%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW470+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:13 AM UTC 2026
% Result : Theorem 102.45s 24.70s
% Output : Refutation 98.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 154
% Syntax : Number of formulae : 732 ( 322 unt; 0 typ; 10 def)
% Number of atoms : 1791 ( 788 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 10071 ( 672 ~; 402 |; 100 &;8596 @)
% ( 22 <=>; 279 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 102 usr; 32 con; 0-6 aty)
% Number of variables : 1681 ( 27 ^;1581 !; 63 ?;1681 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_f1753944735l_bool_decl,type,
hAPP_f1753944735l_bool: $i > $i > $i ).
thf(hoare_472868247rivs_a_decl,type,
hoare_472868247rivs_a: $i > $i ).
thf(g_decl,type,
g: $i ).
thf(hAPP_f1400872321a_bool_decl,type,
hAPP_f1400872321a_bool: $i > $i > $i ).
thf(hAPP_H1816261935a_bool_decl,type,
hAPP_H1816261935a_bool: $i > $i > $i ).
thf(insert1871499715iple_a_decl,type,
insert1871499715iple_a: $i ).
thf(hoare_1050552211iple_a_decl,type,
hoare_1050552211iple_a: $i > $i > $i > $i ).
thf(cOMBK_1458035955bool_a_decl,type,
cOMBK_1458035955bool_a: $i > $i ).
thf(cOMBK_bool_state_decl,type,
cOMBK_bool_state: $i > $i ).
thf(fFalse_decl,type,
fFalse: $i ).
thf(c_decl,type,
c: $i ).
thf(hAPP_f762886889e_bool_decl,type,
hAPP_f762886889e_bool: $i > $i > $i ).
thf(hAPP_f1261923407e_bool_decl,type,
hAPP_f1261923407e_bool: $i > $i > $i ).
thf(cOMBC_892787026e_bool_decl,type,
cOMBC_892787026e_bool: $i ).
thf(hAPP_f963367678e_bool_decl,type,
hAPP_f963367678e_bool: $i > $i > $i ).
thf(cOMBB_145932198bool_a_decl,type,
cOMBB_145932198bool_a: $i > $i ).
thf(cOMBS_1378840469l_bool_decl,type,
cOMBS_1378840469l_bool: $i ).
thf(hAPP_f1509969235l_bool_decl,type,
hAPP_f1509969235l_bool: $i > $i > $i ).
thf(cOMBB_1355796797bool_a_decl,type,
cOMBB_1355796797bool_a: $i > $i ).
thf(cOMBB_188601460_state_decl,type,
cOMBB_188601460_state: $i > $i ).
thf(fconj_decl,type,
fconj: $i ).
thf(p_decl,type,
p: $i ).
thf(hAPP_f1759915619e_bool_decl,type,
hAPP_f1759915619e_bool: $i > $i > $i ).
thf(cOMBB_160679318_state_decl,type,
cOMBB_160679318_state: $i > $i ).
thf(fNot_decl,type,
fNot: $i ).
thf(b_decl,type,
b: $i ).
thf(bot_bo1687970473a_bool_decl,type,
bot_bo1687970473a_bool: $i ).
thf(is_bool_decl,type,
is_bool: $i > $o ).
thf(bot_bot_bool_decl,type,
bot_bot_bool: $i ).
thf(hAPP_f1826273671iple_a_decl,type,
hAPP_f1826273671iple_a: $i > $i > $i ).
thf(finite233325225iple_a_decl,type,
finite233325225iple_a: $i > $i ).
thf(the_Ho1745054714iple_a_decl,type,
the_Ho1745054714iple_a: $i ).
thf(finite388748825iple_a_decl,type,
finite388748825iple_a: $i > $i > $i ).
thf(hAPP_a2036067514e_bool_decl,type,
hAPP_a2036067514e_bool: $i > $i > $i ).
thf(hAPP_b540892988e_bool_decl,type,
hAPP_b540892988e_bool: $i > $i > $i ).
thf(hAPP_f1824947087e_bool_decl,type,
hAPP_f1824947087e_bool: $i > $i > $i ).
thf(cOMBC_41962815e_bool_decl,type,
cOMBC_41962815e_bool: $i ).
thf(hAPP_b2019457360e_bool_decl,type,
hAPP_b2019457360e_bool: $i > $i > $i ).
thf(hAPP_a723219176e_bool_decl,type,
hAPP_a723219176e_bool: $i > $i > $i ).
thf(hAPP_f340725611e_bool_decl,type,
hAPP_f340725611e_bool: $i > $i > $i ).
thf(cOMBB_1348041619bool_a_decl,type,
cOMBB_1348041619bool_a: $i > $i ).
thf(hAPP_f167292325e_bool_decl,type,
hAPP_f167292325e_bool: $i > $i > $i ).
thf(hAPP_a849909144l_bool_decl,type,
hAPP_a849909144l_bool: $i > $i > $i ).
thf(skip_decl,type,
skip: $i ).
thf(semi_decl,type,
semi: $i > $i > $i ).
thf(hAPP_state_bool_decl,type,
hAPP_state_bool: $i > $i > $i ).
thf(cOMBC_231445413l_bool_decl,type,
cOMBC_231445413l_bool: $i ).
thf(hAPP_bool_bool_decl,type,
hAPP_bool_bool: $i > $i > $i ).
thf(hAPP_s58564346l_bool_decl,type,
hAPP_s58564346l_bool: $i > $i > $i ).
thf(hAPP_H562195827a_bool_decl,type,
hAPP_H562195827a_bool: $i > $i > $i ).
thf(fequal1878252616iple_a_decl,type,
fequal1878252616iple_a: $i ).
thf(hAPP_H1877746411l_bool_decl,type,
hAPP_H1877746411l_bool: $i > $i > $i ).
thf(hAPP_f13210641l_bool_decl,type,
hAPP_f13210641l_bool: $i > $i > $i ).
thf(cOMBB_633860163iple_a_decl,type,
cOMBB_633860163iple_a: $i > $i ).
thf(hAPP_b589554111l_bool_decl,type,
hAPP_b589554111l_bool: $i > $i > $i ).
thf(hAPP_H1927961489a_bool_decl,type,
hAPP_H1927961489a_bool: $i > $i > $i ).
thf(collec1266446174iple_a_decl,type,
collec1266446174iple_a: $i > $i ).
thf(cOMBK_1150238960iple_a_decl,type,
cOMBK_1150238960iple_a: $i > $i ).
thf(fTrue_decl,type,
fTrue: $i ).
thf(finite1948426435iple_a_decl,type,
finite1948426435iple_a: $i > $i > $i ).
thf(finite520909254iple_a_decl,type,
finite520909254iple_a: $i > $i > $i ).
thf(hAPP_s1806633685e_bool_decl,type,
hAPP_s1806633685e_bool: $i > $i > $i ).
thf(hAPP_f817621513e_bool_decl,type,
hAPP_f817621513e_bool: $i > $i > $i ).
thf(cOMBC_2027030106e_bool_decl,type,
cOMBC_2027030106e_bool: $i ).
thf(hAPP_f1915402821a_bool_decl,type,
hAPP_f1915402821a_bool: $i > $i > $i ).
thf(cOMBC_2049287834a_bool_decl,type,
cOMBC_2049287834a_bool: $i ).
thf(hAPP_H1926610125l_bool_decl,type,
hAPP_H1926610125l_bool: $i > $i > $i ).
thf(member564727580iple_a_decl,type,
member564727580iple_a: $i ).
thf(finite506133020iple_a_decl,type,
finite506133020iple_a: $i ).
thf(hAPP_H401672213iple_a_decl,type,
hAPP_H401672213iple_a: $i > $i > $i ).
thf(hAPP_H568064713iple_a_decl,type,
hAPP_H568064713iple_a: $i > $i > $i ).
thf(fimplies_decl,type,
fimplies: $i ).
thf(hAPP_f1447988451a_bool_decl,type,
hAPP_f1447988451a_bool: $i > $i > $i ).
thf(cOMBB_545742339iple_a_decl,type,
cOMBB_545742339iple_a: $i > $i ).
thf(hAPP_f1104866853a_bool_decl,type,
hAPP_f1104866853a_bool: $i > $i > $i ).
thf(cOMBS_213702372l_bool_decl,type,
cOMBS_213702372l_bool: $i ).
thf(cOMBB_650444389iple_a_decl,type,
cOMBB_650444389iple_a: $i > $i ).
thf(hAPP_f644196280e_bool_decl,type,
hAPP_f644196280e_bool: $i > $i > $i ).
thf(hAPP_f1259673775l_bool_decl,type,
hAPP_f1259673775l_bool: $i > $i > $i ).
thf(finite1734202118iple_a_decl,type,
finite1734202118iple_a: $i > $i > $i > $i ).
thf(fdisj_decl,type,
fdisj: $i ).
thf(hAPP_f945663555a_bool_decl,type,
hAPP_f945663555a_bool: $i > $i > $i ).
thf(cOMBC_2067518550l_bool_decl,type,
cOMBC_2067518550l_bool: $i ).
thf(fequal_state_decl,type,
fequal_state: $i ).
thf(the_el287271400iple_a_decl,type,
the_el287271400iple_a: $i ).
thf(hAPP_f1945881407l_bool_decl,type,
hAPP_f1945881407l_bool: $i > $i > $i ).
thf(fequal1765155200a_bool_decl,type,
fequal1765155200a_bool: $i ).
thf(hAPP_f1170963427a_bool_decl,type,
hAPP_f1170963427a_bool: $i > $i > $i ).
thf(hAPP_f1874567875a_bool_decl,type,
hAPP_f1874567875a_bool: $i > $i > $i ).
thf(cOMBC_1089176504a_bool_decl,type,
cOMBC_1089176504a_bool: $i ).
thf(hAPP_a1200519163e_bool_decl,type,
hAPP_a1200519163e_bool: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i > $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i > $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i > $i > $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i ).
thf(sk20_decl,type,
sk20: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ semi ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ semi ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ! [E: $i] : ( bot_bo1687970473a_bool @ ( E @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( E @ ( D @ ( B @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( bot_bo1687970473a_bool @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ ( B @ ( A @ sk4 ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( D @ ( C @ ( B @ ( A @ sk4 ) ) @ ( B @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
@+[G: $i] :
~ ! [H: $i] :
( ( H @ ( G @ ( E @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ! [I: $i] :
( ! [J: $i] :
( ( H @ ( J @ ( C @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( I @ ( J @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( I @ ( G @ ( F @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
@+[G: $i] :
~ ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ sk6 ) ) ) ) ) @ ( E @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ! [H: $i] :
( ! [I: $i] :
( ( G @ ( I @ ( C @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( H @ ( I @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( H @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ sk6 ) ) ) ) ) @ ( F @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
@+[G: $i] :
~ ( ! [H: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ sk7 ) ) ) ) ) @ ( H @ ( C @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( G @ ( H @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ sk6 ) ) ) ) ) @ ( F @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ? [C: $i] :
( A
= ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( A @ sk19 @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
<=> ( ? [B: $i,C: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
| ( A = bot_bo1687970473a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite_Osimps) ).
thf(357,plain,
! [A: $i] :
( ( ( ? [B: $i,C: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
| ( A = bot_bo1687970473a_bool ) )
=> ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ? [B: $i,C: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
| ( A = bot_bo1687970473a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(358,plain,
( ! [A: $i] :
( ( ? [B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ? [C: $i] :
( A
= ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
| ( A = bot_bo1687970473a_bool ) )
=> ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ! [A: $i] :
( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ? [B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ? [C: $i] :
( A
= ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
| ( A = bot_bo1687970473a_bool ) ) ) ),
inference(miniscope,[status(thm)],[357]) ).
thf(359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ~ ( C @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( B
!= ( C @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
& ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( B != bot_bo1687970473a_bool ) )
& ( ( A @ sk19 @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A = bot_bo1687970473a_bool )
| ~ ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( A
= ( A @ sk19 @ ( A @ sk20 @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
| ( A = bot_bo1687970473a_bool )
| ~ ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(cnf,[status(esa)],[358]) ).
thf(362,plain,
! [A: $i] :
( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A != bot_bo1687970473a_bool ) ),
inference(cnfConj,[status(thm)],[359]) ).
thf(366,plain,
! [A: $i] :
( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A != bot_bo1687970473a_bool ) ),
inference(lifteq,[status(thm)],[362]) ).
thf(367,plain,
bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL,
inference(simp,[status(thm)],[366]) ).
thf(144,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(758,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(759,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(cnf,[status(esa)],[758]) ).
thf(877,plain,
! [A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ ( A @ hBOOL )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,759]) ).
thf(878,plain,
! [A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ ( A @ hBOOL ) ),
inference(simp,[status(thm)],[877]) ).
thf(892,plain,
! [A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) )
| ~ ( A @ hBOOL ) ),
inference(simp,[status(thm)],[878]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( B @ ( A @ finite520909254iple_a ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____jfehddehev__Otriple) ).
thf(196,plain,
! [A: $i,B: $i] : ( B @ ( A @ finite520909254iple_a ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(197,plain,
! [B: $i,A: $i] : ( B @ ( A @ finite520909254iple_a ) @ is_bool ),
inference(cnf,[status(esa)],[196]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( B @ is_bool )
=> ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ hAPP_bool_bool ) @ is_bool )
| ~ ( B @ is_bool ) ),
inference(cnf,[status(esa)],[170]) ).
thf(1021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ finite520909254iple_a ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[197,171]) ).
thf(1022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ finite520909254iple_a ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1021]) ).
thf(1023,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ finite520909254iple_a ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1022:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ finite520909254iple_a ) ))]]) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ finite520909254iple_a ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1023]) ).
thf(79,axiom,
! [A: $i,B: $i] : ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_fold__graph_OemptyI) ).
thf(455,plain,
! [A: $i,B: $i] : ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(456,plain,
! [B: $i,A: $i] : ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(cnf,[status(esa)],[455]) ).
thf(24,axiom,
~ ( fFalse @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(215,plain,
~ ( fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(216,plain,
~ ( fFalse @ hBOOL ),
inference(polarity_switch,[status(thm)],[215]) ).
thf(1684,plain,
! [B: $i,A: $i] :
( ( ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[456,216]) ).
thf(1685,plain,
! [B: $i,A: $i] :
( ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[1684]) ).
thf(1718,plain,
! [B: $i,A: $i] :
( ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[1685]) ).
thf(145,axiom,
bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_finite_OemptyI) ).
thf(760,plain,
bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(42,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1753944735l_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_Mtc) ).
thf(302,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1753944735l_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(303,plain,
! [B: $i,A: $i] : ( B @ ( A @ hAPP_f1753944735l_bool ) @ is_bool ),
inference(cnf,[status(esa)],[302]) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP_f1753944735l_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[303,171]) ).
thf(1011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP_f1753944735l_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1010]) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ hAPP_f1753944735l_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1011:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ hAPP_f1753944735l_bool ) ))]]) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ hAPP_f1753944735l_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1012]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ! [C: $i] : ( bot_bo1687970473a_bool @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( D @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( D != bot_bo1687970473a_bool )
=> ( ~ ( D @ ( C @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__ne__induct) ).
thf(518,plain,
! [A: $i,B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ! [C: $i] : ( bot_bo1687970473a_bool @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( D @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( D != bot_bo1687970473a_bool )
=> ( ~ ( D @ ( C @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_545742339iple_a @ hAPP_f1447988451a_bool ) @ hAPP_H1927961489a_bool ) )
= ( C @ ( B @ hAPP_H562195827a_bool ) @ ( A @ hAPP_f1753944735l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) ).
thf(232,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_545742339iple_a @ hAPP_f1447988451a_bool ) @ hAPP_H1927961489a_bool ) )
= ( C @ ( B @ hAPP_H562195827a_bool ) @ ( A @ hAPP_f1753944735l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(233,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cOMBB_545742339iple_a @ hAPP_f1447988451a_bool ) @ hAPP_H1927961489a_bool ) )
= ( C @ ( B @ hAPP_H562195827a_bool ) @ ( A @ hAPP_f1753944735l_bool ) ) ),
inference(cnf,[status(esa)],[232]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cOMBB_545742339iple_a @ hAPP_f1447988451a_bool ) @ hAPP_H1927961489a_bool ) )
= ( C @ ( B @ hAPP_H562195827a_bool ) @ ( A @ hAPP_f1753944735l_bool ) ) ),
inference(lifteq,[status(thm)],[233]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_) ).
thf(345,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A != B ) ),
inference(cnf,[status(esa)],[345]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A != B ) ),
inference(lifteq,[status(thm)],[346]) ).
thf(348,plain,
! [A: $i] : ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(simp,[status(thm)],[347]) ).
thf(879,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ $true
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[367,759]) ).
thf(880,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[879]) ).
thf(881,plain,
~ ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[880:[bind(A,$thf( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ))]]) ).
thf(934,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,881]) ).
thf(935,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[934]) ).
thf(950,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) ) ),
inference(simp,[status(thm)],[935]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
thf(381,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(382,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(cnf,[status(esa)],[381]) ).
thf(383,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(lifteq,[status(thm)],[382]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ collec1266446174iple_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__def) ).
thf(186,plain,
! [A: $i] :
( ( A @ collec1266446174iple_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(187,plain,
! [A: $i] :
( ( A @ collec1266446174iple_a )
= A ),
inference(cnf,[status(esa)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( A @ collec1266446174iple_a )
= A ),
inference(lifteq,[status(thm)],[187]) ).
thf(1219,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(rewrite,[status(thm)],[383,188]) ).
thf(1406,plain,
! [A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) ) ),
inference(rewrite,[status(thm)],[950,1219]) ).
thf(54,axiom,
fFalse @ is_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).
thf(349,plain,
fFalse @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(190,plain,
! [A: $i] :
( ( A @ is_bool )
=> ! [B: $i] :
( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(miniscope,[status(thm)],[189]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A )
| ~ ( A @ is_bool ) ),
inference(cnf,[status(esa)],[190]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ~ ( A @ is_bool )
| ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ( ( fFalse @ is_bool )
!= ( A @ is_bool ) )
| ~ $true
| ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[349,192]) ).
thf(1441,plain,
! [B: $i,A: $i] :
( ( ( fFalse @ is_bool )
!= ( A @ is_bool ) )
| ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(simp,[status(thm)],[1440]) ).
thf(1442,plain,
! [A: $i] :
( ( A @ ( fFalse @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= fFalse ),
inference(pattern_uni,[status(thm)],[1441:[bind(A,$thf( fFalse ))]]) ).
thf(1525,plain,
! [A: $i] :
( ( A @ ( fFalse @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= fFalse ),
inference(simp,[status(thm)],[1442]) ).
thf(48,axiom,
( bot_bo1687970473a_bool
= ( fFalse @ cOMBK_1150238960iple_a @ collec1266446174iple_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_empty__def) ).
thf(325,plain,
( bot_bo1687970473a_bool
= ( fFalse @ cOMBK_1150238960iple_a @ collec1266446174iple_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(326,plain,
( ( fFalse @ cOMBK_1150238960iple_a @ collec1266446174iple_a )
= bot_bo1687970473a_bool ),
inference(lifteq,[status(thm)],[325]) ).
thf(783,plain,
( ( fFalse @ cOMBK_1150238960iple_a )
= bot_bo1687970473a_bool ),
inference(rewrite,[status(thm)],[326,188]) ).
thf(1608,plain,
! [A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
= fFalse ),
inference(rewrite,[status(thm)],[1525,783]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ hAPP_H1877746411l_bool ) )
= ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
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] :
( ( C @ ( B @ ( A @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ hAPP_H1877746411l_bool ) )
= ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ hAPP_H1877746411l_bool ) )
= ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(cnf,[status(esa)],[167]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( A @ hAPP_b589554111l_bool ) )
= ( C @ ( B @ ( A @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ hAPP_H1877746411l_bool ) ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( D @ ( C @ hAPP_H1927961489a_bool ) ) )
| ( ( fFalse @ ( B @ hAPP_b589554111l_bool ) )
= ( D @ ( C @ ( B @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ hAPP_H1877746411l_bool ) ) ) ),
inference(paramod_ordered,[status(thm)],[1608,169]) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ( fFalse @ ( B @ hAPP_b589554111l_bool ) )
= ( A @ ( bot_bo1687970473a_bool @ ( B @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ hAPP_H1877746411l_bool ) ) ),
inference(pattern_uni,[status(thm)],[1617:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( bot_bo1687970473a_bool )),bind(D,$thf( A ))]]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ! [C: $i] :
( ( C @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C = B ) )
=> ( ( A @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_the__equality) ).
thf(449,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ! [C: $i] :
( ( C @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C = B ) )
=> ( ( A @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
= ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( C @ ( A @ hAPP_H1877746411l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00) ).
thf(677,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
= ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( C @ ( A @ hAPP_H1877746411l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(19,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_H1927961489a_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc__HOL__) ).
thf(201,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_H1927961489a_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(202,plain,
! [B: $i,A: $i] : ( B @ ( A @ hAPP_H1927961489a_bool ) @ is_bool ),
inference(cnf,[status(esa)],[201]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ is_bool )
=> ( ( A = fFalse )
| ( A = fTrue ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(408,plain,
! [A: $i] :
( ( A @ is_bool )
=> ( ( A = fFalse )
| ( A = fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(25,axiom,
! [A: $i] :
( ! [B: $i] :
~ ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A = bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_equals0I) ).
thf(217,plain,
! [A: $i] :
( ! [B: $i] :
~ ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A = bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_insert__code) ).
thf(276,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Ostate_T) ).
thf(466,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(467,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ( A != B ) ),
inference(cnf,[status(esa)],[466]) ).
thf(468,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ( A != B ) ),
inference(lifteq,[status(thm)],[467]) ).
thf(469,plain,
! [A: $i] : ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL ),
inference(simp,[status(thm)],[468]) ).
thf(1133,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ( ( B @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,892]) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ( ( B @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ) ),
inference(simp,[status(thm)],[1133]) ).
thf(1135,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(pattern_uni,[status(thm)],[1134:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) ))]]) ).
thf(1142,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[1135]) ).
thf(60,axiom,
! [A: $i,B: $i] : ( bot_bo1687970473a_bool @ ( B @ ( skip @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hoare__derivs_OSkip) ).
thf(379,plain,
! [A: $i,B: $i] : ( bot_bo1687970473a_bool @ ( B @ ( skip @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
<=> ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite__insert) ).
thf(384,plain,
! [A: $i,B: $i] :
( ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ( A @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( B @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_finite__Collect__conjI) ).
thf(533,plain,
! [A: $i,B: $i] :
( ( ( A @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( B @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_bot__apply) ).
thf(500,plain,
! [A: $i] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_empty__fold__graphE) ).
thf(715,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(129,axiom,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_el287271400iple_a @ hAPP_f1826273671iple_a ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_the__elem__eq) ).
thf(696,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_el287271400iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(697,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_el287271400iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(cnf,[status(esa)],[696]) ).
thf(698,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_el287271400iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(lifteq,[status(thm)],[697]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( B = bot_bo1687970473a_bool )
=> ~ ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_equals0D) ).
thf(747,plain,
! [A: $i,B: $i] :
( ( B = bot_bo1687970473a_bool )
=> ~ ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(941,plain,
( ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,881]) ).
thf(942,plain,
( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[941]) ).
thf(945,plain,
( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[942]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) )
= ( B @ ( C @ ( A @ hAPP_a723219176e_bool ) @ hAPP_b2019457360e_bool ) ) ),
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] :
( ( C @ ( B @ ( A @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) )
= ( B @ ( C @ ( A @ hAPP_a723219176e_bool ) @ hAPP_b2019457360e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) )
= ( B @ ( C @ ( A @ hAPP_a723219176e_bool ) @ hAPP_b2019457360e_bool ) ) ),
inference(cnf,[status(esa)],[151]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ hAPP_a723219176e_bool ) @ hAPP_b2019457360e_bool ) )
= ( C @ ( B @ ( A @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(1,conjecture,
bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(146,plain,
~ ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(823,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,146]) ).
thf(824,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[823]) ).
thf(826,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[824]) ).
thf(1222,plain,
! [A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(rewrite,[status(thm)],[826,1219]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) ).
thf(462,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A != B ) ),
inference(cnf,[status(esa)],[462]) ).
thf(464,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A != B ) ),
inference(lifteq,[status(thm)],[463]) ).
thf(465,plain,
! [A: $i] : ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(simp,[status(thm)],[464]) ).
thf(838,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[465,146]) ).
thf(839,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[838]) ).
thf(842,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[839]) ).
thf(929,plain,
! [A: $i] :
( ( A
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
| ( ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(simp,[status(thm)],[842]) ).
thf(930,plain,
( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ),
inference(simp,[status(thm)],[929]) ).
thf(101,axiom,
! [A: $i] : ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).
thf(557,plain,
! [A: $i] : ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(558,plain,
! [A: $i] : ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(cnf,[status(esa)],[557]) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ $true
| ~ ( B @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[558,759]) ).
thf(875,plain,
! [B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ ( B @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[874]) ).
thf(876,plain,
! [A: $i] :
~ ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[875:[bind(A,$thf( E )),bind(B,$thf( bot_bo1687970473a_bool @ ( E @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ))]]) ).
thf(898,plain,
! [A: $i] :
~ ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(simp,[status(thm)],[876]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ hAPP_a2036067514e_bool ) )
= ( B @ ( C @ ( A @ hAPP_a1200519163e_bool ) @ hAPP_f1759915619e_bool ) ) ),
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(417,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ hAPP_a2036067514e_bool ) )
= ( B @ ( C @ ( A @ hAPP_a1200519163e_bool ) @ hAPP_f1759915619e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B != bot_bo1687970473a_bool )
=> ? [C: $i] : ( C @ ( B @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__nonempty__imp__fold1Set) ).
thf(651,plain,
! [A: $i,B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B != bot_bo1687970473a_bool )
=> ? [C: $i] : ( C @ ( B @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(724,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ hAPP_a849909144l_bool ) )
= ( C @ ( B @ hAPP_a2036067514e_bool ) @ ( A @ hAPP_f1259673775l_bool ) ) ),
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(619,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ hAPP_a849909144l_bool ) )
= ( C @ ( B @ hAPP_a2036067514e_bool ) @ ( A @ hAPP_f1259673775l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_singleton__conv) ).
thf(577,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(578,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(cnf,[status(esa)],[577]) ).
thf(579,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(lifteq,[status(thm)],[578]) ).
thf(1826,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) )
= ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(rewrite,[status(thm)],[579,188]) ).
thf(939,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,881]) ).
thf(940,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[939]) ).
thf(949,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) ) ),
inference(simp,[status(thm)],[940]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ semi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_com_Osimps_I12_J) ).
thf(157,plain,
! [A: $i,B: $i] :
( skip
!= ( B @ ( A @ semi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ! [C: $i] :
( ( C @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C = B ) )
=> ( A @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_theI) ).
thf(702,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ! [C: $i] :
( ( C @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C = B ) )
=> ( A @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_singletonE) ).
thf(751,plain,
! [A: $i,B: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_insert__iff) ).
thf(559,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(3,axiom,
bot_bot_bool @ is_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).
thf(147,plain,
bot_bot_bool @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ( ( bot_bot_bool @ is_bool )
!= ( A @ is_bool ) )
| ~ $true
| ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[147,192]) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( ( bot_bot_bool @ is_bool )
!= ( A @ is_bool ) )
| ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(simp,[status(thm)],[1437]) ).
thf(1439,plain,
! [A: $i] :
( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= bot_bot_bool ),
inference(pattern_uni,[status(thm)],[1438:[bind(A,$thf( bot_bot_bool ))]]) ).
thf(1524,plain,
! [A: $i] :
( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= bot_bot_bool ),
inference(simp,[status(thm)],[1439]) ).
thf(1790,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( C @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) ) )
| ( bot_bot_bool != fFalse ) ),
inference(paramod_ordered,[status(thm)],[1524,1718]) ).
thf(1795,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( bot_bo1687970473a_bool @ ( C @ ( B @ finite1734202118iple_a ) ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( bot_bot_bool != fFalse ) ),
inference(simp,[status(thm)],[1790]) ).
thf(1800,plain,
! [B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( bot_bot_bool != fFalse ) ),
inference(simp,[status(thm)],[1795]) ).
thf(965,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,898]) ).
thf(966,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[965]) ).
thf(969,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[966]) ).
thf(15,axiom,
fTrue @ is_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fTrue) ).
thf(193,plain,
fTrue @ is_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ( ( fTrue @ is_bool )
!= ( A @ is_bool ) )
| ~ $true
| ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[193,192]) ).
thf(1417,plain,
! [B: $i,A: $i] :
( ( ( fTrue @ is_bool )
!= ( A @ is_bool ) )
| ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= A ) ),
inference(simp,[status(thm)],[1416]) ).
thf(1418,plain,
! [A: $i] :
( ( A @ ( fTrue @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= fTrue ),
inference(pattern_uni,[status(thm)],[1417:[bind(A,$thf( fTrue ))]]) ).
thf(1505,plain,
! [A: $i] :
( ( A @ ( fTrue @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= fTrue ),
inference(simp,[status(thm)],[1418]) ).
thf(1541,plain,
! [B: $i,A: $i] :
( ( ( A @ ( fTrue @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= fTrue ) ),
inference(paramod_ordered,[status(thm)],[1505,1222]) ).
thf(1561,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1541]) ).
thf(1568,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1561]) ).
thf(218,plain,
! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A = bot_bo1687970473a_bool ) ),
inference(miniscope,[status(thm)],[217]) ).
thf(219,plain,
! [A: $i] :
( ( A = bot_bo1687970473a_bool )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(cnf,[status(esa)],[218]) ).
thf(220,plain,
! [A: $i] :
( ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A = bot_bo1687970473a_bool ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_singleton__iff) ).
thf(394,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(395,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ! [A: $i,B: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[394]) ).
thf(396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( C != D ) )
& ( ( A = B )
| ~ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(cnf,[status(esa)],[395]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[396]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A != B ) ),
inference(lifteq,[status(thm)],[398]) ).
thf(401,plain,
! [A: $i] : ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(simp,[status(thm)],[400]) ).
thf(1356,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,146]) ).
thf(1357,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[1356]) ).
thf(1364,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[1357]) ).
thf(1371,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
| ( ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(simp,[status(thm)],[1364]) ).
thf(1372,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool != bot_bo1687970473a_bool )
| ( ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) )
!= ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) ) )
| ( ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(simp,[status(thm)],[1371]) ).
thf(1373,plain,
! [A: $i] :
( ( ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) )
!= ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) ) )
| ( ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(simp,[status(thm)],[1372]) ).
thf(1414,plain,
! [A: $i] :
( ( A
!= ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) ) )
| ( insert1871499715iple_a != insert1871499715iple_a )
| ( ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(simp,[status(thm)],[1373]) ).
thf(1415,plain,
( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ),
inference(simp,[status(thm)],[1414]) ).
thf(2402,plain,
! [A: $i] :
( ( A
!= ( fconj @ cOMBB_188601460_state ) )
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( bot_bo1687970473a_bool @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,1415]) ).
thf(2403,plain,
( ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( bot_bo1687970473a_bool @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( fconj @ cOMBB_188601460_state @ ( fconj @ cOMBB_188601460_state @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2402:[bind(A,$thf( fconj @ cOMBB_188601460_state ))]]) ).
thf(277,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(miniscope,[status(thm)],[276]) ).
thf(278,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
| ~ ( F @ ( E @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ( ( F @ ( E @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( D != F ) )
& ( ( C @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A = C )
| ~ ( C @ ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
inference(cnf,[status(esa)],[277]) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A != C ) ),
inference(cnfConj,[status(thm)],[278]) ).
thf(283,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
| ( A != C ) ),
inference(lifteq,[status(thm)],[280]) ).
thf(284,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(simp,[status(thm)],[283]) ).
thf(67,axiom,
! [A: $i] :
~ ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_empty__iff) ).
thf(405,plain,
! [A: $i] :
~ ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(406,plain,
~ ? [A: $i] : ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(miniscope,[status(thm)],[405]) ).
thf(407,plain,
! [A: $i] :
~ ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(cnf,[status(esa)],[406]) ).
thf(766,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,407]) ).
thf(767,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[766]) ).
thf(770,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[767]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_1089176504a_bool @ hAPP_f1874567875a_bool ) @ hAPP_f1170963427a_bool ) @ hAPP_H562195827a_bool ) )
= ( B @ ( C @ ( A @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_004) ).
thf(475,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_1089176504a_bool @ hAPP_f1874567875a_bool ) @ hAPP_f1170963427a_bool ) @ hAPP_H562195827a_bool ) )
= ( B @ ( C @ ( A @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_the__sym__eq__trivial) ).
thf(164,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_) ).
thf(591,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
= ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).
thf(376,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
= ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( bot_bo1687970473a_bool @ ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( B @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ! [I: $i] :
( ! [J: $i] :
( ( H @ ( J @ ( D @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( I @ ( J @ ( F @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( I @ ( G @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) ) )
=> ( bot_bo1687970473a_bool @ ( A @ ( E @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_conseq12) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( bot_bo1687970473a_bool @ ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( B @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ! [I: $i] :
( ! [J: $i] :
( ( H @ ( J @ ( D @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( I @ ( J @ ( F @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( I @ ( G @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) ) )
=> ( bot_bo1687970473a_bool @ ( A @ ( E @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ( ( fFalse @ is_bool )
!= ( B @ is_bool ) )
| ( B @ ( A @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[349,171]) ).
thf(1019,plain,
! [B: $i,A: $i] :
( ( ( fFalse @ is_bool )
!= ( B @ is_bool ) )
| ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1018]) ).
thf(1020,plain,
! [A: $i] : ( fFalse @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1019:[bind(A,$thf( A )),bind(B,$thf( fFalse ))]]) ).
thf(3092,plain,
! [A: $i] :
( ( A
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) )
| ( bot_bo1687970473a_bool @ hBOOL )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,367]) ).
thf(3093,plain,
( ( bot_bo1687970473a_bool @ hBOOL )
| ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[3092:[bind(A,$thf( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ))]]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( F @ ( E @ ( D @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( bot_bo1687970473a_bool @ ( E @ ( C @ hAPP_a2036067514e_bool ) @ cOMBK_1458035955bool_a @ ( B @ ( F @ ( fequal_state @ ( cOMBC_2027030106e_bool @ hAPP_f817621513e_bool ) @ hAPP_s1806633685e_bool ) @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
=> ( bot_bo1687970473a_bool @ ( C @ ( B @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).
thf(353,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( F @ ( E @ ( D @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( bot_bo1687970473a_bool @ ( E @ ( C @ hAPP_a2036067514e_bool ) @ cOMBK_1458035955bool_a @ ( B @ ( F @ ( fequal_state @ ( cOMBC_2027030106e_bool @ hAPP_f817621513e_bool ) @ hAPP_s1806633685e_bool ) @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
=> ( bot_bo1687970473a_bool @ ( C @ ( B @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( bot_bo1687970473a_bool @ ( E @ ( D @ ( C @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( G @ ( F @ ( C @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( bot_bo1687970473a_bool @ ( E @ ( D @ ( A @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_conseq1) ).
thf(480,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( bot_bo1687970473a_bool @ ( E @ ( D @ ( C @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( G @ ( F @ ( C @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( bot_bo1687970473a_bool @ ( E @ ( D @ ( A @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(392,plain,
! [A: $i] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(393,plain,
! [A: $i] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(cnf,[status(esa)],[392]) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( C @ hBOOL ) )
| ~ $true
| ~ ( C @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[456,759]) ).
thf(1700,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( C @ hBOOL ) )
| ~ ( C @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[1699]) ).
thf(1701,plain,
! [B: $i,A: $i] :
~ ( A @ ( bot_bo1687970473a_bool @ ( A @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[1700:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E @ ( bot_bo1687970473a_bool @ ( E @ ( F @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) ))]]) ).
thf(1723,plain,
! [B: $i,A: $i] :
~ ( A @ ( bot_bo1687970473a_bool @ ( A @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(simp,[status(thm)],[1701]) ).
thf(9771,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( C @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) )
| ~ $true
| ( A @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[393,1723]) ).
thf(9772,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( C @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) )
| ( A @ hBOOL ) ),
inference(simp,[status(thm)],[9771]) ).
thf(9773,plain,
! [B: $i,A: $i] : ( A @ ( bot_bo1687970473a_bool @ ( A @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[9772:[bind(A,$thf( E @ ( bot_bo1687970473a_bool @ ( E @ ( F @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) )),bind(B,$thf( E )),bind(C,$thf( F ))]]) ).
thf(9854,plain,
! [B: $i,A: $i] : ( A @ ( bot_bo1687970473a_bool @ ( A @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(simp,[status(thm)],[9773]) ).
thf(10210,plain,
! [B: $i,A: $i] :
( ( ( A @ ( bot_bo1687970473a_bool @ ( A @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9854,216]) ).
thf(10211,plain,
! [B: $i,A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ ( A @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[10210]) ).
thf(10303,plain,
! [B: $i,A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ ( A @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[10211]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ finite520909254iple_a ) @ hBOOL )
=> ( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( A != bot_bo1687970473a_bool )
=> ( ! [D: $i,E: $i] : ( bot_bo1687970473a_bool @ ( E @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( E @ ( D @ ( B @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A @ ( A @ ( C @ hAPP_f1826273671iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_folding__one_Oclosed) ).
thf(221,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ finite520909254iple_a ) @ hBOOL )
=> ( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( A != bot_bo1687970473a_bool )
=> ( ! [D: $i,E: $i] : ( bot_bo1687970473a_bool @ ( E @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( E @ ( D @ ( B @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A @ ( A @ ( C @ hAPP_f1826273671iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(2423,plain,
! [A: $i] :
( ( A
!= ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a ) )
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( bot_bo1687970473a_bool @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,1415]) ).
thf(2424,plain,
( ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( bot_bo1687970473a_bool @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2423:[bind(A,$thf( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a ))]]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(411,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ hBOOL )
=> ( B
= ( B @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( C @ ( fNot @ hAPP_bool_bool ) @ ( fimplies @ hAPP_b589554111l_bool ) @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( C @ ( fimplies @ hAPP_b589554111l_bool ) @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ) )
& ( ( C @ hBOOL )
=> ( A
= ( B @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( C @ ( fNot @ hAPP_bool_bool ) @ ( fimplies @ hAPP_b589554111l_bool ) @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( C @ ( fimplies @ hAPP_b589554111l_bool ) @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_If__def) ).
thf(243,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ hBOOL )
=> ( B
= ( B @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( C @ ( fNot @ hAPP_bool_bool ) @ ( fimplies @ hAPP_b589554111l_bool ) @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( C @ ( fimplies @ hAPP_b589554111l_bool ) @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ) )
& ( ( C @ hBOOL )
=> ( A
= ( B @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( C @ ( fNot @ hAPP_bool_bool ) @ ( fimplies @ hAPP_b589554111l_bool ) @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( C @ ( fimplies @ hAPP_b589554111l_bool ) @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2067518550l_bool @ hAPP_f945663555a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
= ( B @ ( C @ ( A @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_002) ).
thf(428,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2067518550l_bool @ hAPP_f945663555a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
= ( B @ ( C @ ( A @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(817,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,216]) ).
thf(818,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[817]) ).
thf(828,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[818]) ).
thf(1224,plain,
! [A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
!= fFalse ),
inference(rewrite,[status(thm)],[828,1219]) ).
thf(1586,plain,
! [B: $i,A: $i] :
( ( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) )
| ( bot_bot_bool != fFalse ) ),
inference(paramod_ordered,[status(thm)],[1524,1224]) ).
thf(1590,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( bot_bot_bool != fFalse ) ),
inference(simp,[status(thm)],[1586]) ).
thf(1600,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( bot_bot_bool != fFalse ) ),
inference(simp,[status(thm)],[1590]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_188601460_state @ hAPP_f1259673775l_bool ) @ hAPP_s58564346l_bool ) )
= ( C @ ( B @ hAPP_state_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(265,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_188601460_state @ hAPP_f1259673775l_bool ) @ hAPP_s58564346l_bool ) )
= ( C @ ( B @ hAPP_state_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1434,plain,
! [C: $i,B: $i,A: $i] :
( ( ( fFalse @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( B @ is_bool ) )
| ~ $true
| ( ( C @ ( B @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1020,192]) ).
thf(1435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( fFalse @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( B @ is_bool ) )
| ( ( C @ ( B @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= B ) ),
inference(simp,[status(thm)],[1434]) ).
thf(1436,plain,
! [B: $i,A: $i] :
( ( A @ ( fFalse @ ( B @ hAPP_bool_bool ) @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= ( fFalse @ ( B @ hAPP_bool_bool ) ) ),
inference(pattern_uni,[status(thm)],[1435:[bind(A,$thf( D )),bind(B,$thf( fFalse @ ( D @ hAPP_bool_bool ) )),bind(C,$thf( C ))]]) ).
thf(1521,plain,
! [B: $i,A: $i] :
( ( A @ ( fFalse @ ( B @ hAPP_bool_bool ) @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= ( fFalse @ ( B @ hAPP_bool_bool ) ) ),
inference(simp,[status(thm)],[1436]) ).
thf(21,axiom,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_state_bool ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) ).
thf(206,plain,
! [A: $i,B: $i] : ( B @ ( A @ hAPP_state_bool ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cOMBK_1458035955bool_a @ hAPP_a2036067514e_bool ) )
= 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(439,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cOMBK_1458035955bool_a @ hAPP_a2036067514e_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cOMBK_1458035955bool_a @ hAPP_a2036067514e_bool ) )
= A ),
inference(cnf,[status(esa)],[439]) ).
thf(441,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cOMBK_1458035955bool_a @ hAPP_a2036067514e_bool ) )
= A ),
inference(lifteq,[status(thm)],[440]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ hAPP_a723219176e_bool ) )
= ( C @ ( B @ hAPP_a849909144l_bool ) @ ( A @ hAPP_f167292325e_bool ) ) ),
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] :
( ( C @ ( B @ ( A @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ hAPP_a723219176e_bool ) )
= ( C @ ( B @ hAPP_a849909144l_bool ) @ ( A @ hAPP_f167292325e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ hAPP_a723219176e_bool ) )
= ( C @ ( B @ hAPP_a849909144l_bool ) @ ( A @ hAPP_f167292325e_bool ) ) ),
inference(cnf,[status(esa)],[154]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP_a849909144l_bool ) @ ( A @ hAPP_f167292325e_bool ) )
= ( C @ ( B @ ( A @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ hAPP_a723219176e_bool ) ) ),
inference(lifteq,[status(thm)],[155]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
= ( B @ ( C @ ( A @ hAPP_s58564346l_bool ) @ hAPP_bool_bool ) ) ),
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] :
( ( C @ ( B @ ( A @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
= ( B @ ( C @ ( A @ hAPP_s58564346l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
= ( B @ ( C @ ( A @ hAPP_s58564346l_bool ) @ hAPP_bool_bool ) ) ),
inference(cnf,[status(esa)],[161]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ hAPP_s58564346l_bool ) @ hAPP_bool_bool ) )
= ( C @ ( B @ ( A @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) ) ),
inference(lifteq,[status(thm)],[162]) ).
thf(916,plain,
! [A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true
| ( A @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[393,146]) ).
thf(917,plain,
! [A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ( A @ hBOOL ) ),
inference(simp,[status(thm)],[916]) ).
thf(920,plain,
! [A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( A @ hBOOL ) ),
inference(simp,[status(thm)],[917]) ).
thf(1068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ hAPP_s58564346l_bool ) @ hAPP_bool_bool ) )
!= ( D @ ( fNot @ hAPP_bool_bool ) ) )
| ( ( C @ ( B @ ( A @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( D @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[163,920]) ).
thf(1069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( C @ ( A @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( C @ ( B @ ( A @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( D @ hBOOL ) ),
inference(simp,[status(thm)],[1068]) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( B @ ( C @ ( A @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( C @ hBOOL ) ),
inference(simp,[status(thm)],[1069]) ).
thf(1072,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ hAPP_a849909144l_bool ) @ ( A @ hAPP_f167292325e_bool ) )
!= ( D @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) ) )
| ( ( E @ ( D @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( E @ ( F @ ( C @ ( B @ ( A @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ hAPP_a723219176e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( F @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[156,1070]) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ hAPP_a849909144l_bool ) @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( A @ ( B @ ( D @ ( C @ ( cOMBC_231445413l_bool @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ hAPP_a723219176e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( B @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[1072:[bind(A,$thf( cOMBC_231445413l_bool )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ hAPP_a849909144l_bool ) ))]]) ).
thf(1075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ hAPP_a849909144l_bool ) @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( A @ ( B @ ( D @ ( C @ ( cOMBC_231445413l_bool @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ hAPP_a723219176e_bool ) @ hAPP_b2019457360e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( B @ hBOOL ) ),
inference(simp,[status(thm)],[1073]) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( C @ hAPP_a849909144l_bool ) @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( A @ ( D @ ( B @ ( C @ ( cOMBC_231445413l_bool @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( B @ hBOOL ) ),
inference(rewrite,[status(thm)],[1075,153]) ).
thf(1167,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cOMBK_1458035955bool_a @ hAPP_a2036067514e_bool ) )
!= ( F @ ( D @ ( E @ ( cOMBC_231445413l_bool @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) ) )
| ( ( C @ ( F @ ( E @ hAPP_a849909144l_bool ) @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( C @ ( A @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( D @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[441,1166]) ).
thf(1168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != F )
| ( ( A @ cOMBK_1458035955bool_a )
!= ( D @ ( E @ ( cOMBC_231445413l_bool @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) ) )
| ( ( C @ ( F @ ( E @ hAPP_a849909144l_bool ) @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( C @ ( A @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( D @ hBOOL ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1169,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ cOMBK_1458035955bool_a )
!= ( C @ ( D @ ( cOMBC_231445413l_bool @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) ) )
| ( ( B @ ( E @ ( D @ hAPP_a849909144l_bool ) @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( B @ ( A @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( C @ hBOOL ) ),
inference(simp,[status(thm)],[1168]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_insertCI) ).
thf(687,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(2019,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[284,216]) ).
thf(2020,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[2019]) ).
thf(2061,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[2020]) ).
thf(2408,plain,
! [A: $i] :
( ( A
!= ( fNot @ cOMBB_160679318_state ) )
| ( ( b @ ( bot_bo1687970473a_bool @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,1415]) ).
thf(2409,plain,
( ( ( b @ ( bot_bo1687970473a_bool @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( fNot @ cOMBB_160679318_state @ ( fNot @ cOMBB_160679318_state @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2408:[bind(A,$thf( fNot @ cOMBB_160679318_state ))]]) ).
thf(869,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ $true
| ~ ( B @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[348,759]) ).
thf(870,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ ( B @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[869]) ).
thf(871,plain,
! [A: $i] :
~ ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[870:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) ))]]) ).
thf(897,plain,
! [A: $i] :
~ ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(simp,[status(thm)],[871]) ).
thf(1223,plain,
! [A: $i] :
~ ( A @ ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(rewrite,[status(thm)],[897,1219]) ).
thf(772,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,216]) ).
thf(773,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[772]) ).
thf(778,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[773]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( B @ ( A @ hoare_1050552211iple_a ) ) )
= ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) ) )
<=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_triple_Oinject) ).
thf(729,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = F )
& ( B = E )
& ( A = D ) )
=> ( ( C @ ( B @ ( A @ hoare_1050552211iple_a ) ) )
= ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ hoare_1050552211iple_a ) ) )
= ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) ) )
=> ( ( C = F )
& ( B = E )
& ( A = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( B
= ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mk__disjoint__insert) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ? [C: $i] :
( ~ ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( B
= ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ hAPP_a1200519163e_bool ) )
= ( C @ ( B @ hAPP_a849909144l_bool ) @ ( A @ hAPP_f644196280e_bool ) ) ),
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(598,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ hAPP_a1200519163e_bool ) )
= ( C @ ( B @ hAPP_a849909144l_bool ) @ ( A @ hAPP_f644196280e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(158,plain,
~ ? [A: $i,B: $i] :
( skip
= ( B @ ( A @ semi ) ) ),
inference(miniscope,[status(thm)],[157]) ).
thf(159,plain,
! [B: $i,A: $i] :
( skip
!= ( B @ ( A @ semi ) ) ),
inference(cnf,[status(esa)],[158]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ semi ) )
!= skip ),
inference(lifteq,[status(thm)],[159]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite233325225iple_a @ hAPP_f1826273671iple_a ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_fold1__singleton) ).
thf(693,plain,
! [A: $i,B: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite233325225iple_a @ hAPP_f1826273671iple_a ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ finite520909254iple_a ) @ hBOOL )
=> ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( D @ hAPP_f1826273671iple_a ) )
= ( B @ ( D @ hAPP_f1826273671iple_a ) @ ( A @ ( C @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_folding__one_Oinsert) ).
thf(484,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ finite520909254iple_a ) @ hBOOL )
=> ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( D @ hAPP_f1826273671iple_a ) )
= ( B @ ( D @ hAPP_f1826273671iple_a ) @ ( A @ ( C @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(16,axiom,
! [A: $i,B: $i] : ( B @ ( A @ finite1948426435iple_a ) @ is_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____jfehddehev__O) ).
thf(194,plain,
! [A: $i,B: $i] : ( B @ ( A @ finite1948426435iple_a ) @ is_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(195,plain,
! [B: $i,A: $i] : ( B @ ( A @ finite1948426435iple_a ) @ is_bool ),
inference(cnf,[status(esa)],[194]) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ finite1948426435iple_a ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,171]) ).
thf(1028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ finite1948426435iple_a ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1027]) ).
thf(1029,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ finite1948426435iple_a ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1028:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ finite1948426435iple_a ) ))]]) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ finite1948426435iple_a ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1029]) ).
thf(90,axiom,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( A
!= ( D @ ( C @ ( B @ hoare_1050552211iple_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_triple_Oexhaust) ).
thf(493,plain,
! [A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( A
!= ( D @ ( C @ ( B @ hoare_1050552211iple_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ finite1948426435iple_a ) @ hBOOL )
=> ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( D @ hAPP_f1826273671iple_a ) )
= ( B @ ( D @ hAPP_f1826273671iple_a ) @ ( A @ ( C @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_folding__one__idem_Oinsert__idem) ).
thf(710,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ finite1948426435iple_a ) @ hBOOL )
=> ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B != bot_bo1687970473a_bool )
=> ( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( D @ hAPP_f1826273671iple_a ) )
= ( B @ ( D @ hAPP_f1826273671iple_a ) @ ( A @ ( C @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(224,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1338,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[401,216]) ).
thf(1339,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[1338]) ).
thf(1360,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[1339]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( bot_bo1687970473a_bool @ ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( bot_bo1687970473a_bool @ ( B @ ( A @ ( F @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( bot_bo1687970473a_bool @ ( B @ ( A @ ( E @ semi ) @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Comp) ).
thf(317,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( bot_bo1687970473a_bool @ ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( bot_bo1687970473a_bool @ ( B @ ( A @ ( F @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( bot_bo1687970473a_bool @ ( B @ ( A @ ( E @ semi ) @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1004,plain,
! [B: $i,A: $i] :
( ( ( bot_bot_bool @ is_bool )
!= ( B @ is_bool ) )
| ( B @ ( A @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[147,171]) ).
thf(1005,plain,
! [B: $i,A: $i] :
( ( ( bot_bot_bool @ is_bool )
!= ( B @ is_bool ) )
| ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1004]) ).
thf(1006,plain,
! [A: $i] : ( bot_bot_bool @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1005:[bind(A,$thf( A )),bind(B,$thf( bot_bot_bool ))]]) ).
thf(847,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,216]) ).
thf(848,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[847]) ).
thf(857,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[848]) ).
thf(1051,plain,
! [C: $i,B: $i,A: $i] :
( ( ( fFalse @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( C @ is_bool ) )
| ( C @ ( B @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1020,171]) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ( ( fFalse @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( C @ is_bool ) )
| ( C @ ( B @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1051]) ).
thf(1053,plain,
! [B: $i,A: $i] : ( fFalse @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1052:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( fFalse @ ( D @ hAPP_bool_bool ) ))]]) ).
thf(1056,plain,
! [B: $i,A: $i] : ( fFalse @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1053]) ).
thf(1089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( fFalse @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1056,171]) ).
thf(1090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( fFalse @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1089]) ).
thf(1091,plain,
! [C: $i,B: $i,A: $i] : ( fFalse @ ( C @ hAPP_bool_bool ) @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1090:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( fFalse @ ( G @ hAPP_bool_bool ) @ ( E @ hAPP_bool_bool ) ))]]) ).
thf(1096,plain,
! [C: $i,B: $i,A: $i] : ( fFalse @ ( C @ hAPP_bool_bool ) @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1091]) ).
thf(72,axiom,
! [A: $i] :
( ( bot_bo1687970473a_bool
= ( A @ collec1266446174iple_a ) )
<=> ! [B: $i] :
~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_empty__Collect__eq) ).
thf(420,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( bot_bo1687970473a_bool
= ( A @ collec1266446174iple_a ) ) )
& ( ( bot_bo1687970473a_bool
= ( A @ collec1266446174iple_a ) )
=> ! [B: $i] :
~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(cnf,[status(esa)],[224]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_the__eq__trivial) ).
thf(212,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Ostate_T) ).
thf(537,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(117,axiom,
! [A: $i] :
( ( A != bot_bo1687970473a_bool )
<=> ? [B: $i,C: $i] :
( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A
= ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nonempty__iff) ).
thf(622,plain,
! [A: $i] :
( ( ? [B: $i,C: $i] :
( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A
= ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
=> ( A != bot_bo1687970473a_bool ) )
& ( ( A != bot_bo1687970473a_bool )
=> ? [B: $i,C: $i] :
( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A
= ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_insertI2) ).
thf(654,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( F @ ( E @ ( D @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ? [G: $i,H: $i] :
( ! [I: $i] :
( ! [J: $i] :
( ( F @ ( J @ ( G @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( I @ ( J @ ( H @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( I @ ( E @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
& ( bot_bo1687970473a_bool @ ( H @ ( C @ ( G @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) )
=> ( bot_bo1687970473a_bool @ ( A @ ( C @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_conseq) ).
thf(457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( F @ ( E @ ( D @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ? [G: $i,H: $i] :
( ! [I: $i] :
( ! [J: $i] :
( ( F @ ( J @ ( G @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( I @ ( J @ ( H @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( I @ ( E @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
& ( bot_bo1687970473a_bool @ ( H @ ( C @ ( G @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) )
=> ( bot_bo1687970473a_bool @ ( A @ ( C @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(137,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) ).
thf(721,plain,
! [A: $i,B: $i] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ finite520909254iple_a ) @ hBOOL )
=> ( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( A @ ( C @ hAPP_f1826273671iple_a ) )
= ( A @ ( B @ finite233325225iple_a @ hAPP_f1826273671iple_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_folding__one_Oeq__fold) ).
thf(569,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ finite520909254iple_a ) @ hBOOL )
=> ( ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( A @ ( C @ hAPP_f1826273671iple_a ) )
= ( A @ ( B @ finite233325225iple_a @ hAPP_f1826273671iple_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1706,plain,
! [B: $i,A: $i] :
( ( ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[456,146]) ).
thf(1707,plain,
! [B: $i,A: $i] :
( ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[1706]) ).
thf(1715,plain,
! [B: $i,A: $i] :
( ( B @ ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[1707]) ).
thf(774,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,146]) ).
thf(775,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[774]) ).
thf(779,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[775]) ).
thf(7564,plain,
! [B: $i,A: $i] :
( ( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) )
| ~ ( bot_bot_bool @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[1524,1223]) ).
thf(7605,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ~ ( bot_bot_bool @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[7564]) ).
thf(7624,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ~ ( bot_bot_bool @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[7605]) ).
thf(30,axiom,
! [A: $i,B: $i] :
~ ( B @ ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_empty__fold1SetE) ).
thf(235,plain,
! [A: $i,B: $i] :
~ ( B @ ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(236,plain,
~ ? [A: $i,B: $i] : ( B @ ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(miniscope,[status(thm)],[235]) ).
thf(237,plain,
! [B: $i,A: $i] :
~ ( B @ ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(cnf,[status(esa)],[236]) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ( ( fTrue @ is_bool )
!= ( B @ is_bool ) )
| ( B @ ( A @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[193,171]) ).
thf(1008,plain,
! [B: $i,A: $i] :
( ( ( fTrue @ is_bool )
!= ( B @ is_bool ) )
| ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1007]) ).
thf(1009,plain,
! [A: $i] : ( fTrue @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1008:[bind(A,$thf( A )),bind(B,$thf( fTrue ))]]) ).
thf(1044,plain,
! [C: $i,B: $i,A: $i] :
( ( ( fTrue @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( C @ is_bool ) )
| ( C @ ( B @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1009,171]) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ( ( fTrue @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( C @ is_bool ) )
| ( C @ ( B @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1044]) ).
thf(1046,plain,
! [B: $i,A: $i] : ( fTrue @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1045:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( fTrue @ ( D @ hAPP_bool_bool ) ))]]) ).
thf(1049,plain,
! [B: $i,A: $i] : ( fTrue @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1046]) ).
thf(1079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( fTrue @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1049,171]) ).
thf(1080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( fTrue @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1079]) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] : ( fTrue @ ( C @ hAPP_bool_bool ) @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1080:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( fTrue @ ( G @ hAPP_bool_bool ) @ ( E @ hAPP_bool_bool ) ))]]) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] : ( fTrue @ ( C @ hAPP_bool_bool ) @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1081]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) )
= ( B @ ( C @ ( A @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00) ).
thf(203,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) )
= ( B @ ( C @ ( A @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) )
= ( B @ ( C @ ( A @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) ) ),
inference(cnf,[status(esa)],[203]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) )
= ( B @ ( C @ ( A @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a )
= bot_bo1687970473a_bool ) )
& ( ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Collect__conv__if2) ).
thf(508,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a )
= bot_bo1687970473a_bool ) )
& ( ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ( ( A @ ( fTrue @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) )
| ( fTrue != fFalse ) ),
inference(paramod_ordered,[status(thm)],[1505,1224]) ).
thf(1555,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ( fTrue != fFalse ) ),
inference(simp,[status(thm)],[1552]) ).
thf(1563,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ( fTrue != fFalse ) ),
inference(simp,[status(thm)],[1555]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ semi ) )
= ( D @ ( C @ semi ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_com_Osimps_I3_J) ).
thf(172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ semi ) )
= ( D @ ( C @ semi ) ) ) )
& ( ( ( B @ ( A @ semi ) )
= ( D @ ( C @ semi ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(173,plain,
( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ semi ) )
= ( D @ ( C @ semi ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ semi ) )
= ( D @ ( C @ semi ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(miniscope,[status(thm)],[172]) ).
thf(174,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( F @ ( E @ semi ) )
= ( H @ ( G @ semi ) ) )
| ( F != H )
| ( E != G ) )
& ( ( B = D )
| ( ( B @ ( A @ semi ) )
!= ( D @ ( C @ semi ) ) ) )
& ( ( A = C )
| ( ( B @ ( A @ semi ) )
!= ( D @ ( C @ semi ) ) ) ) ),
inference(cnf,[status(esa)],[173]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ semi ) )
!= ( D @ ( C @ semi ) ) ) ),
inference(cnfConj,[status(thm)],[174]) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ semi ) )
!= ( D @ ( C @ semi ) ) ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(179,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ semi ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[178]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ semi ) @ ( B @ sk1 ) )
= A ),
inference(cnf,[status(esa)],[179]) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ semi ) @ ( B @ sk1 ) )
= A ),
inference(lifteq,[status(thm)],[180]) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP_H1927961489a_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[202,171]) ).
thf(1002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP_H1927961489a_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1001]) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1002:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ hAPP_H1927961489a_bool ) ))]]) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ hAPP_H1927961489a_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1003]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_insertE) ).
thf(530,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__absorb) ).
thf(718,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ finite1948426435iple_a ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_folding__one__idem_Oidem) ).
thf(298,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ finite1948426435iple_a ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1488,plain,
! [C: $i,B: $i,A: $i] :
( ( ( fTrue @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( B @ is_bool ) )
| ~ $true
| ( ( C @ ( B @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1009,192]) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ( ( fTrue @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( B @ is_bool ) )
| ( ( C @ ( B @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= B ) ),
inference(simp,[status(thm)],[1488]) ).
thf(1490,plain,
! [B: $i,A: $i] :
( ( A @ ( fTrue @ ( B @ hAPP_bool_bool ) @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= ( fTrue @ ( B @ hAPP_bool_bool ) ) ),
inference(pattern_uni,[status(thm)],[1489:[bind(A,$thf( D )),bind(B,$thf( fTrue @ ( D @ hAPP_bool_bool ) )),bind(C,$thf( C ))]]) ).
thf(1510,plain,
! [B: $i,A: $i] :
( ( A @ ( fTrue @ ( B @ hAPP_bool_bool ) @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= ( fTrue @ ( B @ hAPP_bool_bool ) ) ),
inference(simp,[status(thm)],[1490]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ finite233325225iple_a @ hAPP_f1826273671iple_a ) )
= ( B @ ( A @ finite388748825iple_a ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fold1__def) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ finite233325225iple_a @ hAPP_f1826273671iple_a ) )
= ( B @ ( A @ finite388748825iple_a ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ semi ) )
!= ( D @ ( C @ semi ) ) ) ),
inference(cnfConj,[status(thm)],[174]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ semi ) )
!= ( D @ ( C @ semi ) ) ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(182,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ semi ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[181]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ semi ) @ ( A @ sk2 ) )
= B ),
inference(cnf,[status(esa)],[182]) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ semi ) @ ( A @ sk2 ) )
= B ),
inference(lifteq,[status(thm)],[183]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( C @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cut) ).
thf(601,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( C @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ hAPP_state_bool ) )
= ( C @ ( B @ hAPP_state_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
thf(402,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ hAPP_state_bool ) )
= ( C @ ( B @ hAPP_state_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(832,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[465,216]) ).
thf(833,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[832]) ).
thf(843,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[833]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
<=> ? [D: $i,E: $i,F: $i] :
( ~ ( E @ ( D @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( F @ ( E @ ( D @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
& ( C = F )
& ( B
= ( E @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_fold1Set_Osimps) ).
thf(286,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i,F: $i] :
( ~ ( E @ ( D @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( F @ ( E @ ( D @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
& ( C = F )
& ( B
= ( E @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
=> ( C @ ( B @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ? [D: $i,E: $i,F: $i] :
( ~ ( E @ ( D @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( F @ ( E @ ( D @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
& ( C = F )
& ( B
= ( E @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_bool_state @ hAPP_state_bool ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) ).
thf(445,plain,
! [A: $i,B: $i] :
( ( A @ is_bool )
=> ( ( B @ ( A @ cOMBK_bool_state @ hAPP_state_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( B != bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_fold1Set__nonempty) ).
thf(572,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( B != bot_bo1687970473a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(786,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool != bot_bo1687970473a_bool )
| ( ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= finite506133020iple_a ) ),
inference(simp,[status(thm)],[770]) ).
thf(787,plain,
! [A: $i] :
( ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= finite506133020iple_a ),
inference(simp,[status(thm)],[786]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ? [D: $i] : ( D @ ( C @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__imp__fold__graph) ).
thf(713,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ? [D: $i] : ( D @ ( C @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_insert__commute) ).
thf(350,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( bot_bo1687970473a_bool @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_doubleton__eq__iff) ).
thf(540,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( bot_bo1687970473a_bool @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
& ( ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( bot_bo1687970473a_bool @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(2473,plain,
! [A: $i] :
( ( A != bot_bot_bool )
| ( bot_bo1687970473a_bool @ is_bool )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,147]) ).
thf(2474,plain,
( ( bot_bo1687970473a_bool @ is_bool )
| ( bot_bot_bool @ ( bot_bot_bool @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2473:[bind(A,$thf( bot_bot_bool ))]]) ).
thf(943,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[465,881]) ).
thf(944,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[943]) ).
thf(947,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) ) ),
inference(simp,[status(thm)],[944]) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( ( B @ ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,237]) ).
thf(794,plain,
! [B: $i,A: $i] :
( ( B @ ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[793]) ).
thf(796,plain,
! [B: $i,A: $i] :
( ( B @ ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[794]) ).
thf(1587,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) ) )
| ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(paramod_ordered,[status(thm)],[1524,796]) ).
thf(1593,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(simp,[status(thm)],[1587]) ).
thf(1603,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(simp,[status(thm)],[1593]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ semi ) )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_com_Osimps_I13_J) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ semi ) )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(120,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insertI1) ).
thf(649,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( ( bot_bot_bool @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( C @ is_bool ) )
| ( C @ ( B @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1006,171]) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
( ( ( bot_bot_bool @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( C @ is_bool ) )
| ( C @ ( B @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1037]) ).
thf(1039,plain,
! [B: $i,A: $i] : ( bot_bot_bool @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1038:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( bot_bot_bool @ ( D @ hAPP_bool_bool ) ))]]) ).
thf(1043,plain,
! [B: $i,A: $i] : ( bot_bot_bool @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1039]) ).
thf(887,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ ( A @ hBOOL ) ),
inference(eqfactor_ordered,[status(thm)],[759]) ).
thf(890,plain,
! [A: $i] :
( ( ( A @ ( fNot @ hAPP_bool_bool ) )
!= A )
| ~ ( A @ hBOOL ) ),
inference(simp,[status(thm)],[887]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(594,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(139,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_insert__absorb2) ).
thf(726,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(764,plain,
( ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,146]) ).
thf(765,plain,
( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[764]) ).
thf(769,plain,
( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[765]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2027030106e_bool @ hAPP_f817621513e_bool ) @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) )
= ( B @ ( C @ ( A @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) ).
thf(198,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2027030106e_bool @ hAPP_f817621513e_bool ) @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) )
= ( B @ ( C @ ( A @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).
thf(330,plain,
! [A: $i] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(853,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,146]) ).
thf(854,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[853]) ).
thf(858,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[854]) ).
thf(239,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( E @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ sk8 ) ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ sk6 ) ) ) ) ) @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ~ ( bot_bo1687970473a_bool @ ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( bot_bo1687970473a_bool @ ( A @ ( E @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ sk8 ) ) ) ) ) @ ( G @ ( F @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ sk7 ) ) ) ) ) @ ( G @ ( D @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ~ ( bot_bo1687970473a_bool @ ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( bot_bo1687970473a_bool @ ( A @ ( E @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ sk7 ) ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ sk6 ) ) ) ) ) @ ( B @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ~ ( bot_bo1687970473a_bool @ ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(cnf,[status(esa)],[238]) ).
thf(240,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( E @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ sk7 ) ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ sk6 ) ) ) ) ) @ ( B @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
| ~ ( bot_bo1687970473a_bool @ ( F @ ( E @ ( D @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(cnfConj,[status(thm)],[239]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBS_1378840469l_bool @ hAPP_f644196280e_bool ) @ hAPP_f1759915619e_bool ) @ hAPP_state_bool ) )
= ( C @ ( B @ hAPP_state_bool ) @ ( C @ ( A @ hAPP_s58564346l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(251,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( cOMBS_1378840469l_bool @ hAPP_f644196280e_bool ) @ hAPP_f1759915619e_bool ) @ hAPP_state_bool ) )
= ( C @ ( B @ hAPP_state_bool ) @ ( C @ ( A @ hAPP_s58564346l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(2417,plain,
! [A: $i] :
( ( A
!= ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a ) )
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( bot_bo1687970473a_bool @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,1415]) ).
thf(2418,plain,
( ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( bot_bo1687970473a_bool @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2417:[bind(A,$thf( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a ))]]) ).
thf(2400,plain,
! [A: $i] :
( ( A != member564727580iple_a )
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( bot_bo1687970473a_bool @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,1415]) ).
thf(2401,plain,
( ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( bot_bo1687970473a_bool @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( member564727580iple_a @ ( member564727580iple_a @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2400:[bind(A,$thf( member564727580iple_a ))]]) ).
thf(762,plain,
( ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,216]) ).
thf(763,plain,
( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) ),
inference(simp,[status(thm)],[762]) ).
thf(768,plain,
( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) )
!= fFalse ),
inference(simp,[status(thm)],[763]) ).
thf(1449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( bot_bot_bool @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( B @ is_bool ) )
| ~ $true
| ( ( C @ ( B @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1006,192]) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ( ( bot_bot_bool @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( B @ is_bool ) )
| ( ( C @ ( B @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= B ) ),
inference(simp,[status(thm)],[1449]) ).
thf(1451,plain,
! [B: $i,A: $i] :
( ( A @ ( bot_bot_bool @ ( B @ hAPP_bool_bool ) @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= ( bot_bot_bool @ ( B @ hAPP_bool_bool ) ) ),
inference(pattern_uni,[status(thm)],[1450:[bind(A,$thf( D )),bind(B,$thf( bot_bot_bool @ ( D @ hAPP_bool_bool ) )),bind(C,$thf( C ))]]) ).
thf(1528,plain,
! [B: $i,A: $i] :
( ( A @ ( bot_bot_bool @ ( B @ hAPP_bool_bool ) @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
= ( bot_bot_bool @ ( B @ hAPP_bool_bool ) ) ),
inference(simp,[status(thm)],[1451]) ).
thf(776,plain,
! [B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,407]) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[776]) ).
thf(780,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[777]) ).
thf(74,axiom,
! [A: $i] :
( ( ( A @ collec1266446174iple_a )
= bot_bo1687970473a_bool )
<=> ! [B: $i] :
~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Collect__empty__eq) ).
thf(431,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ collec1266446174iple_a )
= bot_bo1687970473a_bool ) )
& ( ( ( A @ collec1266446174iple_a )
= bot_bo1687970473a_bool )
=> ! [B: $i] :
~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( fTrue @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) ) )
| ~ ( fTrue @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[1505,237]) ).
thf(1554,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ~ ( fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[1549]) ).
thf(1562,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ~ ( fTrue @ hBOOL ) ),
inference(simp,[status(thm)],[1554]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ hAPP_f1826273671iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ~ ( bot_bo1687970473a_bool @ ( A @ ( B @ ( C @ sk5 ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( B @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A = bot_bo1687970473a_bool )
| ~ ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ~ ( C @ ( B @ finite520909254iple_a ) @ hBOOL ) ),
inference(cnf,[status(esa)],[221]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ hAPP_f1826273671iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ~ ( bot_bo1687970473a_bool @ ( A @ ( B @ ( C @ sk5 ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( B @ ( C @ sk5 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( B @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
| ~ ( A @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
| ~ ( C @ ( B @ finite520909254iple_a ) @ hBOOL )
| ( A = bot_bo1687970473a_bool ) ),
inference(lifteq,[status(thm)],[222]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_insert__not__empty) ).
thf(608,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ finite520909254iple_a ) @ hBOOL )
=> ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hAPP_f1826273671iple_a ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_folding__one_Osingleton) ).
thf(306,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ finite520909254iple_a ) @ hBOOL )
=> ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( C @ hAPP_f1826273671iple_a ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL )
<=> ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_bot__empty__eq) ).
thf(226,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1071,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ hAPP_a723219176e_bool ) @ hAPP_b2019457360e_bool ) )
!= ( F @ ( D @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) @ hAPP_b2019457360e_bool ) ) )
| ( ( E @ ( D @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( E @ ( C @ ( B @ ( A @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( F @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[153,1070]) ).
thf(1074,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != F )
| ( ( C @ ( A @ hAPP_a723219176e_bool ) )
!= ( D @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) ) )
| ( ( E @ ( D @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( E @ ( C @ ( B @ ( A @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( F @ hBOOL ) ),
inference(simp,[status(thm)],[1071]) ).
thf(1076,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP_a723219176e_bool ) )
!= ( C @ ( cOMBC_231445413l_bool @ hAPP_f167292325e_bool ) ) )
| ( ( D @ ( C @ hAPP_s58564346l_bool ) )
!= fNot )
| ( ( D @ ( B @ ( E @ ( A @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) )
| ( E @ hBOOL ) ),
inference(simp,[status(thm)],[1074]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( bot_bo1687970473a_bool
!= ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_empty__not__insert) ).
thf(487,plain,
! [A: $i,B: $i] :
( bot_bo1687970473a_bool
!= ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( D @ ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_fold1Set_Ointros) ).
thf(516,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( D @ ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( B @ ( member564727580iple_a @ ( cOMBC_2067518550l_bool @ hAPP_f945663555a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fdisj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_insert__compr) ).
thf(342,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( B @ ( member564727580iple_a @ ( cOMBC_2067518550l_bool @ hAPP_f945663555a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fdisj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ hBOOL )
=> ( bot_bo1687970473a_bool @ ( D @ ( C @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
=> ( bot_bo1687970473a_bool @ ( D @ ( C @ ( E @ ( B @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBC_231445413l_bool @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_constant) ).
thf(754,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ hBOOL )
=> ( bot_bo1687970473a_bool @ ( D @ ( C @ ( B @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
=> ( bot_bo1687970473a_bool @ ( D @ ( C @ ( E @ ( B @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBC_231445413l_bool @ cOMBB_1348041619bool_a @ hAPP_f340725611e_bool ) @ ( cOMBC_41962815e_bool @ hAPP_f1824947087e_bool ) @ hAPP_b540892988e_bool ) @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(488,plain,
~ ? [A: $i,B: $i] :
( bot_bo1687970473a_bool
= ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(miniscope,[status(thm)],[487]) ).
thf(489,plain,
! [B: $i,A: $i] :
( bot_bo1687970473a_bool
!= ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ),
inference(cnf,[status(esa)],[488]) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool ),
inference(lifteq,[status(thm)],[489]) ).
thf(124,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(675,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( C @ ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,237]) ).
thf(792,plain,
! [C: $i,B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( C @ ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[791]) ).
thf(795,plain,
! [C: $i,B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) ) ),
inference(simp,[status(thm)],[792]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( A @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insert__ident) ).
thf(680,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( A @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
& ( ( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( A @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ~ ! [C: $i] :
( ( B
= ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
=> ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Set_Oset__insert) ).
thf(580,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ~ ! [C: $i] :
( ( B
= ( C @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
=> ( C @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(119,axiom,
! [A: $i] :
( ? [B: $i] : ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
<=> ( A != bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_ex__in__conv) ).
thf(640,plain,
! [A: $i] :
( ( ( A != bot_bo1687970473a_bool )
=> ? [B: $i] : ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ? [B: $i] : ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A != bot_bo1687970473a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( fTrue @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) ) )
| ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) )
!= fTrue ) ),
inference(paramod_ordered,[status(thm)],[1505,796]) ).
thf(1559,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1553]) ).
thf(1566,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) )
!= fTrue ) ),
inference(simp,[status(thm)],[1559]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ finite233325225iple_a @ hAPP_f1826273671iple_a ) )
= ( B @ ( A @ finite388748825iple_a ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ),
inference(cnf,[status(esa)],[148]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ finite233325225iple_a @ hAPP_f1826273671iple_a ) )
= ( B @ ( A @ finite388748825iple_a ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(132,axiom,
! [A: $i] :
~ ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_emptyE) ).
thf(707,plain,
! [A: $i] :
~ ( bot_bo1687970473a_bool @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ ( the_el287271400iple_a @ hAPP_f1826273671iple_a ) )
= ( bot_bo1687970473a_bool @ ( insert1871499715iple_a @ ( cOMBC_1089176504a_bool @ hAPP_f1874567875a_bool ) @ hAPP_f1170963427a_bool ) @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ cOMBB_545742339iple_a @ hAPP_f1447988451a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_the__elem__def) ).
thf(414,plain,
! [A: $i] :
( ( A @ ( the_el287271400iple_a @ hAPP_f1826273671iple_a ) )
= ( bot_bo1687970473a_bool @ ( insert1871499715iple_a @ ( cOMBC_1089176504a_bool @ hAPP_f1874567875a_bool ) @ hAPP_f1170963427a_bool ) @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ cOMBB_545742339iple_a @ hAPP_f1447988451a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(963,plain,
! [B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,898]) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[963]) ).
thf(971,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= ( bot_bo1687970473a_bool @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) ) ),
inference(simp,[status(thm)],[964]) ).
thf(1583,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) ) )
| ~ ( bot_bot_bool @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[1524,237]) ).
thf(1595,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ~ ( bot_bot_bool @ hBOOL ) ),
inference(simp,[status(thm)],[1583]) ).
thf(1605,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ~ ( bot_bot_bool @ hBOOL ) ),
inference(simp,[status(thm)],[1595]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_singleton__inject) ).
thf(327,plain,
! [A: $i,B: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1117,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ( ( B @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[348,892]) ).
thf(1118,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ( ( B @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ) ),
inference(simp,[status(thm)],[1117]) ).
thf(1119,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(pattern_uni,[status(thm)],[1118:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) ))]]) ).
thf(1141,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[1119]) ).
thf(1987,plain,
! [A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(rewrite,[status(thm)],[1141,1219]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( B
= ( C @ finite233325225iple_a ) )
=> ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hAPP_f1826273671iple_a ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_fold1__singleton__def) ).
thf(470,plain,
! [A: $i,B: $i,C: $i] :
( ( B
= ( C @ finite233325225iple_a ) )
=> ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hAPP_f1826273671iple_a ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(165,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(cnf,[status(esa)],[164]) ).
thf(166,plain,
! [A: $i] :
( ( A @ ( fequal1878252616iple_a @ hAPP_H562195827a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(lifteq,[status(thm)],[165]) ).
thf(1220,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(rewrite,[status(thm)],[166,1219]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ! [D: $i] :
( ( D @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( D = C ) )
& ( C @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL ) )
=> ( ( A @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( B @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_the1__equality) ).
thf(585,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ! [D: $i] :
( ( D @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( D = C ) )
& ( C @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL ) )
=> ( ( A @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( B @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( bot_bo1687970473a_bool @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( D @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__induct) ).
thf(370,plain,
! [A: $i,B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( bot_bo1687970473a_bool @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [C: $i,D: $i] :
( ( D @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1217,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool != bot_bo1687970473a_bool )
| ( ( A @ hoare_472868247rivs_a )
!= ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) ) ) ),
inference(simp,[status(thm)],[780]) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ( A @ hoare_472868247rivs_a )
!= ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) ) ),
inference(simp,[status(thm)],[1217]) ).
thf(3094,plain,
! [A: $i] :
( ( A != finite506133020iple_a )
| ( bot_bo1687970473a_bool @ ( bot_bo1687970473a_bool @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,367]) ).
thf(3095,plain,
( ( bot_bo1687970473a_bool @ ( bot_bo1687970473a_bool @ hAPP_f1753944735l_bool ) @ hBOOL )
| ( finite506133020iple_a @ ( finite506133020iple_a @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[3094:[bind(A,$thf( finite506133020iple_a ))]]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( F @ ( E @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
=> ( ( D @ ( F @ ( E @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( F @ ( E @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__fold1SetE) ).
thf(336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( ( C @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( F @ ( E @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) )
=> ( ( D @ ( F @ ( E @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( F @ ( E @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
<=> ( ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
& ~ ( F @ ( E @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( D
= ( G @ ( E @ ( A @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) ) )
& ( C
= ( F @ ( E @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
| ( ( D = B )
& ( C = bot_bo1687970473a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_fold__graph_Osimps) ).
thf(656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
& ~ ( F @ ( E @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( D
= ( G @ ( E @ ( A @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) ) )
& ( C
= ( F @ ( E @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
| ( ( D = B )
& ( C = bot_bo1687970473a_bool ) ) )
=> ( D @ ( C @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ( ( D @ ( C @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ? [E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
& ~ ( F @ ( E @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( D
= ( G @ ( E @ ( A @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) ) )
& ( C
= ( F @ ( E @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) )
| ( ( D = B )
& ( C = bot_bo1687970473a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(8531,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( C @ ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) )
| ( fFalse != fFalse ) ),
inference(paramod_ordered,[status(thm)],[1608,2061]) ).
thf(8532,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( C @ ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) ),
inference(simp,[status(thm)],[8531]) ).
thf(8554,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool ) ),
inference(simp,[status(thm)],[8532]) ).
thf(8564,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool ),
inference(simp,[status(thm)],[8554]) ).
thf(7591,plain,
! [B: $i,A: $i] :
( ( ( A @ ( fTrue @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) )
| ~ ( fTrue @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[1505,1223]) ).
thf(7597,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ~ ( fTrue @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[7591]) ).
thf(7621,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( fTrue @ cOMBK_1150238960iple_a ) )
| ~ ( fTrue @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[7597]) ).
thf(1129,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ( ( B @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[465,892]) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ( ( B @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1131,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(pattern_uni,[status(thm)],[1130:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) ))]]) ).
thf(1140,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[1131]) ).
thf(1787,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( C @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) ) )
| ( fFalse != fFalse ) ),
inference(paramod_ordered,[status(thm)],[1608,1718]) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( C @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) ) ),
inference(simp,[status(thm)],[1787]) ).
thf(1792,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( bot_bo1687970473a_bool @ ( C @ ( B @ finite1734202118iple_a ) ) )
!= bot_bo1687970473a_bool ) ),
inference(simp,[status(thm)],[1788]) ).
thf(1797,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) )
!= bot_bo1687970473a_bool ),
inference(simp,[status(thm)],[1792]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
<=> ( ( B @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite__Collect__disjI) ).
thf(612,plain,
! [A: $i,B: $i] :
( ( ( ( B @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
& ( A @ collec1266446174iple_a @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ finite1948426435iple_a ) @ hBOOL )
=> ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ ( D @ hAPP_f1826273671iple_a ) @ ( A @ ( C @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) )
= ( B @ ( D @ hAPP_f1826273671iple_a ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_folding__one__idem_Oin__idem) ).
thf(497,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ finite1948426435iple_a ) @ hBOOL )
=> ( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( B @ ( D @ hAPP_f1826273671iple_a ) @ ( A @ ( C @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) )
= ( B @ ( D @ hAPP_f1826273671iple_a ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1221,plain,
! [A: $i] : ( A @ ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) @ hBOOL ),
inference(rewrite,[status(thm)],[348,1219]) ).
thf(1622,plain,
! [B: $i,A: $i] :
( ( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) )
| ( fFalse != fFalse ) ),
inference(paramod_ordered,[status(thm)],[1608,1224]) ).
thf(1623,plain,
! [B: $i,A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) ),
inference(simp,[status(thm)],[1622]) ).
thf(1640,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool ) ),
inference(simp,[status(thm)],[1623]) ).
thf(1649,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool ),
inference(simp,[status(thm)],[1640]) ).
thf(2087,plain,
! [A: $i] :
( ( A != fTrue )
| ( bot_bo1687970473a_bool @ is_bool )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,193]) ).
thf(2088,plain,
( ( bot_bo1687970473a_bool @ is_bool )
| ( fTrue @ ( fTrue @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2087:[bind(A,$thf( fTrue ))]]) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( C @ ( bot_bo1687970473a_bool @ ( C @ ( B @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(paramod_ordered,[status(thm)],[1524,1715]) ).
thf(1841,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( bot_bo1687970473a_bool @ ( C @ ( B @ finite1734202118iple_a ) ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(simp,[status(thm)],[1836]) ).
thf(1844,plain,
! [B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( B @ ( A @ finite1734202118iple_a ) ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(simp,[status(thm)],[1841]) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( B @ ( member564727580iple_a @ ( cOMBC_2067518550l_bool @ hAPP_f945663555a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fdisj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_insert__compr__raw) ).
thf(699,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( B @ ( member564727580iple_a @ ( cOMBC_2067518550l_bool @ hAPP_f945663555a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fdisj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(319,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ $true
| ~ ( B @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[469,759]) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ ( B @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[864]) ).
thf(866,plain,
! [A: $i] :
~ ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[865:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) ))]]) ).
thf(896,plain,
! [A: $i] :
~ ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(simp,[status(thm)],[866]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(304,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( E @ ( D @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( C @ ( E @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C @ ( D @ ( A @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) @ ( E @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_fold__graph_OinsertI) ).
thf(390,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( E @ ( D @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( C @ ( E @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C @ ( D @ ( A @ hAPP_H568064713iple_a ) @ hAPP_H401672213iple_a ) @ ( E @ ( D @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ ( A @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(118,axiom,
! [A: $i] :
( ! [B: $i] :
~ ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
<=> ( A = bot_bo1687970473a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_all__not__in__conv) ).
thf(632,plain,
! [A: $i] :
( ( ( A = bot_bo1687970473a_bool )
=> ! [B: $i] :
~ ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) )
& ( ! [B: $i] :
~ ( A @ ( B @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A = bot_bo1687970473a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(2415,plain,
! [A: $i] :
( ( A
!= ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a ) )
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( bot_bo1687970473a_bool @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,1415]) ).
thf(2416,plain,
( ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( bot_bo1687970473a_bool @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2415:[bind(A,$thf( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a ))]]) ).
thf(2393,plain,
! [A: $i] :
( ( A
!= ( fFalse @ cOMBK_bool_state ) )
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( bot_bo1687970473a_bool @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( A @ ( A @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[220,1415]) ).
thf(2394,plain,
( ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( bot_bo1687970473a_bool @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) )
| ( fFalse @ cOMBK_bool_state @ ( fFalse @ cOMBK_bool_state @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[2393:[bind(A,$thf( fFalse @ cOMBK_bool_state ))]]) ).
thf(932,plain,
! [A: $i] :
( ( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[469,881]) ).
thf(933,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) @ hBOOL )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[932]) ).
thf(946,plain,
! [A: $i] :
( ( A @ ( A @ ( fequal_state @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) ) ),
inference(simp,[status(thm)],[933]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_finite_OinsertI) ).
thf(258,plain,
! [A: $i,B: $i] :
( ( B @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(207,plain,
! [B: $i,A: $i] : ( B @ ( A @ hAPP_state_bool ) @ is_bool ),
inference(cnf,[status(esa)],[206]) ).
thf(1024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP_state_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,171]) ).
thf(1025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP_state_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1024]) ).
thf(1026,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ hAPP_state_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1025:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ hAPP_state_bool ) ))]]) ).
thf(1030,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ hAPP_state_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1026]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(478,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(884,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ $true
| ~ ( B @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[465,759]) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ ( B @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(simp,[status(thm)],[884]) ).
thf(886,plain,
! [A: $i] :
~ ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[885:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) ))]]) ).
thf(899,plain,
! [A: $i] :
~ ( A @ ( A @ ( fequal1765155200a_bool @ hAPP_f1945881407l_bool ) @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) @ hBOOL ),
inference(simp,[status(thm)],[886]) ).
thf(788,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool )
| ( ( A @ hoare_472868247rivs_a )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(simp,[status(thm)],[779]) ).
thf(789,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool )
| ( A != g ) ),
inference(simp,[status(thm)],[788]) ).
thf(790,plain,
( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= bot_bo1687970473a_bool ),
inference(simp,[status(thm)],[789]) ).
thf(113,axiom,
! [A: $i] :
( ? [B: $i] :
( ! [C: $i] :
( ( C @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C = B ) )
& ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) )
=> ( A @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_theI_H) ).
thf(603,plain,
! [A: $i] :
( ? [B: $i] :
( ! [C: $i] :
( ( C @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( C = B ) )
& ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) )
=> ( A @ ( the_Ho1745054714iple_a @ hAPP_f1826273671iple_a ) @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(471,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ finite233325225iple_a ) )
=> ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hAPP_f1826273671iple_a ) )
= A ) ),
inference(miniscope,[status(thm)],[470]) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hAPP_f1826273671iple_a ) )
= A )
| ( B
!= ( C @ finite233325225iple_a ) ) ),
inference(cnf,[status(esa)],[471]) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hAPP_f1826273671iple_a ) )
= A )
| ( B
!= ( C @ finite233325225iple_a ) ) ),
inference(lifteq,[status(thm)],[472]) ).
thf(474,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ finite233325225iple_a @ hAPP_f1826273671iple_a ) )
= A ),
inference(simp,[status(thm)],[473]) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( bot_bot_bool @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1043,171]) ).
thf(1059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( bot_bot_bool @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool )
!= ( D @ is_bool ) )
| ( D @ ( C @ hAPP_bool_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1058]) ).
thf(1060,plain,
! [C: $i,B: $i,A: $i] : ( bot_bot_bool @ ( C @ hAPP_bool_bool ) @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(pattern_uni,[status(thm)],[1059:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( bot_bot_bool @ ( G @ hAPP_bool_bool ) @ ( E @ hAPP_bool_bool ) ))]]) ).
thf(1065,plain,
! [C: $i,B: $i,A: $i] : ( bot_bot_bool @ ( C @ hAPP_bool_bool ) @ ( B @ hAPP_bool_bool ) @ ( A @ hAPP_bool_bool ) @ is_bool ),
inference(simp,[status(thm)],[1060]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(506,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a )
= bot_bo1687970473a_bool ) )
& ( ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Collect__conv__if) ).
thf(268,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a )
= bot_bo1687970473a_bool ) )
& ( ( B @ ( A @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fconj @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a )
= ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( B @ collec1266446174iple_a @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( B @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fNot @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( fimplies @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_insert__Collect) ).
thf(442,plain,
! [A: $i,B: $i] :
( ( B @ collec1266446174iple_a @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
= ( B @ ( A @ ( fequal1878252616iple_a @ ( cOMBC_2049287834a_bool @ hAPP_f1915402821a_bool ) @ hAPP_H562195827a_bool ) @ ( fNot @ cOMBB_650444389iple_a @ hAPP_f1400872321a_bool ) @ ( fimplies @ cOMBB_633860163iple_a @ hAPP_f13210641l_bool ) @ ( cOMBS_213702372l_bool @ hAPP_f1104866853a_bool ) @ hAPP_f1400872321a_bool ) @ collec1266446174iple_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( D @ ( bot_bo1687970473a_bool @ ( C @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) ) )
| ( A
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) ) )
| ~ ( A @ is_bool ) ),
inference(paramod_ordered,[status(thm)],[192,796]) ).
thf(1494,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( bot_bo1687970473a_bool @ ( B @ finite388748825iple_a ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ cOMBK_1150238960iple_a ) )
| ~ ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1487]) ).
thf(1514,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ cOMBK_1150238960iple_a ) )
| ~ ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ is_bool ) ),
inference(simp,[status(thm)],[1494]) ).
thf(8642,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ cOMBK_1150238960iple_a ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1514,303]) ).
thf(8643,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ finite388748825iple_a ) )
!= ( bot_bo1687970473a_bool @ ( finite506133020iple_a @ hAPP_f1753944735l_bool ) @ cOMBK_1150238960iple_a ) ),
inference(simp,[status(thm)],[8642]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( bot_bo1687970473a_bool @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( A @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
thf(596,plain,
! [A: $i,B: $i,C: $i] :
( ( bot_bo1687970473a_bool @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ( A @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( A @ ( C @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2027030106e_bool @ hAPP_f817621513e_bool ) @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) )
= ( B @ ( C @ ( A @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( cOMBC_2027030106e_bool @ hAPP_f817621513e_bool ) @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) )
= ( B @ ( C @ ( A @ hAPP_s1806633685e_bool ) @ hAPP_state_bool ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(10330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( C @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) ) )
| ( fFalse != fFalse ) ),
inference(paramod_ordered,[status(thm)],[1608,10303]) ).
thf(10331,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( bot_bo1687970473a_bool @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( C @ finite1734202118iple_a ) ) @ hAPP_H1927961489a_bool ) ) ),
inference(simp,[status(thm)],[10330]) ).
thf(10356,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( ( bot_bo1687970473a_bool @ ( B @ ( C @ finite1734202118iple_a ) ) )
!= bot_bo1687970473a_bool ) ),
inference(simp,[status(thm)],[10331]) ).
thf(10372,plain,
! [B: $i,A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ ( B @ finite1734202118iple_a ) ) )
!= bot_bo1687970473a_bool ),
inference(simp,[status(thm)],[10356]) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ( ( B @ ( fNot @ hAPP_bool_bool ) )
!= B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,890]) ).
thf(1303,plain,
! [B: $i,A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( B @ hBOOL ) )
| ( ( B @ ( fNot @ hAPP_bool_bool ) )
!= B ) ),
inference(simp,[status(thm)],[1302]) ).
thf(1304,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(pattern_uni,[status(thm)],[1303:[bind(A,$thf( E )),bind(B,$thf( bot_bo1687970473a_bool @ ( E @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ))]]) ).
thf(1320,plain,
! [A: $i] :
( ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ ( fNot @ hAPP_bool_bool ) )
!= ( bot_bo1687970473a_bool @ ( A @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) ) ),
inference(simp,[status(thm)],[1304]) ).
thf(4552,plain,
( ( ( member564727580iple_a @ ( member564727580iple_a @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ~ $true
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( bot_bo1687970473a_bool @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(paramod_ordered,[status(thm)],[2401,216]) ).
thf(4553,plain,
( ( ( member564727580iple_a @ ( member564727580iple_a @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) @ hBOOL )
!= ( fFalse @ hBOOL ) )
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( bot_bo1687970473a_bool @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(simp,[status(thm)],[4552]) ).
thf(4627,plain,
( ( ( member564727580iple_a @ ( member564727580iple_a @ sk3 @ ( member564727580iple_a @ hAPP_H1926610125l_bool ) @ hAPP_f1753944735l_bool ) )
!= fFalse )
| ( ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( bot_bo1687970473a_bool @ hAPP_H1926610125l_bool ) )
!= ( g @ hoare_472868247rivs_a ) ) ),
inference(simp,[status(thm)],[4553]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_fold1Set__sing) ).
thf(309,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = C )
=> ( C @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL ) )
& ( ( C @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( A @ finite388748825iple_a ) @ hAPP_H1927961489a_bool ) @ hBOOL )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(491,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( bot_bo1687970473a_bool @ ( E @ ( D @ ( C @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( E @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( G @ ( F @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( bot_bo1687970473a_bool @ ( A @ ( D @ ( C @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_conseq2) ).
thf(254,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( bot_bo1687970473a_bool @ ( E @ ( D @ ( C @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL )
=> ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( E @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL )
=> ( G @ ( F @ ( A @ hAPP_a2036067514e_bool ) @ hAPP_state_bool ) @ hBOOL ) )
=> ( bot_bo1687970473a_bool @ ( A @ ( D @ ( C @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( B @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1575,plain,
! [B: $i,A: $i] :
( ( ( A @ ( bot_bot_bool @ cOMBK_1150238960iple_a @ hAPP_H1927961489a_bool ) )
!= ( B @ ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ hAPP_H1927961489a_bool ) ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(paramod_ordered,[status(thm)],[1524,1222]) ).
thf(1596,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( bot_bo1687970473a_bool @ ( B @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(simp,[status(thm)],[1575]) ).
thf(1606,plain,
! [A: $i] :
( ( ( bot_bo1687970473a_bool @ ( A @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) )
!= ( bot_bot_bool @ cOMBK_1150238960iple_a ) )
| ( ( bot_bo1687970473a_bool @ ( b @ ( fNot @ cOMBB_160679318_state @ hAPP_f1759915619e_bool ) @ ( p @ ( fconj @ cOMBB_188601460_state @ cOMBB_1355796797bool_a @ hAPP_f1509969235l_bool ) @ ( cOMBS_1378840469l_bool @ cOMBB_145932198bool_a @ hAPP_f963367678e_bool ) @ ( cOMBC_892787026e_bool @ hAPP_f1261923407e_bool ) @ hAPP_f762886889e_bool ) @ ( c @ ( fFalse @ cOMBK_bool_state @ cOMBK_1458035955bool_a @ hoare_1050552211iple_a ) ) @ ( insert1871499715iple_a @ hAPP_H1816261935a_bool ) @ hAPP_f1400872321a_bool ) @ ( g @ hoare_472868247rivs_a @ hAPP_f1753944735l_bool ) )
!= bot_bot_bool ) ),
inference(simp,[status(thm)],[1596]) ).
thf(17703,plain,
$false,
inference(e,[status(thm)],[892,1036,1718,760,1031,518,234,1406,1618,449,677,202,408,170,217,276,1142,379,1608,384,533,500,715,698,747,945,153,1222,930,898,417,651,724,619,1826,357,196,949,157,702,751,559,1800,969,881,325,1568,2403,189,284,770,216,475,164,591,1373,376,238,1020,3093,353,480,9854,1415,147,10303,221,2424,411,243,428,1600,265,1521,206,1169,687,920,439,201,381,220,2061,2409,1723,1223,778,302,392,729,260,349,598,160,192,407,693,484,1032,197,493,710,224,456,842,1360,317,156,1006,169,857,1096,188,783,420,225,212,193,537,622,393,654,457,721,569,1715,779,7624,237,1086,205,508,1563,1170,1035,558,530,718,298,1510,1219,148,161,1374,601,402,843,286,577,445,572,1371,787,713,466,181,1224,350,540,2474,947,172,1524,1603,303,208,649,1043,890,758,594,726,769,198,330,462,345,858,367,240,251,2418,2401,768,1528,780,455,431,167,1562,223,608,394,306,226,1364,1076,1166,487,516,342,754,194,1049,490,675,795,680,557,580,640,1070,1566,150,707,414,971,1605,327,1987,441,470,1220,585,370,1218,3095,336,656,8564,7621,1140,1797,612,497,1221,154,465,1649,2088,203,1844,759,699,319,896,304,390,186,632,401,171,2416,2394,946,258,1030,235,207,478,899,151,146,405,790,603,195,474,1056,1065,696,796,506,268,178,442,1505,8643,596,163,200,10372,1320,469,4627,1009,309,215,491,232,254,1606]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW470+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 16:02:31 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.51/1.29 % [INFO] Parsing done (309ms).
% 1.98/1.30 % [INFO] Running in sequential loop mode.
% 2.41/1.69 % [INFO] eprover registered as external prover.
% 2.62/1.70 % [INFO] Scanning for conjecture ...
% 2.83/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 143 axioms. Running axiom selection ...
% 3.03/2.02 % [INFO] Axiom selection finished. Selected 143 axioms (removed 0 axioms).
% 4.23/2.21 % [INFO] Problem is first-order (TPTP FOF).
% 4.23/2.23 % [INFO] Type checking passed.
% 4.23/2.24 % [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 ...
% 102.45/24.69 % External prover 'e' found a proof!
% 102.45/24.69 % [INFO] Killing All external provers ...
% 102.45/24.69 % Time passed: 24161ms (effective reasoning time: 23382ms)
% 102.45/24.69 % 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)>
% 102.45/24.69 % 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
% 102.45/24.69 % No. of inferences in proof: 722
% 102.45/24.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24161 ms resp. 23382 ms w/o parsing
% 98.88/25.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 98.88/25.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------