TSTP Solution File: SWW470+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW470+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:23:57 EDT 2023
% Result : Theorem 8.51s 2.91s
% Output : Refutation 9.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 236
% Syntax : Number of formulae : 382 ( 114 unt; 92 typ; 0 def)
% Number of atoms : 712 ( 270 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 4038 ( 130 ~; 59 |; 81 &;3486 @)
% ( 22 <=>; 260 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 110 ( 110 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 31 con; 0-3 aty)
% Number of variables : 780 ( 0 ^; 733 !; 47 ?; 780 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_f1753944735l_bool_type,type,
hAPP_f1753944735l_bool: $i > $i > $i ).
thf(hoare_472868247rivs_a_type,type,
hoare_472868247rivs_a: $i > $i ).
thf(g_type,type,
g: $i ).
thf(hAPP_f1400872321a_bool_type,type,
hAPP_f1400872321a_bool: $i > $i > $i ).
thf(hAPP_H1816261935a_bool_type,type,
hAPP_H1816261935a_bool: $i > $i > $i ).
thf(insert1871499715iple_a_type,type,
insert1871499715iple_a: $i ).
thf(hoare_1050552211iple_a_type,type,
hoare_1050552211iple_a: $i > $i > $i > $i ).
thf(cOMBK_1458035955bool_a_type,type,
cOMBK_1458035955bool_a: $i > $i ).
thf(cOMBK_bool_state_type,type,
cOMBK_bool_state: $i > $i ).
thf(fFalse_type,type,
fFalse: $i ).
thf(c_type,type,
c: $i ).
thf(hAPP_f762886889e_bool_type,type,
hAPP_f762886889e_bool: $i > $i > $i ).
thf(hAPP_f1261923407e_bool_type,type,
hAPP_f1261923407e_bool: $i > $i > $i ).
thf(cOMBC_892787026e_bool_type,type,
cOMBC_892787026e_bool: $i ).
thf(hAPP_f963367678e_bool_type,type,
hAPP_f963367678e_bool: $i > $i > $i ).
thf(cOMBB_145932198bool_a_type,type,
cOMBB_145932198bool_a: $i > $i ).
thf(cOMBS_1378840469l_bool_type,type,
cOMBS_1378840469l_bool: $i ).
thf(hAPP_f1509969235l_bool_type,type,
hAPP_f1509969235l_bool: $i > $i > $i ).
thf(cOMBB_1355796797bool_a_type,type,
cOMBB_1355796797bool_a: $i > $i ).
thf(cOMBB_188601460_state_type,type,
cOMBB_188601460_state: $i > $i ).
thf(fconj_type,type,
fconj: $i ).
thf(p_type,type,
p: $i ).
thf(hAPP_f1759915619e_bool_type,type,
hAPP_f1759915619e_bool: $i > $i > $i ).
thf(cOMBB_160679318_state_type,type,
cOMBB_160679318_state: $i > $i ).
thf(fNot_type,type,
fNot: $i ).
thf(b_type,type,
b: $i ).
thf(bot_bo1687970473a_bool_type,type,
bot_bo1687970473a_bool: $i ).
thf(is_bool_type,type,
is_bool: $i > $o ).
thf(bot_bot_bool_type,type,
bot_bot_bool: $i ).
thf(hAPP_f1826273671iple_a_type,type,
hAPP_f1826273671iple_a: $i > $i > $i ).
thf(finite233325225iple_a_type,type,
finite233325225iple_a: $i > $i ).
thf(the_Ho1745054714iple_a_type,type,
the_Ho1745054714iple_a: $i ).
thf(finite388748825iple_a_type,type,
finite388748825iple_a: $i > $i > $i ).
thf(hAPP_a2036067514e_bool_type,type,
hAPP_a2036067514e_bool: $i > $i > $i ).
thf(hAPP_b540892988e_bool_type,type,
hAPP_b540892988e_bool: $i > $i > $i ).
thf(hAPP_f1824947087e_bool_type,type,
hAPP_f1824947087e_bool: $i > $i > $i ).
thf(cOMBC_41962815e_bool_type,type,
cOMBC_41962815e_bool: $i ).
thf(hAPP_b2019457360e_bool_type,type,
hAPP_b2019457360e_bool: $i > $i > $i ).
thf(hAPP_a723219176e_bool_type,type,
hAPP_a723219176e_bool: $i > $i > $i ).
thf(hAPP_f340725611e_bool_type,type,
hAPP_f340725611e_bool: $i > $i > $i ).
thf(cOMBB_1348041619bool_a_type,type,
cOMBB_1348041619bool_a: $i > $i ).
thf(hAPP_f167292325e_bool_type,type,
hAPP_f167292325e_bool: $i > $i > $i ).
thf(hAPP_a849909144l_bool_type,type,
hAPP_a849909144l_bool: $i > $i > $i ).
thf(skip_type,type,
skip: $i ).
thf(semi_type,type,
semi: $i > $i > $i ).
thf(hAPP_state_bool_type,type,
hAPP_state_bool: $i > $i > $i ).
thf(cOMBC_231445413l_bool_type,type,
cOMBC_231445413l_bool: $i ).
thf(hAPP_bool_bool_type,type,
hAPP_bool_bool: $i > $i > $i ).
thf(hAPP_s58564346l_bool_type,type,
hAPP_s58564346l_bool: $i > $i > $i ).
thf(hAPP_H562195827a_bool_type,type,
hAPP_H562195827a_bool: $i > $i > $i ).
thf(fequal1878252616iple_a_type,type,
fequal1878252616iple_a: $i ).
thf(hAPP_H1877746411l_bool_type,type,
hAPP_H1877746411l_bool: $i > $i > $i ).
thf(hAPP_f13210641l_bool_type,type,
hAPP_f13210641l_bool: $i > $i > $i ).
thf(cOMBB_633860163iple_a_type,type,
cOMBB_633860163iple_a: $i > $i ).
thf(hAPP_b589554111l_bool_type,type,
hAPP_b589554111l_bool: $i > $i > $i ).
thf(hAPP_H1927961489a_bool_type,type,
hAPP_H1927961489a_bool: $i > $i > $i ).
thf(collec1266446174iple_a_type,type,
collec1266446174iple_a: $i > $i ).
thf(cOMBK_1150238960iple_a_type,type,
cOMBK_1150238960iple_a: $i > $i ).
thf(fTrue_type,type,
fTrue: $i ).
thf(finite1948426435iple_a_type,type,
finite1948426435iple_a: $i > $i > $i ).
thf(finite520909254iple_a_type,type,
finite520909254iple_a: $i > $i > $i ).
thf(hAPP_s1806633685e_bool_type,type,
hAPP_s1806633685e_bool: $i > $i > $i ).
thf(hAPP_f817621513e_bool_type,type,
hAPP_f817621513e_bool: $i > $i > $i ).
thf(cOMBC_2027030106e_bool_type,type,
cOMBC_2027030106e_bool: $i ).
thf(hAPP_f1915402821a_bool_type,type,
hAPP_f1915402821a_bool: $i > $i > $i ).
thf(cOMBC_2049287834a_bool_type,type,
cOMBC_2049287834a_bool: $i ).
thf(hAPP_H1926610125l_bool_type,type,
hAPP_H1926610125l_bool: $i > $i > $i ).
thf(member564727580iple_a_type,type,
member564727580iple_a: $i ).
thf(finite506133020iple_a_type,type,
finite506133020iple_a: $i ).
thf(hAPP_H401672213iple_a_type,type,
hAPP_H401672213iple_a: $i > $i > $i ).
thf(hAPP_H568064713iple_a_type,type,
hAPP_H568064713iple_a: $i > $i > $i ).
thf(fimplies_type,type,
fimplies: $i ).
thf(hAPP_f1447988451a_bool_type,type,
hAPP_f1447988451a_bool: $i > $i > $i ).
thf(cOMBB_545742339iple_a_type,type,
cOMBB_545742339iple_a: $i > $i ).
thf(hAPP_f1104866853a_bool_type,type,
hAPP_f1104866853a_bool: $i > $i > $i ).
thf(cOMBS_213702372l_bool_type,type,
cOMBS_213702372l_bool: $i ).
thf(cOMBB_650444389iple_a_type,type,
cOMBB_650444389iple_a: $i > $i ).
thf(hAPP_f644196280e_bool_type,type,
hAPP_f644196280e_bool: $i > $i > $i ).
thf(hAPP_f1259673775l_bool_type,type,
hAPP_f1259673775l_bool: $i > $i > $i ).
thf(finite1734202118iple_a_type,type,
finite1734202118iple_a: $i > $i > $i > $i ).
thf(fdisj_type,type,
fdisj: $i ).
thf(hAPP_f945663555a_bool_type,type,
hAPP_f945663555a_bool: $i > $i > $i ).
thf(cOMBC_2067518550l_bool_type,type,
cOMBC_2067518550l_bool: $i ).
thf(fequal_state_type,type,
fequal_state: $i ).
thf(the_el287271400iple_a_type,type,
the_el287271400iple_a: $i ).
thf(hAPP_f1945881407l_bool_type,type,
hAPP_f1945881407l_bool: $i > $i > $i ).
thf(fequal1765155200a_bool_type,type,
fequal1765155200a_bool: $i ).
thf(hAPP_f1170963427a_bool_type,type,
hAPP_f1170963427a_bool: $i > $i > $i ).
thf(hAPP_f1874567875a_bool_type,type,
hAPP_f1874567875a_bool: $i > $i > $i ).
thf(cOMBC_1089176504a_bool_type,type,
cOMBC_1089176504a_bool: $i ).
thf(hAPP_a1200519163e_bool_type,type,
hAPP_a1200519163e_bool: $i > $i > $i ).
thf(90,axiom,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( A
!= ( hoare_1050552211iple_a @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_triple_Oexhaust) ).
thf(468,plain,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( A
!= ( hoare_1050552211iple_a @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ E @ F ) ) @ bot_bo1687970473a_bool ) ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ B @ G ) @ H ) )
=> ! [I: $i] :
( ! [J: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ J ) @ H ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ F @ J ) @ I ) ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ G ) @ I ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ B @ E @ A ) ) @ bot_bo1687970473a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_conseq12) ).
thf(234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ E @ F ) ) @ bot_bo1687970473a_bool ) ) )
=> ( ! [G: $i,H: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ B @ G ) @ H ) )
=> ! [I: $i] :
( ! [J: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ J ) @ H ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ F @ J ) @ I ) ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ G ) @ I ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ B @ E @ A ) ) @ bot_bo1687970473a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( is_bool @ B )
=> ( is_bool @ ( hAPP_bool_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( is_bool @ B )
=> ( is_bool @ ( hAPP_bool_bool @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ B ) @ C ) )
<=> ? [D: $i,E: $i,F: $i] :
( ( B
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ E ) )
& ( C = F )
& ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ D @ E ) @ F ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_fold1Set_Osimps) ).
thf(276,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ B ) @ C ) )
=> ? [D: $i,E: $i,F: $i] :
( ( B
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ E ) )
& ( C = F )
& ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ D @ E ) @ F ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ D ) @ E ) ) ) )
& ( ? [D: $i,E: $i,F: $i] :
( ( B
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ E ) )
& ( C = F )
& ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ D @ E ) @ F ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(129,axiom,
! [A: $i] :
( ( hAPP_f1826273671iple_a @ the_el287271400iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_the__elem__eq) ).
thf(655,plain,
! [A: $i] :
( ( hAPP_f1826273671iple_a @ the_el287271400iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ bot_bo1687970473a_bool ) ) )
<=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_doubleton__eq__iff) ).
thf(511,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ bot_bo1687970473a_bool ) ) )
=> ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) )
& ( ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) )
=> ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ bot_bo1687970473a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(67,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_empty__iff) ).
thf(385,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( finite1948426435iple_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ( ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ C @ A ) @ ( hAPP_f1826273671iple_a @ D @ B ) )
= ( hAPP_f1826273671iple_a @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_folding__one__idem_Oin__idem) ).
thf(472,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( finite1948426435iple_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ( ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ C @ A ) @ ( hAPP_f1826273671iple_a @ D @ B ) )
= ( hAPP_f1826273671iple_a @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( finite520909254iple_a @ B @ C ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ A ) )
=> ( ( hAPP_f1826273671iple_a @ C @ A )
= ( hAPP_f1826273671iple_a @ ( finite233325225iple_a @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_folding__one_Oeq__fold) ).
thf(538,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( finite520909254iple_a @ B @ C ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ A ) )
=> ( ( hAPP_f1826273671iple_a @ C @ A )
= ( hAPP_f1826273671iple_a @ ( finite233325225iple_a @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( hAPP_a2036067514e_bool @ ( cOMBK_1458035955bool_a @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) ).
thf(417,plain,
! [A: $i,B: $i] :
( ( hAPP_a2036067514e_bool @ ( cOMBK_1458035955bool_a @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a1200519163e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ A ) @ B ) @ C )
= ( hAPP_f644196280e_bool @ A @ ( hAPP_a849909144l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_003) ).
thf(565,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a1200519163e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ A ) @ B ) @ C )
= ( hAPP_f644196280e_bool @ A @ ( hAPP_a849909144l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_s58564346l_bool @ ( hAPP_f1259673775l_bool @ ( cOMBB_188601460_state @ A ) @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_state_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(257,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_s58564346l_bool @ ( hAPP_f1259673775l_bool @ ( cOMBB_188601460_state @ A ) @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_state_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(113,axiom,
! [A: $i] :
( ? [B: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
& ! [C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ C ) )
=> ( C = B ) ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_theI_H) ).
thf(570,plain,
! [A: $i] :
( ? [B: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
& ! [C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ C ) )
=> ( C = B ) ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(117,axiom,
! [A: $i] :
( ( A != bot_bo1687970473a_bool )
<=> ? [B: $i,C: $i] :
( ( A
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nonempty__iff) ).
thf(587,plain,
! [A: $i] :
( ( ( A != bot_bo1687970473a_bool )
=> ? [B: $i,C: $i] :
( ( A
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) ) ) )
& ( ? [B: $i,C: $i] :
( ( A
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) ) )
=> ( A != bot_bo1687970473a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( skip
!= ( semi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_com_Osimps_I12_J) ).
thf(157,plain,
! [A: $i,B: $i] :
( skip
!= ( semi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_H1877746411l_bool @ A @ C ) @ ( hAPP_H1927961489a_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00) ).
thf(638,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_H1877746411l_bool @ A @ C ) @ ( hAPP_H1927961489a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_f1447988451a_bool @ ( cOMBB_545742339iple_a @ A ) @ B ) @ C )
= ( hAPP_f1753944735l_bool @ A @ ( hAPP_H562195827a_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) ).
thf(228,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_f1447988451a_bool @ ( cOMBB_545742339iple_a @ A ) @ B ) @ C )
= ( hAPP_f1753944735l_bool @ A @ ( hAPP_H562195827a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(92,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_bot__apply) ).
thf(475,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(9,axiom,
! [A: $i] :
( ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_the__sym__eq__trivial) ).
thf(164,plain,
! [A: $i] :
( ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ? [C: $i] :
( ( B
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mk__disjoint__insert) ).
thf(253,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ? [C: $i] :
( ( B
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ C )
=> ( A
= ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ ( hAPP_b589554111l_bool @ fimplies @ C ) ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ ( hAPP_b589554111l_bool @ fimplies @ ( hAPP_bool_bool @ fNot @ C ) ) ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ B ) ) ) ) ) )
& ( ~ ( hBOOL @ C )
=> ( B
= ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ ( hAPP_b589554111l_bool @ fimplies @ C ) ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ ( hAPP_b589554111l_bool @ fimplies @ ( hAPP_bool_bool @ fNot @ C ) ) ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_If__def) ).
thf(238,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ C )
=> ( A
= ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ ( hAPP_b589554111l_bool @ fimplies @ C ) ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ ( hAPP_b589554111l_bool @ fimplies @ ( hAPP_bool_bool @ fNot @ C ) ) ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ B ) ) ) ) ) )
& ( ~ ( hBOOL @ C )
=> ( B
= ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ ( hAPP_b589554111l_bool @ fimplies @ C ) ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ ( hAPP_b589554111l_bool @ fimplies @ ( hAPP_bool_bool @ fNot @ C ) ) ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B )
!= bot_bo1687970473a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_insert__not__empty) ).
thf(574,plain,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B )
!= bot_bo1687970473a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ bot_bo1687970473a_bool ) )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ D ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__induct) ).
thf(353,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ bot_bo1687970473a_bool ) )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ D ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(480,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(3,axiom,
is_bool @ bot_bot_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).
thf(147,plain,
is_bool @ bot_bot_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(221,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(293,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a2036067514e_bool @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ A ) @ B ) @ C )
= ( hAPP_f1759915619e_bool @ ( hAPP_a1200519163e_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc) ).
thf(397,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a2036067514e_bool @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ A ) @ B ) @ C )
= ( hAPP_f1759915619e_bool @ ( hAPP_a1200519163e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hoare_1050552211iple_a @ A @ B @ C )
= ( hoare_1050552211iple_a @ D @ E @ F ) )
<=> ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_triple_Oinject) ).
thf(687,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hoare_1050552211iple_a @ A @ B @ C )
= ( hoare_1050552211iple_a @ D @ E @ F ) )
=> ( ( A = D )
& ( B = E )
& ( C = F ) ) )
& ( ( ( A = D )
& ( B = E )
& ( C = F ) )
=> ( ( hoare_1050552211iple_a @ A @ B @ C )
= ( hoare_1050552211iple_a @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(101,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
thf(527,plain,
! [A: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(48,axiom,
( bot_bo1687970473a_bool
= ( collec1266446174iple_a @ ( cOMBK_1150238960iple_a @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_empty__def) ).
thf(312,plain,
( bot_bo1687970473a_bool
= ( collec1266446174iple_a @ ( cOMBK_1150238960iple_a @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(307,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ A ) ) )
& ( ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ A ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ C @ D @ E ) ) @ bot_bo1687970473a_bool ) ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ E @ F ) @ G ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ F ) @ G ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ C @ D @ A ) ) @ bot_bo1687970473a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conseq2) ).
thf(248,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ C @ D @ E ) ) @ bot_bo1687970473a_bool ) ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ E @ F ) @ G ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ F ) @ G ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ C @ D @ A ) ) @ bot_bo1687970473a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) )
<=> ( ( A = B )
| ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_insert__iff) ).
thf(529,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) )
=> ( ( A = B )
| ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) ) )
& ( ( ( A = B )
| ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ C ) )
=> ( C = B ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_theI) ).
thf(661,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ C ) )
=> ( C = B ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(105,axiom,
! [A: $i] :
( ( collec1266446174iple_a @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_singleton__conv) ).
thf(546,plain,
! [A: $i] :
( ( collec1266446174iple_a @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite__insert) ).
thf(366,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) ) )
& ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(54,axiom,
is_bool @ fFalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).
thf(334,plain,
is_bool @ fFalse,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ B ) ) ) @ A ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ B ) ) ) @ A ) )
= bot_bo1687970473a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Collect__conv__if) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ B ) ) ) @ A ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ B ) ) ) @ A ) )
= bot_bo1687970473a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(561,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( hAPP_f945663555a_bool @ cOMBC_2067518550l_bool @ A ) @ B ) @ C )
= ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_002) ).
thf(407,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( hAPP_f945663555a_bool @ cOMBC_2067518550l_bool @ A ) @ B ) @ C )
= ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(60,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ B @ skip @ B ) ) @ bot_bo1687970473a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hoare__derivs_OSkip) ).
thf(361,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ B @ skip @ B ) ) @ bot_bo1687970473a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(132,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_emptyE) ).
thf(665,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(682,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ C @ D @ E ) ) @ bot_bo1687970473a_bool ) ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ F ) @ G ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ C @ F ) @ G ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ A @ D @ E ) ) @ bot_bo1687970473a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_conseq1) ).
thf(456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ C @ D @ E ) ) @ bot_bo1687970473a_bool ) ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ F ) @ G ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ C @ F ) @ G ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ A @ D @ E ) ) @ bot_bo1687970473a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fdisj ) @ A ) ) @ B ) ) ) )
<=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ A ) ) )
& ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite__Collect__disjI) ).
thf(578,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fdisj ) @ A ) ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ A ) ) )
& ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ B ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ A ) ) )
& ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fdisj ) @ A ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(50,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).
thf(317,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) )
=> ( hBOOL @ bot_bot_bool ) )
& ( ( hBOOL @ bot_bot_bool )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(68,axiom,
! [A: $i] :
( ( is_bool @ A )
=> ( ( A = fTrue )
| ( A = fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(388,plain,
! [A: $i] :
( ( is_bool @ A )
=> ( ( A = fTrue )
| ( A = fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( collec1266446174iple_a @ B ) )
= ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fimplies ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ fNot ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_insert__Collect) ).
thf(420,plain,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( collec1266446174iple_a @ B ) )
= ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fimplies ) @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ fNot ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( is_bool @ ( finite520909254iple_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____jfehddehev__Otriple) ).
thf(193,plain,
! [A: $i,B: $i] : ( is_bool @ ( finite520909254iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_fold1Set_Ointros) ).
thf(489,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_f1945881407l_bool @ fequal1765155200a_bool @ A ) @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) ).
thf(679,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_f1945881407l_bool @ fequal1765155200a_bool @ A ) @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(24,axiom,
~ ( hBOOL @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(212,plain,
~ ( hBOOL @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) )
=> ( B = A ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_insertCI) ).
thf(647,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) )
=> ( B = A ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( B = bot_bo1687970473a_bool )
=> ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_equals0D) ).
thf(701,plain,
! [A: $i,B: $i] :
( ( B = bot_bo1687970473a_bool )
=> ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ E ) @ C ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ E ) ) @ ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_fold__graph_OinsertI) ).
thf(371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ D ) @ E ) )
=> ( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ E ) @ C ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ E ) ) @ ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( semi @ A @ B )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_com_Osimps_I13_J) ).
thf(205,plain,
! [A: $i,B: $i] :
( ( semi @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Ostate_T) ).
thf(508,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ B ) @ C ) )
=> ( B != bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_fold1Set__nonempty) ).
thf(541,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ B ) @ C ) )
=> ( B != bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_H1927961489a_bool @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ A ) @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_) ).
thf(558,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_H1927961489a_bool @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ A ) @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_fold1Set__sing) ).
thf(298,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ C ) @ D ) )
<=> ( ( ( C = bot_bo1687970473a_bool )
& ( D = B ) )
| ? [E: $i,F: $i,G: $i] :
( ( C
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ E ) @ F ) )
& ( D
= ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ A @ E ) @ G ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ E ) @ F ) )
& ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_fold__graph_Osimps) ).
thf(618,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ C ) @ D ) )
=> ( ( ( C = bot_bo1687970473a_bool )
& ( D = B ) )
| ? [E: $i,F: $i,G: $i] :
( ( C
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ E ) @ F ) )
& ( D
= ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ A @ E ) @ G ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ E ) @ F ) )
& ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ F ) @ G ) ) ) ) )
& ( ( ( ( C = bot_bo1687970473a_bool )
& ( D = B ) )
| ? [E: $i,F: $i,G: $i] :
( ( C
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ E ) @ F ) )
& ( D
= ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ A @ E ) @ G ) )
& ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ E ) @ F ) )
& ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ F ) @ G ) ) ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( hAPP_f1826273671iple_a @ ( finite233325225iple_a @ A ) @ B )
= ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( finite388748825iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fold1__def) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( hAPP_f1826273671iple_a @ ( finite233325225iple_a @ A ) @ B )
= ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( finite388748825iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_state_bool @ ( hAPP_b2019457360e_bool @ ( hAPP_f167292325e_bool @ cOMBC_231445413l_bool @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_s58564346l_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(161,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_state_bool @ ( hAPP_b2019457360e_bool @ ( hAPP_f167292325e_bool @ cOMBC_231445413l_bool @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_s58564346l_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_singleton__iff) ).
thf(375,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a849909144l_bool @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ A ) @ B ) @ C )
= ( hAPP_f1259673775l_bool @ A @ ( hAPP_a2036067514e_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(584,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a849909144l_bool @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ A ) @ B ) @ C )
= ( hAPP_f1259673775l_bool @ A @ ( hAPP_a2036067514e_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_state_bool @ ( cOMBK_bool_state @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
thf(423,plain,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_state_bool @ ( cOMBK_bool_state @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(16,axiom,
! [A: $i,B: $i] : ( is_bool @ ( finite1948426435iple_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____jfehddehev__O) ).
thf(191,plain,
! [A: $i,B: $i] : ( is_bool @ ( finite1948426435iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(144,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(711,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(42,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1753944735l_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_Mtc) ).
thf(291,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_f1753944735l_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) )
=> ( ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ A ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insert__ident) ).
thf(641,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) )
=> ( ( ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ A ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(391,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_state_bool @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_state_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
thf(382,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_state_bool @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_state_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(120,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insertI1) ).
thf(611,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(145,axiom,
hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ bot_bo1687970473a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_finite_OemptyI) ).
thf(713,plain,
hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ bot_bo1687970473a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(466,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_insert__commute) ).
thf(335,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
<=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_com_Osimps_I3_J) ).
thf(172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) )
& ( ( ( A = C )
& ( B = D ) )
=> ( ( semi @ A @ B )
= ( semi @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H562195827a_bool @ ( hAPP_f1170963427a_bool @ ( hAPP_f1874567875a_bool @ cOMBC_1089176504a_bool @ A ) @ B ) @ C )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_004) ).
thf(451,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H562195827a_bool @ ( hAPP_f1170963427a_bool @ ( hAPP_f1874567875a_bool @ cOMBC_1089176504a_bool @ A ) @ B ) @ C )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_state_bool @ ( hAPP_f1759915619e_bool @ ( hAPP_f644196280e_bool @ cOMBS_1378840469l_bool @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_s58564346l_bool @ A @ C ) @ ( hAPP_state_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(245,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_state_bool @ ( hAPP_f1759915619e_bool @ ( hAPP_f644196280e_bool @ cOMBS_1378840469l_bool @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ ( hAPP_s58564346l_bool @ A @ C ) @ ( hAPP_state_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ E ) @ F ) )
=> ? [G: $i,H: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ G @ C @ H ) ) @ bot_bo1687970473a_bool ) ) )
& ! [I: $i] :
( ! [J: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ G @ J ) @ F ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ H @ J ) @ I ) ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ E ) @ I ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ C @ A ) ) @ bot_bo1687970473a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_conseq) ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ E ) @ F ) )
=> ? [G: $i,H: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ G @ C @ H ) ) @ bot_bo1687970473a_bool ) ) )
& ! [I: $i] :
( ! [J: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ G @ J ) @ F ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ H @ J ) @ I ) ) )
=> ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ A @ E ) @ I ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ C @ A ) ) @ bot_bo1687970473a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_insertI2) ).
thf(616,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_finite_OinsertI) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( finite1948426435iple_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ( hAPP_f1826273671iple_a @ D @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) )
= ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ C @ A ) @ ( hAPP_f1826273671iple_a @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_folding__one__idem_Oinsert__idem) ).
thf(668,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( finite1948426435iple_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ( hAPP_f1826273671iple_a @ D @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) )
= ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ C @ A ) @ ( hAPP_f1826273671iple_a @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(19,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_H1927961489a_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc__HOL__) ).
thf(198,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_H1927961489a_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_H1927961489a_bool @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_) ).
thf(330,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_H1927961489a_bool @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( bot_bo1687970473a_bool
!= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_empty__not__insert) ).
thf(462,plain,
! [A: $i,B: $i] :
( bot_bo1687970473a_bool
!= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(636,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(28,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) )
<=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ bot_bo1687970473a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_bot__empty__eq) ).
thf(223,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ bot_bo1687970473a_bool ) ) )
& ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ bot_bo1687970473a_bool ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ bot_bo1687970473a_bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(70,axiom,
! [A: $i] :
( ( hAPP_f1826273671iple_a @ the_el287271400iple_a @ A )
= ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_f1447988451a_bool @ ( cOMBB_545742339iple_a @ ( hAPP_f1945881407l_bool @ fequal1765155200a_bool @ A ) ) @ ( hAPP_f1170963427a_bool @ ( hAPP_f1874567875a_bool @ cOMBC_1089176504a_bool @ insert1871499715iple_a ) @ bot_bo1687970473a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_the__elem__def) ).
thf(394,plain,
! [A: $i] :
( ( hAPP_f1826273671iple_a @ the_el287271400iple_a @ A )
= ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_f1447988451a_bool @ ( cOMBB_545742339iple_a @ ( hAPP_f1945881407l_bool @ fequal1765155200a_bool @ A ) ) @ ( hAPP_f1170963427a_bool @ ( hAPP_f1874567875a_bool @ cOMBC_1089176504a_bool @ insert1871499715iple_a ) @ bot_bo1687970473a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ bot_bo1687970473a_bool ) ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
thf(563,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ bot_bo1687970473a_bool ) ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ A ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) @ C ) )
<=> ( ( A = C )
| ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_insert__code) ).
thf(267,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) @ C ) )
=> ( ( A = C )
| ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ C ) ) ) )
& ( ( ( A = C )
| ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ C ) ) )
=> ( hBOOL @ ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1877746411l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ A ) @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_H1927961489a_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_001) ).
thf(167,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1877746411l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ A ) @ B ) @ C )
= ( hAPP_b589554111l_bool @ A @ ( hAPP_H1927961489a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B )
= ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fdisj ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) @ ( hAPP_f1400872321a_bool @ ( hAPP_f945663555a_bool @ cOMBC_2067518550l_bool @ member564727580iple_a ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_insert__compr__raw) ).
thf(658,plain,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B )
= ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fdisj ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) @ ( hAPP_f1400872321a_bool @ ( hAPP_f945663555a_bool @ cOMBC_2067518550l_bool @ member564727580iple_a ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ B ) ) )
| ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_finite__Collect__conjI) ).
thf(505,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ B ) ) )
| ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ A ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_f1945881407l_bool @ fequal1765155200a_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) ).
thf(438,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_f1945881407l_bool @ fequal1765155200a_bool @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(23,axiom,
! [A: $i] :
( ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_the__eq__trivial) ).
thf(209,plain,
! [A: $i] :
( ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ C ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ D ) )
=> ( D = C ) ) )
=> ( ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ A ) )
=> ( ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_the1__equality) ).
thf(553,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ C ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ D ) )
=> ( D = C ) ) )
=> ( ( hBOOL @ ( hAPP_H1927961489a_bool @ B @ A ) )
=> ( ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( finite520909254iple_a @ B @ C ) )
=> ( ( hAPP_f1826273671iple_a @ C @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_folding__one_Osingleton) ).
thf(295,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( finite520909254iple_a @ B @ C ) )
=> ( ( hAPP_f1826273671iple_a @ C @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_singletonE) ).
thf(705,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B )
= ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fdisj ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) @ ( hAPP_f1400872321a_bool @ ( hAPP_f945663555a_bool @ cOMBC_2067518550l_bool @ member564727580iple_a ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_insert__compr) ).
thf(327,plain,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B )
= ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fdisj ) @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ fequal1878252616iple_a ) @ A ) ) ) @ ( hAPP_f1400872321a_bool @ ( hAPP_f945663555a_bool @ cOMBC_2067518550l_bool @ member564727580iple_a ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ bot_bo1687970473a_bool ) @ C ) )
=> ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_empty__fold__graphE) ).
thf(673,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ bot_bo1687970473a_bool ) @ C ) )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_insertE) ).
thf(502,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) )
=> ( ( A != B )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ ( cOMBK_1458035955bool_a @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ fequal_state ) @ F ) ) @ B @ ( cOMBK_1458035955bool_a @ ( hAPP_a2036067514e_bool @ C @ E ) ) ) ) @ bot_bo1687970473a_bool ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ B @ C ) ) @ bot_bo1687970473a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).
thf(338,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( hBOOL @ ( hAPP_state_bool @ ( hAPP_a2036067514e_bool @ D @ E ) @ F ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ ( cOMBK_1458035955bool_a @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ fequal_state ) @ F ) ) @ B @ ( cOMBK_1458035955bool_a @ ( hAPP_a2036067514e_bool @ C @ E ) ) ) ) @ bot_bo1687970473a_bool ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ B @ C ) ) @ bot_bo1687970473a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( B != bot_bo1687970473a_bool )
=> ? [C: $i] : ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__nonempty__imp__fold1Set) ).
thf(613,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( B != bot_bo1687970473a_bool )
=> ? [C: $i] : ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a723219176e_bool @ ( hAPP_f340725611e_bool @ ( cOMBB_1348041619bool_a @ A ) @ B ) @ C )
= ( hAPP_f167292325e_bool @ A @ ( hAPP_a849909144l_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) ).
thf(154,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a723219176e_bool @ ( hAPP_f340725611e_bool @ ( cOMBB_1348041619bool_a @ A ) @ B ) @ C )
= ( hAPP_f167292325e_bool @ A @ ( hAPP_a849909144l_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_singleton__inject) ).
thf(314,plain,
! [A: $i,B: $i] :
( ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( B
= ( finite233325225iple_a @ C ) )
=> ( ( hAPP_f1826273671iple_a @ B @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_fold1__singleton__def) ).
thf(446,plain,
! [A: $i,B: $i,C: $i] :
( ( B
= ( finite233325225iple_a @ C ) )
=> ( ( hAPP_f1826273671iple_a @ B @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(30,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ bot_bo1687970473a_bool ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_empty__fold1SetE) ).
thf(231,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ bot_bo1687970473a_bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(61,axiom,
! [A: $i] :
( ( collec1266446174iple_a @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ A ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
thf(363,plain,
! [A: $i] :
( ( collec1266446174iple_a @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ A ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ C ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__imp__fold__graph) ).
thf(671,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ C ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( finite520909254iple_a @ B @ C ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ A ) )
=> ( ( A != bot_bo1687970473a_bool )
=> ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ B @ D ) @ E ) ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ E ) @ bot_bo1687970473a_bool ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ ( hAPP_f1826273671iple_a @ C @ A ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_folding__one_Oclosed) ).
thf(218,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( finite520909254iple_a @ B @ C ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ A ) )
=> ( ( A != bot_bo1687970473a_bool )
=> ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ B @ D ) @ E ) ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ D ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ E ) @ bot_bo1687970473a_bool ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ ( hAPP_f1826273671iple_a @ C @ A ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ B ) ) ) @ A ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ B ) ) ) @ A ) )
= bot_bo1687970473a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Collect__conv__if2) ).
thf(482,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ B ) ) ) @ A ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) ) )
& ( ~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ ( hAPP_f1400872321a_bool @ ( hAPP_f1104866853a_bool @ cOMBS_213702372l_bool @ ( hAPP_f13210641l_bool @ ( cOMBB_633860163iple_a @ fconj ) @ ( hAPP_H562195827a_bool @ fequal1878252616iple_a @ B ) ) ) @ A ) )
= bot_bo1687970473a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(21,axiom,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_state_bool @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) ).
thf(203,plain,
! [A: $i,B: $i] : ( is_bool @ ( hAPP_state_bool @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( hAPP_f1826273671iple_a @ ( finite233325225iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_fold1__singleton) ).
thf(652,plain,
! [A: $i,B: $i] :
( ( hAPP_f1826273671iple_a @ ( finite233325225iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ bot_bo1687970473a_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_H1927961489a_bool @ ( cOMBK_1150238960iple_a @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( is_bool @ A )
=> ( ( hAPP_H1927961489a_bool @ ( cOMBK_1150238960iple_a @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cut) ).
thf(568,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_insert__absorb2) ).
thf(684,plain,
! [A: $i,B: $i] :
( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ~ ! [C: $i] :
( ( B
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Set_Oset__insert) ).
thf(549,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ~ ! [C: $i] :
( ( B
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ C ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(25,axiom,
! [A: $i] :
( ! [B: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) )
=> ( A = bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_equals0I) ).
thf(214,plain,
! [A: $i] :
( ! [B: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) )
=> ( A = bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( finite1948426435iple_a @ B @ C ) )
=> ( ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ B @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_folding__one__idem_Oidem) ).
thf(287,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( finite1948426435iple_a @ B @ C ) )
=> ( ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ B @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a2036067514e_bool @ ( hAPP_b540892988e_bool @ ( hAPP_f1824947087e_bool @ cOMBC_41962815e_bool @ A ) @ B ) @ C )
= ( hAPP_b2019457360e_bool @ ( hAPP_a723219176e_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_a2036067514e_bool @ ( hAPP_b540892988e_bool @ ( hAPP_f1824947087e_bool @ cOMBC_41962815e_bool @ A ) @ B ) @ C )
= ( hAPP_b2019457360e_bool @ ( hAPP_a723219176e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(79,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ bot_bo1687970473a_bool ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_fold__graph_OemptyI) ).
thf(432,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ B @ bot_bo1687970473a_bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(74,axiom,
! [A: $i] :
( ( ( collec1266446174iple_a @ A )
= bot_bo1687970473a_bool )
<=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Collect__empty__eq) ).
thf(410,plain,
! [A: $i] :
( ( ( ( collec1266446174iple_a @ A )
= bot_bo1687970473a_bool )
=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) ) )
& ( ! [B: $i] :
~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ( collec1266446174iple_a @ A )
= bot_bo1687970473a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1,conjecture,
hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ g ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ ( cOMBK_1458035955bool_a @ ( cOMBK_bool_state @ fFalse ) ) @ c @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ cOMBS_1378840469l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ p ) ) ) @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ fNot ) @ b ) ) ) ) @ bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ g ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ ( cOMBK_1458035955bool_a @ ( cOMBK_bool_state @ fFalse ) ) @ c @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ cOMBS_1378840469l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ p ) ) ) @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ fNot ) @ b ) ) ) ) @ bot_bo1687970473a_bool ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(146,plain,
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ g ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ ( cOMBK_1458035955bool_a @ ( cOMBK_bool_state @ fFalse ) ) @ c @ ( hAPP_f762886889e_bool @ ( hAPP_f1261923407e_bool @ cOMBC_892787026e_bool @ ( hAPP_f963367678e_bool @ ( cOMBB_145932198bool_a @ cOMBS_1378840469l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ p ) ) ) @ ( hAPP_f1759915619e_bool @ ( cOMBB_160679318_state @ fNot ) @ b ) ) ) ) @ bot_bo1687970473a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
is_bool @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fTrue) ).
thf(190,plain,
is_bool @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [A: $i] :
( ( collec1266446174iple_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__def) ).
thf(183,plain,
! [A: $i] :
( ( collec1266446174iple_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(64,axiom,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(373,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(119,axiom,
! [A: $i] :
( ? [B: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) )
<=> ( A != bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_ex__in__conv) ).
thf(603,plain,
! [A: $i] :
( ( ? [B: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) )
=> ( A != bot_bo1687970473a_bool ) )
& ( ( A != bot_bo1687970473a_bool )
=> ? [B: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ E @ F ) ) @ bot_bo1687970473a_bool ) ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ F @ A @ B ) ) @ bot_bo1687970473a_bool ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ ( semi @ E @ A ) @ B ) ) @ bot_bo1687970473a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Comp) ).
thf(305,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ E @ F ) ) @ bot_bo1687970473a_bool ) ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ F @ A @ B ) ) @ bot_bo1687970473a_bool ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ C ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ D @ ( semi @ E @ A ) @ B ) ) @ bot_bo1687970473a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(57,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ A ) )
<=> ( ( A = bot_bo1687970473a_bool )
| ? [B: $i,C: $i] :
( ( A
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ B ) )
& ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite_Osimps) ).
thf(341,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ A ) )
=> ( ( A = bot_bo1687970473a_bool )
| ? [B: $i,C: $i] :
( ( A
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ B ) )
& ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) ) ) ) )
& ( ( ( A = bot_bo1687970473a_bool )
| ? [B: $i,C: $i] :
( ( A
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ B ) )
& ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_H1927961489a_bool @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).
thf(358,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_f1400872321a_bool @ ( cOMBB_650444389iple_a @ A ) @ B ) @ C )
= ( hAPP_bool_bool @ A @ ( hAPP_H1927961489a_bool @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ A ) @ B ) @ C )
= ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) ).
thf(195,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ ( hAPP_f817621513e_bool @ cOMBC_2027030106e_bool @ A ) @ B ) @ C )
= ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(72,axiom,
! [A: $i] :
( ( bot_bo1687970473a_bool
= ( collec1266446174iple_a @ A ) )
<=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_empty__Collect__eq) ).
thf(400,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool
= ( collec1266446174iple_a @ A ) )
=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) ) )
& ( ! [B: $i] :
~ ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( bot_bo1687970473a_bool
= ( collec1266446174iple_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ C ) )
=> ( C = B ) )
=> ( ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_the__equality) ).
thf(427,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ B ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ A @ C ) )
=> ( C = B ) )
=> ( ( hAPP_f1826273671iple_a @ the_Ho1745054714iple_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(118,axiom,
! [A: $i] :
( ! [B: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) )
<=> ( A = bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_all__not__in__conv) ).
thf(596,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) )
=> ( A = bot_bo1687970473a_bool ) )
& ( ( A = bot_bo1687970473a_bool )
=> ! [B: $i] :
~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( finite520909254iple_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ( hAPP_f1826273671iple_a @ D @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) )
= ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ C @ A ) @ ( hAPP_f1826273671iple_a @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_folding__one_Oinsert) ).
thf(459,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( finite520909254iple_a @ C @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ( hAPP_f1826273671iple_a @ D @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B ) )
= ( hAPP_H401672213iple_a @ ( hAPP_H568064713iple_a @ C @ A ) @ ( hAPP_f1826273671iple_a @ D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ A ) @ B ) @ C )
= ( hAPP_H1927961489a_bool @ ( hAPP_H562195827a_bool @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00) ).
thf(200,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP_H1927961489a_bool @ ( hAPP_H562195827a_bool @ ( hAPP_f1915402821a_bool @ cOMBC_2049287834a_bool @ A ) @ B ) @ C )
= ( hAPP_H1927961489a_bool @ ( hAPP_H562195827a_bool @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Ostate_T) ).
thf(442,plain,
! [A: $i,B: $i] :
( ( A != B )
| ( hBOOL @ ( hAPP_state_bool @ ( hAPP_s1806633685e_bool @ fequal_state @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) @ D ) )
=> ~ ! [E: $i,F: $i] :
( ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ E @ F ) @ D ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ E ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__fold1SetE) ).
thf(322,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite388748825iple_a @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C ) ) @ D ) )
=> ~ ! [E: $i,F: $i] :
( ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ B ) @ C )
= ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP_H1927961489a_bool @ ( finite1734202118iple_a @ A @ E @ F ) @ D ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ E ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__absorb) ).
thf(676,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ A ) @ B ) )
=> ( ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ bot_bo1687970473a_bool ) ) )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ D ) )
=> ( ( D != bot_bo1687970473a_bool )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ D ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__ne__induct) ).
thf(491,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ B ) )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ bot_bo1687970473a_bool ) ) )
=> ( ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP_f1753944735l_bool @ finite506133020iple_a @ D ) )
=> ( ( D != bot_bo1687970473a_bool )
=> ( ~ ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hAPP_H1926610125l_bool @ member564727580iple_a @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ D ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ C ) @ D ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(454,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ E )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ B @ C @ D ) ) @ bot_bo1687970473a_bool ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ ( hAPP_b540892988e_bool @ ( hAPP_f1824947087e_bool @ cOMBC_41962815e_bool @ ( hAPP_f340725611e_bool @ ( cOMBB_1348041619bool_a @ cOMBC_231445413l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ B ) ) ) @ E ) @ C @ D ) ) @ bot_bo1687970473a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_constant) ).
thf(708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ E )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ B @ C @ D ) ) @ bot_bo1687970473a_bool ) ) ) )
=> ( hBOOL @ ( hAPP_f1753944735l_bool @ ( hoare_472868247rivs_a @ A ) @ ( hAPP_f1400872321a_bool @ ( hAPP_H1816261935a_bool @ insert1871499715iple_a @ ( hoare_1050552211iple_a @ ( hAPP_b540892988e_bool @ ( hAPP_f1824947087e_bool @ cOMBC_41962815e_bool @ ( hAPP_f340725611e_bool @ ( cOMBB_1348041619bool_a @ cOMBC_231445413l_bool ) @ ( hAPP_f1509969235l_bool @ ( cOMBB_1355796797bool_a @ ( cOMBB_188601460_state @ fconj ) ) @ B ) ) ) @ E ) @ C @ D ) ) @ bot_bo1687970473a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(735,plain,
$false,
inference(cvc4,[status(thm)],[468,234,170,276,655,511,385,472,538,417,565,257,570,587,157,638,228,475,164,253,238,574,353,480,147,221,293,397,687,527,312,307,248,529,661,546,366,334,260,561,407,361,665,682,456,578,317,388,420,193,489,679,212,647,701,371,205,508,541,558,298,618,148,161,375,584,423,191,711,291,641,391,382,611,713,466,335,172,451,245,434,616,251,668,198,330,462,636,223,394,563,267,167,658,505,438,209,553,295,705,327,673,502,338,613,154,314,446,231,363,671,218,482,203,652,186,568,684,549,214,287,151,432,410,146,190,183,373,603,305,341,358,195,400,427,596,459,200,442,322,676,491,454,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SWW470+1 : TPTP v8.1.2. Released v5.3.0.
% 0.09/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 22:20:19 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.87/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/1.02 % [INFO] Parsing done (193ms).
% 1.56/1.03 % [INFO] Running in sequential loop mode.
% 2.12/1.23 % [INFO] eprover registered as external prover.
% 2.12/1.23 % [INFO] cvc4 registered as external prover.
% 2.12/1.24 % [INFO] Scanning for conjecture ...
% 2.50/1.33 % [INFO] Found a conjecture and 143 axioms. Running axiom selection ...
% 2.72/1.42 % [INFO] Axiom selection finished. Selected 143 axioms (removed 0 axioms).
% 3.27/1.54 % [INFO] Problem is first-order (TPTP FOF).
% 3.27/1.56 % [INFO] Type checking passed.
% 3.27/1.56 % [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 ...
% 8.51/2.90 % External prover 'cvc4' found a proof!
% 8.51/2.90 % [INFO] Killing All external provers ...
% 8.51/2.90 % Time passed: 2396ms (effective reasoning time: 1872ms)
% 8.51/2.90 % 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)>
% 8.51/2.91 % Axioms used in derivation (143): fact_10_insertCI, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00, fact_4_constant, fact_20_ex__in__conv, fact_42_bot__fun__def, fact_23_insert__absorb, help_fimplies_2_1_U, fact_54_If__def, gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____jfehddehev__Otriple, fact_60_conseq, fact_67_fold1Set_Ointros, fact_53_the__eq__trivial, fact_65_empty__fold1SetE, help_fconj_3_1_U, fact_75_folding__one_Oeq__fold, help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_6_conseq2, fact_56_the__equality, fact_46_Set_Oset__insert, help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple, help_fequal_1_1_fequal_000tc__Com__Ostate_T, fact_55_equals0I, fact_3_hoare__derivs_Oinsert, fact_34_singleton__inject, fact_5_escape, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_, fact_80_finite__insert, fact_0_empty, fact_27_insert__iff, fact_92_finite__ne__induct, gsy_c_fFalse, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_003, fact_52_the__sym__eq__trivial, gsy_c_fTrue, fact_16_equals0D, fact_44_Comp, fact_15_Collect__conv__if, help_fNot_2_1_U, fact_90_fold__graph_Osimps, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U, fact_25_insert__ident, help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc, fact_74_Collect__def, help_fNot_1_1_U, fact_87_finite_Osimps, fact_73_mem__def, help_fFalse_1_1_T, fact_8_conseq12, fact_2_cut, fact_37_singleton__iff, fact_85_finite__nonempty__imp__fold1Set, fact_41_bot__apply, help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple, gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool, help_fdisj_1_1_U, fact_78_fold__graph_OinsertI, fact_38_insert__not__empty, gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc__HOL__, help_fconj_2_1_U, fact_50_mk__disjoint__insert, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_002, fact_12_singleton__conv2, fact_29_insert__absorb2, help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_48_com_Osimps_I12_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I, fact_77_empty__fold__graphE, fact_69_fold1__def, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It, fact_93_folding__one__idem_Oidem, fact_79_finite__Collect__disjI, fact_51_com_Osimps_I3_J, fact_36_doubleton__eq__iff, fact_47_com_Osimps_I13_J, fact_58_the1__equality, fact_91_folding__one__idem_Oinsert__idem, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_001, help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00, fact_14_Collect__conv__if2, fact_49_the__elem__def, fact_62_fold1Set__sing, fact_18_empty__iff, fact_22_empty__def, fact_68_folding__one_Oinsert, fact_17_Collect__empty__eq, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U, help_fdisj_2_1_U, fact_64_bot__empty__eq, fact_70_finite__Collect__conjI, fact_1_triple_Oinject, fact_59_theI_H, fact_35_singletonE, gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_Mtc, help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U, fact_28_insert__commute, fact_19_empty__Collect__eq, fact_31_insert__compr, fact_76_fold__graph_OemptyI, fact_13_singleton__conv, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__, fact_33_insert__compr__raw, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo, fact_24_insertI2, fact_86_finite__induct, help_fconj_1_1_U, help_fdisj_3_1_U, gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool, fact_63_folding__one_Osingleton, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_, fact_21_all__not__in__conv, fact_89_fold1Set_Osimps, fact_39_empty__not__insert, help_fFalse_1_1_U, fact_11_emptyE, fact_30_insert__Collect, gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____jfehddehev__O, fact_84_insert__fold1SetE, help_fequal_2_1_fequal_000tc__Com__Ostate_T, fact_26_insert__code, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_004, fact_83_folding__one_Oclosed, fact_45_triple_Oexhaust, fact_40_the__elem__eq, fact_72_finite_OinsertI, fact_43_hoare__derivs_OSkip, help_fimplies_1_1_U, help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U, fact_57_theI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel, fact_66_fold1Set__nonempty, help_fimplies_3_1_U, fact_81_fold1__singleton__def, fact_9_insertE, help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__, fact_71_finite_OemptyI, fact_32_insertI1, fact_94_folding__one__idem_Oin__idem, gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool, fact_88_finite__imp__fold__graph, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H, fact_61_nonempty__iff, fact_82_fold1__singleton, fact_7_conseq1
% 8.51/2.91 % No. of inferences in proof: 290
% 8.51/2.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2396 ms resp. 1872 ms w/o parsing
% 9.51/3.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.51/3.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------