%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW470^3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:13 AM UTC 2026
% Result : Theorem 32.70s 7.46s
% Output : Refutation 31.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 366
% Syntax : Number of formulae : 796 ( 406 unt; 0 typ; 0 def)
% Number of atoms : 3073 ( 985 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 6994 ( 253 ~; 49 |; 137 &;5863 @)
% ( 0 <=>; 692 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 1309 (1309 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 6 con; 0-4 aty)
% Number of variables : 2470 ( 257 ^;2162 !; 51 ?;2470 :)
% Comments :
%------------------------------------------------------------------------------
thf(x_a_type,type,
x_a: $tType ).
thf(com_type,type,
com: $tType ).
thf(state_type,type,
state: $tType ).
thf(vname_type,type,
vname: $tType ).
thf(hoare_2091234717iple_a_type,type,
hoare_2091234717iple_a: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(big_co1555037566_a_int_decl,type,
big_co1555037566_a_int: ( hoare_2091234717iple_a > int ) > ( hoare_2091234717iple_a > $o ) > int ).
thf(big_co917763874_a_nat_decl,type,
big_co917763874_a_nat: ( hoare_2091234717iple_a > nat ) > ( hoare_2091234717iple_a > $o ) > nat ).
thf(big_co387207925at_nat_decl,type,
big_co387207925at_nat: ( nat > nat ) > ( nat > $o ) > nat ).
thf(big_co2030419055_a_int_decl,type,
big_co2030419055_a_int: ( hoare_2091234717iple_a > int ) > ( hoare_2091234717iple_a > $o ) > int ).
thf(big_co1393145363_a_nat_decl,type,
big_co1393145363_a_nat: ( hoare_2091234717iple_a > nat ) > ( hoare_2091234717iple_a > $o ) > nat ).
thf(big_se96866163iple_a_decl,type,
big_se96866163iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ) > $o ).
thf(ass_decl,type,
ass: vname > ( state > nat ) > com ).
thf(skip_decl,type,
skip: com ).
thf(semi_decl,type,
semi: com > com > com ).
thf(finite2078358188le_a_o_decl,type,
finite2078358188le_a_o: ( hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > $o ).
thf(finite408405521iple_a_decl,type,
finite408405521iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > $o ).
thf(finite438582129le_a_o_decl,type,
finite438582129le_a_o: ( hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > $o ).
thf(finite1776604428iple_a_decl,type,
finite1776604428iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > $o ).
thf(finite1829014797le_a_o_decl,type,
finite1829014797le_a_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > $o ).
thf(finite232261744iple_a_decl,type,
finite232261744iple_a: ( hoare_2091234717iple_a > $o ) > $o ).
thf(finite114877549iple_a_decl,type,
finite114877549iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
thf(finite2106937597iple_a_decl,type,
finite2106937597iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ).
thf(finite2010064629le_a_o_decl,type,
finite2010064629le_a_o: ( hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
thf(finite186236040iple_a_decl,type,
finite186236040iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ).
thf(finite1003551991le_a_o_decl,type,
finite1003551991le_a_o: ( hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
thf(finite1218641926iple_a_decl,type,
finite1218641926iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
thf(finite247037978iple_a_decl,type,
finite247037978iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ) > $o ).
thf(finite1674555159iple_a_decl,type,
finite1674555159iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ) > $o ).
thf(minus_836160335le_a_o_decl,type,
minus_836160335le_a_o: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
thf(minus_minus_int_decl,type,
minus_minus_int: int > int > int ).
thf(plus_plus_int_decl,type,
plus_plus_int: int > int > int ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(times_times_int_decl,type,
times_times_int: int > int > int ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(the_Ho1471183438iple_a_decl,type,
the_Ho1471183438iple_a: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ).
thf(hoare_1467856363rivs_a_decl,type,
hoare_1467856363rivs_a: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
thf(hoare_657976383iple_a_decl,type,
hoare_657976383iple_a: ( x_a > state > $o ) > com > ( x_a > state > $o ) > hoare_2091234717iple_a ).
thf(if_nat_decl,type,
if_nat: $o > nat > nat > nat ).
thf(update_decl,type,
update: state > vname > nat > state ).
thf(bot_bo1791335050le_a_o_decl,type,
bot_bo1791335050le_a_o: hoare_2091234717iple_a > $o ).
thf(bot_bot_int_o_decl,type,
bot_bot_int_o: int > $o ).
thf(bot_bot_nat_o_decl,type,
bot_bot_nat_o: nat > $o ).
thf(bot_bot_o_decl,type,
bot_bot_o: $o ).
thf(ord_le35180118le_a_o_decl,type,
ord_le35180118le_a_o: ( hoare_2091234717iple_a > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
thf(partia443170835iple_a_decl,type,
partia443170835iple_a: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ).
thf(collec1008234059le_a_o_decl,type,
collec1008234059le_a_o: ( ( hoare_2091234717iple_a > $o ) > $o ) > ( hoare_2091234717iple_a > $o ) > $o ).
thf(collec992574898iple_a_decl,type,
collec992574898iple_a: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
thf(collect_int_decl,type,
collect_int: ( int > $o ) > int > $o ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > nat > $o ).
thf(image_1661191109iple_a_decl,type,
image_1661191109iple_a: ( hoare_2091234717iple_a > hoare_2091234717iple_a ) > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
thf(image_1773322034_a_nat_decl,type,
image_1773322034_a_nat: ( hoare_2091234717iple_a > nat ) > ( hoare_2091234717iple_a > $o ) > nat > $o ).
thf(image_int_nat_decl,type,
image_int_nat: ( int > nat ) > ( int > $o ) > nat > $o ).
thf(image_359186840iple_a_decl,type,
image_359186840iple_a: ( nat > hoare_2091234717iple_a ) > ( nat > $o ) > hoare_2091234717iple_a > $o ).
thf(insert1597628439iple_a_decl,type,
insert1597628439iple_a: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o ).
thf(insert_nat_decl,type,
insert_nat: nat > ( nat > $o ) > nat > $o ).
thf(the_el13400124iple_a_decl,type,
the_el13400124iple_a: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a ).
thf(the_elem_nat_decl,type,
the_elem_nat: ( nat > $o ) > nat ).
thf(fequal1604381340iple_a_decl,type,
fequal1604381340iple_a: hoare_2091234717iple_a > hoare_2091234717iple_a > $o ).
thf(fequal_nat_decl,type,
fequal_nat: nat > nat > $o ).
thf(member290856304iple_a_decl,type,
member290856304iple_a: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > $o ).
thf(g_decl,type,
g: hoare_2091234717iple_a > $o ).
thf(p_decl,type,
p: x_a > state > $o ).
thf(b_decl,type,
b: state > $o ).
thf(c_decl,type,
c: com ).
thf(sk59_decl,type,
sk59: hoare_2091234717iple_a ).
thf(197,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ B @ C )
=> ( ( B @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_folding__one__idem_Oidem) ).
thf(1024,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ B @ C )
=> ( ( B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(254,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( B != bot_bo1791335050le_a_o )
=> ? [C: hoare_2091234717iple_a] : ( finite114877549iple_a @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_finite__nonempty__imp__fold1Set) ).
thf(1237,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( B != bot_bo1791335050le_a_o )
=> ? [C: hoare_2091234717iple_a] : ( finite114877549iple_a @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(199,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_setsum__diff1_H) ).
thf(1031,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(155,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( collect_nat @ B ) )
= ( collect_nat
@ ^ [C: nat] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_insert__Collect) ).
thf(893,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( collect_nat @ B ) )
= ( collect_nat
@ ^ [C: nat] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(276,axiom,
! [A: nat,B: nat] :
( ( if_nat @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).
thf(1315,plain,
! [A: nat,B: nat] :
( ( if_nat @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(211,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a > int,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co2030419055_a_int
@ ^ [D: hoare_2091234717iple_a] : ( times_times_int @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( times_times_int @ ( big_co2030419055_a_int @ A @ C ) @ ( big_co2030419055_a_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_setprod_Odistrib) ).
thf(1083,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a > int,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co2030419055_a_int
@ ^ [D: hoare_2091234717iple_a] : ( times_times_int @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( times_times_int @ ( big_co2030419055_a_int @ A @ C ) @ ( big_co2030419055_a_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(171,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: $o] :
( ( C
=> ( A
= ( the_Ho1471183438iple_a
@ ^ [D: hoare_2091234717iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) )
& ( ~ C
=> ( B
= ( the_Ho1471183438iple_a
@ ^ [D: hoare_2091234717iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_If__def) ).
thf(941,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: $o] :
( ( C
=> ( A
= ( the_Ho1471183438iple_a
@ ^ [D: hoare_2091234717iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) )
& ( ~ C
=> ( B
= ( the_Ho1471183438iple_a
@ ^ [D: hoare_2091234717iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(344,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( ! [B: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ B @ A ) )
= ( A = bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_all__not__in__conv) ).
thf(1554,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( ! [B: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ B @ A ) )
= ( A = bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(244,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_nat__mult__assoc) ).
thf(1200,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(232,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_zmult__commute) ).
thf(1158,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(305,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( bot_bo1791335050le_a_o
!= ( insert1597628439iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_empty__not__insert) ).
thf(1406,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( bot_bo1791335050le_a_o
!= ( insert1597628439iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(334,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( ( A = bot_bo1791335050le_a_o )
| ( A
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_893_subset__singletonD) ).
thf(1522,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( ( A = bot_bo1791335050le_a_o )
| ( A
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(354,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( ? [B: hoare_2091234717iple_a] : ( member290856304iple_a @ B @ A ) )
= ( A != bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_ex__in__conv) ).
thf(1618,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( ? [B: hoare_2091234717iple_a] : ( member290856304iple_a @ B @ A ) )
= ( A != bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(304,axiom,
! [A: x_a > state > $o,B: x_a > state > $o,C: hoare_2091234717iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ E @ F ) @ bot_bo1791335050le_a_o ) )
=> ( ! [G: x_a,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: x_a] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ B @ E @ A ) @ bot_bo1791335050le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_conseq12) ).
thf(1401,plain,
! [A: x_a > state > $o,B: x_a > state > $o,C: hoare_2091234717iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ E @ F ) @ bot_bo1791335050le_a_o ) )
=> ( ! [G: x_a,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: x_a] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ B @ E @ A ) @ bot_bo1791335050le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(111,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ~ ( fequal1604381340iple_a @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_) ).
thf(741,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ~ ( fequal1604381340iple_a @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(341,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( minus_836160335le_a_o @ A @ B )
= ( finite2010064629le_a_o
@ ^ [C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] : ( minus_836160335le_a_o @ D @ ( insert1597628439iple_a @ C @ bot_bo1791335050le_a_o ) )
@ A
@ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_minus__fold__remove) ).
thf(1544,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( minus_836160335le_a_o @ A @ B )
= ( finite2010064629le_a_o
@ ^ [C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] : ( minus_836160335le_a_o @ D @ ( insert1597628439iple_a @ C @ bot_bo1791335050le_a_o ) )
@ A
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(144,axiom,
! [A: int] :
( ( bot_bot_int_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_bot__apply) ).
thf(861,plain,
! [A: int] :
( ( bot_bot_int_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(236,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ! [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ C )
=> ( member290856304iple_a @ ( A @ D ) @ B ) )
=> ( ord_le35180118le_a_o @ ( image_1661191109iple_a @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_927_image__subsetI) ).
thf(1173,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ! [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ C )
=> ( member290856304iple_a @ ( A @ D ) @ B ) )
=> ( ord_le35180118le_a_o @ ( image_1661191109iple_a @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(76,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_zadd__zmult__distrib) ).
thf(614,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(94,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
!= bot_bot_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_insert__not__empty) ).
thf(677,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
!= bot_bot_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(332,axiom,
! [A: ( hoare_2091234717iple_a > $o ) > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( B != bot_bo1791335050le_a_o )
=> ( ! [C: hoare_2091234717iple_a] : ( A @ ( insert1597628439iple_a @ C @ bot_bo1791335050le_a_o ) )
=> ( ! [C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ D )
=> ( ( D != bot_bo1791335050le_a_o )
=> ( ~ ( member290856304iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert1597628439iple_a @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_finite__ne__induct) ).
thf(1497,plain,
! [A: ( hoare_2091234717iple_a > $o ) > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( B != bot_bo1791335050le_a_o )
=> ( ! [C: hoare_2091234717iple_a] : ( A @ ( insert1597628439iple_a @ C @ bot_bo1791335050le_a_o ) )
=> ( ! [C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ D )
=> ( ( D != bot_bo1791335050le_a_o )
=> ( ~ ( member290856304iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert1597628439iple_a @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(8,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > $o,C: nat > nat,D: nat > $o] :
( ( times_times_nat @ ( big_co917763874_a_nat @ A @ B ) @ ( big_co387207925at_nat @ C @ D ) )
= ( big_co917763874_a_nat
@ ^ [E: hoare_2091234717iple_a] :
( big_co387207925at_nat
@ ^ [F: nat] : ( times_times_nat @ ( A @ E ) @ ( C @ F ) )
@ D )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_setsum__product) ).
thf(384,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > $o,C: nat > nat,D: nat > $o] :
( ( times_times_nat @ ( big_co917763874_a_nat @ A @ B ) @ ( big_co387207925at_nat @ C @ D ) )
= ( big_co917763874_a_nat
@ ^ [E: hoare_2091234717iple_a] :
( big_co387207925at_nat
@ ^ [F: nat] : ( times_times_nat @ ( A @ E ) @ ( C @ F ) )
@ D )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(263,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite1776604428iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( finite186236040iple_a @ D @ ( D @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_comp__fun__idem_Ofold__insert__idem2) ).
thf(1275,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite1776604428iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( finite186236040iple_a @ D @ ( D @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(252,axiom,
! [A: hoare_2091234717iple_a] :
( ( bot_bo1791335050le_a_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_bot__apply) ).
thf(1231,plain,
! [A: hoare_2091234717iple_a] :
( ( bot_bo1791335050le_a_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1232,plain,
! [A: hoare_2091234717iple_a] :
( ( bot_bo1791335050le_a_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[1231]) ).
thf(1233,plain,
! [A: hoare_2091234717iple_a] :
( ( bot_bo1791335050le_a_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[1232]) ).
thf(130,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co2030419055_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_int @ ( A @ B ) @ ( big_co2030419055_a_int @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_setprod__insert) ).
thf(814,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co2030419055_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_int @ ( A @ B ) @ ( big_co2030419055_a_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(162,axiom,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_insert__absorb2) ).
thf(913,plain,
! [A: nat,B: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(291,axiom,
! [A: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite2010064629le_a_o @ A @ B @ bot_bo1791335050le_a_o )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_fold__empty) ).
thf(1354,plain,
! [A: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite2010064629le_a_o @ A @ B @ bot_bo1791335050le_a_o )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(167,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( big_se96866163iple_a @ B @ C )
=> ( ( finite232261744iple_a @ A )
=> ( ( C @ A )
= ( finite2106937597iple_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_semilattice__big_OF__eq) ).
thf(930,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( big_se96866163iple_a @ B @ C )
=> ( ( finite232261744iple_a @ A )
=> ( ( C @ A )
= ( finite2106937597iple_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(319,axiom,
( finite438582129le_a_o
@ ^ [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] : ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_comp__fun__idem__remove) ).
thf(1458,plain,
( finite438582129le_a_o
@ ^ [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] : ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(91,axiom,
! [A: vname,B: state > nat] :
( ( ass @ A @ B )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_com_Osimps_I9_J) ).
thf(667,plain,
! [A: vname,B: state > nat] :
( ( ass @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(668,plain,
~ ? [A: vname,B: state > nat] :
( ( ass @ A @ B )
= skip ),
inference(miniscope,[status(thm)],[667]) ).
thf(669,plain,
! [B: state > nat,A: vname] :
( ( ass @ A @ B )
!= skip ),
inference(cnf,[status(esa)],[668]) ).
thf(670,plain,
! [B: state > nat,A: vname] :
( ( ass @ A @ B )
!= skip ),
inference(lifteq,[status(thm)],[669]) ).
thf(274,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ord_le35180118le_a_o @ ( insert1597628439iple_a @ A @ B ) @ ( insert1597628439iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_insert__mono) ).
thf(1310,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ord_le35180118le_a_o @ ( insert1597628439iple_a @ A @ B ) @ ( insert1597628439iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(533,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(188,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ C @ D )
=> ( ( ord_le35180118le_a_o @ A @ B )
=> ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ C @ B ) @ ( minus_836160335le_a_o @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_Diff__mono) ).
thf(1001,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ C @ D )
=> ( ( ord_le35180118le_a_o @ A @ B )
=> ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ C @ B ) @ ( minus_836160335le_a_o @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(315,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( ( B = bot_bo1791335050le_a_o )
=> ( ( image_1661191109iple_a
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= bot_bo1791335050le_a_o ) )
& ( ( B != bot_bo1791335050le_a_o )
=> ( ( image_1661191109iple_a
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_image__constant__conv) ).
thf(1441,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( ( B = bot_bo1791335050le_a_o )
=> ( ( image_1661191109iple_a
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= bot_bo1791335050le_a_o ) )
& ( ( B != bot_bo1791335050le_a_o )
=> ( ( image_1661191109iple_a
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(364,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ A )
= bot_bo1791335050le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_Diff__cancel) ).
thf(1645,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ A )
= bot_bo1791335050le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(299,axiom,
finite438582129le_a_o @ insert1597628439iple_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_comp__fun__idem__insert) ).
thf(1386,plain,
finite438582129le_a_o @ insert1597628439iple_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(61,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co917763874_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_setsum_Oinsert) ).
thf(565,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co917763874_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(258,axiom,
( bot_bot_int_o
= ( collect_int
@ ^ [A: int] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_empty__def) ).
thf(1265,plain,
( bot_bot_int_o
= ( collect_int
@ ^ [A: int] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(356,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( image_1661191109iple_a
@ ^ [D: hoare_2091234717iple_a] : A
@ C )
= ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_image__constant) ).
thf(1623,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( image_1661191109iple_a
@ ^ [D: hoare_2091234717iple_a] : A
@ C )
= ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(179,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite438582129le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite2010064629le_a_o @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_comp__fun__idem_Ofold__insert__idem) ).
thf(973,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite438582129le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite2010064629le_a_o @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(204,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member290856304iple_a @ A @ ( image_1661191109iple_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_rev__image__eqI) ).
thf(1046,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ C @ D )
=> ( ( A
= ( B @ C ) )
=> ( member290856304iple_a @ A @ ( image_1661191109iple_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(270,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite186236040iple_a @ D @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_comp__fun__commute_Ofold__insert__remove) ).
thf(1298,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite186236040iple_a @ D @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(4,axiom,
! [A: nat,B: nat > nat,C: nat > $o] :
( ( times_times_nat @ A @ ( big_co387207925at_nat @ B @ C ) )
= ( big_co387207925at_nat
@ ^ [D: nat] : ( times_times_nat @ A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_setsum__right__distrib) ).
thf(372,plain,
! [A: nat,B: nat > nat,C: nat > $o] :
( ( times_times_nat @ A @ ( big_co387207925at_nat @ B @ C ) )
= ( big_co387207925at_nat
@ ^ [D: nat] : ( times_times_nat @ A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
! [A: nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( times_times_nat @ A @ ( big_co917763874_a_nat @ B @ C ) )
= ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( times_times_nat @ A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_setsum__right__distrib) ).
thf(504,plain,
! [A: nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( times_times_nat @ A @ ( big_co917763874_a_nat @ B @ C ) )
= ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( times_times_nat @ A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(282,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ~ ( member290856304iple_a @ B @ C )
=> ( ~ ( member290856304iple_a @ B @ A )
=> ( ( ( insert1597628439iple_a @ B @ C )
= ( insert1597628439iple_a @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_insert__ident) ).
thf(1330,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ~ ( member290856304iple_a @ B @ C )
=> ( ~ ( member290856304iple_a @ B @ A )
=> ( ( ( insert1597628439iple_a @ B @ C )
= ( insert1597628439iple_a @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(126,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( D @ A @ ( finite186236040iple_a @ D @ B @ C ) )
= ( finite186236040iple_a @ D @ ( D @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_comp__fun__commute_Ofold__fun__comm) ).
thf(802,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( D @ A @ ( finite186236040iple_a @ D @ B @ C ) )
= ( finite186236040iple_a @ D @ ( D @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(318,axiom,
! [A: hoare_2091234717iple_a] :
( ( collec992574898iple_a
@ ^ [B: hoare_2091234717iple_a] : ( B = A ) )
= ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_singleton__conv) ).
thf(1455,plain,
! [A: hoare_2091234717iple_a] :
( ( collec992574898iple_a
@ ^ [B: hoare_2091234717iple_a] : ( B = A ) )
= ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(321,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a,D: hoare_2091234717iple_a] :
( ( ( insert1597628439iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
= ( insert1597628439iple_a @ C @ ( insert1597628439iple_a @ D @ bot_bo1791335050le_a_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_doubleton__eq__iff) ).
thf(1462,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a,D: hoare_2091234717iple_a] :
( ( ( insert1597628439iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
= ( insert1597628439iple_a @ C @ ( insert1597628439iple_a @ D @ bot_bo1791335050le_a_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(172,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ ( image_1661191109iple_a @ A @ B ) @ ( image_1661191109iple_a @ A @ C ) ) @ ( image_1661191109iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_899_image__diff__subset) ).
thf(949,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ ( image_1661191109iple_a @ A @ B ) @ ( image_1661191109iple_a @ A @ C ) ) @ ( image_1661191109iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_crossproduct__noteq) ).
thf(587,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ D @ B ) )
!= ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ ( times_times_nat @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(279,axiom,
! [A: hoare_2091234717iple_a > $o,B: x_a > state > $o,C: vname,D: state > nat] :
( hoare_1467856363rivs_a @ A
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [E: x_a,F: state] : ( B @ E @ ( update @ F @ C @ ( D @ F ) ) )
@ ( ass @ C @ D )
@ B )
@ bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Ass) ).
thf(1323,plain,
! [A: hoare_2091234717iple_a > $o,B: x_a > state > $o,C: vname,D: state > nat] :
( hoare_1467856363rivs_a @ A
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [E: x_a,F: state] : ( B @ E @ ( update @ F @ C @ ( D @ F ) ) )
@ ( ass @ C @ D )
@ B )
@ bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(100,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( member290856304iple_a @ A @ B )
=> ( ( ( ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= bot_bo1791335050le_a_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
!= bot_bo1791335050le_a_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_folding__one_Oremove) ).
thf(702,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( member290856304iple_a @ A @ B )
=> ( ( ( ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= bot_bo1791335050le_a_o )
=> ( ( D @ B )
= A ) )
& ( ( ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
!= bot_bo1791335050le_a_o )
=> ( ( D @ B )
= ( C @ A @ ( D @ ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(114,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( collec992574898iple_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Collect__def) ).
thf(751,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( collec992574898iple_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(55,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co1555037566_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_setsum_Oinsert__remove) ).
thf(542,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co1555037566_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_add__diff__cancel) ).
thf(460,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(131,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( ord_le35180118le_a_o @ A @ ( image_1661191109iple_a @ B @ C ) )
=> ( finite232261744iple_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_finite__surj) ).
thf(817,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( ord_le35180118le_a_o @ A @ ( image_1661191109iple_a @ B @ C ) )
=> ( finite232261744iple_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(83,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co917763874_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_setsum__insert) ).
thf(638,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co917763874_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(297,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ! [B: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ B @ A )
=> ( A = bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_equals0I) ).
thf(1379,plain,
! [A: hoare_2091234717iple_a > $o] :
( ! [B: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ B @ A )
=> ( A = bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(228,axiom,
! [A: vname,B: state > nat,C: vname,D: state > nat] :
( ( ( ass @ A @ B )
= ( ass @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_com_Osimps_I1_J) ).
thf(1147,plain,
! [A: vname,B: state > nat,C: vname,D: state > nat] :
( ( ( ass @ A @ B )
= ( ass @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(148,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ! [C: hoare_2091234717iple_a] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le35180118le_a_o @ ( collec992574898iple_a @ B ) @ ( collec992574898iple_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_Collect__mono) ).
thf(870,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ! [C: hoare_2091234717iple_a] :
( ( B @ C )
=> ( A @ C ) )
=> ( ord_le35180118le_a_o @ ( collec992574898iple_a @ B ) @ ( collec992574898iple_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(193,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) )
=> ~ ( member290856304iple_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_DiffD2) ).
thf(1013,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) )
=> ~ ( member290856304iple_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(348,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ B )
=> ( hoare_1467856363rivs_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_890_asm) ).
thf(1568,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ B )
=> ( hoare_1467856363rivs_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(362,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Nat__Onat_T) ).
thf(1641,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(331,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
=> ( ( insert1597628439iple_a @ A @ ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_insert__Diff) ).
thf(1494,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
=> ( ( insert1597628439iple_a @ A @ ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(288,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( finite232261744iple_a @ ( insert1597628439iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_finite_OinsertI) ).
thf(1347,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( finite232261744iple_a @ ( insert1597628439iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(350,axiom,
! [A: ( hoare_2091234717iple_a > $o ) > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( A @ bot_bo1791335050le_a_o )
=> ( ! [C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ D )
=> ( ~ ( member290856304iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert1597628439iple_a @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_finite__induct) ).
thf(1572,plain,
! [A: ( hoare_2091234717iple_a > $o ) > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( A @ bot_bo1791335050le_a_o )
=> ( ! [C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ D )
=> ( ~ ( member290856304iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert1597628439iple_a @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(95,axiom,
! [A: nat,B: hoare_2091234717iple_a > $o] :
( ( ( B = bot_bo1791335050le_a_o )
=> ( ( image_1773322034_a_nat
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= bot_bot_nat_o ) )
& ( ( B != bot_bo1791335050le_a_o )
=> ( ( image_1773322034_a_nat
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_image__constant__conv) ).
thf(681,plain,
! [A: nat,B: hoare_2091234717iple_a > $o] :
( ( ( B = bot_bo1791335050le_a_o )
=> ( ( image_1773322034_a_nat
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= bot_bot_nat_o ) )
& ( ( B != bot_bo1791335050le_a_o )
=> ( ( image_1773322034_a_nat
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(682,plain,
( ! [A: nat,B: hoare_2091234717iple_a > $o] :
( ( B = bot_bo1791335050le_a_o )
=> ( ( image_1773322034_a_nat
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= bot_bot_nat_o ) )
& ! [A: nat,B: hoare_2091234717iple_a > $o] :
( ( B != bot_bo1791335050le_a_o )
=> ( ( image_1773322034_a_nat
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
inference(miniscope,[status(thm)],[681]) ).
thf(683,plain,
! [D: hoare_2091234717iple_a > $o,C: nat,B: hoare_2091234717iple_a > $o,A: nat] :
( ( ( B != bot_bo1791335050le_a_o )
| ( ( image_1773322034_a_nat
@ ^ [E: hoare_2091234717iple_a] : A
@ B )
= bot_bot_nat_o ) )
& ( ( D = bot_bo1791335050le_a_o )
| ( ( image_1773322034_a_nat
@ ^ [E: hoare_2091234717iple_a] : C
@ D )
= ( insert_nat @ C @ bot_bot_nat_o ) ) ) ),
inference(cnf,[status(esa)],[682]) ).
thf(684,plain,
! [B: hoare_2091234717iple_a > $o,A: nat] :
( ( B != bot_bo1791335050le_a_o )
| ( ( image_1773322034_a_nat
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= bot_bot_nat_o ) ),
inference(cnfConj,[status(thm)],[683]) ).
thf(686,plain,
! [B: hoare_2091234717iple_a > $o,A: nat] :
( ( B != bot_bo1791335050le_a_o )
| ( ( image_1773322034_a_nat
@ ^ [C: hoare_2091234717iple_a] : A
@ B )
= bot_bot_nat_o ) ),
inference(lifteq,[status(thm)],[684]) ).
thf(687,plain,
! [A: nat] :
( ( image_1773322034_a_nat
@ ^ [B: hoare_2091234717iple_a] : A
@ bot_bo1791335050le_a_o )
= bot_bot_nat_o ),
inference(simp,[status(thm)],[686]) ).
thf(103,axiom,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_bot__apply) ).
thf(714,plain,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(715,plain,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[714]) ).
thf(716,plain,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[715]) ).
thf(1741,plain,
! [A: nat] :
( ( image_1773322034_a_nat
@ ^ [B: hoare_2091234717iple_a] : A
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o )
= ( ^ [B: nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[687,1233,716]) ).
thf(303,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( ( A = B )
| ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_insert__iff) ).
thf(1398,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( ( A = B )
| ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(18,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_nat__add__left__cancel) ).
thf(416,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(308,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( ( ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= bot_bo1791335050le_a_o )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= A ) )
& ( ( ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
!= bot_bo1791335050le_a_o )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( C @ A @ ( D @ ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_folding__one_Oinsert__remove) ).
thf(1415,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( ( ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= bot_bo1791335050le_a_o )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= A ) )
& ( ( ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
!= bot_bo1791335050le_a_o )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( C @ A @ ( D @ ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(166,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( ord_le35180118le_a_o @ C @ ( image_1661191109iple_a @ A @ B ) )
=> ? [D: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ D @ B )
& ( finite232261744iple_a @ D )
& ( C
= ( image_1661191109iple_a @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_920_finite__subset__image) ).
thf(924,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( ord_le35180118le_a_o @ C @ ( image_1661191109iple_a @ A @ B ) )
=> ? [D: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ D @ B )
& ( finite232261744iple_a @ D )
& ( C
= ( image_1661191109iple_a @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(265,axiom,
! [A: hoare_2091234717iple_a > $o] : ( hoare_1467856363rivs_a @ A @ bot_bo1791335050le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).
thf(1281,plain,
! [A: hoare_2091234717iple_a > $o] : ( hoare_1467856363rivs_a @ A @ bot_bo1791335050le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1282,plain,
! [A: hoare_2091234717iple_a > $o] : ( hoare_1467856363rivs_a @ A @ bot_bo1791335050le_a_o ),
inference(cnf,[status(esa)],[1281]) ).
thf(1707,plain,
! [A: hoare_2091234717iple_a > $o] :
( hoare_1467856363rivs_a @ A
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o ),
inference(rewrite,[status(thm)],[1282,1233]) ).
thf(1,conjecture,
( hoare_1467856363rivs_a @ g
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hoare_1467856363rivs_a @ g
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo1791335050le_a_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(368,plain,
~ ( hoare_1467856363rivs_a @ g
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1682,plain,
~ ( hoare_1467856363rivs_a @ g
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_2091234717iple_a] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[368,1233]) ).
thf(1708,plain,
! [A: hoare_2091234717iple_a > $o] :
( ~ $true
| ( ( hoare_1467856363rivs_a @ A
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o )
!= ( hoare_1467856363rivs_a @ g
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [B: x_a,C: state] : $false
@ c
@ ^ [B: x_a,C: state] :
( ( p @ B @ C )
& ~ ( b @ C ) ) )
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o ) ) ) ),
inference(paramod_ordered,[status(thm)],[1707,1682]) ).
thf(1709,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( hoare_1467856363rivs_a @ A
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o )
!= ( hoare_1467856363rivs_a @ g
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [B: x_a,C: state] : $false
@ c
@ ^ [B: x_a,C: state] :
( ( p @ B @ C )
& ~ ( b @ C ) ) )
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o ) ) ),
inference(simp,[status(thm)],[1708]) ).
thf(1710,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( A != g )
| ( ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [B: x_a,C: state] : $false
@ c
@ ^ [B: x_a,C: state] :
( ( p @ B @ C )
& ~ ( b @ C ) ) )
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o )
!= ( ^ [B: hoare_2091234717iple_a] : bot_bot_o ) ) ),
inference(simp,[status(thm)],[1709]) ).
thf(1711,plain,
( ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_2091234717iple_a] : bot_bot_o )
!= ( ^ [A: hoare_2091234717iple_a] : bot_bot_o ) ),
inference(simp,[status(thm)],[1710]) ).
thf(1714,plain,
( ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_2091234717iple_a] : bot_bot_o
@ sk59 )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[1711]) ).
thf(316,axiom,
! [A: hoare_2091234717iple_a] :
( ( bot_bo1791335050le_a_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_bot__fun__def) ).
thf(1450,plain,
! [A: hoare_2091234717iple_a] :
( ( bot_bo1791335050le_a_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(79,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_comm__semiring__class_Odistrib) ).
thf(623,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(266,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( insert1597628439iple_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_insert__code) ).
thf(1283,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( insert1597628439iple_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(133,axiom,
! [A: hoare_2091234717iple_a] :
( ( the_Ho1471183438iple_a @ ( fequal1604381340iple_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_the__sym__eq__trivial) ).
thf(821,plain,
! [A: hoare_2091234717iple_a] :
( ( the_Ho1471183438iple_a @ ( fequal1604381340iple_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(35,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a > int,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co1555037566_a_int
@ ^ [D: hoare_2091234717iple_a] : ( plus_plus_int @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus_int @ ( big_co1555037566_a_int @ A @ C ) @ ( big_co1555037566_a_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_setsum_Odistrib) ).
thf(480,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a > int,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co1555037566_a_int
@ ^ [D: hoare_2091234717iple_a] : ( plus_plus_int @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus_int @ ( big_co1555037566_a_int @ A @ C ) @ ( big_co1555037566_a_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(39,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(492,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(322,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ bot_bo1791335050le_a_o )
= ( A = bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_subset__empty) ).
thf(1465,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ bot_bo1791335050le_a_o )
= ( A = bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(202,axiom,
! [A: com,B: com,C: vname,D: state > nat] :
( ( semi @ A @ B )
!= ( ass @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_com_Osimps_I25_J) ).
thf(1040,plain,
! [A: com,B: com,C: vname,D: state > nat] :
( ( semi @ A @ B )
!= ( ass @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(218,axiom,
! [A: hoare_2091234717iple_a] :
( ( the_Ho1471183438iple_a
@ ^ [B: hoare_2091234717iple_a] : ( B = A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_the__eq__trivial) ).
thf(1109,plain,
! [A: hoare_2091234717iple_a] :
( ( the_Ho1471183438iple_a
@ ^ [B: hoare_2091234717iple_a] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(359,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( B != bot_bo1791335050le_a_o )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_folding__one__idem_Oinsert__idem) ).
thf(1632,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( B != bot_bo1791335050le_a_o )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(298,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o )
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_singleton__inject) ).
thf(1383,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o )
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(64,axiom,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(574,plain,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_add__left__cancel) ).
thf(602,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(249,axiom,
! [A: int > $o] :
( ( bot_bot_int_o
= ( collect_int @ A ) )
= ( ! [B: int] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_empty__Collect__eq) ).
thf(1215,plain,
! [A: int > $o] :
( ( bot_bot_int_o
= ( collect_int @ A ) )
= ( ! [B: int] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(877,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(146,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a,D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > $o] :
( ~ ( member290856304iple_a @ D @ E )
=> ( ( finite1218641926iple_a @ A @ B @ E @ C )
=> ( finite1218641926iple_a @ A @ B @ ( insert1597628439iple_a @ D @ E ) @ ( A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_fold__graph_OinsertI) ).
thf(866,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a,D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > $o] :
( ~ ( member290856304iple_a @ D @ E )
=> ( ( finite1218641926iple_a @ A @ B @ E @ C )
=> ( finite1218641926iple_a @ A @ B @ ( insert1597628439iple_a @ D @ E ) @ ( A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(12,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(396,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(187,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ~ ( member290856304iple_a @ A @ B )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( finite186236040iple_a @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_folding__one_Oeq__fold_H) ).
thf(998,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ~ ( member290856304iple_a @ A @ B )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( finite186236040iple_a @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(44,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(507,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(347,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( B = bot_bo1791335050le_a_o )
=> ~ ( member290856304iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_equals0D) ).
thf(1564,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( B = bot_bo1791335050le_a_o )
=> ~ ( member290856304iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(366,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( finite2106937597iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_fold1__singleton) ).
thf(1651,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( finite2106937597iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(6,axiom,
! [A: nat > hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > $o,C: nat > $o] :
( ( big_co387207925at_nat
@ ^ [D: nat] : ( big_co917763874_a_nat @ ( A @ D ) @ B )
@ C )
= ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] :
( big_co387207925at_nat
@ ^ [E: nat] : ( A @ E @ D )
@ C )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_setsum__commute) ).
thf(378,plain,
! [A: nat > hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > $o,C: nat > $o] :
( ( big_co387207925at_nat
@ ^ [D: nat] : ( big_co917763874_a_nat @ ( A @ D ) @ B )
@ C )
= ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] :
( big_co387207925at_nat
@ ^ [E: nat] : ( A @ E @ D )
@ C )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(379,plain,
! [C: nat > $o,B: hoare_2091234717iple_a > $o,A: nat > hoare_2091234717iple_a > nat] :
( ( big_co387207925at_nat
@ ^ [D: nat] : ( big_co917763874_a_nat @ ( A @ D ) @ B )
@ C )
= ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] :
( big_co387207925at_nat
@ ^ [E: nat] : ( A @ E @ D )
@ C )
@ B ) ),
inference(cnf,[status(esa)],[378]) ).
thf(380,plain,
! [C: nat > $o,B: hoare_2091234717iple_a > $o,A: nat > hoare_2091234717iple_a > nat] :
( ( big_co387207925at_nat
@ ^ [D: nat] : ( big_co917763874_a_nat @ ( A @ D ) @ B )
@ C )
= ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] :
( big_co387207925at_nat
@ ^ [E: nat] : ( A @ E @ D )
@ C )
@ B ) ),
inference(lifteq,[status(thm)],[379]) ).
thf(314,axiom,
! [A: nat > hoare_2091234717iple_a,B: nat,C: nat > $o] :
( ( image_359186840iple_a @ A @ ( insert_nat @ B @ C ) )
= ( insert1597628439iple_a @ ( A @ B ) @ ( image_359186840iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_image__insert) ).
thf(1438,plain,
! [A: nat > hoare_2091234717iple_a,B: nat,C: nat > $o] :
( ( image_359186840iple_a @ A @ ( insert_nat @ B @ C ) )
= ( insert1597628439iple_a @ ( A @ B ) @ ( image_359186840iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(117,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(761,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(7,axiom,
! [A: nat > nat,B: nat > $o,C: nat] :
( ( times_times_nat @ ( big_co387207925at_nat @ A @ B ) @ C )
= ( big_co387207925at_nat
@ ^ [D: nat] : ( times_times_nat @ ( A @ D ) @ C )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_setsum__left__distrib) ).
thf(381,plain,
! [A: nat > nat,B: nat > $o,C: nat] :
( ( times_times_nat @ ( big_co387207925at_nat @ A @ B ) @ C )
= ( big_co387207925at_nat
@ ^ [D: nat] : ( times_times_nat @ ( A @ D ) @ C )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(324,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( member290856304iple_a @ B @ ( insert1597628439iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_insertI2) ).
thf(1470,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( member290856304iple_a @ B @ ( insert1597628439iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(208,axiom,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Collect__conv__if2) ).
thf(1067,plain,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(246,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) )
=> ( member290856304iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_DiffD1) ).
thf(1206,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) )
=> ( member290856304iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(28,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > $o] :
( ( C = D )
=> ( ! [E: hoare_2091234717iple_a] :
( ( member290856304iple_a @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co917763874_a_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_setsum_OF__cong) ).
thf(452,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > $o] :
( ( C = D )
=> ( ! [E: hoare_2091234717iple_a] :
( ( member290856304iple_a @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co917763874_a_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(251,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( ( partia443170835iple_a @ B @ A )
= B ) )
& ( ~ ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( ( partia443170835iple_a @ B @ A )
= ( the_Ho1471183438iple_a
@ ^ [C: hoare_2091234717iple_a] : ( member290856304iple_a @ C @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_flat__lub__def) ).
thf(1223,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( ( partia443170835iple_a @ B @ A )
= B ) )
& ( ~ ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( ( partia443170835iple_a @ B @ A )
= ( the_Ho1471183438iple_a
@ ^ [C: hoare_2091234717iple_a] : ( member290856304iple_a @ C @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(214,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(1091,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(196,axiom,
! [A: int] :
( ( bot_bot_int_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_bot__fun__def) ).
thf(1021,plain,
! [A: int] :
( ( bot_bot_int_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(333,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( minus_836160335le_a_o @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_Diff__insert2) ).
thf(1519,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( minus_836160335le_a_o @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(220,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( minus_836160335le_a_o @ ( insert1597628439iple_a @ B @ A ) @ C )
= ( minus_836160335le_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_insert__Diff1) ).
thf(1123,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( minus_836160335le_a_o @ ( insert1597628439iple_a @ B @ A ) @ C )
= ( minus_836160335le_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(349,axiom,
! [A: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ bot_bo1791335050le_a_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_empty__subsetI) ).
thf(1570,plain,
! [A: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ bot_bo1791335050le_a_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(20,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_diff__add__cancel) ).
thf(424,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(97,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1393145363_a_nat @ A @ C )
= ( times_times_nat @ ( A @ B ) @ ( big_co1393145363_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_setprod_Oremove) ).
thf(693,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1393145363_a_nat @ A @ C )
= ( times_times_nat @ ( A @ B ) @ ( big_co1393145363_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(346,axiom,
! [A: hoare_2091234717iple_a > $o,B: com,C: x_a > state > $o,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ( hoare_1467856363rivs_a @ A
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [G: x_a,H: state] : ( H = F )
@ B
@ ^ [G: x_a] : ( C @ E ) )
@ bot_bo1791335050le_a_o ) ) )
=> ( hoare_1467856363rivs_a @ A @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ B @ C ) @ bot_bo1791335050le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_escape) ).
thf(1560,plain,
! [A: hoare_2091234717iple_a > $o,B: com,C: x_a > state > $o,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ( hoare_1467856363rivs_a @ A
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [G: x_a,H: state] : ( H = F )
@ B
@ ^ [G: x_a] : ( C @ E ) )
@ bot_bo1791335050le_a_o ) ) )
=> ( hoare_1467856363rivs_a @ A @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ B @ C ) @ bot_bo1791335050le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(300,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ bot_bo1791335050le_a_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_Diff__empty) ).
thf(1387,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ bot_bo1791335050le_a_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(161,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ ( minus_836160335le_a_o @ A @ B ) @ B )
= ( minus_836160335le_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_Diff__idemp) ).
thf(910,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ ( minus_836160335le_a_o @ A @ B ) @ B )
= ( minus_836160335le_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(163,axiom,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(916,plain,
! [A: int,B: int] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ( insert_nat @ A @ bot_bot_nat_o )
= ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_singleton__inject) ).
thf(847,plain,
! [A: nat,B: nat] :
( ( ( insert_nat @ A @ bot_bot_nat_o )
= ( insert_nat @ B @ bot_bot_nat_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(294,axiom,
! [A: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ A @ bot_bo1791335050le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_empty__iff) ).
thf(1365,plain,
! [A: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ A @ bot_bo1791335050le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(23,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_add__left__cancel) ).
thf(435,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(243,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( image_1661191109iple_a @ B @ C ) )
=> ~ ! [D: hoare_2091234717iple_a] :
( ( A
= ( B @ D ) )
=> ~ ( member290856304iple_a @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_imageE) ).
thf(1195,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( image_1661191109iple_a @ B @ C ) )
=> ~ ! [D: hoare_2091234717iple_a] :
( ( A
= ( B @ D ) )
=> ~ ( member290856304iple_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_nat__add__assoc) ).
thf(551,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(268,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite1776604428iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite186236040iple_a @ D @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_comp__fun__idem_Ofold__insert__idem) ).
thf(1291,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite1776604428iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite186236040iple_a @ D @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(217,axiom,
! [A: int > $o] :
( ( collect_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_Collect__def) ).
thf(1106,plain,
! [A: int > $o] :
( ( collect_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(49,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_eq__add__iff1) ).
thf(522,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ D ) @ B ) @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(136,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( A != bot_bo1791335050le_a_o )
=> ( ( ord_le35180118le_a_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_910_folding__one__idem_Osubset__idem) ).
thf(830,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( A != bot_bo1791335050le_a_o )
=> ( ( ord_le35180118le_a_o @ A @ B )
=> ( ( C @ ( D @ A ) @ ( D @ B ) )
= ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(48,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( C
= ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_eq__add__iff2) ).
thf(519,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ D @ B ) @ E ) )
= ( C
= ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(149,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite2010064629le_a_o @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_comp__fun__commute_Ofold__insert) ).
thf(874,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite2010064629le_a_o @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(261,axiom,
! [A: hoare_2091234717iple_a] :
( ( collec992574898iple_a @ ( fequal1604381340iple_a @ A ) )
= ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_singleton__conv2) ).
thf(1270,plain,
! [A: hoare_2091234717iple_a] :
( ( collec992574898iple_a @ ( fequal1604381340iple_a @ A ) )
= ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(650,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(281,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( hoare_1467856363rivs_a @ B @ C )
=> ( ( hoare_1467856363rivs_a @ A @ B )
=> ( hoare_1467856363rivs_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cut) ).
thf(1328,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( hoare_1467856363rivs_a @ B @ C )
=> ( ( hoare_1467856363rivs_a @ A @ B )
=> ( hoare_1467856363rivs_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(1266,plain,
( ( collect_int
@ ^ [A: int] : $false )
= bot_bot_int_o ),
inference(lifteq,[status(thm)],[1265]) ).
thf(862,plain,
! [A: int] :
( ( bot_bot_int_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[861]) ).
thf(863,plain,
! [A: int] :
( ( bot_bot_int_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[862]) ).
thf(1672,plain,
( ( collect_int
@ ^ [A: int] : $false )
= ( ^ [A: int] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1266,863]) ).
thf(190,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_Diff__subset) ).
thf(1006,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(225,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) ) )
= ( finite232261744iple_a @ ( minus_836160335le_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_finite__Diff__insert) ).
thf(1138,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) ) )
= ( finite232261744iple_a @ ( minus_836160335le_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(593,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_doubleton__eq__iff) ).
thf(783,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_nat_o ) )
= ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(184,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ B )
= ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C = A )
| ( member290856304iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_insert__compr__raw) ).
thf(989,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ B )
= ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C = A )
| ( member290856304iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(253,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( insert1597628439iple_a @ B @ C ) )
=> ( ( A != B )
=> ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_insertE) ).
thf(1234,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( insert1597628439iple_a @ B @ C ) )
=> ( ( A != B )
=> ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(340,axiom,
! [A: x_a > state > $o,B: com,C: x_a > state > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( ( hoare_657976383iple_a @ A @ B @ C )
= ( hoare_657976383iple_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_triple_Oinject) ).
thf(1541,plain,
! [A: x_a > state > $o,B: com,C: x_a > state > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( ( hoare_657976383iple_a @ A @ B @ C )
= ( hoare_657976383iple_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_nat__add__right__cancel) ).
thf(471,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1683,plain,
( finite438582129le_a_o
@ ^ [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( minus_836160335le_a_o @ B
@ ( insert1597628439iple_a @ A
@ ^ [C: hoare_2091234717iple_a] : bot_bot_o ) ) ),
inference(rewrite,[status(thm)],[1458,1233]) ).
thf(152,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co2030419055_a_int @ A @ C )
= ( times_times_int @ ( A @ B ) @ ( big_co2030419055_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_setprod_Oremove) ).
thf(884,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co2030419055_a_int @ A @ C )
= ( times_times_int @ ( A @ B ) @ ( big_co2030419055_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(198,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ C )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_setsum__diff1_H) ).
thf(1028,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ C )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(293,axiom,
! [A: x_a > state > $o,B: hoare_2091234717iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ C @ D @ E ) @ bot_bo1791335050le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ C @ D @ A ) @ bot_bo1791335050le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_conseq2) ).
thf(1361,plain,
! [A: x_a > state > $o,B: hoare_2091234717iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ C @ D @ E ) @ bot_bo1791335050le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ C @ D @ A ) @ bot_bo1791335050le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(168,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a
@ ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite232261744iple_a @ ( collec992574898iple_a @ A ) )
& ( finite232261744iple_a @ ( collec992574898iple_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_finite__Collect__disjI) ).
thf(933,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a
@ ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite232261744iple_a @ ( collec992574898iple_a @ A ) )
& ( finite232261744iple_a @ ( collec992574898iple_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(59,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(554,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(90,axiom,
! [A: nat,B: int > $o] :
( ( ( B = bot_bot_int_o )
=> ( ( image_int_nat
@ ^ [C: int] : A
@ B )
= bot_bot_nat_o ) )
& ( ( B != bot_bot_int_o )
=> ( ( image_int_nat
@ ^ [C: int] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_image__constant__conv) ).
thf(658,plain,
! [A: nat,B: int > $o] :
( ( ( B = bot_bot_int_o )
=> ( ( image_int_nat
@ ^ [C: int] : A
@ B )
= bot_bot_nat_o ) )
& ( ( B != bot_bot_int_o )
=> ( ( image_int_nat
@ ^ [C: int] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(659,plain,
( ! [A: nat,B: int > $o] :
( ( B = bot_bot_int_o )
=> ( ( image_int_nat
@ ^ [C: int] : A
@ B )
= bot_bot_nat_o ) )
& ! [A: nat,B: int > $o] :
( ( B != bot_bot_int_o )
=> ( ( image_int_nat
@ ^ [C: int] : A
@ B )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ) ),
inference(miniscope,[status(thm)],[658]) ).
thf(660,plain,
! [D: int > $o,C: nat,B: int > $o,A: nat] :
( ( ( B != bot_bot_int_o )
| ( ( image_int_nat
@ ^ [E: int] : A
@ B )
= bot_bot_nat_o ) )
& ( ( D = bot_bot_int_o )
| ( ( image_int_nat
@ ^ [E: int] : C
@ D )
= ( insert_nat @ C @ bot_bot_nat_o ) ) ) ),
inference(cnf,[status(esa)],[659]) ).
thf(661,plain,
! [B: int > $o,A: nat] :
( ( B != bot_bot_int_o )
| ( ( image_int_nat
@ ^ [C: int] : A
@ B )
= bot_bot_nat_o ) ),
inference(cnfConj,[status(thm)],[660]) ).
thf(663,plain,
! [B: int > $o,A: nat] :
( ( B != bot_bot_int_o )
| ( ( image_int_nat
@ ^ [C: int] : A
@ B )
= bot_bot_nat_o ) ),
inference(lifteq,[status(thm)],[661]) ).
thf(664,plain,
! [A: nat] :
( ( image_int_nat
@ ^ [B: int] : A
@ bot_bot_int_o )
= bot_bot_nat_o ),
inference(simp,[status(thm)],[663]) ).
thf(1739,plain,
! [A: nat] :
( ( image_int_nat
@ ^ [B: int] : A
@ ^ [B: int] : bot_bot_o )
= ( ^ [B: nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[664,716,863]) ).
thf(310,axiom,
! [A: hoare_2091234717iple_a,B: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( B
= ( finite2106937597iple_a @ C ) )
=> ( ( B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_fold1__singleton__def) ).
thf(1424,plain,
! [A: hoare_2091234717iple_a,B: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( B
= ( finite2106937597iple_a @ C ) )
=> ( ( B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_comm__semiring__class_Odistrib) ).
thf(489,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(590,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ B ) )
= ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(231,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1393145363_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_nat @ ( A @ B ) @ ( big_co1393145363_a_nat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_setprod_Oinsert) ).
thf(1155,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1393145363_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_nat @ ( A @ B ) @ ( big_co1393145363_a_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(158,axiom,
! [A: nat,B: nat > $o,C: nat] :
( ( insert_nat @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_insert__code) ).
thf(901,plain,
! [A: nat,B: nat > $o,C: nat] :
( ( insert_nat @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(209,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ E )
=> ( ( finite1218641926iple_a @ E @ B @ C @ D )
=> ( ( member290856304iple_a @ A @ C )
=> ? [F: hoare_2091234717iple_a] :
( ( D
= ( E @ A @ F ) )
& ( finite1218641926iple_a @ E @ B @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_comp__fun__commute_Ofold__graph__insertE__aux) ).
thf(1075,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ E )
=> ( ( finite1218641926iple_a @ E @ B @ C @ D )
=> ( ( member290856304iple_a @ A @ C )
=> ? [F: hoare_2091234717iple_a] :
( ( D
= ( E @ A @ F ) )
& ( finite1218641926iple_a @ E @ B @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(11,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(393,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(647,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(229,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ? [D: hoare_2091234717iple_a] : ( finite1218641926iple_a @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_finite__imp__fold__graph) ).
thf(1150,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ? [D: hoare_2091234717iple_a] : ( finite1218641926iple_a @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(110,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(738,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(339,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ C @ bot_bo1791335050le_a_o ) )
=> ( ( hoare_1467856363rivs_a @ B @ A )
=> ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
thf(1539,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ C @ bot_bo1791335050le_a_o ) )
=> ( ( hoare_1467856363rivs_a @ B @ A )
=> ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(242,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(1192,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(205,axiom,
! [A: nat,B: nat] :
( ( if_nat @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T) ).
thf(1050,plain,
! [A: nat,B: nat] :
( ( if_nat @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(311,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ B @ C )
=> ( ( finite232261744iple_a @ A )
=> ( ( A != bot_bo1791335050le_a_o )
=> ( ! [D: hoare_2091234717iple_a,E: hoare_2091234717iple_a] : ( member290856304iple_a @ ( B @ D @ E ) @ ( insert1597628439iple_a @ D @ ( insert1597628439iple_a @ E @ bot_bo1791335050le_a_o ) ) )
=> ( member290856304iple_a @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_folding__one_Oclosed) ).
thf(1429,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ B @ C )
=> ( ( finite232261744iple_a @ A )
=> ( ( A != bot_bo1791335050le_a_o )
=> ( ! [D: hoare_2091234717iple_a,E: hoare_2091234717iple_a] : ( member290856304iple_a @ ( B @ D @ E ) @ ( insert1597628439iple_a @ D @ ( insert1597628439iple_a @ E @ bot_bo1791335050le_a_o ) ) )
=> ( member290856304iple_a @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(1715,plain,
( ~ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_2091234717iple_a] : bot_bot_o
@ sk59 )
| ~ bot_bot_o ),
inference(bool_ext,[status(thm)],[1714]) ).
thf(3,axiom,
! [A: nat > nat,B: nat > $o,C: hoare_2091234717iple_a > nat,D: hoare_2091234717iple_a > $o] :
( ( times_times_nat @ ( big_co387207925at_nat @ A @ B ) @ ( big_co917763874_a_nat @ C @ D ) )
= ( big_co387207925at_nat
@ ^ [E: nat] :
( big_co917763874_a_nat
@ ^ [F: hoare_2091234717iple_a] : ( times_times_nat @ ( A @ E ) @ ( C @ F ) )
@ D )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_setsum__product) ).
thf(369,plain,
! [A: nat > nat,B: nat > $o,C: hoare_2091234717iple_a > nat,D: hoare_2091234717iple_a > $o] :
( ( times_times_nat @ ( big_co387207925at_nat @ A @ B ) @ ( big_co917763874_a_nat @ C @ D ) )
= ( big_co387207925at_nat
@ ^ [E: nat] :
( big_co917763874_a_nat
@ ^ [F: hoare_2091234717iple_a] : ( times_times_nat @ ( A @ E ) @ ( C @ F ) )
@ D )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(370,plain,
! [D: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > nat,B: nat > $o,A: nat > nat] :
( ( times_times_nat @ ( big_co387207925at_nat @ A @ B ) @ ( big_co917763874_a_nat @ C @ D ) )
= ( big_co387207925at_nat
@ ^ [E: nat] :
( big_co917763874_a_nat
@ ^ [F: hoare_2091234717iple_a] : ( times_times_nat @ ( A @ E ) @ ( C @ F ) )
@ D )
@ B ) ),
inference(cnf,[status(esa)],[369]) ).
thf(371,plain,
! [D: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > nat,B: nat > $o,A: nat > nat] :
( ( times_times_nat @ ( big_co387207925at_nat @ A @ B ) @ ( big_co917763874_a_nat @ C @ D ) )
= ( big_co387207925at_nat
@ ^ [E: nat] :
( big_co917763874_a_nat
@ ^ [F: hoare_2091234717iple_a] : ( times_times_nat @ ( A @ E ) @ ( C @ F ) )
@ D )
@ B ) ),
inference(lifteq,[status(thm)],[370]) ).
thf(73,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(605,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(335,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( image_1661191109iple_a @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( insert1597628439iple_a @ ( A @ B ) @ ( image_1661191109iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_image__insert) ).
thf(1525,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( image_1661191109iple_a @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( insert1597628439iple_a @ ( A @ B ) @ ( image_1661191109iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(283,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( member290856304iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_singletonE) ).
thf(1333,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( member290856304iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(277,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( A != bot_bo1791335050le_a_o )
= ( ? [B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( A
= ( insert1597628439iple_a @ B @ C ) )
& ~ ( member290856304iple_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_nonempty__iff) ).
thf(1318,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( A != bot_bo1791335050le_a_o )
= ( ? [B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( A
= ( insert1597628439iple_a @ B @ C ) )
& ~ ( member290856304iple_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(212,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( member290856304iple_a @ ( A @ B ) @ ( image_1661191109iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_imageI) ).
thf(1086,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( member290856304iple_a @ ( A @ B ) @ ( image_1661191109iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(127,axiom,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_nat_o )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Collect__empty__eq) ).
thf(805,plain,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_nat_o )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(165,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_zmult__assoc) ).
thf(921,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(235,axiom,
! [A: nat] :
( ( collect_nat @ ( fequal_nat @ A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_singleton__conv2) ).
thf(1170,plain,
! [A: nat] :
( ( collect_nat @ ( fequal_nat @ A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(267,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
=> ~ ! [C: hoare_2091234717iple_a > $o] :
( ( B
= ( insert1597628439iple_a @ A @ C ) )
=> ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Set_Oset__insert) ).
thf(1286,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
=> ~ ! [C: hoare_2091234717iple_a > $o] :
( ( B
= ( insert1597628439iple_a @ A @ C ) )
=> ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_nat__mult__commute) ).
thf(674,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(260,axiom,
( bot_bot_nat_o
= ( collect_nat
@ ^ [A: nat] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_empty__def) ).
thf(1268,plain,
( bot_bot_nat_o
= ( collect_nat
@ ^ [A: nat] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(1269,plain,
( ( collect_nat
@ ^ [A: nat] : $false )
= bot_bot_nat_o ),
inference(lifteq,[status(thm)],[1268]) ).
thf(1663,plain,
( ( collect_nat
@ ^ [A: nat] : $false )
= ( ^ [A: nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1269,716]) ).
thf(234,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( D @ A @ ( finite2010064629le_a_o @ D @ B @ C ) )
= ( finite2010064629le_a_o @ D @ ( D @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_comp__fun__commute_Ofold__fun__comm) ).
thf(1167,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( D @ A @ ( finite2010064629le_a_o @ D @ B @ C ) )
= ( finite2010064629le_a_o @ D @ ( D @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(125,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > $o] :
( ( C = D )
=> ( ! [E: hoare_2091234717iple_a] :
( ( member290856304iple_a @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( image_1661191109iple_a @ A @ C )
= ( image_1661191109iple_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_image__cong) ).
thf(794,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > $o] :
( ( C = D )
=> ( ! [E: hoare_2091234717iple_a] :
( ( member290856304iple_a @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( image_1661191109iple_a @ A @ C )
= ( image_1661191109iple_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(264,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a] :
( ( finite1218641926iple_a @ A @ B @ bot_bo1791335050le_a_o @ C )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_empty__fold__graphE) ).
thf(1278,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a] :
( ( finite1218641926iple_a @ A @ B @ bot_bo1791335050le_a_o @ C )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(46,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( image_1773322034_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( insert_nat @ ( A @ B ) @ ( image_1773322034_a_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_image__insert) ).
thf(513,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( image_1773322034_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( insert_nat @ ( A @ B ) @ ( image_1773322034_a_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(285,axiom,
( bot_bo1791335050le_a_o
= ( collec992574898iple_a
@ ^ [A: hoare_2091234717iple_a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_empty__def) ).
thf(1339,plain,
( bot_bo1791335050le_a_o
= ( collec992574898iple_a
@ ^ [A: hoare_2091234717iple_a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1340,plain,
( ( collec992574898iple_a
@ ^ [A: hoare_2091234717iple_a] : $false )
= bot_bo1791335050le_a_o ),
inference(lifteq,[status(thm)],[1339]) ).
thf(1680,plain,
( ( collec992574898iple_a
@ ^ [A: hoare_2091234717iple_a] : $false )
= ( ^ [A: hoare_2091234717iple_a] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1340,1233]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(824,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(262,axiom,
! [A: hoare_2091234717iple_a > $o,B: x_a > state > $o] : ( hoare_1467856363rivs_a @ A @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ B @ skip @ B ) @ bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_hoare__derivs_OSkip) ).
thf(1273,plain,
! [A: hoare_2091234717iple_a > $o,B: x_a > state > $o] : ( hoare_1467856363rivs_a @ A @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ B @ skip @ B ) @ bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(271,axiom,
! [A: hoare_2091234717iple_a] :
( ( the_el13400124iple_a @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_the__elem__eq) ).
thf(1301,plain,
! [A: hoare_2091234717iple_a] :
( ( the_el13400124iple_a @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(26,axiom,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ D ) )
= ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_combine__common__factor) ).
thf(444,plain,
! [A: int,B: int,C: int,D: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ D ) )
= ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(224,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ B )
= ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( member290856304iple_a @ C @ A )
& ~ ( member290856304iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_set__diff__eq) ).
thf(1135,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ B )
= ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( member290856304iple_a @ C @ A )
& ~ ( member290856304iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(365,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
~ ( finite114877549iple_a @ A @ bot_bo1791335050le_a_o @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_empty__fold1SetE) ).
thf(1648,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
~ ( finite114877549iple_a @ A @ bot_bo1791335050le_a_o @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(5,axiom,
! [A: hoare_2091234717iple_a > nat > nat,B: nat > $o,C: hoare_2091234717iple_a > $o] :
( ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( big_co387207925at_nat @ ( A @ D ) @ B )
@ C )
= ( big_co387207925at_nat
@ ^ [D: nat] :
( big_co917763874_a_nat
@ ^ [E: hoare_2091234717iple_a] : ( A @ E @ D )
@ C )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_setsum__commute) ).
thf(375,plain,
! [A: hoare_2091234717iple_a > nat > nat,B: nat > $o,C: hoare_2091234717iple_a > $o] :
( ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( big_co387207925at_nat @ ( A @ D ) @ B )
@ C )
= ( big_co387207925at_nat
@ ^ [D: nat] :
( big_co917763874_a_nat
@ ^ [E: hoare_2091234717iple_a] : ( A @ E @ D )
@ C )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(108,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ C )
=> ( ( finite232261744iple_a @ B )
=> ( finite1218641926iple_a @ C @ A @ B @ ( finite186236040iple_a @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_comp__fun__commute_Ofold__graph__fold) ).
thf(733,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ C )
=> ( ( finite232261744iple_a @ B )
=> ( finite1218641926iple_a @ C @ A @ B @ ( finite186236040iple_a @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(67,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_crossproduct__eq) ).
thf(584,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(132,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( ord_le35180118le_a_o @ C @ A )
=> ( member290856304iple_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_set__rev__mp) ).
thf(819,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( ord_le35180118le_a_o @ C @ A )
=> ( member290856304iple_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(159,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite186236040iple_a @ D @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_comp__fun__commute_Ofold__insert) ).
thf(904,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite186236040iple_a @ D @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(14,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( plus_plus_nat @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus_nat @ ( big_co917763874_a_nat @ A @ C ) @ ( big_co917763874_a_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_setsum_Odistrib) ).
thf(402,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( plus_plus_nat @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus_nat @ ( big_co917763874_a_nat @ A @ C ) @ ( big_co917763874_a_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(353,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ~ ( member290856304iple_a @ A @ B )
=> ( ( minus_836160335le_a_o @ ( insert1597628439iple_a @ A @ B ) @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_Diff__insert__absorb) ).
thf(1615,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ~ ( member290856304iple_a @ A @ B )
=> ( ( minus_836160335le_a_o @ ( insert1597628439iple_a @ A @ B ) @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(140,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( A != B )
| ( fequal1604381340iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_) ).
thf(843,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( A != B )
| ( fequal1604381340iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(120,axiom,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_bot__fun__def) ).
thf(772,plain,
! [A: nat] :
( ( bot_bot_nat_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(175,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( finite186236040iple_a @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_folding__one__idem_Oeq__fold__idem_H) ).
thf(958,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( finite186236040iple_a @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(17,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_zadd__zmult__distrib2) ).
thf(413,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( A != B )
| ( fequal_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(577,plain,
! [A: nat,B: nat] :
( ( A != B )
| ( fequal_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(102,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite1003551991le_a_o @ D @ A @ B @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ B )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_comp__fun__commute_Ofold__equality) ).
thf(711,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite1003551991le_a_o @ D @ A @ B @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(56,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_zadd__left__commute) ).
thf(545,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(329,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ bot_bo1791335050le_a_o )
= ( A = bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_bot__unique) ).
thf(1488,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ bot_bo1791335050le_a_o )
= ( A = bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_nat__add__left__commute) ).
thf(641,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(169,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(936,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(275,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ B @ C )
=> ( ( C @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_folding__one_Osingleton) ).
thf(1312,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ B @ C )
=> ( ( C @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(611,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(498,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(360,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ ( collec992574898iple_a @ B ) )
= ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_insert__Collect) ).
thf(1635,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ ( collec992574898iple_a @ B ) )
= ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(31,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_add__right__imp__eq) ).
thf(466,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(164,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ B )
=> ( ( finite232261744iple_a @ B )
=> ( finite232261744iple_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_finite__subset) ).
thf(919,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ B )
=> ( ( finite232261744iple_a @ B )
=> ( finite232261744iple_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(361,axiom,
! [A: hoare_2091234717iple_a] :
( ( bot_bo1791335050le_a_o @ A )
= ( member290856304iple_a @ A @ bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_bot__empty__eq) ).
thf(1638,plain,
! [A: hoare_2091234717iple_a] :
( ( bot_bo1791335050le_a_o @ A )
= ( member290856304iple_a @ A @ bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(247,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ! [E: hoare_2091234717iple_a,F: hoare_2091234717iple_a] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite232261744iple_a @ A )
=> ( ( A != bot_bo1791335050le_a_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_1661191109iple_a @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_folding__one__idem_Ohom__commute) ).
thf(1209,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ! [E: hoare_2091234717iple_a,F: hoare_2091234717iple_a] :
( ( B @ ( C @ E @ F ) )
= ( C @ ( B @ E ) @ ( B @ F ) ) )
=> ( ( finite232261744iple_a @ A )
=> ( ( A != bot_bo1791335050le_a_o )
=> ( ( B @ ( D @ A ) )
= ( D @ ( image_1661191109iple_a @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(289,axiom,
! [A: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ A @ bot_bo1791335050le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_emptyE) ).
thf(1349,plain,
! [A: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ A @ bot_bo1791335050le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(376,plain,
! [C: hoare_2091234717iple_a > $o,B: nat > $o,A: hoare_2091234717iple_a > nat > nat] :
( ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( big_co387207925at_nat @ ( A @ D ) @ B )
@ C )
= ( big_co387207925at_nat
@ ^ [D: nat] :
( big_co917763874_a_nat
@ ^ [E: hoare_2091234717iple_a] : ( A @ E @ D )
@ C )
@ B ) ),
inference(cnf,[status(esa)],[375]) ).
thf(377,plain,
! [C: hoare_2091234717iple_a > $o,B: nat > $o,A: hoare_2091234717iple_a > nat > nat] :
( ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( big_co387207925at_nat @ ( A @ D ) @ B )
@ C )
= ( big_co387207925at_nat
@ ^ [D: nat] :
( big_co917763874_a_nat
@ ^ [E: hoare_2091234717iple_a] : ( A @ E @ D )
@ C )
@ B ) ),
inference(lifteq,[status(thm)],[376]) ).
thf(227,axiom,
! [A: nat > $o] :
( ( collect_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Collect__def) ).
thf(1144,plain,
! [A: nat > $o] :
( ( collect_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(151,axiom,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_com_Osimps_I12_J) ).
thf(880,plain,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(296,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( member290856304iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_singleton__iff) ).
thf(1376,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( member290856304iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(273,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
=> ( ( insert1597628439iple_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_insert__absorb) ).
thf(1307,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
=> ( ( insert1597628439iple_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(118,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ! [C: hoare_2091234717iple_a] :
( ( member290856304iple_a @ C @ B )
=> ( member290856304iple_a @ C @ A ) )
=> ( ord_le35180118le_a_o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_subsetI) ).
thf(764,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ! [C: hoare_2091234717iple_a] :
( ( member290856304iple_a @ C @ B )
=> ( member290856304iple_a @ C @ A ) )
=> ( ord_le35180118le_a_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(181,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( finite114877549iple_a @ A @ B @ C )
= ( ? [D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > $o,F: hoare_2091234717iple_a] :
( ( B
= ( insert1597628439iple_a @ D @ E ) )
& ( C = F )
& ( finite1218641926iple_a @ A @ D @ E @ F )
& ~ ( member290856304iple_a @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_fold1Set_Osimps) ).
thf(979,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( finite114877549iple_a @ A @ B @ C )
= ( ? [D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > $o,F: hoare_2091234717iple_a] :
( ( B
= ( insert1597628439iple_a @ D @ E ) )
& ( C = F )
& ( finite1218641926iple_a @ A @ D @ E @ F )
& ~ ( member290856304iple_a @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(192,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ( member290856304iple_a @ A @ B )
=> ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_in__mono) ).
thf(1011,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ( member290856304iple_a @ A @ B )
=> ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(19,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_add__right__imp__eq) ).
thf(419,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(154,axiom,
! [A: nat] :
( ( collect_nat
@ ^ [B: nat] : ( B = A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_singleton__conv) ).
thf(890,plain,
! [A: nat] :
( ( collect_nat
@ ^ [B: nat] : ( B = A ) )
= ( insert_nat @ A @ bot_bot_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(34,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_add__right__cancel) ).
thf(477,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(210,axiom,
! [A: nat] :
( ( the_elem_nat @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_the__elem__eq) ).
thf(1080,plain,
! [A: nat] :
( ( the_elem_nat @ ( insert_nat @ A @ bot_bot_nat_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(345,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( bot_bo1791335050le_a_o
= ( image_1661191109iple_a @ A @ B ) )
= ( B = bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_empty__is__image) ).
thf(1557,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( bot_bo1791335050le_a_o
= ( image_1661191109iple_a @ A @ B ) )
= ( B = bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(36,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(483,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(280,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a] :
( ( finite114877549iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) @ C )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_fold1Set__sing) ).
thf(1325,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a] :
( ( finite114877549iple_a @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) @ C )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(177,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co2030419055_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_int @ ( A @ B ) @ ( big_co2030419055_a_int @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_setprod_Oinsert) ).
thf(964,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co2030419055_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_int @ ( A @ B ) @ ( big_co2030419055_a_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(80,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ! [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co917763874_a_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_setsum_Ocong) ).
thf(626,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ! [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co917763874_a_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(287,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ~ ( member290856304iple_a @ A @ B )
=> ( ( B != bot_bo1791335050le_a_o )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_folding__one_Oinsert) ).
thf(1344,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ~ ( member290856304iple_a @ A @ B )
=> ( ( B != bot_bo1791335050le_a_o )
=> ( ( D @ ( insert1597628439iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(237,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o
@ ^ [C: hoare_2091234717iple_a] : ( member290856304iple_a @ C @ A )
@ ^ [C: hoare_2091234717iple_a] : ( member290856304iple_a @ C @ B ) )
= ( ord_le35180118le_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_pred__subset__eq) ).
thf(1177,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o
@ ^ [C: hoare_2091234717iple_a] : ( member290856304iple_a @ C @ A )
@ ^ [C: hoare_2091234717iple_a] : ( member290856304iple_a @ C @ B ) )
= ( ord_le35180118le_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(219,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ? [B: hoare_2091234717iple_a] :
( ( A @ B )
& ! [C: hoare_2091234717iple_a] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_Ho1471183438iple_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_theI_H) ).
thf(1112,plain,
! [A: hoare_2091234717iple_a > $o] :
( ? [B: hoare_2091234717iple_a] :
( ( A @ B )
& ! [C: hoare_2091234717iple_a] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_Ho1471183438iple_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(129,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1393145363_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_nat @ ( A @ B ) @ ( big_co1393145363_a_nat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_setprod__insert) ).
thf(811,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1393145363_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_nat @ ( A @ B ) @ ( big_co1393145363_a_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(9,axiom,
! [A: nat > nat,B: nat > nat,C: nat > $o] :
( ( big_co387207925at_nat
@ ^ [D: nat] : ( plus_plus_nat @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus_nat @ ( big_co387207925at_nat @ A @ C ) @ ( big_co387207925at_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_setsum__addf) ).
thf(387,plain,
! [A: nat > nat,B: nat > nat,C: nat > $o] :
( ( big_co387207925at_nat
@ ^ [D: nat] : ( plus_plus_nat @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus_nat @ ( big_co387207925at_nat @ A @ C ) @ ( big_co387207925at_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(758,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(302,axiom,
! [A: com,B: x_a > state > $o,C: hoare_2091234717iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ E @ F ) @ bot_bo1791335050le_a_o ) )
=> ( ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ F @ A @ B ) @ bot_bo1791335050le_a_o ) )
=> ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ ( semi @ E @ A ) @ B ) @ bot_bo1791335050le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Comp) ).
thf(1396,plain,
! [A: com,B: x_a > state > $o,C: hoare_2091234717iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ E @ F ) @ bot_bo1791335050le_a_o ) )
=> ( ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ F @ A @ B ) @ bot_bo1791335050le_a_o ) )
=> ( hoare_1467856363rivs_a @ C @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ ( semi @ E @ A ) @ B ) @ bot_bo1791335050le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(13,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_setsum__insert) ).
thf(399,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(326,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ ( insert1597628439iple_a @ A @ B ) )
= ( finite232261744iple_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_finite__insert) ).
thf(1474,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ ( insert1597628439iple_a @ A @ B ) )
= ( finite232261744iple_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(203,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( finite232261744iple_a @ ( minus_836160335le_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_finite__Diff) ).
thf(1044,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( finite232261744iple_a @ ( minus_836160335le_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(122,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ( ord_le35180118le_a_o @ C @ A )
=> ( ( minus_836160335le_a_o @ C @ ( minus_836160335le_a_o @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_double__diff) ).
thf(780,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ( ord_le35180118le_a_o @ C @ A )
=> ( ( minus_836160335le_a_o @ C @ ( minus_836160335le_a_o @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(194,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( image_1661191109iple_a @ B @ C ) )
= ( ? [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_image__iff) ).
thf(1015,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( image_1661191109iple_a @ B @ C ) )
= ( ? [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_nat__add__commute) ).
thf(608,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(183,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ B )
= ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C = A )
| ( member290856304iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_insert__compr) ).
thf(986,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ B )
= ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C = A )
| ( member290856304iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(313,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite2010064629le_a_o @ D @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_comp__fun__commute_Ofold__insert__remove) ).
thf(1435,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( D @ B @ ( finite2010064629le_a_o @ D @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(327,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a] :
( ( finite1218641926iple_a @ A @ B @ C @ D )
= ( ( ( C = bot_bo1791335050le_a_o )
& ( D = B ) )
| ? [E: hoare_2091234717iple_a,F: hoare_2091234717iple_a > $o,G: hoare_2091234717iple_a] :
( ( C
= ( insert1597628439iple_a @ E @ F ) )
& ( D
= ( A @ E @ G ) )
& ~ ( member290856304iple_a @ E @ F )
& ( finite1218641926iple_a @ A @ B @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_fold__graph_Osimps) ).
thf(1477,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a] :
( ( finite1218641926iple_a @ A @ B @ C @ D )
= ( ( ( C = bot_bo1791335050le_a_o )
& ( D = B ) )
| ? [E: hoare_2091234717iple_a,F: hoare_2091234717iple_a > $o,G: hoare_2091234717iple_a] :
( ( C
= ( insert1597628439iple_a @ E @ F ) )
& ( D
= ( A @ E @ G ) )
& ~ ( member290856304iple_a @ E @ F )
& ( finite1218641926iple_a @ A @ B @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_add__mult__distrib2) ).
thf(438,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(88,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_com_Osimps_I3_J) ).
thf(653,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)],[88]) ).
thf(119,axiom,
! [A: nat,B: nat > $o] :
( bot_bot_nat_o
!= ( insert_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_empty__not__insert) ).
thf(768,plain,
! [A: nat,B: nat > $o] :
( bot_bot_nat_o
!= ( insert_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(135,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ~ ( member290856304iple_a @ B @ C )
=> ( ( ord_le35180118le_a_o @ C @ ( insert1597628439iple_a @ B @ A ) )
= ( ord_le35180118le_a_o @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_subset__insert) ).
thf(827,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ~ ( member290856304iple_a @ B @ C )
=> ( ( ord_le35180118le_a_o @ C @ ( insert1597628439iple_a @ B @ A ) )
= ( ord_le35180118le_a_o @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(336,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( image_1661191109iple_a @ A @ bot_bo1791335050le_a_o )
= bot_bo1791335050le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_image__empty) ).
thf(1528,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( image_1661191109iple_a @ A @ bot_bo1791335050le_a_o )
= bot_bo1791335050le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(147,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( ord_le35180118le_a_o @ A @ B )
=> ( finite232261744iple_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_rev__finite__subset) ).
thf(868,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( ord_le35180118le_a_o @ A @ B )
=> ( finite232261744iple_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(307,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) @ C )
=> ( ( member290856304iple_a @ B @ A )
=> ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_906_diff__single__insert) ).
thf(1413,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) @ C )
=> ( ( member290856304iple_a @ B @ A )
=> ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(357,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ A )
= ( ( A = bot_bo1791335050le_a_o )
| ? [B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( A
= ( insert1597628439iple_a @ C @ B ) )
& ( finite232261744iple_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_finite_Osimps) ).
thf(1626,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ A )
= ( ( A = bot_bo1791335050le_a_o )
| ? [B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( A
= ( insert1597628439iple_a @ C @ B ) )
& ( finite232261744iple_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(200,axiom,
! [A: nat > $o] :
( ( bot_bot_nat_o
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_empty__Collect__eq) ).
thf(1034,plain,
! [A: nat > $o] :
( ( bot_bot_nat_o
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(272,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( bot_bo1791335050le_a_o
= ( collec992574898iple_a @ A ) )
= ( ! [B: hoare_2091234717iple_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_empty__Collect__eq) ).
thf(1304,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( bot_bo1791335050le_a_o
= ( collec992574898iple_a @ A ) )
= ( ! [B: hoare_2091234717iple_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(245,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(1203,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(57,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(548,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(373,plain,
! [C: nat > $o,B: nat > nat,A: nat] :
( ( times_times_nat @ A @ ( big_co387207925at_nat @ B @ C ) )
= ( big_co387207925at_nat
@ ^ [D: nat] : ( times_times_nat @ A @ ( B @ D ) )
@ C ) ),
inference(cnf,[status(esa)],[372]) ).
thf(374,plain,
! [C: nat > $o,B: nat > nat,A: nat] :
( ( times_times_nat @ A @ ( big_co387207925at_nat @ B @ C ) )
= ( big_co387207925at_nat
@ ^ [D: nat] : ( times_times_nat @ A @ ( B @ D ) )
@ C ) ),
inference(lifteq,[status(thm)],[373]) ).
thf(170,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ord_le35180118le_a_o @ ( image_1661191109iple_a @ A @ B ) @ ( image_1661191109iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_image__mono) ).
thf(939,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ord_le35180118le_a_o @ ( image_1661191109iple_a @ A @ B ) @ ( image_1661191109iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(325,axiom,
! [A: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ bot_bo1791335050le_a_o @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_bot__least) ).
thf(1472,plain,
! [A: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ bot_bo1791335050le_a_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(195,axiom,
! [A: nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( image_1773322034_a_nat
@ ^ [D: hoare_2091234717iple_a] : A
@ C )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_image__constant) ).
thf(1018,plain,
! [A: nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( image_1773322034_a_nat
@ ^ [D: hoare_2091234717iple_a] : A
@ C )
= ( insert_nat @ A @ bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(115,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > hoare_2091234717iple_a,D: hoare_2091234717iple_a] :
( ( B
= ( C @ D ) )
=> ( ( member290856304iple_a @ D @ A )
=> ( member290856304iple_a @ B @ ( image_1661191109iple_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_image__eqI) ).
thf(754,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > hoare_2091234717iple_a,D: hoare_2091234717iple_a] :
( ( B
= ( C @ D ) )
=> ( ( member290856304iple_a @ D @ A )
=> ( member290856304iple_a @ B @ ( image_1661191109iple_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(138,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( insert1597628439iple_a @ ( A @ B ) @ ( image_1661191109iple_a @ A @ C ) )
= ( image_1661191109iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_insert__image) ).
thf(836,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ( insert1597628439iple_a @ ( A @ B ) @ ( image_1661191109iple_a @ A @ C ) )
= ( image_1661191109iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(77,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > $o,C: nat] :
( ( times_times_nat @ ( big_co917763874_a_nat @ A @ B ) @ C )
= ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( times_times_nat @ ( A @ D ) @ C )
@ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_setsum__left__distrib) ).
thf(617,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > $o,C: nat] :
( ( times_times_nat @ ( big_co917763874_a_nat @ A @ B ) @ C )
= ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( times_times_nat @ ( A @ D ) @ C )
@ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_left__add__mult__distrib) ).
thf(516,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(342,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( the_el13400124iple_a @ A )
= ( the_Ho1471183438iple_a
@ ^ [B: hoare_2091234717iple_a] :
( A
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_the__elem__def) ).
thf(1547,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( the_el13400124iple_a @ A )
= ( the_Ho1471183438iple_a
@ ^ [B: hoare_2091234717iple_a] :
( A
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(50,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_add__right__cancel) ).
thf(525,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(96,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( finite232261744iple_a @ ( minus_836160335le_a_o @ A @ B ) )
= ( finite232261744iple_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_finite__Diff2) ).
thf(690,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( finite232261744iple_a @ ( minus_836160335le_a_o @ A @ B ) )
= ( finite232261744iple_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(678,plain,
~ ? [A: nat,B: nat > $o] :
( ( insert_nat @ A @ B )
= bot_bot_nat_o ),
inference(miniscope,[status(thm)],[677]) ).
thf(679,plain,
! [B: nat > $o,A: nat] :
( ( insert_nat @ A @ B )
!= bot_bot_nat_o ),
inference(cnf,[status(esa)],[678]) ).
thf(680,plain,
! [B: nat > $o,A: nat] :
( ( insert_nat @ A @ B )
!= bot_bot_nat_o ),
inference(lifteq,[status(thm)],[679]) ).
thf(1743,plain,
! [B: nat > $o,A: nat] :
( ( insert_nat @ A @ B )
!= ( ^ [C: nat] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[680,716]) ).
thf(153,axiom,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(887,plain,
! [A: int,B: int,C: int,D: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(174,axiom,
! [A: vname,B: state > nat] :
( skip
!= ( ass @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_com_Osimps_I8_J) ).
thf(954,plain,
! [A: vname,B: state > nat] :
( skip
!= ( ass @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(295,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( ( A @ B )
=> ( ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo1791335050le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Collect__conv__if) ).
thf(1368,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( ( A @ B )
=> ( ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo1791335050le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(259,axiom,
finite232261744iple_a @ bot_bo1791335050le_a_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_finite_OemptyI) ).
thf(1267,plain,
finite232261744iple_a @ bot_bo1791335050le_a_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(337,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
=> ? [C: hoare_2091234717iple_a > $o] :
( ( B
= ( insert1597628439iple_a @ A @ C ) )
& ~ ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_mk__disjoint__insert) ).
thf(1531,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
=> ? [C: hoare_2091234717iple_a > $o] :
( ( B
= ( insert1597628439iple_a @ A @ C ) )
& ~ ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(60,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > $o] :
( ( C = D )
=> ( ! [E: hoare_2091234717iple_a] :
( ( member290856304iple_a @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co917763874_a_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_setsum__cong) ).
thf(557,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > $o] :
( ( C = D )
=> ( ! [E: hoare_2091234717iple_a] :
( ( member290856304iple_a @ E @ D )
=> ( ( A @ E )
= ( B @ E ) ) )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co917763874_a_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(189,axiom,
! [A: int > $o] :
( ( ( collect_int @ A )
= bot_bot_int_o )
= ( ! [B: int] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Collect__empty__eq) ).
thf(1003,plain,
! [A: int > $o] :
( ( ( collect_int @ A )
= bot_bot_int_o )
= ( ! [B: int] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1716,plain,
( ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_2091234717iple_a] : bot_bot_o
@ sk59 )
| bot_bot_o ),
inference(bool_ext,[status(thm)],[1714]) ).
thf(312,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ bot_bo1791335050le_a_o )
=> ( A = bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_le__bot) ).
thf(1432,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ bot_bo1791335050le_a_o )
=> ( A = bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(1186,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(25,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_combine__common__factor) ).
thf(441,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(104,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co1393145363_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( times_times_nat @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( times_times_nat @ ( big_co1393145363_a_nat @ A @ C ) @ ( big_co1393145363_a_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_setprod_Odistrib) ).
thf(717,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co1393145363_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( times_times_nat @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( times_times_nat @ ( big_co1393145363_a_nat @ A @ C ) @ ( big_co1393145363_a_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(358,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ bot_bo1791335050le_a_o @ A )
= bot_bo1791335050le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_empty__Diff) ).
thf(1629,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ bot_bo1791335050le_a_o @ A )
= bot_bo1791335050le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(1630,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ bot_bo1791335050le_a_o @ A )
= bot_bo1791335050le_a_o ),
inference(cnf,[status(esa)],[1629]) ).
thf(1631,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ bot_bo1791335050le_a_o @ A )
= bot_bo1791335050le_a_o ),
inference(lifteq,[status(thm)],[1630]) ).
thf(1785,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o
@ A )
= ( ^ [B: hoare_2091234717iple_a] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1631,1233]) ).
thf(257,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( ( ( member290856304iple_a @ B @ A )
=> ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) @ C ) )
& ( ~ ( member290856304iple_a @ B @ A )
=> ( ord_le35180118le_a_o @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_subset__insert__iff) ).
thf(1262,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( ( ( member290856304iple_a @ B @ A )
=> ( ord_le35180118le_a_o @ ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) @ C ) )
& ( ~ ( member290856304iple_a @ B @ A )
=> ( ord_le35180118le_a_o @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(30,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(463,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1350,plain,
~ ? [A: hoare_2091234717iple_a] : ( member290856304iple_a @ A @ bot_bo1791335050le_a_o ),
inference(miniscope,[status(thm)],[1349]) ).
thf(1351,plain,
! [A: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ A @ bot_bo1791335050le_a_o ),
inference(cnf,[status(esa)],[1350]) ).
thf(1679,plain,
! [A: hoare_2091234717iple_a] :
~ ( member290856304iple_a @ A
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o ),
inference(rewrite,[status(thm)],[1351,1233]) ).
thf(222,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_insert__commute) ).
thf(1130,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
= ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(250,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( finite114877549iple_a @ A @ B @ C )
=> ( B != bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_fold1Set__nonempty) ).
thf(1218,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a] :
( ( finite114877549iple_a @ A @ B @ C )
=> ( B != bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(284,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( ( collec992574898iple_a @ A )
= bot_bo1791335050le_a_o )
= ( ! [B: hoare_2091234717iple_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Collect__empty__eq) ).
thf(1336,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( ( collec992574898iple_a @ A )
= bot_bo1791335050le_a_o )
= ( ! [B: hoare_2091234717iple_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(160,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( image_1661191109iple_a
@ ^ [B: hoare_2091234717iple_a] : B
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_image__ident) ).
thf(907,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( image_1661191109iple_a
@ ^ [B: hoare_2091234717iple_a] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(206,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( finite2010064629le_a_o @ D @ ( D @ B @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_comp__fun__commute_Ofold__insert2) ).
thf(1053,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( finite2010064629le_a_o @ D @ ( D @ B @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(173,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite2106937597iple_a @ A @ B )
= ( the_Ho1471183438iple_a @ ( finite114877549iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_fold1__def) ).
thf(951,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite2106937597iple_a @ A @ B )
= ( the_Ho1471183438iple_a @ ( finite114877549iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(128,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ C )
= ( D @ B @ ( finite2010064629le_a_o @ D @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_comp__fun__commute_Ofold__rec) ).
thf(808,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ C )
= ( D @ B @ ( finite2010064629le_a_o @ D @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(112,axiom,
! [A: vname,B: state > nat,C: com,D: com] :
( ( ass @ A @ B )
!= ( semi @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_com_Osimps_I24_J) ).
thf(744,plain,
! [A: vname,B: state > nat,C: com,D: com] :
( ( ass @ A @ B )
!= ( semi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(89,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ C )
=> ( ( finite232261744iple_a @ B )
=> ( finite1003551991le_a_o @ C @ A @ B @ ( finite2010064629le_a_o @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_comp__fun__commute_Ofold__graph__fold) ).
thf(656,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite2078358188le_a_o @ C )
=> ( ( finite232261744iple_a @ B )
=> ( finite1003551991le_a_o @ C @ A @ B @ ( finite2010064629le_a_o @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(145,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( finite232261744iple_a @ ( image_1661191109iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_finite__imageI) ).
thf(864,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( finite232261744iple_a @ ( image_1661191109iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(215,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ ( image_1661191109iple_a @ B @ C ) )
= ( ? [D: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ D @ C )
& ( A
= ( image_1661191109iple_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_877_subset__image__iff) ).
thf(1094,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ A @ ( image_1661191109iple_a @ B @ C ) )
= ( ? [D: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ D @ C )
& ( A
= ( image_1661191109iple_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(191,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(1008,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(63,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_zadd__assoc) ).
thf(571,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(143,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a] :
( ( finite1218641926iple_a @ A @ B @ C @ D )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( finite114877549iple_a @ A @ ( insert1597628439iple_a @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_fold1Set_Ointros) ).
thf(859,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a] :
( ( finite1218641926iple_a @ A @ B @ C @ D )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( finite114877549iple_a @ A @ ( insert1597628439iple_a @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(255,axiom,
! [A: hoare_2091234717iple_a > $o,B: x_a > state > $o,C: com,D: x_a > state > $o,E: $o] :
( ( E
=> ( hoare_1467856363rivs_a @ A @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ B @ C @ D ) @ bot_bo1791335050le_a_o ) ) )
=> ( hoare_1467856363rivs_a @ A
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [F: x_a,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo1791335050le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_constant) ).
thf(1240,plain,
! [A: hoare_2091234717iple_a > $o,B: x_a > state > $o,C: com,D: x_a > state > $o,E: $o] :
( ( E
=> ( hoare_1467856363rivs_a @ A @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ B @ C @ D ) @ bot_bo1791335050le_a_o ) ) )
=> ( hoare_1467856363rivs_a @ A
@ ( insert1597628439iple_a
@ ( hoare_657976383iple_a
@ ^ [F: x_a,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo1791335050le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(226,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_setsum_Oremove) ).
thf(1141,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(338,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( ( image_1661191109iple_a @ A @ B )
= bot_bo1791335050le_a_o )
= ( B = bot_bo1791335050le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_image__is__empty) ).
thf(1536,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( ( image_1661191109iple_a @ A @ B )
= bot_bo1791335050le_a_o )
= ( B = bot_bo1791335050le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(309,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( minus_836160335le_a_o @ ( minus_836160335le_a_o @ A @ C ) @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_Diff__insert) ).
thf(1421,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( minus_836160335le_a_o @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( minus_836160335le_a_o @ ( minus_836160335le_a_o @ A @ C ) @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(320,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( finite186236040iple_a @ A @ B @ bot_bo1791335050le_a_o )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_fold__empty) ).
thf(1459,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a] :
( ( finite186236040iple_a @ A @ B @ bot_bo1791335050le_a_o )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(238,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) )
=> ~ ( ( member290856304iple_a @ A @ B )
=> ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_DiffE) ).
thf(1180,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) )
=> ~ ( ( member290856304iple_a @ A @ B )
=> ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(54,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(539,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(92,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ E )
=> ( ( finite1218641926iple_a @ E @ B @ C @ D )
=> ( ( finite1218641926iple_a @ E @ B @ C @ A )
=> ( A = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_comp__fun__commute_Ofold__graph__determ) ).
thf(671,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ E )
=> ( ( finite1218641926iple_a @ E @ B @ C @ D )
=> ( ( finite1218641926iple_a @ E @ B @ C @ A )
=> ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(278,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ord_le35180118le_a_o @ B @ ( insert1597628439iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_subset__insertI2) ).
thf(1321,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ord_le35180118le_a_o @ B @ ( insert1597628439iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(180,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite186236040iple_a @ A @ B @ C )
= ( the_Ho1471183438iple_a @ ( finite1218641926iple_a @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_fold__def) ).
thf(976,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite186236040iple_a @ A @ B @ C )
= ( the_Ho1471183438iple_a @ ( finite1218641926iple_a @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(66,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co917763874_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_setsum_Oinsert__remove) ).
thf(581,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co917763874_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_nat @ ( A @ B ) @ ( big_co917763874_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1529,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( image_1661191109iple_a @ A @ bot_bo1791335050le_a_o )
= bot_bo1791335050le_a_o ),
inference(cnf,[status(esa)],[1528]) ).
thf(1530,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( image_1661191109iple_a @ A @ bot_bo1791335050le_a_o )
= bot_bo1791335050le_a_o ),
inference(lifteq,[status(thm)],[1529]) ).
thf(1781,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( image_1661191109iple_a @ A
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o )
= ( ^ [B: hoare_2091234717iple_a] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[1530,1233]) ).
thf(221,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( ( finite232261744iple_a @ ( collec992574898iple_a @ B ) )
| ( finite232261744iple_a @ ( collec992574898iple_a @ A ) ) )
=> ( finite232261744iple_a
@ ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_finite__Collect__conjI) ).
thf(1126,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o] :
( ( ( finite232261744iple_a @ ( collec992574898iple_a @ B ) )
| ( finite232261744iple_a @ ( collec992574898iple_a @ A ) ) )
=> ( finite232261744iple_a
@ ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(241,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
= ( minus_minus_int @ ( big_co1555037566_a_int @ A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_setsum__diff1__ring) ).
thf(1189,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
= ( minus_minus_int @ ( big_co1555037566_a_int @ A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(301,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ~ ( member290856304iple_a @ B @ C )
=> ( B = A ) )
=> ( member290856304iple_a @ B @ ( insert1597628439iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_insertCI) ).
thf(1390,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ~ ( member290856304iple_a @ B @ C )
=> ( B = A ) )
=> ( member290856304iple_a @ B @ ( insert1597628439iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(40,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_zdiff__zmult__distrib2) ).
thf(495,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(367,axiom,
! [A: x_a > state > $o,B: hoare_2091234717iple_a > $o,C: com,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ? [G: x_a > state > $o,H: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ G @ C @ H ) @ bot_bo1791335050le_a_o ) )
& ! [I: state] :
( ! [J: x_a] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ C @ A ) @ bot_bo1791335050le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_conseq) ).
thf(1654,plain,
! [A: x_a > state > $o,B: hoare_2091234717iple_a > $o,C: com,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ? [G: x_a > state > $o,H: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ G @ C @ H ) @ bot_bo1791335050le_a_o ) )
& ! [I: state] :
( ! [J: x_a] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ D @ C @ A ) @ bot_bo1791335050le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(317,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a] : ( finite1218641926iple_a @ A @ B @ bot_bo1791335050le_a_o @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_fold__graph_OemptyI) ).
thf(1453,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a] : ( finite1218641926iple_a @ A @ B @ bot_bo1791335050le_a_o @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(351,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co2030419055_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_int @ ( A @ B ) @ ( big_co2030419055_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_setprod_Oinsert__remove) ).
thf(1590,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co2030419055_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_int @ ( A @ B ) @ ( big_co2030419055_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(99,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_mem__def) ).
thf(699,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(176,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite438582129le_a_o @ C )
=> ( ( C @ A @ ( C @ A @ B ) )
= ( C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_comp__fun__idem_Ofun__left__idem) ).
thf(961,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite438582129le_a_o @ C )
=> ( ( C @ A @ ( C @ A @ B ) )
= ( C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(10,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_zadd__commute) ).
thf(390,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(81,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(632,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ B ) )
= ( times_times_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(256,axiom,
! [A: ( hoare_2091234717iple_a > $o ) > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( A @ B )
=> ( ! [C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ D )
=> ( ( member290856304iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_836160335le_a_o @ D @ ( insert1597628439iple_a @ C @ bot_bo1791335050le_a_o ) ) ) ) ) )
=> ( A @ bot_bo1791335050le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_finite__empty__induct) ).
thf(1244,plain,
! [A: ( hoare_2091234717iple_a > $o ) > $o,B: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ B )
=> ( ( A @ B )
=> ( ! [C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ D )
=> ( ( member290856304iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( minus_836160335le_a_o @ D @ ( insert1597628439iple_a @ C @ bot_bo1791335050le_a_o ) ) ) ) ) )
=> ( A @ bot_bo1791335050le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(186,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(995,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(286,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co1393145363_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_nat @ ( A @ B ) @ ( big_co1393145363_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_setprod_Oinsert__remove) ).
thf(1341,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co1393145363_a_nat @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( times_times_nat @ ( A @ B ) @ ( big_co1393145363_a_nat @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(896,plain,
! [A: nat,B: nat] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(113,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(748,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(107,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ( member290856304iple_a @ A @ B )
=> ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_subsetD) ).
thf(731,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ( member290856304iple_a @ A @ B )
=> ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(124,axiom,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Collect__conv__if) ).
thf(786,plain,
! [A: nat > $o,B: nat] :
( ( ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_nat @ B @ bot_bot_nat_o ) ) )
& ( ~ ( A @ B )
=> ( ( collect_nat
@ ^ [C: nat] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(330,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ ( insert1597628439iple_a @ A @ B ) )
= ( insert1597628439iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_insert__absorb2) ).
thf(1491,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ ( insert1597628439iple_a @ A @ B ) )
= ( insert1597628439iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(62,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_setsum_Oinsert) ).
thf(568,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(510,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(248,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite438582129le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( finite2010064629le_a_o @ D @ ( D @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_comp__fun__idem_Ofold__insert__idem2) ).
thf(1212,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a > $o] :
( ( finite438582129le_a_o @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( finite2010064629le_a_o @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( finite2010064629le_a_o @ D @ ( D @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(157,axiom,
! [A: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ A )
=> ( finite1829014797le_a_o
@ ( collec1008234059le_a_o
@ ^ [B: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_finite__Collect__subsets) ).
thf(899,plain,
! [A: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ A )
=> ( finite1829014797le_a_o
@ ( collec1008234059le_a_o
@ ^ [B: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ~ ( fequal_nat @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(536,plain,
! [A: nat,B: nat] :
( ~ ( fequal_nat @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(269,axiom,
! [A: x_a > state > $o,B: hoare_2091234717iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ C @ D @ E ) @ bot_bo1791335050le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ A @ D @ E ) @ bot_bo1791335050le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_conseq1) ).
thf(1294,plain,
! [A: x_a > state > $o,B: hoare_2091234717iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ C @ D @ E ) @ bot_bo1791335050le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_1467856363rivs_a @ B @ ( insert1597628439iple_a @ ( hoare_657976383iple_a @ A @ D @ E ) @ bot_bo1791335050le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(233,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
= ( minus_minus_int @ ( big_co1555037566_a_int @ A @ C ) @ ( A @ B ) ) ) )
& ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
= ( big_co1555037566_a_int @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_setsum__diff1) ).
thf(1161,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
= ( minus_minus_int @ ( big_co1555037566_a_int @ A @ C ) @ ( A @ B ) ) ) )
& ( ~ ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
= ( big_co1555037566_a_int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(223,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ~ ( member290856304iple_a @ B @ A )
=> ( member290856304iple_a @ B @ ( minus_836160335le_a_o @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_DiffI) ).
thf(1133,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ B @ C )
=> ( ~ ( member290856304iple_a @ B @ A )
=> ( member290856304iple_a @ B @ ( minus_836160335le_a_o @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(78,axiom,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1089_zdiff__zmult__distrib) ).
thf(620,plain,
! [A: int,B: int,C: int] :
( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(363,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) )
= ( insert1597628439iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_insert__Diff__single) ).
thf(1642,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ ( minus_836160335le_a_o @ B @ ( insert1597628439iple_a @ A @ bot_bo1791335050le_a_o ) ) )
= ( insert1597628439iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(27,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_add__left__imp__eq) ).
thf(447,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(22,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co387207925at_nat
@ ^ [D: nat] :
( big_co917763874_a_nat @ A
@ ( collec992574898iple_a
@ ^ [E: hoare_2091234717iple_a] :
( ( member290856304iple_a @ E @ C )
& ( ( B @ E )
= D ) ) ) )
@ ( image_1773322034_a_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_setsum__image__gen) ).
thf(432,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co387207925at_nat
@ ^ [D: nat] :
( big_co917763874_a_nat @ A
@ ( collec992574898iple_a
@ ^ [E: hoare_2091234717iple_a] :
( ( member290856304iple_a @ E @ C )
& ( ( B @ E )
= D ) ) ) )
@ ( image_1773322034_a_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(216,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ? [C: hoare_2091234717iple_a] :
( ( B @ C )
& ! [D: hoare_2091234717iple_a] :
( ( B @ D )
=> ( D = C ) ) )
=> ( ( B @ A )
=> ( ( the_Ho1471183438iple_a @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_the1__equality) ).
thf(1097,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ? [C: hoare_2091234717iple_a] :
( ( B @ C )
& ! [D: hoare_2091234717iple_a] :
( ( B @ D )
=> ( D = C ) ) )
=> ( ( B @ A )
=> ( ( the_Ho1471183438iple_a @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(352,axiom,
! [A: ( hoare_2091234717iple_a > $o ) > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( ord_le35180118le_a_o @ C @ B )
=> ( ( A @ bot_bo1791335050le_a_o )
=> ( ! [D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ E )
=> ( ( member290856304iple_a @ D @ B )
=> ( ~ ( member290856304iple_a @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert1597628439iple_a @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_finite__subset__induct) ).
thf(1593,plain,
! [A: ( hoare_2091234717iple_a > $o ) > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( ord_le35180118le_a_o @ C @ B )
=> ( ( A @ bot_bo1791335050le_a_o )
=> ( ! [D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ E )
=> ( ( member290856304iple_a @ D @ B )
=> ( ~ ( member290856304iple_a @ D @ E )
=> ( ( A @ E )
=> ( A @ ( insert1597628439iple_a @ D @ E ) ) ) ) ) )
=> ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_add__imp__eq) ).
thf(405,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(328,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( ( A @ B )
=> ( ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo1791335050le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Collect__conv__if2) ).
thf(1480,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( ( A @ B )
=> ( ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec992574898iple_a
@ ^ [C: hoare_2091234717iple_a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo1791335050le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(109,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(735,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(137,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( finite186236040iple_a @ D @ ( D @ B @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_comp__fun__commute_Ofold__insert2) ).
thf(833,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ( ( finite186236040iple_a @ D @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( finite186236040iple_a @ D @ ( D @ B @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(16,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_diff__eq__diff__eq) ).
thf(410,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(178,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a] :
( ( finite114877549iple_a @ A @ ( insert1597628439iple_a @ B @ C ) @ D )
=> ~ ! [E: hoare_2091234717iple_a,F: hoare_2091234717iple_a > $o] :
( ( ( insert1597628439iple_a @ B @ C )
= ( insert1597628439iple_a @ E @ F ) )
=> ( ( finite1218641926iple_a @ A @ E @ F @ D )
=> ( member290856304iple_a @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_insert__fold1SetE) ).
thf(967,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a] :
( ( finite114877549iple_a @ A @ ( insert1597628439iple_a @ B @ C ) @ D )
=> ~ ! [E: hoare_2091234717iple_a,F: hoare_2091234717iple_a > $o] :
( ( ( insert1597628439iple_a @ B @ C )
= ( insert1597628439iple_a @ E @ F ) )
=> ( ( finite1218641926iple_a @ A @ E @ F @ D )
=> ( member290856304iple_a @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(207,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( A @ B )
=> ( ! [C: hoare_2091234717iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_Ho1471183438iple_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_theI) ).
thf(1056,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( A @ B )
=> ( ! [C: hoare_2091234717iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_Ho1471183438iple_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_add__mult__distrib) ).
thf(635,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(98,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( finite186236040iple_a @ D @ A @ C )
= ( D @ B @ ( finite186236040iple_a @ D @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_comp__fun__commute_Ofold__rec) ).
thf(696,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( finite186236040iple_a @ D @ A @ C )
= ( D @ B @ ( finite186236040iple_a @ D @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(105,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ( member290856304iple_a @ B @ C )
=> ( ( minus_836160335le_a_o @ ( insert1597628439iple_a @ B @ A ) @ C )
= ( minus_836160335le_a_o @ A @ C ) ) )
& ( ~ ( member290856304iple_a @ B @ C )
=> ( ( minus_836160335le_a_o @ ( insert1597628439iple_a @ B @ A ) @ C )
= ( insert1597628439iple_a @ B @ ( minus_836160335le_a_o @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_insert__Diff__if) ).
thf(720,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( ( member290856304iple_a @ B @ C )
=> ( ( minus_836160335le_a_o @ ( insert1597628439iple_a @ B @ A ) @ C )
= ( minus_836160335le_a_o @ A @ C ) ) )
& ( ~ ( member290856304iple_a @ B @ C )
=> ( ( minus_836160335le_a_o @ ( insert1597628439iple_a @ B @ A ) @ C )
= ( insert1597628439iple_a @ B @ ( minus_836160335le_a_o @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(33,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_crossproduct__noteq) ).
thf(474,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( C != D )
& ( A != B ) )
= ( ( plus_plus_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ D @ B ) )
!= ( plus_plus_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(306,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( insert1597628439iple_a @ B @ ( insert1597628439iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_insert__commute) ).
thf(1410,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ ( insert1597628439iple_a @ B @ C ) )
= ( insert1597628439iple_a @ B @ ( insert1597628439iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(139,axiom,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_com_Osimps_I13_J) ).
thf(839,plain,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(106,axiom,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ C )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_setsum_Oremove) ).
thf(728,plain,
! [A: hoare_2091234717iple_a > int,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o] :
( ( finite232261744iple_a @ C )
=> ( ( member290856304iple_a @ B @ C )
=> ( ( big_co1555037566_a_int @ A @ C )
= ( plus_plus_int @ ( A @ B ) @ ( big_co1555037566_a_int @ A @ ( minus_836160335le_a_o @ C @ ( insert1597628439iple_a @ B @ bot_bo1791335050le_a_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(290,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] : ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_subset__insertI) ).
thf(1352,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] : ( ord_le35180118le_a_o @ A @ ( insert1597628439iple_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(71,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ! [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co917763874_a_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_setsum__cong2) ).
thf(596,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ! [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) )
=> ( ( big_co917763874_a_nat @ A @ C )
= ( big_co917763874_a_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(51,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_add__imp__eq) ).
thf(528,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(292,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ B )
!= bot_bo1791335050le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insert__not__empty) ).
thf(1357,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ( insert1597628439iple_a @ A @ B )
!= bot_bo1791335050le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(185,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ B @ C )
=> ( ( finite232261744iple_a @ A )
=> ( ( C @ A )
= ( finite2106937597iple_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_folding__one_Oeq__fold) ).
thf(992,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,C: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite247037978iple_a @ B @ C )
=> ( ( finite232261744iple_a @ A )
=> ( ( C @ A )
= ( finite2106937597iple_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(142,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( A @ B )
=> ( ! [C: hoare_2091234717iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_Ho1471183438iple_a @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_the__equality) ).
thf(850,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a] :
( ( A @ B )
=> ( ! [C: hoare_2091234717iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_Ho1471183438iple_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(182,axiom,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ~ ( finite232261744iple_a @ B )
=> ( ( finite232261744iple_a @ ( image_1661191109iple_a @ A @ B ) )
=> ? [C: hoare_2091234717iple_a] :
( ( member290856304iple_a @ C @ B )
& ~ ( finite232261744iple_a
@ ( collec992574898iple_a
@ ^ [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_pigeonhole__infinite) ).
thf(982,plain,
! [A: hoare_2091234717iple_a > hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] :
( ~ ( finite232261744iple_a @ B )
=> ( ( finite232261744iple_a @ ( image_1661191109iple_a @ A @ B ) )
=> ? [C: hoare_2091234717iple_a] :
( ( member290856304iple_a @ C @ B )
& ~ ( finite232261744iple_a
@ ( collec992574898iple_a
@ ^ [D: hoare_2091234717iple_a] :
( ( member290856304iple_a @ D @ B )
& ( ( A @ D )
= ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(355,axiom,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( hoare_1467856363rivs_a @ B @ C )
=> ( ( ord_le35180118le_a_o @ A @ C )
=> ( hoare_1467856363rivs_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_889_weaken) ).
thf(1621,plain,
! [A: hoare_2091234717iple_a > $o,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( hoare_1467856363rivs_a @ B @ C )
=> ( ( ord_le35180118le_a_o @ A @ C )
=> ( hoare_1467856363rivs_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(42,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_crossproduct__eq) ).
thf(501,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) )
= ( ( A = C )
| ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(230,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) )
= ( ( member290856304iple_a @ A @ B )
& ~ ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_Diff__iff) ).
thf(1152,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( member290856304iple_a @ A @ ( minus_836160335le_a_o @ B @ C ) )
= ( ( member290856304iple_a @ A @ B )
& ~ ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_add__left__imp__eq) ).
thf(427,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(85,axiom,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( plus_plus_nat @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus_nat @ ( big_co917763874_a_nat @ A @ C ) @ ( big_co917763874_a_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_setsum__addf) ).
thf(644,plain,
! [A: hoare_2091234717iple_a > nat,B: hoare_2091234717iple_a > nat,C: hoare_2091234717iple_a > $o] :
( ( big_co917763874_a_nat
@ ^ [D: hoare_2091234717iple_a] : ( plus_plus_nat @ ( A @ D ) @ ( B @ D ) )
@ C )
= ( plus_plus_nat @ ( big_co917763874_a_nat @ A @ C ) @ ( big_co917763874_a_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(343,axiom,
! [A: hoare_2091234717iple_a] :
~ ! [B: x_a > state > $o,C: com,D: x_a > state > $o] :
( A
!= ( hoare_657976383iple_a @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_triple_Oexhaust) ).
thf(1550,plain,
! [A: hoare_2091234717iple_a] :
~ ! [B: x_a > state > $o,C: com,D: x_a > state > $o] :
( A
!= ( hoare_657976383iple_a @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(486,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1473,plain,
! [A: hoare_2091234717iple_a > $o] : ( ord_le35180118le_a_o @ bot_bo1791335050le_a_o @ A ),
inference(cnf,[status(esa)],[1472]) ).
thf(1737,plain,
! [A: hoare_2091234717iple_a > $o] :
( ord_le35180118le_a_o
@ ^ [B: hoare_2091234717iple_a] : bot_bot_o
@ A ),
inference(rewrite,[status(thm)],[1473,1233]) ).
thf(213,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite1218641926iple_a @ D @ A @ B @ C )
=> ( ( finite186236040iple_a @ D @ A @ B )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_comp__fun__commute_Ofold__equality) ).
thf(1088,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a,D: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ D )
=> ( ( finite1218641926iple_a @ D @ A @ B @ C )
=> ( ( finite186236040iple_a @ D @ A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(323,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] : ( member290856304iple_a @ A @ ( insert1597628439iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_insertI1) ).
thf(1468,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o] : ( member290856304iple_a @ A @ ( insert1597628439iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(101,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( member290856304iple_a @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_folding__one__idem_Oin__idem) ).
thf(708,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a,D: ( hoare_2091234717iple_a > $o ) > hoare_2091234717iple_a] :
( ( finite1674555159iple_a @ C @ D )
=> ( ( finite232261744iple_a @ B )
=> ( ( member290856304iple_a @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1681,plain,
( finite232261744iple_a
@ ^ [A: hoare_2091234717iple_a] : bot_bot_o ),
inference(rewrite,[status(thm)],[1267,1233]) ).
thf(239,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ( member290856304iple_a @ A @ B )
=> ( member290856304iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_set__mp) ).
thf(1184,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ B @ C )
=> ( ( member290856304iple_a @ A @ B )
=> ( member290856304iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(201,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ ( insert1597628439iple_a @ A @ B ) @ C )
= ( ( member290856304iple_a @ A @ C )
& ( ord_le35180118le_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_insert__subset) ).
thf(1037,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a > $o,C: hoare_2091234717iple_a > $o] :
( ( ord_le35180118le_a_o @ ( insert1597628439iple_a @ A @ B ) @ C )
= ( ( member290856304iple_a @ A @ C )
& ( ord_le35180118le_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(121,axiom,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ E )
=> ( ( finite1218641926iple_a @ E @ A @ ( insert1597628439iple_a @ B @ C ) @ D )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ~ ! [F: hoare_2091234717iple_a] :
( ( D
= ( E @ B @ F ) )
=> ~ ( finite1218641926iple_a @ E @ A @ C @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_comp__fun__commute_Ofold__graph__insertE) ).
thf(775,plain,
! [A: hoare_2091234717iple_a,B: hoare_2091234717iple_a,C: hoare_2091234717iple_a > $o,D: hoare_2091234717iple_a,E: hoare_2091234717iple_a > hoare_2091234717iple_a > hoare_2091234717iple_a] :
( ( finite408405521iple_a @ E )
=> ( ( finite1218641926iple_a @ E @ A @ ( insert1597628439iple_a @ B @ C ) @ D )
=> ( ~ ( member290856304iple_a @ B @ C )
=> ~ ! [F: hoare_2091234717iple_a] :
( ( D
= ( E @ B @ F ) )
=> ~ ( finite1218641926iple_a @ E @ A @ C @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(2825,plain,
$false,
inference(e,[status(thm)],[1024,1237,1031,893,1315,1083,941,1554,1200,1158,1406,1522,1618,1401,741,1544,861,1173,614,677,1497,384,1275,1233,814,913,1354,930,1458,670,1310,533,1001,1441,1645,1386,565,1265,1623,973,1046,1298,372,504,1330,802,1455,1462,949,587,1323,702,751,542,460,817,638,1379,1147,870,1013,1568,1641,1494,1347,1572,1741,1398,416,1415,924,1714,1450,623,1682,1283,821,480,492,1465,1040,1109,1632,1383,574,602,1215,877,866,396,998,507,1564,1651,380,1438,761,381,1470,1067,714,1206,452,1223,1091,1021,1519,1123,1570,424,693,1560,1387,910,916,847,1365,435,1195,551,1281,1291,1106,522,830,519,874,1270,650,1328,1672,1006,1138,593,783,989,1234,1541,471,1683,884,1028,1361,933,554,1739,1424,489,590,1155,901,1075,393,647,1150,738,1539,1231,1192,1050,1429,1715,371,605,1525,1333,1318,1086,805,921,1170,1286,674,1663,1167,794,1278,513,1680,824,1273,1301,444,1135,1648,375,733,584,819,904,402,1615,843,772,958,413,577,711,545,1488,641,936,1707,1312,611,498,1635,466,919,1638,1209,681,1349,377,1144,880,1376,1307,863,764,979,1011,419,890,477,1080,1557,483,1325,964,626,1344,1177,1112,811,387,758,1339,1396,399,1474,1044,780,1015,608,986,1435,1477,438,653,658,768,827,1528,868,1413,1626,1034,1304,1203,548,374,939,1472,1018,754,836,617,516,1547,525,690,1743,887,954,1368,1267,1531,557,1003,1716,1432,1186,441,717,1785,1262,463,1679,1130,1218,1336,907,1711,1053,951,808,744,656,864,1094,1008,571,859,1240,1141,1536,1421,1459,1180,539,671,1321,976,581,1781,1126,1189,1390,495,1654,368,1453,1590,699,961,390,1629,632,1244,995,1341,896,748,731,786,1491,568,378,510,1212,899,536,667,1294,716,1161,1133,620,1642,447,432,1097,1593,405,1480,735,833,410,967,1056,635,696,720,474,1410,839,728,1352,1268,596,528,1357,992,850,982,1621,501,369,1152,427,644,1550,486,1737,1088,1468,708,1681,1184,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW470^3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n005.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:04:46 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.08/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.29/1.42 % [INFO] Parsing done (611ms).
% 3.29/1.44 % [INFO] Running in sequential loop mode.
% 4.55/1.83 % [INFO] eprover registered as external prover.
% 4.55/1.83 % [INFO] Scanning for conjecture ...
% 5.23/2.05 % [INFO] Found a conjecture (or negated_conjecture) and 1207 axioms. Running axiom selection ...
% 5.81/2.25 % [INFO] Axiom selection finished. Selected 365 axioms (removed 842 axioms).
% 6.65/2.45 % [INFO] Problem is higher-order (TPTP THF).
% 6.65/2.47 % [INFO] Type checking passed.
% 6.65/2.47 % [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 ...
% 32.70/7.45 % External prover 'e' found a proof!
% 32.70/7.45 % [INFO] Killing All external provers ...
% 32.70/7.45 % Time passed: 7107ms (effective reasoning time: 6006ms)
% 32.70/7.45 % 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)>
% 32.70/7.46 % Axioms used in derivation (365): fact_206_image__empty, fact_686_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_67_insert__commute, fact_235_image__constant, fact_4_constant, fact_107_bot__apply, fact_681_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_318_finite__induct, fact_223_image__insert, fact_497_comp__fun__commute_Ofold__equality, fact_530_setsum__right__distrib, fact_424_insert__Diff, fact_76_insert__compr, fact_72_insert__Collect, fact_674_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, help_If_3_1_If_000tc__Nat__Onat_T, fact_920_finite__subset__image, fact_36_empty__iff, fact_27_Collect__conv__if, fact_797_set__rev__mp, fact_150_image__constant__conv, fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_397_Diff__cancel, fact_1088_zmult__commute, fact_19_singleton__conv2, fact_661_add__right__cancel, fact_35_Collect__empty__eq, fact_507_comp__fun__commute_Ofold__insert2, fact_201_com_Osimps_I9_J, fact_360_folding__one_Oinsert__remove, fact_421_Diff__insert__absorb, fact_64_insert__iff, fact_691_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_88_singletonE, fact_106_bot__apply, fact_1050_nat__add__left__commute, fact_697_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_82_insert__compr__raw, fact_499_fold__empty, fact_118_mk__disjoint__insert, fact_6_conseq2, fact_370_finite__Diff, fact_220_image__insert, fact_367_DiffE, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_394_Diff__empty, fact_1051_nat__add__commute, fact_193_com_Osimps_I25_J, fact_455_comp__fun__idem__insert, fact_164_fold1__def, fact_1089_zdiff__zmult__distrib, fact_407_insert__Diff1, fact_868_insert__subset, fact_683_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_94_singleton__iff, fact_659_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_336_theI, fact_309_insert__fold1SetE, fact_845_bot__least, fact_708_setsum__cong, fact_3_hoare__derivs_Oinsert, fact_916_subsetI, fact_5_escape, fact_476_setprod_Oremove, fact_692_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_492_setsum__commute, fact_705_setsum__cong2, fact_1053_add__mult__distrib, fact_190_image__ident, fact_1046_nat__mult__commute, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_, fact_1093_zadd__commute, fact_649_combine__common__factor, fact_464_setsum__diff1__ring, fact_553_setprod__insert, fact_0_empty, fact_640_setsum_Oinsert, fact_651_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_851_finite__subset, fact_481_comp__fun__commute_Ofold__fun__comm, fact_388_DiffD2, fact_385_DiffD1, fact_73_insert__Collect, fact_279_finite_OemptyI, fact_850_subset__empty, fact_733_pred__subset__eq, fact_694_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_628_setsum__addf, fact_270_folding__one_Oeq__fold, fact_1090_zdiff__zmult__distrib2, fact_646_add__diff__cancel, fact_200_Collect__def, fact_345_fold__graph_Osimps, fact_110_bot__fun__def, fact_648_crossproduct__eq, fact_700_comm__semiring__class_Odistrib, fact_431_folding__one__idem_Oin__idem, fact_610_setsum_Oremove, fact_351_finite__ne__induct, fact_274_folding__one_Oclosed, fact_112_Comp, fact_199_Collect__def, fact_311_finite__nonempty__imp__fold1Set, fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_1096_zadd__zmult__distrib, fact_537_comp__fun__commute_Ofold__graph__determ, fact_99_empty__not__insert, fact_418_insert__Diff__single, fact_215_insert__image, fact_147_fold1__singleton__def, fact_467_setprod_Oinsert__remove, fact_111_hoare__derivs_OSkip, fact_1048_nat__add__left__cancel, fact_490_setsum__commute, fact_134_fold1Set__sing, fact_695_diff__eq__diff__eq, fact_127_com_Osimps_I13_J, fact_34_Collect__empty__eq, fact_415_Diff__insert2, fact_684_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_1091_zadd__assoc, fact_675_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_616_setsum__diff1_H, fact_8_conseq12, fact_2_cut, fact_15_emptyE, fact_696_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_374_folding__one__idem_Oidem, fact_508_comp__fun__commute_Ofold__insert2, fact_333_fold1Set_Osimps, fact_21_singleton__conv, fact_320_pigeonhole__infinite, fact_624_setsum_Oinsert__remove, fact_941_Collect__mono, fact_687_ab__semigroup__mult__class_Omult__ac_I1_J, fact_862_subset__insertI2, fact_557_setprod_Oinsert, fact_85_singleton__inject, fact_673_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_529_setsum__left__distrib, fact_302_empty__fold__graphE, fact_52_insert__absorb, fact_440_finite__empty__induct, fact_1095_zadd__zmult__distrib2, fact_30_equals0D, fact_578_comp__fun__idem_Ofold__insert__idem, fact_636_setsum__insert, fact_194_com_Osimps_I8_J, fact_652_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_548_comp__fun__commute_Ofold__insert__remove, fact_192_com_Osimps_I24_J, fact_641_setsum_Oinsert, fact_222_image__insert, fact_889_weaken, fact_877_subset__image__iff, fact_679_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_532_setsum__right__distrib, fact_479_minus__fold__remove, fact_909_subset__insert__iff, fact_1045_nat__mult__assoc, fact_61_insert__code, fact_198_Collect__def, fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_125_nonempty__iff, fact_572_comp__fun__idem_Ofold__insert__idem2, fact_91_doubleton__eq__iff, fact_252_the__eq__trivial, help_fequal_1_1_fequal_000tc__Nat__Onat_T, fact_670_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_202_image__is__empty, fact_668_ab__semigroup__add__class_Oadd__ac_I1_J, fact_881_double__diff, fact_513_comp__fun__commute_Ofold__insert, fact_559_setprod_Oinsert, fact_915_finite__subset__induct, fact_167_rev__image__eqI, fact_268_folding__one_Oinsert, fact_255_If__def, fact_899_image__diff__subset, fact_25_Collect__conv__if2, fact_933_flat__lub__def, fact_1052_add__mult__distrib2, fact_840_bot__unique, fact_348_folding__one__idem_Oinsert__idem, fact_910_folding__one__idem_Osubset__idem, fact_452_comp__fun__idem_Ofun__left__idem, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It__a_J_, fact_890_asm, fact_60_insert__code, fact_906_diff__single__insert, fact_376_set__diff__eq, fact_626_setsum__addf, fact_249_the__sym__eq__trivial, fact_45_all__not__in__conv, fact_1047_nat__add__right__cancel, fact_55_insertI2, fact_794_set__mp, fact_342_theI_H, fact_590_comp__fun__commute_Ofold__graph__insertE, fact_105_bot__apply, fact_102_the__elem__eq, fact_412_Diff__insert, fact_109_bot__fun__def, fact_33_Collect__empty__eq, fact_555_setprod__insert, fact_24_Collect__conv__if2, fact_233_image__constant, fact_461_setsum__diff1, fact_458_comp__fun__commute_Ofold__graph__insertE__aux, fact_285_finite__imageI, fact_653_add__right__imp__eq, fact_195_mem__def, fact_656_add__imp__eq, fact_230_empty__fold1SetE, fact_103_the__elem__eq, fact_183_image__iff, fact_66_insert__commute, fact_663_add__left__cancel, fact_650_combine__common__factor, fact_630_setsum_Odistrib, fact_69_insert__absorb2, fact_495_comp__fun__commute_Ofold__equality, fact_132_com_Osimps_I3_J, fact_41_empty__Collect__eq, fact_662_add__right__cancel, fact_339_the1__equality, fact_48_empty__def, fact_592_setsum__image__gen, fact_357_folding__one_Oremove, fact_565_fold__def, fact_644_eq__add__iff1, fact_893_subset__singletonD, fact_227_fold1Set__nonempty, fact_643_eq__add__iff2, fact_672_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_100_empty__not__insert, fact_128_com_Osimps_I12_J, fact_669_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_698_crossproduct__noteq, fact_645_diff__add__cancel, fact_473_setprod_Oremove, fact_383_Diff__idemp, fact_149_image__constant__conv, fact_139_bot__empty__eq, fact_315_finite_Osimps, fact_364_DiffI, fact_50_empty__def, fact_500_fold__empty, fact_671_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_1_triple_Oinject, fact_598_setsum_Ocong, fact_142_Ass, fact_703_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_549_comp__fun__commute_Ofold__insert__remove, fact_526_setsum__product, fact_517_comp__fun__commute_Ofold__graph__fold, fact_524_setsum__product, fact_676_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_667_ab__semigroup__add__class_Oadd__ac_I1_J, fact_449_comp__fun__idem__remove, fact_329_finite__imp__fold__graph, fact_297_finite__insert, fact_276_finite__Collect__conjI, fact_13_insertCI, fact_90_doubleton__eq__iff, fact_729_empty__subsetI, fact_39_empty__Collect__eq, fact_658_add__left__imp__eq, fact_470_setprod_Oinsert__remove, fact_265_the__equality, fact_800_in__mono, fact_631_setsum_Odistrib, fact_680_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_28_Collect__conv__if, fact_690_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_514_comp__fun__commute_Ofold__insert, fact_654_add__right__imp__eq, fact_482_comp__fun__commute_Ofold__fun__comm, fact_22_singleton__conv, fact_635_setsum__insert, fact_283_finite_OinsertI, fact_582_folding__one_Oeq__fold_H, fact_427_finite__Diff__insert, fact_884_Diff__mono, fact_79_insertI1, fact_895_finite__surj, fact_612_setsum_Oremove, fact_379_Diff__iff, fact_1092_zadd__left__commute, fact_97_insert__not__empty, help_If_1_1_If_000tc__Nat__Onat_T, fact_542_comp__fun__commute_Ofold__rec, fact_10_insertE, fact_724_subsetD, fact_693_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_58_insert__ident, fact_155_image__eqI, fact_257_image__cong, fact_657_add__left__imp__eq, fact_120_equals0I, fact_299_fold__graph_OemptyI, fact_123_conseq, fact_682_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_436_folding__one__idem_Ohom__commute, fact_618_setsum__diff1_H, fact_353_semilattice__big_OF__eq, fact_678_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_664_add__left__cancel, fact_873_image__mono, fact_391_empty__Diff, fact_151_image__constant__conv, fact_927_image__subsetI, fact_571_comp__fun__idem_Ofold__insert__idem2, fact_622_setsum_Oinsert__remove, fact_113_triple_Oexhaust, fact_1054_left__add__mult__distrib, fact_543_comp__fun__commute_Ofold__rec, fact_210_empty__is__image, fact_404_insert__Diff__if, fact_539_setprod_Odistrib, fact_585_folding__one__idem_Oeq__fold__idem_H, fact_677_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_84_singleton__inject, fact_689_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_40_empty__Collect__eq, fact_730_finite__Collect__subsets, fact_701_comm__semiring__class_Odistrib, fact_854_rev__finite__subset, fact_144_fold1__singleton, fact_293_finite__Collect__disjI, fact_18_singleton__conv2, fact_655_add__imp__eq, help_If_2_1_If_000tc__Nat__Onat_T, fact_115_Set_Oset__insert, fact_865_subset__insert, fact_42_ex__in__conv, fact_108_bot__fun__def, fact_137_folding__one_Osingleton, fact_96_insert__not__empty, fact_240_imageE, fact_70_insert__absorb2, fact_647_crossproduct__eq, fact_400_finite__Diff2, fact_527_setsum__left__distrib, fact_175_imageI, fact_685_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_835_le__bot, fact_166_com_Osimps_I1_J, fact_49_empty__def, fact_887_Diff__subset, fact_306_fold__graph_OinsertI, fact_538_setprod_Odistrib, fact_660_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_1049_nat__add__assoc, fact_1086_zmult__assoc, fact_130_the__elem__def, fact_262_fold1Set_Ointros, fact_518_comp__fun__commute_Ofold__graph__fold, fact_859_insert__mono, fact_577_comp__fun__idem_Ofold__insert__idem, fact_699_crossproduct__noteq, fact_871_subset__insertI, fact_688_ab__semigroup__mult__class_Omult__ac_I1_J, fact_7_conseq1, fact_711_setsum_OF__cong
% 32.70/7.46 % No. of inferences in proof: 796
% 32.70/7.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7107 ms resp. 6006 ms w/o parsing
% 31.24/7.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.24/7.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------