_bot_pname_o )
= ( ( A = bot_bot_pname_o )
& ( B = bot_bot_pname_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_Un__empty) ).
thf(1449,plain,
! [A: pname > $o,B: pname > $o] :
( ( ( semila1780557381name_o @ A @ B )
= bot_bot_pname_o )
= ( ( A = bot_bot_pname_o )
& ( B = bot_bot_pname_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(34,axiom,
! [A: pname,B: pname > $o] :
( ~ ( member_pname @ A @ B )
=> ( ( minus_minus_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ bot_bot_pname_o ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_Diff__insert__absorb) ).
thf(708,plain,
! [A: pname,B: pname > $o] :
( ~ ( member_pname @ A @ B )
=> ( ( minus_minus_pname_o @ ( insert_pname @ A @ B ) @ ( insert_pname @ A @ bot_bot_pname_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(415,axiom,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila1172322802tate_o @ A @ B @ C )
= ( semila10642723_sup_o @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_sup__apply) ).
thf(1912,plain,
! [A: hoare_1167836817_state > $o,B: hoare_1167836817_state > $o,C: hoare_1167836817_state] :
( ( semila1172322802tate_o @ A @ B @ C )
= ( semila10642723_sup_o @ ( A @ C ) @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(130,axiom,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_Int__absorb2) ).
thf(1014,plain,
! [A: pname > $o,B: pname > $o] :
( ( ord_less_eq_pname_o @ A @ B )
=> ( ( semila1673364395name_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(253,axiom,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_folding__one_Oremove) ).
thf(1417,plain,
! [A: pname,B: pname > $o,C: pname > pname > pname,D: ( pname > $o ) > pname] :
( ( finite1282449217_pname @ C @ D )
=> ( ( finite_finite_pname @ B )
=> ( ( member_pname @ A @ B )
=> ( ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
= bot_bot_pname_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) )
!= bot_bot_pname_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_minus_pname_o @ B @ ( insert_pname @ A @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(399,axiom,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( B @ A )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_predicate1D) ).
thf(1870,plain,
! [A: hoare_1167836817_state,B: hoare_1167836817_state > $o,C: hoare_1167836817_state > $o] :
( ( ord_le827224136tate_o @ B @ C )
=> ( ( B @ A )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(2961,plain,
$false,
inference(e,[status(thm)],[2163,1665,1718,1024,2341,2031,1767,1729,1031,1899,2544,1110,2250,1036,2630,1586,1501,2452,2412,846,1315,2595,2499,962,2427,2480,1924,1596,730,1068,2381,1443,741,1205,2114,878,614,861,1486,1200,2077,994,2527,2282,1591,1078,1137,1310,1735,1164,814,2168,913,930,1867,2184,2434,1872,1196,1835,1001,1935,1359,1386,2082,1904,1482,1887,651,1746,898,1127,2491,1243,1650,1921,1724,1475,2400,2067,1628,1409,2603,1298,785,1323,802,1455,1792,1430,1511,751,934,1191,949,2356,1545,902,1514,2520,1875,2388,1704,1890,1479,1609,969,606,1347,1572,924,2616,1302,1373,1632,2236,1864,937,2034,966,1283,905,2456,2007,2178,2222,1828,1978,766,1169,2437,2483,1119,1394,2137,660,2002,1433,2392,2530,2523,1796,988,2286,2103,1405,1104,1697,849,1975,1564,2011,920,678,1691,761,2118,2047,1915,798,1074,1604,1274,2409,910,1021,1519,1255,2414,1883,957,894,1042,2541,1123,862,1570,1676,2133,1217,2147,1824,788,2150,1423,916,1938,1365,1968,1178,1951,1687,1819,1159,2181,757,1392,1291,842,974,1012,625,2477,852,2332,1296,665,1210,1656,1027,2327,682,1407,2547,2344,1350,2157,1851,1017,1804,1064,1970,1672,2537,869,610,783,697,1089,1762,2515,1375,1121,1856,725,980,1587,1540,1006,1878,2631,857,1397,1567,2460,2561,1182,1461,2080,1842,2172,2038,1039,1942,1659,686,2419,1207,2085,622,997,985,2153,1932,2505,1947,1984,779,1150,1249,1131,654,1599,1246,605,1759,1202,1241,633,2057,1286,1167,773,718,926,1466,1071,1906,1754,2253,2585,1927,2602,689,733,2260,618,1764,1959,2556,1833,2188,1752,2568,1403,1965,1520,1488,1784,1389,875,711,2220,2029,1707,1312,611,1635,1239,804,1258,2474,1638,1356,1786,1669,1271,1371,1058,1107,1194,1853,2383,1894,1806,2257,1492,1542,2116,616,2510,764,2361,2311,1771,737,649,1801,1969,1307,811,631,2129,1993,1731,1909,2446,1862,700,1838,1344,943,1381,890,1667,609,2111,1556,769,2289,1293,2553,2329,1061,2350,959,1213,2369,1113,1726,1496,2156,1694,1973,1562,1699,2401,1594,2051,2550,1066,1445,1528,1176,608,1775,2244,1435,2535,2101,1076,1809,1662,1304,1684,1134,2449,1081,1990,1472,754,836,2582,2054,722,675,1583,795,2318,663,2471,1145,2564,1845,1798,1003,855,1516,872,971,2143,739,2175,2386,1531,2160,1547,776,1611,2375,1156,2060,1743,1400,954,1252,2165,791,1188,1262,2337,2276,2322,1679,643,2468,1711,1499,673,2092,1987,1716,1813,1452,1317,1830,2486,951,808,2247,744,1849,656,1702,613,978,1008,612,2584,859,1141,1981,2279,2357,1955,1749,1427,991,1617,1940,845,2088,1180,1553,671,2194,1781,1575,2626,1918,1459,2045,2347,1412,2611,2325,759,1289,2226,1276,1326,1674,2004,1822,2262,1646,2443,1385,1721,2167,2273,2098,748,2135,2406,2532,1508,946,1101,2041,2198,1607,2230,2315,2494,2095,684,716,1161,1614,800,620,2517,1280,1957,1097,2233,1625,2522,1148,865,735,1116,2003,1593,2604,867,1757,1859,1363,1816,2334,2186,2070,1033,1891,2063,886,1172,2417,1056,1789,2091,2404,728,1352,1129,1152,1532,1378,1019,1550,2583,908,2507,1880,1902,1885,2372,607,1930,2353,839,2502,2127,2430,1268,2539,1713,1505,2270,1621,1320,1962,1945,1737,1463,2238,639,2170,2106,1468,1653,1367,940,1681,1184,2074,2191,1449,708,1912,1014,1417,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW474^2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n015.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 16:09:33 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.89/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.84/1.38 % [INFO] Parsing done (580ms).
% 3.27/1.40 % [INFO] Running in sequential loop mode.
% 4.53/1.94 % [INFO] eprover registered as external prover.
% 4.53/1.95 % [INFO] Scanning for conjecture ...
% 5.11/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 722 axioms. Running axiom selection ...
% 5.95/2.43 % [INFO] Axiom selection finished. Selected 602 axioms (removed 120 axioms).
% 7.66/3.04 % [INFO] Problem is higher-order (TPTP THF).
% 8.24/3.10 % [INFO] Type checking passed.
% 8.24/3.11 % [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 ...
% 58.81/14.01 % External prover 'e' found a proof!
% 58.81/14.01 % [INFO] Killing All external provers ...
% 58.81/14.01 % Time passed: 13651ms (effective reasoning time: 12598ms)
% 58.81/14.01 % 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)>
% 58.81/14.02 % Axioms used in derivation (602): fact_389_rev__predicate1D, fact_85_empty__def, fact_215_WT__bodiesD, fact_163_empty__is__image, fact_37_image__constant, help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T, fact_591_inf__Int__eq, fact_72_empty__iff, fact_413_sup__assoc, fact_480_WT_OSkip, fact_67_equals0D, fact_232_finite__subset__image, fact_115_set__mp, fact_475_finite__ne__induct, fact_654_sup__inf__distrib1, fact_325_Un__upper2, fact_606_Int__lower2, fact_664_distrib__inf__le, fact_525_predicate1I, fact_450_inf__sup__ord_I4_J, fact_455_sup__eq__bot__iff, fact_458_sup__bot__right, fact_175_mem__def, fact_504_com_Osimps_I49_J, fact_395_pred__subset__eq, fact_694_Diff__insert__absorb, fact_39_insert__dom, fact_165_finite__subset, fact_194_image__mono, fact_260_the__elem__eq, fact_626_inf__le1, fact_656_sup__inf__distrib2, fact_560_IntE, fact_622_Int__insert__right, fact_601_Int__absorb1, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com, fact_685_DiffI, fact_282_UnI1, fact_478_com_Osimps_I19_J, fact_216_imageE, fact_187_subset__insertI, fact_224_subsetI, fact_45_finite__surj, fact_640_inf__absorb1, fact_596_Int__Un__distrib, fact_15_finite__imageI, fact_202_Collect__conv__if2, fact_641_inf__absorb2, fact_147_singleton__iff, fact_597_Int__mono, fact_201_Collect__conv__if, fact_174_insert__mono, fact_315_Un__mono, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com, fact_454_inf__sup__ord_I3_J, fact_687_DiffE, fact_620_Int__insert__left, fact_514_folding__one_Osingleton, fact_1_asm, fact_328_image__Un, fact_310_Un__insert__left, fact_185_insert__subset, fact_539_evalc_OWhileFalse, fact_409_sup__fun__def, fact_680_folding__one_Oinsert__remove, fact_410_sup__apply, fact_615_Int__insert__right__if0, fact_527_mk__disjoint__insert, fact_447_sup__ge2, fact_364_bot__unique, fact_674_distrib__imp1, fact_229_finite__subset__image, fact_339_xt1_I5_J, fact_35_image__constant__conv, fact_304_finite__UnI, fact_149_insert__not__empty, fact_639_inf__absorb1, fact_522_Collect__mono, fact_698_Diff__insert2, fact_184_subset__insert, fact_384_sup1E, conj_3, fact_333_insert__is__Un, fact_441_le__supI1, fact_603_Int__absorb2, help_fequal_1_1_fequal_000tc__Com__Ostate_T, fact_222_WTs__elim__cases_I7_J, fact_60_equalityI, fact_405_elem__set, fact_192_image__insert, fact_314_Un__mono, fact_176_mem__def, fact_444_le__sup__iff, fact_209_singleton__conv, fact_382_conseq2, fact_352_order__antisym__conv, fact_3_thin, fact_637_le__infI2, fact_316_Un__least, fact_77_empty__Collect__eq, fact_406_elem__set, fact_509_folding__one_Oinsert, fact_491_the__elem__def, fact_561_IntE, fact_257_com_Osimps_I6_J, fact_358_option_Oinject, fact_68_Collect__empty__eq, fact_503_com_Osimps_I17_J, fact_635_le__infI1, fact_79_ex__in__conv, fact_417_inf__sup__aci_I7_J, fact_0_empty, fact_88_insertI2, fact_191_image__insert, fact_305_finite__UnI, fact_261_the__elem__eq, fact_99_insert__absorb2, fact_127_subset__refl, fact_29_finite_OemptyI, fact_129_rev__image__eqI, fact_463_folding__one__idem_Ounion__idem, fact_95_insert__iff, fact_250_pigeonhole__infinite, fact_354_order__eq__refl, help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T, fact_374_bot__apply, fact_686_DiffE, fact_62_subsetD, fact_595_Un__Int__distrib, fact_38_image__constant, fact_264_order__refl, fact_451_sup__ge1, fact_117_set__rev__mp, fact_336_xt1_I6_J, fact_667_Un__Int__assoc__eq, fact_613_Int__insert__left__if0, fact_546_xt1_I15_J, fact_570_Int__empty__left, fact_630_inf__le2, fact_323_subset__Un__eq, fact_313_Un__insert__right, fact_254_pigeonhole__infinite, fact_386_hoare__sound, fact_580_IntD2, fact_568_Int__empty__right, fact_457_sup__bot__right, fact_290_Un__commute, fact_329_insert__def, fact_351_ord__eq__le__trans, fact_446_le__iff__sup, fact_665_image__Int__subset, fact_137_insert__compr__raw, fact_155_finite__insert, fact_164_empty__is__image, fact_289_Un__left__absorb, fact_100_insert__Collect, fact_270_UnCI, fact_487_folding__one__idem_Ohom__commute, fact_448_sup__ge2, fact_255_pigeonhole__infinite, fact_13_finite__imageI, fact_611_Int__insert__right__if1, fact_553_folding__one_Ounion__inter, fact_646_inf__greatest, fact_661_distrib__sup__le, fact_343_order__antisym, fact_652_sup__inf__absorb, fact_340_order__trans, fact_452_sup__ge1, fact_520_image__cong, fact_87_insert__absorb, fact_610_Int__insert__left__if1, fact_684_DiffI, fact_246_pigeonhole__infinite, fact_57_insertCI, fact_356_order__eq__iff, fact_468_folding__one__idem_Osubset__idem, fact_181_subset__insertI2, fact_86_insert__absorb, fact_390_rev__predicate1D, fact_198_Collect__conv__if, fact_474_finite__ne__induct, fact_233_finite__subset__image, fact_426_sup_Oidem, fact_651_inf__sup__absorb, fact_579_IntD1, fact_319_Un__absorb2, fact_220_finite__subset__induct, fact_349_xt1_I3_J, fact_308_finite__Un, fact_124_set__eq__subset, fact_97_insert__commute, fact_533_MGT__alternD, fact_173_insert__mono, fact_50_finite__surj, fact_360_Body1, fact_73_empty__iff, fact_240_finite__induct, fact_599_Int__greatest, fact_244_finite_Osimps, fact_96_insert__commute, fact_217_imageE, fact_436_sup__absorb1, fact_54_emptyE, fact_156_finite__insert, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_660_inf__bot__left, fact_234_finite__subset__image, fact_274_Collect__disj__eq, fact_500_com_Osimps_I58_J, fact_653_inf__sup__distrib1, fact_502_com_Osimps_I16_J, fact_197_domI, fact_111_equalityE, fact_267_nonempty__iff, fact_691_finite__Diff, fact_33_finite__Collect__conjI, fact_421_sup_Oleft__idem, fact_576_Int__iff, fact_40_finite__surj, fact_125_set__eq__subset, fact_22_empty__subsetI, fact_92_insert__code, fact_397_sup__Un__eq, fact_528_mk__disjoint__insert, fact_439_le__supI2, fact_116_set__rev__mp, fact_231_finite__subset__image, fact_206_singleton__conv, fact_259_domD, fact_535_MGT__def, fact_659_inf__bot__left, fact_265_order__refl, fact_531_equals0I, help_fequal_1_1_fequal_000tc__Com__Opname_T, fact_271_UnCI, fact_74_empty__Collect__eq, fact_126_subset__refl, help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate, fact_428_le__supE, fact_624_inf__sup__ord_I1_J, fact_583_Collect__conj__eq, fact_30_finite_OemptyI, fact_557_folding__one_Ounion__disjoint, fact_625_inf__le1, conj_2, fact_593_Un__Int__distrib2, fact_459_sup__bot__left, fact_20_finite__imageI, fact_631_le__iff__inf, fact_122_equalityD1, fact_558_IntI, fact_63_subsetD, fact_21_empty__subsetI, fact_494_WTs__elim__cases_I4_J, fact_587_Int__Collect, fact_98_insert__absorb2, fact_423_inf__sup__aci_I5_J, fact_141_singleton__inject, fact_263_image__subsetI, fact_142_singleton__inject, fact_150_insert__not__empty, fact_521_Collect__mono, fact_177_Collect__def, fact_151_empty__not__insert, fact_378_finite__pointwise, fact_80_all__not__in__conv, fact_608_Int__lower1, fact_326_Un__upper1, fact_168_finite__subset, fact_300_Un__empty__left, fact_605_Int__lower2, fact_616_Int__insert__right__if0, fact_334_insert__is__Un, fact_432_sup__least, fact_65_image__eqI, fact_649_le__infE, fact_388_bot__empty__eq, fact_697_insert__Diff__single, fact_195_subset__image__iff, fact_676_folding__one_Oremove, fact_110_equalityE, fact_543_com__det, fact_144_singletonE, fact_516_folding__one_Oclosed, fact_277_Collect__disj__eq, fact_52_subset__singletonD, fact_221_finite__subset__induct, fact_362_le__bot, fact_350_ord__eq__le__trans, fact_365_bot__least, fact_416_sup__left__commute, fact_268_the_Osimps, fact_547_xt1_I15_J, fact_648_inf__mono, fact_418_sup_Oleft__commute, fact_12_finite__imageI, fact_632_le__iff__inf, fact_193_image__mono, fact_456_sup__eq__bot__iff, fact_324_Un__upper2, fact_104_insert__compr, fact_210_singleton__conv2, fact_498_com_Osimps_I5_J, fact_662_distrib__sup__le, fact_619_Int__insert__left, fact_612_Int__insert__right__if1, fact_82_empty__def, fact_169_rev__finite__subset, fact_537_evalc__elim__cases_I6_J, fact_114_set__mp, fact_435_sup__absorb1, fact_415_sup_Oassoc, fact_666_Un__Int__assoc__eq, fact_262_image__subsetI, fact_492_the__elem__def, fact_681_folding__one_Oinsert__remove, fact_566_disjoint__iff__not__equal, fact_89_insertI2, fact_636_le__infI1, fact_341_order__trans, fact_532_equals0I, fact_437_sup__absorb2, fact_121_equalityD2, fact_317_Un__least, fact_404_Option_Oset_Osimps_I2_J, fact_112_subset__trans, fact_449_inf__sup__ord_I4_J, fact_499_com_Osimps_I59_J, fact_5_hoare__derivs_Oinsert, fact_573_Int__def, fact_278_triple_Oinject, fact_392_predicate1D, fact_559_IntI, fact_482_folding__one__idem_Oin__idem, fact_301_Un__empty__left, fact_66_equals0D, fact_348_xt1_I3_J, fact_425_sup__idem, fact_109_insertI1, fact_25_finite_OinsertI, fact_42_finite__surj, fact_64_image__eqI, fact_618_insert__inter__insert, fact_330_insert__def, help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate, fact_398_sup__Un__eq, fact_617_insert__inter__insert, fact_577_Int__iff, fact_189_insert__image, fact_6_derivs__insertD, fact_342_order__antisym, fact_51_subset__singletonD, fact_146_doubleton__eq__iff, fact_43_finite__surj, fact_669_dom__if, fact_93_insert__code, fact_355_order__eq__refl, fact_34_finite__Collect__conjI, fact_645_inf__greatest, fact_582_Collect__conj__eq, fact_91_insert__ident, fact_145_doubleton__eq__iff, fact_464_folding__one__idem_Ounion__idem, fact_470_folding__one__idem_Oinsert__idem, fact_107_insert__compr, fact_399_conseq12, fact_671_Int__Collect__mono, fact_604_Int__absorb2, fact_152_empty__not__insert, fact_296_Un__empty, fact_140_insert__compr__raw, fact_594_Int__Un__distrib2, fact_526_predicate1I, fact_299_Un__empty__right, fact_629_inf__le2, fact_44_finite__surj, fact_497_com_Osimps_I3_J, help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T, fact_123_equalityD1, fact_385_sup1CI, fact_159_image__is__empty, fact_130_imageI, fact_569_Int__empty__right, fact_581_IntD2, fact_161_image__empty, fact_239_finite__induct, fact_564_finite__Int, fact_132_image__iff, fact_481_folding__one__idem_Oin__idem, fact_320_Un__absorb1, fact_295_Un__absorb, fact_55_emptyE, fact_508_com_Osimps_I13_J, fact_345_xt1_I4_J, fact_279_UnI2, fact_403_Option_Oset_Osimps_I2_J, fact_78_ex__in__conv, fact_170_rev__finite__subset, fact_519_triple_Oexhaust, fact_214_MGF__lemma1, conj_6, fact_167_finite__subset, fact_196_subset__image__iff, fact_190_insert__image, fact_496_com_Osimps_I47_J, fact_571_Int__empty__left, fact_188_subset__insertI, fact_692_insert__Diff, fact_335_hoare__derivs_OBody, fact_285_Un__assoc, fact_160_image__is__empty, fact_431_sup__least, fact_693_insert__Diff, fact_131_imageI, conj_1, fact_552_folding__one_Ounion__inter, fact_318_Un__absorb2, fact_94_insert__iff, fact_376_bot__fun__def, fact_361_le__bot, fact_256_pigeonhole__infinite, fact_258_MGT__Body, fact_148_singleton__iff, fact_41_finite__surj, fact_424_sup_Ocommute, fact_235_finite__subset__image, fact_614_Int__insert__left__if0, fact_548_xt1_I16_J, fact_288_Un__left__commute, fact_283_ball__Un, fact_445_le__iff__sup, fact_166_finite__subset, fact_530_Set_Oset__insert, fact_379_escape, fact_113_subset__trans, fact_469_hoare__derivs_OSkip, fact_387_bot__empty__eq, fact_53_MGF, fact_36_image__constant__conv, fact_411_single__stateE, fact_586_Int__Collect, fact_440_le__supI2, fact_565_finite__Int, fact_647_inf__mono, fact_286_Un__iff, fact_655_inf__sup__distrib2, fact_172_rev__finite__subset, fact_567_disjoint__iff__not__equal, fact_471_folding__one__idem_Oinsert__idem, fact_245_pigeonhole__infinite, fact_143_singletonE, fact_321_Un__absorb1, fact_119_in__mono, fact_467_folding__one__idem_Osubset__idem, fact_529_Set_Oset__insert, fact_284_bex__Un, fact_157_subset__empty, fact_505_com_Osimps_I48_J, fact_658_inf__bot__right, fact_677_folding__one_Oremove, fact_380_Body__sound__lemma, fact_322_subset__Un__eq, fact_633_le__inf__iff, fact_327_Un__upper1, fact_489_LoopF, fact_696_insert__Diff__single, fact_419_sup__left__idem, fact_291_Un__def, fact_534_MGT__alternI, fact_538_evalc__elim__cases_I1_J, fact_510_folding__one_Oinsert, fact_391_predicate1D, fact_344_xt1_I4_J, fact_243_finite_Osimps, fact_600_Int__greatest, fact_230_finite__subset__image, fact_269_weak__Body, fact_353_order__antisym__conv, fact_347_ord__le__eq__trans, help_fequal_2_1_fequal_000tc__Com__Ostate_T, fact_251_pigeonhole__infinite, fact_621_Int__insert__right, fact_598_Int__mono, fact_2_weaken, help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate, fact_623_inf__sup__ord_I1_J, fact_294_Un__def, fact_650_le__infE, fact_381_conseq1, fact_506_WT_OSemi, fact_171_rev__finite__subset, fact_545_evalc__WHILE__case, fact_337_xt1_I6_J, fact_393_sup1I2, fact_359_constant, fact_4_cut, fact_690_finite__Diff, fact_542_evalc_OSkip, fact_429_sup__mono, fact_26_finite_OinsertI, fact_272_UnE, fact_540_evalc_OWhileTrue, fact_460_sup__bot__left, fact_366_bot__least, fact_430_sup__mono, conj_4, fact_312_Un__insert__right, fact_383_MGF__complete, fact_56_insertCI, fact_644_le__infI, fact_643_le__infI, fact_602_Int__absorb1, fact_186_insert__subset, fact_627_inf__sup__ord_I2_J, fact_90_insert__ident, fact_609_Int__insert__left__if1, fact_638_le__infI2, fact_607_Int__lower1, fact_515_folding__one_Oclosed, fact_544_evalc__elim__cases_I4_J, fact_422_sup__commute, fact_136_finite__Collect__disjI, fact_642_inf__absorb2, fact_433_le__supI, fact_71_Collect__empty__eq, fact_695_Diff__insert__absorb, fact_297_Un__empty, fact_158_subset__empty, fact_438_sup__absorb2, fact_120_equalityD2, fact_338_xt1_I5_J, fact_247_pigeonhole__infinite, fact_7_MGT__BodyN, fact_495_com_Osimps_I46_J, fact_592_Un__Int__crazy, fact_81_all__not__in__conv, fact_223_subsetI, fact_394_sup1I1, fact_281_UnI1, fact_128_rev__image__eqI, fact_490_Comp, fact_675_distrib__imp2, fact_311_Un__insert__left, fact_103_insert__Collect, fact_273_UnE, fact_420_inf__sup__aci_I8_J, conj_5, fact_434_le__supI, fact_183_subset__insert, fact_236_finite__dom__body, fact_108_insertI1, fact_668_if__image__distrib, fact_135_finite__Collect__disjI, fact_412_state__not__singleton__def, fact_213_singleton__conv2, fact_375_bot__fun__def, fact_657_inf__bot__right, fact_61_equalityI, conj_0, fact_479_com_Osimps_I18_J, fact_205_Collect__conv__if2, fact_396_pred__subset__eq, fact_549_xt1_I16_J, fact_453_inf__sup__ord_I3_J, fact_118_in__mono, fact_628_inf__sup__ord_I2_J, fact_402_Option_Oset_Osimps_I2_J, fact_309_finite__Un, fact_556_folding__one_Ounion__disjoint, fact_536_evalc_OBody, fact_298_Un__empty__right, fact_357_order__eq__iff, fact_663_distrib__inf__le, fact_443_le__sup__iff, fact_377_BodyN, fact_493_WTs__elim__cases_I6_J, fact_178_Collect__def, fact_182_subset__insertI2, fact_287_Un__iff, fact_162_image__empty, fact_670_Int__Collect__mono, fact_427_le__supE, fact_507_com_Osimps_I12_J, fact_513_folding__one_Osingleton, fact_634_le__inf__iff, fact_59_insertE, fact_442_le__supI1, fact_572_Int__def, fact_590_inf__Int__eq, fact_578_IntD1, fact_58_insertE, fact_363_bot__unique, fact_488_folding__one__idem_Ohom__commute, fact_501_While, fact_414_inf__sup__aci_I6_J, fact_14_finite__imageI, fact_266_nonempty__iff, fact_373_bot__apply, fact_346_ord__le__eq__trans, fact_280_UnI2, fact_541_evalc_OSemi
% 58.81/14.02 % No. of inferences in proof: 1251
% 58.81/14.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13651 ms resp. 12598 ms w/o parsing
% 61.63/14.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 61.63/14.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------