%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP167^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:28 AM UTC 2026
% Result : Theorem 8.05s 1.61s
% Output : CNFRefutation 8.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 19
% Syntax : Number of formulae : 605 ( 158 unt; 0 typ; 0 def)
% Number of atoms : 5475 (1736 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 7306 (1026 ~;1511 |; 14 &;4692 @)
% ( 0 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 2900 (2900 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 82 usr; 6 con; 0-7 aty)
% Number of variables : 1514 ( 94 ^;1420 !; 0 ?;1514 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aexp,type,
aexp: $tType ).
thf(tp_bexp,type,
bexp: $tType ).
thf(tp_com,type,
com: $tType ).
thf(tp_int,type,
int: $tType ).
thf(tp_list_char,type,
list_char: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_produc1166363805nt_com,type,
produc1166363805nt_com: $tType ).
thf(tp_produc1260470173ar_int,type,
produc1260470173ar_int: $tType ).
thf(tp_set_Pr1148378109ar_int,type,
set_Pr1148378109ar_int: $tType ).
thf(tp_set_Pr866150653nt_com,type,
set_Pr866150653nt_com: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_o,type,
set_o: $tType ).
thf(tp_set_set_nat,type,
set_set_nat: $tType ).
thf(tp_assign,type,
assign: list_char > aexp > com ).
thf(tp_aval,type,
aval: aexp > ( list_char > int ) > int ).
thf(tp_big_big_step,type,
big_big_step: produc1260470173ar_int > ( list_char > int ) > $o ).
thf(tp_bval,type,
bval: bexp > ( list_char > int ) > $o ).
thf(tp_c,type,
c: com ).
thf(tp_c2,type,
c2: com ).
thf(tp_collec676690312nt_com,type,
collec676690312nt_com: ( produc1166363805nt_com > $o ) > set_Pr866150653nt_com ).
thf(tp_collec770796680ar_int,type,
collec770796680ar_int: ( produc1260470173ar_int > $o ) > set_Pr1148378109ar_int ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_fun_up103088396ar_int,type,
fun_up103088396ar_int: ( list_char > int ) > list_char > int > list_char > int ).
thf(tp_if,type,
if: bexp > com > com > com ).
thf(tp_if_int,type,
if_int: $o > int > int > int ).
thf(tp_image_1742782760nt_nat,type,
image_1742782760nt_nat: ( produc1260470173ar_int > nat ) > set_Pr1148378109ar_int > set_nat ).
thf(tp_image_1874758725nt_com,type,
image_1874758725nt_com: ( produc1166363805nt_com > produc1166363805nt_com ) > set_Pr866150653nt_com > set_Pr866150653nt_com ).
thf(tp_image_1968865093ar_int,type,
image_1968865093ar_int: ( produc1166363805nt_com > produc1260470173ar_int ) > set_Pr866150653nt_com > set_Pr1148378109ar_int ).
thf(tp_image_244615942nt_com,type,
image_244615942nt_com: ( nat > produc1166363805nt_com ) > set_nat > set_Pr866150653nt_com ).
thf(tp_image_338722310ar_int,type,
image_338722310ar_int: ( nat > produc1260470173ar_int ) > set_nat > set_Pr1148378109ar_int ).
thf(tp_image_522938432_int_o,type,
image_522938432_int_o: ( produc1260470173ar_int > $o ) > set_Pr1148378109ar_int > set_o ).
thf(tp_image_596692520om_nat,type,
image_596692520om_nat: ( produc1166363805nt_com > nat ) > set_Pr866150653nt_com > set_nat ).
thf(tp_image_786684229nt_com,type,
image_786684229nt_com: ( produc1260470173ar_int > produc1166363805nt_com ) > set_Pr1148378109ar_int > set_Pr866150653nt_com ).
thf(tp_image_880790597ar_int,type,
image_880790597ar_int: ( produc1260470173ar_int > produc1260470173ar_int ) > set_Pr1148378109ar_int > set_Pr1148378109ar_int ).
thf(tp_image_989727966et_nat,type,
image_989727966et_nat: ( produc1260470173ar_int > set_nat ) > set_Pr1148378109ar_int > set_set_nat ).
thf(tp_image_nat_nat,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(tp_member2145628230nt_com,type,
member2145628230nt_com: produc1166363805nt_com > set_Pr866150653nt_com > $o ).
thf(tp_member92250950ar_int,type,
member92250950ar_int: produc1260470173ar_int > set_Pr1148378109ar_int > $o ).
thf(tp_member_nat,type,
member_nat: nat > set_nat > $o ).
thf(tp_member_o,type,
member_o: $o > set_o > $o ).
thf(tp_member_set_nat,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(tp_p,type,
p: ( list_char > int ) > ( list_char > int ) > $o ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(tp_produc1139835093nt_com,type,
produc1139835093nt_com: ( list_char > int ) > com > produc1166363805nt_com ).
thf(tp_produc1179280275nt_com,type,
produc1179280275nt_com: ( ( list_char > int ) > com > set_Pr866150653nt_com ) > produc1166363805nt_com > set_Pr866150653nt_com ).
thf(tp_produc1193801173ar_int,type,
produc1193801173ar_int: com > ( list_char > int ) > produc1260470173ar_int ).
thf(tp_produc1194453555nt_com,type,
produc1194453555nt_com: ( com > ( list_char > int ) > produc1166363805nt_com ) > produc1260470173ar_int > produc1166363805nt_com ).
thf(tp_produc1263502010om_nat,type,
produc1263502010om_nat: ( ( list_char > int ) > com > nat ) > produc1166363805nt_com > nat ).
thf(tp_produc128852371ar_int,type,
produc128852371ar_int: ( com > ( list_char > int ) > set_Pr1148378109ar_int ) > produc1260470173ar_int > set_Pr1148378109ar_int ).
thf(tp_produc1288559923ar_int,type,
produc1288559923ar_int: ( com > ( list_char > int ) > produc1260470173ar_int ) > produc1260470173ar_int > produc1260470173ar_int ).
thf(tp_produc1311963066nt_nat,type,
produc1311963066nt_nat: ( com > ( list_char > int ) > nat ) > produc1260470173ar_int > nat ).
thf(tp_produc1461507731ar_int,type,
produc1461507731ar_int: ( ( list_char > int ) > com > set_Pr1148378109ar_int ) > produc1166363805nt_com > set_Pr1148378109ar_int ).
thf(tp_produc1676975923nt_com,type,
produc1676975923nt_com: ( ( list_char > int ) > com > produc1166363805nt_com ) > produc1166363805nt_com > produc1166363805nt_com ).
thf(tp_produc1716235893nt_com,type,
produc1716235893nt_com: produc1166363805nt_com > produc1260470173ar_int ).
thf(tp_produc1754105456et_nat,type,
produc1754105456et_nat: ( ( list_char > int ) > com > set_nat ) > produc1166363805nt_com > set_nat ).
thf(tp_produc1770201973ar_int,type,
produc1770201973ar_int: produc1260470173ar_int > produc1166363805nt_com ).
thf(tp_produc1771082291ar_int,type,
produc1771082291ar_int: ( ( list_char > int ) > com > produc1260470173ar_int ) > produc1166363805nt_com > produc1260470173ar_int ).
thf(tp_produc1791150095et_nat,type,
produc1791150095et_nat: ( produc1260470173ar_int > set_nat ) > com > ( list_char > int ) > set_nat ).
thf(tp_produc1803493327_com_o,type,
produc1803493327_com_o: ( produc1166363805nt_com > $o ) > ( list_char > int ) > com > $o ).
thf(tp_produc1858366159_int_o,type,
produc1858366159_int_o: ( produc1260470173ar_int > $o ) > com > ( list_char > int ) > $o ).
thf(tp_produc1994108563nt_com,type,
produc1994108563nt_com: ( com > ( list_char > int ) > set_Pr866150653nt_com ) > produc1260470173ar_int > set_Pr866150653nt_com ).
thf(tp_produc613711406_com_o,type,
produc613711406_com_o: ( ( list_char > int ) > com > $o ) > produc1166363805nt_com > $o ).
thf(tp_produc641693072nt_nat,type,
produc641693072nt_nat: ( com > ( list_char > int ) > nat ) > produc1260470173ar_int > nat ).
thf(tp_produc668584238_int_o,type,
produc668584238_int_o: ( com > ( list_char > int ) > $o ) > produc1260470173ar_int > $o ).
thf(tp_produc763543641nt_nat,type,
produc763543641nt_nat: ( produc1260470173ar_int > nat ) > com > ( list_char > int ) > nat ).
thf(tp_produc804153044ar_int,type,
produc804153044ar_int: ( produc1260470173ar_int > produc1260470173ar_int ) > com > ( list_char > int ) > produc1260470173ar_int ).
thf(tp_produc837840349ar_int,type,
produc837840349ar_int: ( com > ( list_char > int ) > produc1260470173ar_int ) > produc1260470173ar_int > produc1260470173ar_int ).
thf(tp_produc857153862et_nat,type,
produc857153862et_nat: ( com > ( list_char > int ) > set_nat ) > produc1260470173ar_int > set_nat ).
thf(tp_produc9062872_int_o,type,
produc9062872_int_o: ( com > ( list_char > int ) > $o ) > produc1260470173ar_int > $o ).
thf(tp_produc991755120et_nat,type,
produc991755120et_nat: ( com > ( list_char > int ) > set_nat ) > produc1260470173ar_int > set_nat ).
thf(tp_q,type,
q: ( list_char > int ) > ( list_char > int ) > $o ).
thf(tp_relati1310524937decomp,type,
relati1310524937decomp: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( list_char > int ) > ( list_char > int ) > $o ).
thf(tp_relati186416454e_flip,type,
relati186416454e_flip: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( list_char > int ) > ( list_char > int ) > $o ).
thf(tp_relati2102071307_hoare,type,
relati2102071307_hoare: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > $o ).
thf(tp_relati23543761ar_int,type,
relati23543761ar_int: ( ( list_char > int ) > ( list_char > int ) > $o ) > bexp > com > nat > ( list_char > int ) > ( list_char > int ) > $o ).
thf(tp_relati775585786_valid,type,
relati775585786_valid: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > $o ).
thf(tp_sK10_SY268,type,
sK10_SY268: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK11_SY277,type,
sK11_SY277: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK12_SY278,type,
sK12_SY278: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK1_SY158,type,
sK1_SY158: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK2_SY270,type,
sK2_SY270: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK3_SY245,type,
sK3_SY245: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK4_SY253,type,
sK4_SY253: com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK5_SY271,type,
sK5_SY271: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK6_SY273,type,
sK6_SY273: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK7_SY257,type,
sK7_SY257: com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK8_SY274,type,
sK8_SY274: ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_sK9_SY268,type,
sK9_SY268: ( ( list_char > int ) > ( list_char > int ) > $o ) > com > com > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > ( ( list_char > int ) > ( list_char > int ) > $o ) > list_char > int ).
thf(tp_seq,type,
seq: com > com > com ).
thf(tp_size_com,type,
size_com: com > nat ).
thf(tp_size_size_com,type,
size_size_com: com > nat ).
thf(tp_skip,type,
skip: com ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_while,type,
while: bexp > com > com ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(3,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Int__Oint_T) ).
thf(194,axiom,
! [P_1: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q_1: ( list_char > int ) > ( list_char > int ) > $o,P_2: ( list_char > int ) > ( list_char > int ) > $o,Q_2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P_1 @ C @ C2 @ Q_1 )
=> ( ( relati2102071307_hoare @ P_2 @ C @ C2 @ Q_2 )
=> ( relati2102071307_hoare
@ ^ [S: list_char > int,S2: list_char > int] :
( ( P_1 @ S @ S2 )
| ( P_2 @ S @ S2 ) )
@ C
@ C2
@ ^ [T4: list_char > int,T5: list_char > int] :
( ( Q_1 @ T4 @ T5 )
| ( Q_2 @ T4 @ T5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_ir__disj) ).
thf(284,axiom,
! [X41: bexp,X42: com,X43: com] :
( skip
!= ( if @ X41 @ X42 @ X43 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_com_Odistinct_I5_J) ).
thf(287,axiom,
! [X51: bexp,X52: com] :
( skip
!= ( while @ X51 @ X52 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_com_Odistinct_I7_J) ).
thf(329,axiom,
! [X31: com,X32: com] :
( skip
!= ( seq @ X31 @ X32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_com_Odistinct_I3_J) ).
thf(338,axiom,
! [X21: list_char,X22: aexp] :
( skip
!= ( assign @ X21 @ X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_com_Odistinct_I1_J) ).
thf(344,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ ( relati186416454e_flip @ P ) @ C @ C2 @ ( relati186416454e_flip @ Q ) )
=> ( relati2102071307_hoare @ P @ C2 @ C @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ir__sym) ).
thf(345,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,R: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ( relati2102071307_hoare @ Q @ D @ skip @ R )
=> ( relati2102071307_hoare @ P @ ( seq @ C @ D ) @ C2 @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ir__Seq1) ).
thf(346,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,R: ( list_char > int ) > ( list_char > int ) > $o,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ P @ C @ skip @ R )
& ( relati775585786_valid @ R @ skip @ C2 @ Q ) )
=> ( relati775585786_valid @ P @ C @ C2 @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ir__valid__decomp2) ).
thf(347,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P @ C @ C2 @ Q )
=> ( ( relati775585786_valid @ P @ C @ skip @ ( relati1310524937decomp @ P @ C @ C2 @ Q ) )
& ( relati775585786_valid @ ( relati1310524937decomp @ P @ C @ C2 @ Q ) @ skip @ C2 @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_ir__valid__decomp1) ).
thf(348,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( P @ S3 @ S4 )
=> ( P3 @ S3 @ S4 ) )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( Q3 @ S3 @ S4 )
=> ( Q @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P3 @ C @ C2 @ Q3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ir__conseq) ).
thf(349,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( Q3 @ S3 @ S4 )
=> ( Q @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P @ C @ C2 @ Q3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ir__post) ).
thf(350,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( P @ S3 @ S4 )
=> ( P3 @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P3 @ C @ C2 @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ir__pre) ).
thf(351,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ skip @ skip @ Q )
= ( ! [S: list_char > int,S2: list_char > int] :
( ( Q @ S @ S2 )
=> ( P @ S @ S2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_ir__hoare__Skip__Skip) ).
thf(352,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o] : ( relati2102071307_hoare @ P @ skip @ skip @ P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_ir__Skip__Skip) ).
thf(353,axiom,
( relati775585786_valid
= ( ^ [P2: ( list_char > int ) > ( list_char > int ) > $o,C3: com,C4: com,Q2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P2 @ C3 @ skip @ ( relati1310524937decomp @ P2 @ C3 @ C4 @ Q2 ) )
& ( relati775585786_valid @ ( relati1310524937decomp @ P2 @ C3 @ C4 @ Q2 ) @ skip @ C4 @ Q2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ir__valid__decomp) ).
thf(354,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P @ C @ C2 @ Q )
=> ( relati2102071307_hoare @ P @ C @ C2 @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_completeness) ).
thf(355,axiom,
! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( relati775585786_valid @ P @ C @ C2 @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_soundness) ).
thf(356,conjecture,
( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
& ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(357,negated_conjecture,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
& ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[356]) ).
thf(358,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
& ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $false ),
inference(unfold_def,[status(thm)],[357]) ).
thf(359,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(360,plain,
( ( ! [P_1: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q_1: ( list_char > int ) > ( list_char > int ) > $o,P_2: ( list_char > int ) > ( list_char > int ) > $o,Q_2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P_1 @ C @ C2 @ Q_1 )
=> ( ( relati2102071307_hoare @ P_2 @ C @ C2 @ Q_2 )
=> ( relati2102071307_hoare
@ ^ [S: list_char > int,S2: list_char > int] :
( ( P_1 @ S @ S2 )
| ( P_2 @ S @ S2 ) )
@ C
@ C2
@ ^ [T4: list_char > int,T5: list_char > int] :
( ( Q_1 @ T4 @ T5 )
| ( Q_2 @ T4 @ T5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(361,plain,
( ( ! [X41: bexp,X42: com,X43: com] :
( skip
!= ( if @ X41 @ X42 @ X43 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(362,plain,
( ( ! [X51: bexp,X52: com] :
( skip
!= ( while @ X51 @ X52 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(363,plain,
( ( ! [X31: com,X32: com] :
( skip
!= ( seq @ X31 @ X32 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(364,plain,
( ( ! [X21: list_char,X22: aexp] :
( skip
!= ( assign @ X21 @ X22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(365,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ ( relati186416454e_flip @ P ) @ C @ C2 @ ( relati186416454e_flip @ Q ) )
=> ( relati2102071307_hoare @ P @ C2 @ C @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(366,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,R: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ( relati2102071307_hoare @ Q @ D @ skip @ R )
=> ( relati2102071307_hoare @ P @ ( seq @ C @ D ) @ C2 @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(367,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,R: ( list_char > int ) > ( list_char > int ) > $o,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ P @ C @ skip @ R )
& ( relati775585786_valid @ R @ skip @ C2 @ Q ) )
=> ( relati775585786_valid @ P @ C @ C2 @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(368,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P @ C @ C2 @ Q )
=> ( ( relati775585786_valid @ P @ C @ skip @ ( relati1310524937decomp @ P @ C @ C2 @ Q ) )
& ( relati775585786_valid @ ( relati1310524937decomp @ P @ C @ C2 @ Q ) @ skip @ C2 @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(369,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( P @ S3 @ S4 )
=> ( P3 @ S3 @ S4 ) )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( Q3 @ S3 @ S4 )
=> ( Q @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P3 @ C @ C2 @ Q3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(370,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( Q3 @ S3 @ S4 )
=> ( Q @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P @ C @ C2 @ Q3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(371,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( P @ S3 @ S4 )
=> ( P3 @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P3 @ C @ C2 @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(372,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ skip @ skip @ Q )
= ( ! [S: list_char > int,S2: list_char > int] :
( ( Q @ S @ S2 )
=> ( P @ S @ S2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(373,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o] : ( relati2102071307_hoare @ P @ skip @ skip @ P ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(374,plain,
( ( relati775585786_valid
= ( ^ [P2: ( list_char > int ) > ( list_char > int ) > $o,C3: com,C4: com,Q2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P2 @ C3 @ skip @ ( relati1310524937decomp @ P2 @ C3 @ C4 @ Q2 ) )
& ( relati775585786_valid @ ( relati1310524937decomp @ P2 @ C3 @ C4 @ Q2 ) @ skip @ C4 @ Q2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(375,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P @ C @ C2 @ Q )
=> ( relati2102071307_hoare @ P @ C @ C2 @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(376,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( relati775585786_valid @ P @ C @ C2 @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(377,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
!= ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
& ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[358]) ).
thf(378,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( relati775585786_valid @ P @ C @ C2 @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(379,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P @ C @ C2 @ Q )
=> ( relati2102071307_hoare @ P @ C @ C2 @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(380,plain,
( ( relati775585786_valid
= ( ^ [P2: ( list_char > int ) > ( list_char > int ) > $o,C3: com,C4: com,Q2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P2 @ C3 @ skip @ ( relati1310524937decomp @ P2 @ C3 @ C4 @ Q2 ) )
& ( relati775585786_valid @ ( relati1310524937decomp @ P2 @ C3 @ C4 @ Q2 ) @ skip @ C4 @ Q2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(381,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o] : ( relati2102071307_hoare @ P @ skip @ skip @ P ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(382,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ skip @ skip @ Q )
= ( ! [S: list_char > int,S2: list_char > int] :
( ( Q @ S @ S2 )
=> ( P @ S @ S2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(383,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( P @ S3 @ S4 )
=> ( P3 @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P3 @ C @ C2 @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(384,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( Q3 @ S3 @ S4 )
=> ( Q @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P @ C @ C2 @ Q3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(385,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,P3: ( list_char > int ) > ( list_char > int ) > $o,Q3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( P @ S3 @ S4 )
=> ( P3 @ S3 @ S4 ) )
=> ( ! [S3: list_char > int,S4: list_char > int] :
( ( Q3 @ S3 @ S4 )
=> ( Q @ S3 @ S4 ) )
=> ( relati2102071307_hoare @ P3 @ C @ C2 @ Q3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(386,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ P @ C @ C2 @ Q )
=> ( ( relati775585786_valid @ P @ C @ skip @ ( relati1310524937decomp @ P @ C @ C2 @ Q ) )
& ( relati775585786_valid @ ( relati1310524937decomp @ P @ C @ C2 @ Q ) @ skip @ C2 @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(387,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,R: ( list_char > int ) > ( list_char > int ) > $o,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ P @ C @ skip @ R )
& ( relati775585786_valid @ R @ skip @ C2 @ Q ) )
=> ( relati775585786_valid @ P @ C @ C2 @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(388,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o,D: com,R: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P @ C @ C2 @ Q )
=> ( ( relati2102071307_hoare @ Q @ D @ skip @ R )
=> ( relati2102071307_hoare @ P @ ( seq @ C @ D ) @ C2 @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(389,plain,
( ( ! [P: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ ( relati186416454e_flip @ P ) @ C @ C2 @ ( relati186416454e_flip @ Q ) )
=> ( relati2102071307_hoare @ P @ C2 @ C @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(390,plain,
( ( ! [X21: list_char,X22: aexp] :
( skip
!= ( assign @ X21 @ X22 ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(391,plain,
( ( ! [X31: com,X32: com] :
( skip
!= ( seq @ X31 @ X32 ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(392,plain,
( ( ! [X51: bexp,X52: com] :
( skip
!= ( while @ X51 @ X52 ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(393,plain,
( ( ! [X41: bexp,X42: com,X43: com] :
( skip
!= ( if @ X41 @ X42 @ X43 ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(394,plain,
( ( ! [P_1: ( list_char > int ) > ( list_char > int ) > $o,C: com,C2: com,Q_1: ( list_char > int ) > ( list_char > int ) > $o,P_2: ( list_char > int ) > ( list_char > int ) > $o,Q_2: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ P_1 @ C @ C2 @ Q_1 )
=> ( ( relati2102071307_hoare @ P_2 @ C @ C2 @ Q_2 )
=> ( relati2102071307_hoare
@ ^ [S: list_char > int,S2: list_char > int] :
( ( P_1 @ S @ S2 )
| ( P_2 @ S @ S2 ) )
@ C
@ C2
@ ^ [T4: list_char > int,T5: list_char > int] :
( ( Q_1 @ T4 @ T5 )
| ( Q_2 @ T4 @ T5 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(395,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(396,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
!= ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
& ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(397,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o,SX4: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX5: list_char > int,SX6: list_char > int] :
( ~ ( SX0 @ SX5 @ SX6 )
| ( SX4 @ SX5 @ SX6 ) )
| ( relati2102071307_hoare @ SX4 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(398,plain,
( ( ! [SX0: bexp,SX1: com,SX2: com] :
( skip
!= ( if @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(399,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
!= ( ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(400,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o,SX4: ( list_char > int ) > ( list_char > int ) > $o,SX5: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( relati2102071307_hoare @ SX4 @ SX1 @ SX2 @ SX5 )
| ( relati2102071307_hoare
@ ^ [SX6: list_char > int,SX7: list_char > int] :
( ( SX0 @ SX6 @ SX7 )
| ( SX4 @ SX6 @ SX7 ) )
@ SX1
@ SX2
@ ^ [SX6: list_char > int,SX7: list_char > int] :
( ( SX3 @ SX6 @ SX7 )
| ( SX5 @ SX6 @ SX7 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(401,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati775585786_valid @ SX0 @ SX1 @ SX2 @ SX3 )
| ( relati2102071307_hoare @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(402,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ SX0 @ skip @ skip @ SX1 )
= ( ! [SX2: list_char > int,SX3: list_char > int] :
( ~ ( SX1 @ SX2 @ SX3 )
| ( SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(403,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SX0 @ SX1 @ SX2 @ SX3 )
| ( relati775585786_valid @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(404,plain,
( ( relati775585786_valid
= ( ^ [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SX0 @ SX1 @ skip @ ( relati1310524937decomp @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SX0 @ SX1 @ SX2 @ SX3 ) @ skip @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(405,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o,SX4: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX5: list_char > int,SX6: list_char > int] :
( ~ ( SX4 @ SX5 @ SX6 )
| ( SX3 @ SX5 @ SX6 ) )
| ( relati2102071307_hoare @ SX0 @ SX1 @ SX2 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(406,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o,SX4: com,SX5: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( relati2102071307_hoare @ SX3 @ SX4 @ skip @ SX5 )
| ( relati2102071307_hoare @ SX0 @ ( seq @ SX1 @ SX4 ) @ SX2 @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(407,plain,
( ( ! [SX0: list_char,SX1: aexp] :
( skip
!= ( assign @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(408,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: ( list_char > int ) > ( list_char > int ) > $o,SX3: com,SX4: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ~ ( ~ ( relati775585786_valid @ SX0 @ SX1 @ skip @ SX2 )
| ~ ( relati775585786_valid @ SX2 @ skip @ SX3 @ SX4 ) )
| ( relati775585786_valid @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(409,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ ( relati186416454e_flip @ SX0 ) @ SX1 @ SX2 @ ( relati186416454e_flip @ SX3 ) )
| ( relati2102071307_hoare @ SX0 @ SX2 @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(410,plain,
( ( ! [SX0: com,SX1: com] :
( skip
!= ( seq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(411,plain,
( ( ! [SX0: bexp,SX1: com] :
( skip
!= ( while @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(412,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o,SX4: ( list_char > int ) > ( list_char > int ) > $o,SX5: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ! [SX6: list_char > int,SX7: list_char > int] :
( ~ ( SX0 @ SX6 @ SX7 )
| ( SX4 @ SX6 @ SX7 ) )
| ~ ! [SX6: list_char > int,SX7: list_char > int] :
( ~ ( SX5 @ SX6 @ SX7 )
| ( SX3 @ SX6 @ SX7 ) )
| ( relati2102071307_hoare @ SX4 @ SX1 @ SX2 @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(413,plain,
( ( ! [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati775585786_valid @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( ~ ( relati775585786_valid @ SX0 @ SX1 @ skip @ ( relati1310524937decomp @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SX0 @ SX1 @ SX2 @ SX3 ) @ skip @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(414,plain,
! [SV1: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ SV1 @ skip @ skip @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(415,plain,
! [SV2: $o] :
( ( ( SV2 = $true )
| ( SV2 = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[395]) ).
thf(416,plain,
( ( ( $true = $true )
| ( $true = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[395]) ).
thf(417,plain,
( ( ( $false = $true )
| ( $false = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[395]) ).
thf(418,plain,
! [SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY80: com,SY81: com,SY82: ( list_char > int ) > ( list_char > int ) > $o,SY83: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV3 @ SY80 @ SY81 @ SY82 )
| ~ ! [SY84: list_char > int,SY85: list_char > int] :
( ~ ( SV3 @ SY84 @ SY85 )
| ( SY83 @ SY84 @ SY85 ) )
| ( relati2102071307_hoare @ SY83 @ SY80 @ SY81 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(419,plain,
! [SV4: bexp] :
( ( ! [SY86: com,SY87: com] :
( skip
!= ( if @ SV4 @ SY86 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(420,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= ( ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(421,plain,
! [SV5: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY88: com,SY89: com,SY90: ( list_char > int ) > ( list_char > int ) > $o,SY91: ( list_char > int ) > ( list_char > int ) > $o,SY92: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV5 @ SY88 @ SY89 @ SY90 )
| ~ ( relati2102071307_hoare @ SY91 @ SY88 @ SY89 @ SY92 )
| ( relati2102071307_hoare
@ ^ [SY93: list_char > int,SY94: list_char > int] :
( ( SV5 @ SY93 @ SY94 )
| ( SY91 @ SY93 @ SY94 ) )
@ SY88
@ SY89
@ ^ [SX6: list_char > int,SX7: list_char > int] :
( ( SY90 @ SX6 @ SX7 )
| ( SY92 @ SX6 @ SX7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(422,plain,
! [SV6: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY97: com,SY98: com,SY99: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati775585786_valid @ SV6 @ SY97 @ SY98 @ SY99 )
| ( relati2102071307_hoare @ SV6 @ SY97 @ SY98 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(423,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY100: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SY100 )
= ( ! [SY101: list_char > int,SY102: list_char > int] :
( ~ ( SY100 @ SY101 @ SY102 )
| ( SV7 @ SY101 @ SY102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(424,plain,
! [SV8: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY103: com,SY104: com,SY105: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV8 @ SY103 @ SY104 @ SY105 )
| ( relati775585786_valid @ SV8 @ SY103 @ SY104 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(425,plain,
( ( ! [SV9: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ SV9 )
= ( ^ [SY106: com,SY107: com,SY108: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV9 @ SY106 @ skip @ ( relati1310524937decomp @ SV9 @ SY106 @ SY107 @ SY108 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV9 @ SY106 @ SY107 @ SY108 ) @ skip @ SY107 @ SY108 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[404]) ).
thf(426,plain,
( ( relati775585786_valid
= ( ^ [SX0: ( list_char > int ) > ( list_char > int ) > $o,SX1: com,SX2: com,SX3: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SX0 @ SX1 @ skip @ ( relati1310524937decomp @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SX0 @ SX1 @ SX2 @ SX3 ) @ skip @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[404]) ).
thf(427,plain,
! [SV10: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY109: com,SY110: com,SY111: ( list_char > int ) > ( list_char > int ) > $o,SY112: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV10 @ SY109 @ SY110 @ SY111 )
| ~ ! [SX5: list_char > int,SX6: list_char > int] :
( ~ ( SY112 @ SX5 @ SX6 )
| ( SY111 @ SX5 @ SX6 ) )
| ( relati2102071307_hoare @ SV10 @ SY109 @ SY110 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(428,plain,
! [SV11: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY115: com,SY116: com,SY117: ( list_char > int ) > ( list_char > int ) > $o,SY118: com,SY119: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV11 @ SY115 @ SY116 @ SY117 )
| ~ ( relati2102071307_hoare @ SY117 @ SY118 @ skip @ SY119 )
| ( relati2102071307_hoare @ SV11 @ ( seq @ SY115 @ SY118 ) @ SY116 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(429,plain,
! [SV12: list_char] :
( ( ! [SY120: aexp] :
( skip
!= ( assign @ SV12 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(430,plain,
! [SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY121: com,SY122: ( list_char > int ) > ( list_char > int ) > $o,SY123: com,SY124: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ~ ( ~ ( relati775585786_valid @ SV13 @ SY121 @ skip @ SY122 )
| ~ ( relati775585786_valid @ SY122 @ skip @ SY123 @ SY124 ) )
| ( relati775585786_valid @ SV13 @ SY121 @ SY123 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(431,plain,
! [SV14: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY125: com,SY126: com,SY127: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ ( relati186416454e_flip @ SV14 ) @ SY125 @ SY126 @ ( relati186416454e_flip @ SY127 ) )
| ( relati2102071307_hoare @ SV14 @ SY126 @ SY125 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(432,plain,
! [SV15: com] :
( ( ! [SY128: com] :
( skip
!= ( seq @ SV15 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(433,plain,
! [SV16: bexp] :
( ( ! [SY129: com] :
( skip
!= ( while @ SV16 @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(434,plain,
! [SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY130: com,SY131: com,SY132: ( list_char > int ) > ( list_char > int ) > $o,SY133: ( list_char > int ) > ( list_char > int ) > $o,SY134: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV17 @ SY130 @ SY131 @ SY132 )
| ~ ! [SY135: list_char > int,SY136: list_char > int] :
( ~ ( SV17 @ SY135 @ SY136 )
| ( SY133 @ SY135 @ SY136 ) )
| ~ ! [SX6: list_char > int,SX7: list_char > int] :
( ~ ( SY134 @ SX6 @ SX7 )
| ( SY132 @ SX6 @ SX7 ) )
| ( relati2102071307_hoare @ SY133 @ SY130 @ SY131 @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(435,plain,
! [SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY139: com,SY140: com,SY141: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati775585786_valid @ SV18 @ SY139 @ SY140 @ SY141 )
| ~ ( ~ ( relati775585786_valid @ SV18 @ SY139 @ skip @ ( relati1310524937decomp @ SV18 @ SY139 @ SY140 @ SY141 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SY139 @ SY140 @ SY141 ) @ skip @ SY140 @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(436,plain,
! [SV2: $o] :
( ( ( SV2 = $true )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(437,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(438,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(439,plain,
! [SV19: com,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY142: com,SY143: ( list_char > int ) > ( list_char > int ) > $o,SY144: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV3 @ SV19 @ SY142 @ SY143 )
| ~ ! [SY84: list_char > int,SY85: list_char > int] :
( ~ ( SV3 @ SY84 @ SY85 )
| ( SY144 @ SY84 @ SY85 ) )
| ( relati2102071307_hoare @ SY144 @ SV19 @ SY142 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(440,plain,
! [SV20: com,SV4: bexp] :
( ( ! [SY147: com] :
( skip
!= ( if @ SV4 @ SV20 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(441,plain,
( ( ~ ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
| ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
| ~ ( ~ ( relati2102071307_hoare @ p @ c @ c2 @ q )
| ~ ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[420]) ).
thf(442,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= ( ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ) )
= $false ),
inference(extcnf_equal_neg,[status(thm)],[420]) ).
thf(443,plain,
! [SV21: com,SV5: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY148: com,SY149: ( list_char > int ) > ( list_char > int ) > $o,SY150: ( list_char > int ) > ( list_char > int ) > $o,SY151: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV5 @ SV21 @ SY148 @ SY149 )
| ~ ( relati2102071307_hoare @ SY150 @ SV21 @ SY148 @ SY151 )
| ( relati2102071307_hoare
@ ^ [SY93: list_char > int,SY94: list_char > int] :
( ( SV5 @ SY93 @ SY94 )
| ( SY150 @ SY93 @ SY94 ) )
@ SV21
@ SY148
@ ^ [SX6: list_char > int,SX7: list_char > int] :
( ( SY149 @ SX6 @ SX7 )
| ( SY151 @ SX6 @ SX7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(444,plain,
! [SV22: com,SV6: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY156: com,SY157: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati775585786_valid @ SV6 @ SV22 @ SY156 @ SY157 )
| ( relati2102071307_hoare @ SV6 @ SV22 @ SY156 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(445,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= ( ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(446,plain,
! [SV24: com,SV8: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY160: com,SY161: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV8 @ SV24 @ SY160 @ SY161 )
| ( relati775585786_valid @ SV8 @ SV24 @ SY160 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(447,plain,
! [SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 )
= ( ^ [SY162: com,SY163: com,SY164: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV25 @ SY162 @ skip @ ( relati1310524937decomp @ SV25 @ SY162 @ SY163 @ SY164 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SY162 @ SY163 @ SY164 ) @ skip @ SY163 @ SY164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(448,plain,
! [SV26: com,SV10: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY165: com,SY166: ( list_char > int ) > ( list_char > int ) > $o,SY167: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV10 @ SV26 @ SY165 @ SY166 )
| ~ ! [SX5: list_char > int,SX6: list_char > int] :
( ~ ( SY167 @ SX5 @ SX6 )
| ( SY166 @ SX5 @ SX6 ) )
| ( relati2102071307_hoare @ SV10 @ SV26 @ SY165 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(449,plain,
! [SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY170: com,SY171: ( list_char > int ) > ( list_char > int ) > $o,SY172: com,SY173: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV11 @ SV27 @ SY170 @ SY171 )
| ~ ( relati2102071307_hoare @ SY171 @ SY172 @ skip @ SY173 )
| ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SY172 ) @ SY170 @ SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(450,plain,
! [SV28: aexp,SV12: list_char] :
( ( skip
!= ( assign @ SV12 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(451,plain,
! [SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY174: ( list_char > int ) > ( list_char > int ) > $o,SY175: com,SY176: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ~ ( ~ ( relati775585786_valid @ SV13 @ SV29 @ skip @ SY174 )
| ~ ( relati775585786_valid @ SY174 @ skip @ SY175 @ SY176 ) )
| ( relati775585786_valid @ SV13 @ SV29 @ SY175 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(452,plain,
! [SV30: com,SV14: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY177: com,SY178: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ ( relati186416454e_flip @ SV14 ) @ SV30 @ SY177 @ ( relati186416454e_flip @ SY178 ) )
| ( relati2102071307_hoare @ SV14 @ SY177 @ SV30 @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(453,plain,
! [SV31: com,SV15: com] :
( ( skip
!= ( seq @ SV15 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(454,plain,
! [SV32: com,SV16: bexp] :
( ( skip
!= ( while @ SV16 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(455,plain,
! [SV33: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY179: com,SY180: ( list_char > int ) > ( list_char > int ) > $o,SY181: ( list_char > int ) > ( list_char > int ) > $o,SY182: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV17 @ SV33 @ SY179 @ SY180 )
| ~ ! [SY135: list_char > int,SY136: list_char > int] :
( ~ ( SV17 @ SY135 @ SY136 )
| ( SY181 @ SY135 @ SY136 ) )
| ~ ! [SX6: list_char > int,SX7: list_char > int] :
( ~ ( SY182 @ SX6 @ SX7 )
| ( SY180 @ SX6 @ SX7 ) )
| ( relati2102071307_hoare @ SY181 @ SV33 @ SY179 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(456,plain,
! [SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY187: com,SY188: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati775585786_valid @ SV18 @ SV34 @ SY187 @ SY188 )
| ~ ( ~ ( relati775585786_valid @ SV18 @ SV34 @ skip @ ( relati1310524937decomp @ SV18 @ SV34 @ SY187 @ SY188 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SV34 @ SY187 @ SY188 ) @ skip @ SY187 @ SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(457,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $true )
| ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[436]) ).
thf(458,plain,
! [SV2: $o] :
( ( ( SV2 = $true )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[436]) ).
thf(459,plain,
( ( ( ~ ( $true
| $true )
| ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[437]) ).
thf(460,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[437]) ).
thf(461,plain,
( ( ( ~ ( $false
| $true )
| ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[438]) ).
thf(462,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[438]) ).
thf(463,plain,
! [SV35: com,SV19: com,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY189: ( list_char > int ) > ( list_char > int ) > $o,SY190: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SY189 )
| ~ ! [SY84: list_char > int,SY85: list_char > int] :
( ~ ( SV3 @ SY84 @ SY85 )
| ( SY190 @ SY84 @ SY85 ) )
| ( relati2102071307_hoare @ SY190 @ SV19 @ SV35 @ SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(464,plain,
! [SV36: com,SV20: com,SV4: bexp] :
( ( skip
!= ( if @ SV4 @ SV20 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(465,plain,
( ( ~ ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
| ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(466,plain,
( ( ~ ( ~ ( relati2102071307_hoare @ p @ c @ c2 @ q )
| ~ ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(467,plain,
! [SV37: com,SV21: com,SV5: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY193: ( list_char > int ) > ( list_char > int ) > $o,SY194: ( list_char > int ) > ( list_char > int ) > $o,SY195: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV5 @ SV21 @ SV37 @ SY193 )
| ~ ( relati2102071307_hoare @ SY194 @ SV21 @ SV37 @ SY195 )
| ( relati2102071307_hoare
@ ^ [SY93: list_char > int,SY94: list_char > int] :
( ( SV5 @ SY93 @ SY94 )
| ( SY194 @ SY93 @ SY94 ) )
@ SV21
@ SV37
@ ^ [SX6: list_char > int,SX7: list_char > int] :
( ( SY193 @ SX6 @ SX7 )
| ( SY195 @ SX6 @ SX7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(468,plain,
! [SV38: com,SV22: com,SV6: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY200: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati775585786_valid @ SV6 @ SV22 @ SV38 @ SY200 )
| ( relati2102071307_hoare @ SV6 @ SV22 @ SV38 @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(469,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
| ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[445]) ).
thf(470,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= ( ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[445]) ).
thf(471,plain,
! [SV39: com,SV24: com,SV8: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY201: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV8 @ SV24 @ SV39 @ SY201 )
| ( relati775585786_valid @ SV8 @ SV24 @ SV39 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(472,plain,
! [SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SV40: com] :
( ( relati775585786_valid @ SV25 @ SV40 )
= ( ^ [SY202: com,SY203: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV25 @ SV40 @ skip @ ( relati1310524937decomp @ SV25 @ SV40 @ SY202 @ SY203 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV40 @ SY202 @ SY203 ) @ skip @ SY202 @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[447]) ).
thf(473,plain,
! [SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 )
= ( ^ [SY162: com,SY163: com,SY164: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV25 @ SY162 @ skip @ ( relati1310524937decomp @ SV25 @ SY162 @ SY163 @ SY164 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SY162 @ SY163 @ SY164 ) @ skip @ SY163 @ SY164 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[447]) ).
thf(474,plain,
! [SV41: com,SV26: com,SV10: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY204: ( list_char > int ) > ( list_char > int ) > $o,SY205: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SY204 )
| ~ ! [SX5: list_char > int,SX6: list_char > int] :
( ~ ( SY205 @ SX5 @ SX6 )
| ( SY204 @ SX5 @ SX6 ) )
| ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(475,plain,
! [SV42: com,SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY208: ( list_char > int ) > ( list_char > int ) > $o,SY209: com,SY210: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV11 @ SV27 @ SV42 @ SY208 )
| ~ ( relati2102071307_hoare @ SY208 @ SY209 @ skip @ SY210 )
| ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SY209 ) @ SV42 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(476,plain,
! [SV28: aexp,SV12: list_char] :
( ( skip
= ( assign @ SV12 @ SV28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(477,plain,
! [SV43: ( list_char > int ) > ( list_char > int ) > $o,SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY211: com,SY212: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ~ ( ~ ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 )
| ~ ( relati775585786_valid @ SV43 @ skip @ SY211 @ SY212 ) )
| ( relati775585786_valid @ SV13 @ SV29 @ SY211 @ SY212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(478,plain,
! [SV44: com,SV30: com,SV14: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY213: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ ( relati186416454e_flip @ SV14 ) @ SV30 @ SV44 @ ( relati186416454e_flip @ SY213 ) )
| ( relati2102071307_hoare @ SV14 @ SV44 @ SV30 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(479,plain,
! [SV31: com,SV15: com] :
( ( skip
= ( seq @ SV15 @ SV31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(480,plain,
! [SV32: com,SV16: bexp] :
( ( skip
= ( while @ SV16 @ SV32 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(481,plain,
! [SV45: com,SV33: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY214: ( list_char > int ) > ( list_char > int ) > $o,SY215: ( list_char > int ) > ( list_char > int ) > $o,SY216: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SY214 )
| ~ ! [SY135: list_char > int,SY136: list_char > int] :
( ~ ( SV17 @ SY135 @ SY136 )
| ( SY215 @ SY135 @ SY136 ) )
| ~ ! [SX6: list_char > int,SX7: list_char > int] :
( ~ ( SY216 @ SX6 @ SX7 )
| ( SY214 @ SX6 @ SX7 ) )
| ( relati2102071307_hoare @ SY215 @ SV33 @ SV45 @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(482,plain,
! [SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY221: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SY221 )
| ~ ( ~ ( relati775585786_valid @ SV18 @ SV34 @ skip @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SY221 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SY221 ) @ skip @ SV46 @ SY221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(483,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $true ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(484,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[458]) ).
thf(485,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[458]) ).
thf(486,plain,
( ( ( ~ ( $true
| $true ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(487,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[460]) ).
thf(488,plain,
( ( ( $true = $false )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[460]) ).
thf(489,plain,
( ( ( ~ ( $false
| $true ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(490,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[462]) ).
thf(491,plain,
( ( ( $false = $false )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[462]) ).
thf(492,plain,
! [SV47: ( list_char > int ) > ( list_char > int ) > $o,SV35: com,SV19: com,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY222: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
| ~ ! [SY84: list_char > int,SY85: list_char > int] :
( ~ ( SV3 @ SY84 @ SY85 )
| ( SY222 @ SY84 @ SY85 ) )
| ( relati2102071307_hoare @ SY222 @ SV19 @ SV35 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(493,plain,
! [SV36: com,SV20: com,SV4: bexp] :
( ( skip
= ( if @ SV4 @ SV20 @ SV36 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(494,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
| ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(495,plain,
( ( ~ ( relati2102071307_hoare @ p @ c @ c2 @ q )
| ~ ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(496,plain,
! [SV48: ( list_char > int ) > ( list_char > int ) > $o,SV37: com,SV21: com,SV5: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY225: ( list_char > int ) > ( list_char > int ) > $o,SY226: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV5 @ SV21 @ SV37 @ SV48 )
| ~ ( relati2102071307_hoare @ SY225 @ SV21 @ SV37 @ SY226 )
| ( relati2102071307_hoare
@ ^ [SY93: list_char > int,SY94: list_char > int] :
( ( SV5 @ SY93 @ SY94 )
| ( SY225 @ SY93 @ SY94 ) )
@ SV21
@ SV37
@ ^ [SY229: list_char > int,SY230: list_char > int] :
( ( SV48 @ SY229 @ SY230 )
| ( SY226 @ SY229 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(497,plain,
! [SV49: ( list_char > int ) > ( list_char > int ) > $o,SV38: com,SV22: com,SV6: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati775585786_valid @ SV6 @ SV22 @ SV38 @ SV49 )
| ( relati2102071307_hoare @ SV6 @ SV22 @ SV38 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(498,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(499,plain,
! [SV50: ( list_char > int ) > ( list_char > int ) > $o,SV39: com,SV24: com,SV8: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati2102071307_hoare @ SV8 @ SV24 @ SV39 @ SV50 )
| ( relati775585786_valid @ SV8 @ SV24 @ SV39 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(500,plain,
! [SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 )
= ( ^ [SY231: com,SY232: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SY231 @ SY232 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SY231 @ SY232 ) @ skip @ SY231 @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(501,plain,
! [SV52: ( list_char > int ) > ( list_char > int ) > $o,SV41: com,SV26: com,SV10: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY233: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
| ~ ! [SY234: list_char > int,SY235: list_char > int] :
( ~ ( SY233 @ SY234 @ SY235 )
| ( SV52 @ SY234 @ SY235 ) )
| ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(502,plain,
! [SV53: ( list_char > int ) > ( list_char > int ) > $o,SV42: com,SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY236: com,SY237: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV11 @ SV27 @ SV42 @ SV53 )
| ~ ( relati2102071307_hoare @ SV53 @ SY236 @ skip @ SY237 )
| ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SY236 ) @ SV42 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(503,plain,
! [SV54: com,SV43: ( list_char > int ) > ( list_char > int ) > $o,SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY238: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ~ ( ~ ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 )
| ~ ( relati775585786_valid @ SV43 @ skip @ SV54 @ SY238 ) )
| ( relati775585786_valid @ SV13 @ SV29 @ SV54 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(504,plain,
! [SV55: ( list_char > int ) > ( list_char > int ) > $o,SV44: com,SV30: com,SV14: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati2102071307_hoare @ ( relati186416454e_flip @ SV14 ) @ SV30 @ SV44 @ ( relati186416454e_flip @ SV55 ) )
| ( relati2102071307_hoare @ SV14 @ SV44 @ SV30 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(505,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY239: ( list_char > int ) > ( list_char > int ) > $o,SY240: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
| ~ ! [SY135: list_char > int,SY136: list_char > int] :
( ~ ( SV17 @ SY135 @ SY136 )
| ( SY239 @ SY135 @ SY136 ) )
| ~ ! [SY243: list_char > int,SY244: list_char > int] :
( ~ ( SY240 @ SY243 @ SY244 )
| ( SV56 @ SY243 @ SY244 ) )
| ( relati2102071307_hoare @ SY239 @ SV33 @ SV45 @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(506,plain,
! [SV57: ( list_char > int ) > ( list_char > int ) > $o,SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SV57 )
| ~ ( ~ ( relati775585786_valid @ SV18 @ SV34 @ skip @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) @ skip @ SV46 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(507,plain,
! [SV2: $o] :
( ( ( SV2
| $true )
= $false )
| ( ( ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(508,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(509,plain,
( ( ( $true
| $true )
= $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(510,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(511,plain,
( ( ( $false
| $true )
= $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(512,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(513,plain,
! [SV58: ( list_char > int ) > ( list_char > int ) > $o,SV47: ( list_char > int ) > ( list_char > int ) > $o,SV35: com,SV19: com,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
| ~ ! [SY245: list_char > int,SY246: list_char > int] :
( ~ ( SV3 @ SY245 @ SY246 )
| ( SV58 @ SY245 @ SY246 ) )
| ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(514,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $true )
| ( ( ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(515,plain,
( ( ( ~ ( relati2102071307_hoare @ p @ c @ c2 @ q ) )
= $true )
| ( ( ~ ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(516,plain,
! [SV59: ( list_char > int ) > ( list_char > int ) > $o,SV48: ( list_char > int ) > ( list_char > int ) > $o,SV37: com,SV21: com,SV5: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY247: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV5 @ SV21 @ SV37 @ SV48 )
| ~ ( relati2102071307_hoare @ SV59 @ SV21 @ SV37 @ SY247 )
| ( relati2102071307_hoare
@ ^ [SY248: list_char > int,SY249: list_char > int] :
( ( SV5 @ SY248 @ SY249 )
| ( SV59 @ SY248 @ SY249 ) )
@ SV21
@ SV37
@ ^ [SY229: list_char > int,SY230: list_char > int] :
( ( SV48 @ SY229 @ SY230 )
| ( SY247 @ SY229 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(517,plain,
! [SV49: ( list_char > int ) > ( list_char > int ) > $o,SV38: com,SV22: com,SV6: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV6 @ SV22 @ SV38 @ SV49 ) )
= $true )
| ( ( relati2102071307_hoare @ SV6 @ SV22 @ SV38 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(518,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $false )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(519,plain,
! [SV50: ( list_char > int ) > ( list_char > int ) > $o,SV39: com,SV24: com,SV8: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV8 @ SV24 @ SV39 @ SV50 ) )
= $true )
| ( ( relati775585786_valid @ SV8 @ SV24 @ SV39 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(520,plain,
! [SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SV60: com] :
( ( relati775585786_valid @ SV25 @ SV51 @ SV60 )
= ( ^ [SY252: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV60 @ SY252 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV60 @ SY252 ) @ skip @ SV60 @ SY252 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[500]) ).
thf(521,plain,
! [SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 )
= ( ^ [SY231: com,SY232: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SY231 @ SY232 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SY231 @ SY232 ) @ skip @ SY231 @ SY232 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[500]) ).
thf(522,plain,
! [SV61: ( list_char > int ) > ( list_char > int ) > $o,SV52: ( list_char > int ) > ( list_char > int ) > $o,SV41: com,SV26: com,SV10: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
| ~ ! [SY253: list_char > int,SY254: list_char > int] :
( ~ ( SV61 @ SY253 @ SY254 )
| ( SV52 @ SY253 @ SY254 ) )
| ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(523,plain,
! [SV62: com,SV53: ( list_char > int ) > ( list_char > int ) > $o,SV42: com,SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY255: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV11 @ SV27 @ SV42 @ SV53 )
| ~ ( relati2102071307_hoare @ SV53 @ SV62 @ skip @ SY255 )
| ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SV62 ) @ SV42 @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(524,plain,
! [SV63: ( list_char > int ) > ( list_char > int ) > $o,SV54: com,SV43: ( list_char > int ) > ( list_char > int ) > $o,SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ~ ( ~ ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 )
| ~ ( relati775585786_valid @ SV43 @ skip @ SV54 @ SV63 ) )
| ( relati775585786_valid @ SV13 @ SV29 @ SV54 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(525,plain,
! [SV55: ( list_char > int ) > ( list_char > int ) > $o,SV44: com,SV30: com,SV14: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ ( relati186416454e_flip @ SV14 ) @ SV30 @ SV44 @ ( relati186416454e_flip @ SV55 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV14 @ SV44 @ SV30 @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(526,plain,
! [SV64: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SY256: ( list_char > int ) > ( list_char > int ) > $o] :
( ~ ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
| ~ ! [SY257: list_char > int,SY258: list_char > int] :
( ~ ( SV17 @ SY257 @ SY258 )
| ( SV64 @ SY257 @ SY258 ) )
| ~ ! [SY243: list_char > int,SY244: list_char > int] :
( ~ ( SY256 @ SY243 @ SY244 )
| ( SV56 @ SY243 @ SY244 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(527,plain,
! [SV57: ( list_char > int ) > ( list_char > int ) > $o,SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SV57 ) )
= $true )
| ( ( ~ ( ~ ( relati775585786_valid @ SV18 @ SV34 @ skip @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) @ skip @ SV46 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(528,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(529,plain,
! [SV2: $o] :
( ( $true = $false )
| ( ( ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(530,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(531,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(532,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(533,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(534,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(535,plain,
( ( $true = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(536,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(537,plain,
! [SV58: ( list_char > int ) > ( list_char > int ) > $o,SV47: ( list_char > int ) > ( list_char > int ) > $o,SV35: com,SV19: com,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 ) )
= $true )
| ( ( ~ ! [SY245: list_char > int,SY246: list_char > int] :
( ~ ( SV3 @ SY245 @ SY246 )
| ( SV58 @ SY245 @ SY246 ) )
| ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(538,plain,
( ( ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) )
= $false )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(539,plain,
( ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $false )
| ( ( ~ ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(540,plain,
! [SV65: ( list_char > int ) > ( list_char > int ) > $o,SV59: ( list_char > int ) > ( list_char > int ) > $o,SV48: ( list_char > int ) > ( list_char > int ) > $o,SV37: com,SV21: com,SV5: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati2102071307_hoare @ SV5 @ SV21 @ SV37 @ SV48 )
| ~ ( relati2102071307_hoare @ SV59 @ SV21 @ SV37 @ SV65 )
| ( relati2102071307_hoare
@ ^ [SY248: list_char > int,SY249: list_char > int] :
( ( SV5 @ SY248 @ SY249 )
| ( SV59 @ SY248 @ SY249 ) )
@ SV21
@ SV37
@ ^ [SY263: list_char > int,SY264: list_char > int] :
( ( SV48 @ SY263 @ SY264 )
| ( SV65 @ SY263 @ SY264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(541,plain,
! [SV49: ( list_char > int ) > ( list_char > int ) > $o,SV38: com,SV22: com,SV6: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV6 @ SV22 @ SV38 @ SV49 )
= $false )
| ( ( relati2102071307_hoare @ SV6 @ SV22 @ SV38 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(542,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(543,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $false )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(544,plain,
! [SV50: ( list_char > int ) > ( list_char > int ) > $o,SV39: com,SV24: com,SV8: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV8 @ SV24 @ SV39 @ SV50 )
= $false )
| ( ( relati775585786_valid @ SV8 @ SV24 @ SV39 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(545,plain,
! [SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 )
= ( ^ [SY265: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SY265 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SY265 ) @ skip @ SV66 @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(546,plain,
! [SV61: ( list_char > int ) > ( list_char > int ) > $o,SV52: ( list_char > int ) > ( list_char > int ) > $o,SV41: com,SV26: com,SV10: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 ) )
= $true )
| ( ( ~ ! [SY253: list_char > int,SY254: list_char > int] :
( ~ ( SV61 @ SY253 @ SY254 )
| ( SV52 @ SY253 @ SY254 ) )
| ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(547,plain,
! [SV67: ( list_char > int ) > ( list_char > int ) > $o,SV62: com,SV53: ( list_char > int ) > ( list_char > int ) > $o,SV42: com,SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati2102071307_hoare @ SV11 @ SV27 @ SV42 @ SV53 )
| ~ ( relati2102071307_hoare @ SV53 @ SV62 @ skip @ SV67 )
| ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SV62 ) @ SV42 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(548,plain,
! [SV63: ( list_char > int ) > ( list_char > int ) > $o,SV54: com,SV43: ( list_char > int ) > ( list_char > int ) > $o,SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ~ ( ~ ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 )
| ~ ( relati775585786_valid @ SV43 @ skip @ SV54 @ SV63 ) ) )
= $true )
| ( ( relati775585786_valid @ SV13 @ SV29 @ SV54 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(549,plain,
! [SV55: ( list_char > int ) > ( list_char > int ) > $o,SV44: com,SV30: com,SV14: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ ( relati186416454e_flip @ SV14 ) @ SV30 @ SV44 @ ( relati186416454e_flip @ SV55 ) )
= $false )
| ( ( relati2102071307_hoare @ SV14 @ SV44 @ SV30 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(550,plain,
! [SV68: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
| ~ ! [SY257: list_char > int,SY258: list_char > int] :
( ~ ( SV17 @ SY257 @ SY258 )
| ( SV64 @ SY257 @ SY258 ) )
| ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(551,plain,
! [SV57: ( list_char > int ) > ( list_char > int ) > $o,SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SV57 )
= $false )
| ( ( ~ ( ~ ( relati775585786_valid @ SV18 @ SV34 @ skip @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) @ skip @ SV46 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(552,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $true )
= $false )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(553,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $true )
= $false )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(554,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(555,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(556,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(557,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(558,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(559,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(560,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(561,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(562,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(563,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(564,plain,
! [SV58: ( list_char > int ) > ( list_char > int ) > $o,SV47: ( list_char > int ) > ( list_char > int ) > $o,SV35: com,SV19: com,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
= $false )
| ( ( ~ ! [SY245: list_char > int,SY246: list_char > int] :
( ~ ( SV3 @ SY245 @ SY246 )
| ( SV58 @ SY245 @ SY246 ) )
| ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(565,plain,
( ( ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) ) )
= $false )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(566,plain,
( ( ( ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) )
= $false )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(567,plain,
( ( ( ~ ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) ) )
= $false )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(568,plain,
! [SV65: ( list_char > int ) > ( list_char > int ) > $o,SV59: ( list_char > int ) > ( list_char > int ) > $o,SV48: ( list_char > int ) > ( list_char > int ) > $o,SV37: com,SV21: com,SV5: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV5 @ SV21 @ SV37 @ SV48 ) )
= $true )
| ( ( ~ ( relati2102071307_hoare @ SV59 @ SV21 @ SV37 @ SV65 )
| ( relati2102071307_hoare
@ ^ [SY248: list_char > int,SY249: list_char > int] :
( ( SV5 @ SY248 @ SY249 )
| ( SV59 @ SY248 @ SY249 ) )
@ SV21
@ SV37
@ ^ [SY263: list_char > int,SY264: list_char > int] :
( ( SV48 @ SY263 @ SY264 )
| ( SV65 @ SY263 @ SY264 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(569,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(570,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY270: list_char > int] :
( ~ ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ SY270 )
| ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ SY270 ) ) )
= $false )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[543]) ).
thf(571,plain,
! [SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ! [SV69: ( list_char > int ) > ( list_char > int ) > $o] :
( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV69 )
= ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV69 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV69 ) @ skip @ SV66 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[545]) ).
thf(572,plain,
! [SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 )
= ( ^ [SY265: ( list_char > int ) > ( list_char > int ) > $o] :
~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SY265 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SY265 ) @ skip @ SV66 @ SY265 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[545]) ).
thf(573,plain,
! [SV61: ( list_char > int ) > ( list_char > int ) > $o,SV52: ( list_char > int ) > ( list_char > int ) > $o,SV41: com,SV26: com,SV10: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
= $false )
| ( ( ~ ! [SY253: list_char > int,SY254: list_char > int] :
( ~ ( SV61 @ SY253 @ SY254 )
| ( SV52 @ SY253 @ SY254 ) )
| ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(574,plain,
! [SV67: ( list_char > int ) > ( list_char > int ) > $o,SV62: com,SV53: ( list_char > int ) > ( list_char > int ) > $o,SV42: com,SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV11 @ SV27 @ SV42 @ SV53 ) )
= $true )
| ( ( ~ ( relati2102071307_hoare @ SV53 @ SV62 @ skip @ SV67 )
| ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SV62 ) @ SV42 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(575,plain,
! [SV63: ( list_char > int ) > ( list_char > int ) > $o,SV54: com,SV43: ( list_char > int ) > ( list_char > int ) > $o,SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( ~ ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 )
| ~ ( relati775585786_valid @ SV43 @ skip @ SV54 @ SV63 ) ) )
= $false )
| ( ( relati775585786_valid @ SV13 @ SV29 @ SV54 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(576,plain,
! [SV68: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 ) )
= $true )
| ( ( ~ ! [SY257: list_char > int,SY258: list_char > int] :
( ~ ( SV17 @ SY257 @ SY258 )
| ( SV64 @ SY257 @ SY258 ) )
| ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(577,plain,
! [SV57: ( list_char > int ) > ( list_char > int ) > $o,SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV18 @ SV34 @ skip @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) @ skip @ SV46 @ SV57 ) )
= $false )
| ( ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(578,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(579,plain,
! [SV2: $o] :
( ( ( ~ $true ) = $false )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(580,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(581,plain,
! [SV2: $o] :
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(582,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(583,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(584,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(585,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(586,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(587,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(588,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(589,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(590,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(591,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(592,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(593,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(594,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(595,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(596,plain,
! [SV47: ( list_char > int ) > ( list_char > int ) > $o,SV35: com,SV19: com,SV58: ( list_char > int ) > ( list_char > int ) > $o,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ! [SY245: list_char > int,SY246: list_char > int] :
( ~ ( SV3 @ SY245 @ SY246 )
| ( SV58 @ SY245 @ SY246 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 )
= $true )
| ( ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(597,plain,
( ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
= $true )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(598,plain,
( ( ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q )
= $true )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(599,plain,
( ( ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
| ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) )
= $true )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(600,plain,
! [SV65: ( list_char > int ) > ( list_char > int ) > $o,SV59: ( list_char > int ) > ( list_char > int ) > $o,SV48: ( list_char > int ) > ( list_char > int ) > $o,SV37: com,SV21: com,SV5: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV5 @ SV21 @ SV37 @ SV48 )
= $false )
| ( ( ~ ( relati2102071307_hoare @ SV59 @ SV21 @ SV37 @ SV65 )
| ( relati2102071307_hoare
@ ^ [SY248: list_char > int,SY249: list_char > int] :
( ( SV5 @ SY248 @ SY249 )
| ( SV59 @ SY248 @ SY249 ) )
@ SV21
@ SV37
@ ^ [SY263: list_char > int,SY264: list_char > int] :
( ( SV48 @ SY263 @ SY264 )
| ( SV65 @ SY263 @ SY264 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(601,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 ) )
= $false )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(602,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(603,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
| ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) ) )
= $false )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[570]) ).
thf(604,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(605,plain,
! [SV41: com,SV26: com,SV10: ( list_char > int ) > ( list_char > int ) > $o,SV52: ( list_char > int ) > ( list_char > int ) > $o,SV61: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ! [SY253: list_char > int,SY254: list_char > int] :
( ~ ( SV61 @ SY253 @ SY254 )
| ( SV52 @ SY253 @ SY254 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(606,plain,
! [SV67: ( list_char > int ) > ( list_char > int ) > $o,SV62: com,SV53: ( list_char > int ) > ( list_char > int ) > $o,SV42: com,SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV11 @ SV27 @ SV42 @ SV53 )
= $false )
| ( ( ~ ( relati2102071307_hoare @ SV53 @ SV62 @ skip @ SV67 )
| ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SV62 ) @ SV42 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(607,plain,
! [SV63: ( list_char > int ) > ( list_char > int ) > $o,SV54: com,SV43: ( list_char > int ) > ( list_char > int ) > $o,SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 )
| ~ ( relati775585786_valid @ SV43 @ skip @ SV54 @ SV63 ) )
= $true )
| ( ( relati775585786_valid @ SV13 @ SV29 @ SV54 @ SV63 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(608,plain,
! [SV68: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false )
| ( ( ~ ! [SY257: list_char > int,SY258: list_char > int] :
( ~ ( SV17 @ SY257 @ SY258 )
| ( SV64 @ SY257 @ SY258 ) )
| ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(609,plain,
! [SV57: ( list_char > int ) > ( list_char > int ) > $o,SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV18 @ SV34 @ skip @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) ) )
= $false )
| ( ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(610,plain,
! [SV57: ( list_char > int ) > ( list_char > int ) > $o,SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) @ skip @ SV46 @ SV57 ) )
= $false )
| ( ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(611,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(612,plain,
! [SV2: $o] :
( ( $true = $true )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(613,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(614,plain,
! [SV2: $o] :
( ( $true = $true )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(615,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[582]) ).
thf(616,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[582]) ).
thf(617,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(618,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(619,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(620,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(621,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(622,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(623,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(624,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(625,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(626,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(627,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(628,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(629,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(630,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(631,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(632,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(633,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[595]) ).
thf(634,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[595]) ).
thf(635,plain,
! [SV47: ( list_char > int ) > ( list_char > int ) > $o,SV35: com,SV19: com,SV58: ( list_char > int ) > ( list_char > int ) > $o,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY245: list_char > int,SY246: list_char > int] :
( ~ ( SV3 @ SY245 @ SY246 )
| ( SV58 @ SY245 @ SY246 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 )
= $true )
| ( ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(636,plain,
( ( ( ~ ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) ) )
= $true )
| ( ( ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) )
= $true )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(637,plain,
! [SV48: ( list_char > int ) > ( list_char > int ) > $o,SV5: ( list_char > int ) > ( list_char > int ) > $o,SV65: ( list_char > int ) > ( list_char > int ) > $o,SV37: com,SV21: com,SV59: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV59 @ SV21 @ SV37 @ SV65 ) )
= $true )
| ( ( relati2102071307_hoare
@ ^ [SY248: list_char > int,SY249: list_char > int] :
( ( SV5 @ SY248 @ SY249 )
| ( SV59 @ SY248 @ SY249 ) )
@ SV21
@ SV37
@ ^ [SY263: list_char > int,SY264: list_char > int] :
( ( SV48 @ SY263 @ SY264 )
| ( SV65 @ SY263 @ SY264 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV5 @ SV21 @ SV37 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(638,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $true )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(639,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(640,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) ) )
= $false )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(641,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[603]) ).
thf(642,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ~ ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
| ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[604]) ).
thf(643,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[604]) ).
thf(644,plain,
! [SV41: com,SV26: com,SV10: ( list_char > int ) > ( list_char > int ) > $o,SV52: ( list_char > int ) > ( list_char > int ) > $o,SV61: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY253: list_char > int,SY254: list_char > int] :
( ~ ( SV61 @ SY253 @ SY254 )
| ( SV52 @ SY253 @ SY254 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(645,plain,
! [SV42: com,SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o,SV67: ( list_char > int ) > ( list_char > int ) > $o,SV62: com,SV53: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV53 @ SV62 @ skip @ SV67 ) )
= $true )
| ( ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SV62 ) @ SV42 @ SV67 )
= $true )
| ( ( relati2102071307_hoare @ SV11 @ SV27 @ SV42 @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(646,plain,
! [SV63: ( list_char > int ) > ( list_char > int ) > $o,SV54: com,SV43: ( list_char > int ) > ( list_char > int ) > $o,SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 ) )
= $true )
| ( ( ~ ( relati775585786_valid @ SV43 @ skip @ SV54 @ SV63 ) )
= $true )
| ( ( relati775585786_valid @ SV13 @ SV29 @ SV54 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(647,plain,
! [SV45: com,SV33: com,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ! [SY257: list_char > int,SY258: list_char > int] :
( ~ ( SV17 @ SY257 @ SY258 )
| ( SV64 @ SY257 @ SY258 ) ) )
= $true )
| ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(648,plain,
! [SV57: ( list_char > int ) > ( list_char > int ) > $o,SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV18 @ SV34 @ skip @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) )
= $true )
| ( ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(649,plain,
! [SV57: ( list_char > int ) > ( list_char > int ) > $o,SV46: com,SV34: com,SV18: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ ( relati1310524937decomp @ SV18 @ SV34 @ SV46 @ SV57 ) @ skip @ SV46 @ SV57 )
= $true )
| ( ( relati775585786_valid @ SV18 @ SV34 @ SV46 @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(650,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[611]) ).
thf(651,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[611]) ).
thf(652,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[612]) ).
thf(653,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[612]) ).
thf(654,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[613]) ).
thf(655,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[613]) ).
thf(656,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[614]) ).
thf(657,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[614]) ).
thf(658,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(659,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(660,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(661,plain,
! [SV2: $o] :
( ( $false = $true )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(662,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[619]) ).
thf(663,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[619]) ).
thf(664,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[620]) ).
thf(665,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[620]) ).
thf(666,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[621]) ).
thf(667,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[621]) ).
thf(668,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[622]) ).
thf(669,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[622]) ).
thf(670,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(671,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(672,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(673,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(674,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[627]) ).
thf(675,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[627]) ).
thf(676,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[628]) ).
thf(677,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[628]) ).
thf(678,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[629]) ).
thf(679,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[629]) ).
thf(680,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[630]) ).
thf(681,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[630]) ).
thf(682,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(683,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(684,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(685,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(686,plain,
! [SV58: ( list_char > int ) > ( list_char > int ) > $o,SV19: com,SV35: com,SV47: ( list_char > int ) > ( list_char > int ) > $o,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY271: list_char > int] :
( ~ ( SV3 @ ( sK3_SY245 @ SV47 @ SV35 @ SV19 @ SV58 @ SV3 ) @ SY271 )
| ( SV58 @ ( sK3_SY245 @ SV47 @ SV35 @ SV19 @ SV58 @ SV3 ) @ SY271 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 )
= $true )
| ( ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[635]) ).
thf(687,plain,
( ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
= $false )
| ( ( ~ ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q ) )
= $true )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(688,plain,
! [SV48: ( list_char > int ) > ( list_char > int ) > $o,SV5: ( list_char > int ) > ( list_char > int ) > $o,SV65: ( list_char > int ) > ( list_char > int ) > $o,SV37: com,SV21: com,SV59: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV59 @ SV21 @ SV37 @ SV65 )
= $false )
| ( ( relati2102071307_hoare
@ ^ [SY248: list_char > int,SY249: list_char > int] :
( ( SV5 @ SY248 @ SY249 )
| ( SV59 @ SY248 @ SY249 ) )
@ SV21
@ SV37
@ ^ [SY263: list_char > int,SY264: list_char > int] :
( ( SV48 @ SY263 @ SY264 )
| ( SV65 @ SY263 @ SY264 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV5 @ SV21 @ SV37 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(689,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV71: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY272: list_char > int] :
( ~ ( SV23 @ SV71 @ SY272 )
| ( SV7 @ SV71 @ SY272 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(690,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(691,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $false )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(692,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true )
| ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(693,plain,
! [SV52: ( list_char > int ) > ( list_char > int ) > $o,SV10: ( list_char > int ) > ( list_char > int ) > $o,SV26: com,SV41: com,SV61: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY273: list_char > int] :
( ~ ( SV61 @ ( sK4_SY253 @ SV41 @ SV26 @ SV10 @ SV52 @ SV61 ) @ SY273 )
| ( SV52 @ ( sK4_SY253 @ SV41 @ SV26 @ SV10 @ SV52 @ SV61 ) @ SY273 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[644]) ).
thf(694,plain,
! [SV42: com,SV27: com,SV11: ( list_char > int ) > ( list_char > int ) > $o,SV67: ( list_char > int ) > ( list_char > int ) > $o,SV62: com,SV53: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV53 @ SV62 @ skip @ SV67 )
= $false )
| ( ( relati2102071307_hoare @ SV11 @ ( seq @ SV27 @ SV62 ) @ SV42 @ SV67 )
= $true )
| ( ( relati2102071307_hoare @ SV11 @ SV27 @ SV42 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(695,plain,
! [SV63: ( list_char > int ) > ( list_char > int ) > $o,SV54: com,SV43: ( list_char > int ) > ( list_char > int ) > $o,SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 )
= $false )
| ( ( ~ ( relati775585786_valid @ SV43 @ skip @ SV54 @ SV63 ) )
= $true )
| ( ( relati775585786_valid @ SV13 @ SV29 @ SV54 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(696,plain,
! [SV45: com,SV33: com,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY257: list_char > int,SY258: list_char > int] :
( ~ ( SV17 @ SY257 @ SY258 )
| ( SV64 @ SY257 @ SY258 ) ) )
= $false )
| ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(697,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(698,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(699,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(700,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(701,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(702,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(703,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(704,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(705,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(706,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(707,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(708,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(709,plain,
! [SV58: ( list_char > int ) > ( list_char > int ) > $o,SV19: com,SV35: com,SV47: ( list_char > int ) > ( list_char > int ) > $o,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV3 @ ( sK3_SY245 @ SV47 @ SV35 @ SV19 @ SV58 @ SV3 ) @ ( sK5_SY271 @ SV58 @ SV19 @ SV35 @ SV47 @ SV3 ) )
| ( SV58 @ ( sK3_SY245 @ SV47 @ SV35 @ SV19 @ SV58 @ SV3 ) @ ( sK5_SY271 @ SV58 @ SV19 @ SV35 @ SV47 @ SV3 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 )
= $true )
| ( ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[686]) ).
thf(710,plain,
( ( ( relati2102071307_hoare @ ( relati1310524937decomp @ p @ c @ c2 @ q ) @ skip @ c2 @ q )
= $false )
| ( ( relati2102071307_hoare @ p @ c @ skip @ ( relati1310524937decomp @ p @ c @ c2 @ q ) )
= $false )
| ( ( relati2102071307_hoare @ p @ c @ c2 @ q )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(711,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV72: list_char > int,SV71: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV23 @ SV71 @ SV72 )
| ( SV7 @ SV71 @ SV72 ) )
= $true )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(712,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
| ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $false )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(713,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 ) )
= $false )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(714,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $false )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(715,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
= $false )
| ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(716,plain,
! [SV52: ( list_char > int ) > ( list_char > int ) > $o,SV10: ( list_char > int ) > ( list_char > int ) > $o,SV26: com,SV41: com,SV61: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV61 @ ( sK4_SY253 @ SV41 @ SV26 @ SV10 @ SV52 @ SV61 ) @ ( sK6_SY273 @ SV52 @ SV10 @ SV26 @ SV41 @ SV61 ) )
| ( SV52 @ ( sK4_SY253 @ SV41 @ SV26 @ SV10 @ SV52 @ SV61 ) @ ( sK6_SY273 @ SV52 @ SV10 @ SV26 @ SV41 @ SV61 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[693]) ).
thf(717,plain,
! [SV29: com,SV13: ( list_char > int ) > ( list_char > int ) > $o,SV63: ( list_char > int ) > ( list_char > int ) > $o,SV54: com,SV43: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV43 @ skip @ SV54 @ SV63 )
= $false )
| ( ( relati775585786_valid @ SV13 @ SV29 @ skip @ SV43 )
= $false )
| ( ( relati775585786_valid @ SV13 @ SV29 @ SV54 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(718,plain,
! [SV64: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY274: list_char > int] :
( ~ ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ SY274 )
| ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ SY274 ) ) )
= $false )
| ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[696]) ).
thf(719,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(720,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(721,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(722,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(723,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(724,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(725,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(726,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(727,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(728,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(729,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(730,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(731,plain,
! [SV58: ( list_char > int ) > ( list_char > int ) > $o,SV19: com,SV35: com,SV47: ( list_char > int ) > ( list_char > int ) > $o,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV3 @ ( sK3_SY245 @ SV47 @ SV35 @ SV19 @ SV58 @ SV3 ) @ ( sK5_SY271 @ SV58 @ SV19 @ SV35 @ SV47 @ SV3 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 )
= $true )
| ( ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(732,plain,
! [SV3: ( list_char > int ) > ( list_char > int ) > $o,SV19: com,SV35: com,SV47: ( list_char > int ) > ( list_char > int ) > $o,SV58: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV58 @ ( sK3_SY245 @ SV47 @ SV35 @ SV19 @ SV58 @ SV3 ) @ ( sK5_SY271 @ SV58 @ SV19 @ SV35 @ SV47 @ SV3 ) )
= $false )
| ( ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 )
= $true )
| ( ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(733,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV72: list_char > int,SV71: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV23 @ SV71 @ SV72 ) )
= $true )
| ( ( SV7 @ SV71 @ SV72 )
= $true )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(734,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 ) )
= $false )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(735,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $false )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(736,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $true )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(737,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $true )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(738,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false )
| ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(739,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
= $false )
| ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(740,plain,
! [SV52: ( list_char > int ) > ( list_char > int ) > $o,SV10: ( list_char > int ) > ( list_char > int ) > $o,SV26: com,SV41: com,SV61: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV61 @ ( sK4_SY253 @ SV41 @ SV26 @ SV10 @ SV52 @ SV61 ) @ ( sK6_SY273 @ SV52 @ SV10 @ SV26 @ SV41 @ SV61 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(741,plain,
! [SV61: ( list_char > int ) > ( list_char > int ) > $o,SV10: ( list_char > int ) > ( list_char > int ) > $o,SV26: com,SV41: com,SV52: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV52 @ ( sK4_SY253 @ SV41 @ SV26 @ SV10 @ SV52 @ SV61 ) @ ( sK6_SY273 @ SV52 @ SV10 @ SV26 @ SV41 @ SV61 ) )
= $false )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(742,plain,
! [SV64: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
| ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) ) )
= $false )
| ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[718]) ).
thf(743,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[719]) ).
thf(744,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[719]) ).
thf(745,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(746,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(747,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(748,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(749,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(750,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[722]) ).
thf(751,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(752,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(753,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(754,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(755,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(756,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(757,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(758,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(759,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[727]) ).
thf(760,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[727]) ).
thf(761,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(762,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(763,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(764,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(765,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(766,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(767,plain,
! [SV58: ( list_char > int ) > ( list_char > int ) > $o,SV19: com,SV35: com,SV47: ( list_char > int ) > ( list_char > int ) > $o,SV3: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV3 @ ( sK3_SY245 @ SV47 @ SV35 @ SV19 @ SV58 @ SV3 ) @ ( sK5_SY271 @ SV58 @ SV19 @ SV35 @ SV47 @ SV3 ) )
= $true )
| ( ( relati2102071307_hoare @ SV58 @ SV19 @ SV35 @ SV47 )
= $true )
| ( ( relati2102071307_hoare @ SV3 @ SV19 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(768,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV72: list_char > int,SV71: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV23 @ SV71 @ SV72 )
= $false )
| ( ( SV7 @ SV71 @ SV72 )
= $true )
| ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(769,plain,
! [SV23: ( list_char > int ) > ( list_char > int ) > $o,SV7: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati2102071307_hoare @ SV7 @ skip @ skip @ SV23 )
= $true )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[734]) ).
thf(770,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY158: list_char > int,SY159: list_char > int] :
( ~ ( SV23 @ SY158 @ SY159 )
| ( SV7 @ SY158 @ SY159 ) ) )
= $true )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(771,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV73: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY275: list_char > int] :
( ~ ( SV23 @ SV73 @ SY275 )
| ( SV7 @ SV73 @ SY275 ) ) )
= $true )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(772,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(773,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(774,plain,
! [SV52: ( list_char > int ) > ( list_char > int ) > $o,SV10: ( list_char > int ) > ( list_char > int ) > $o,SV26: com,SV41: com,SV61: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV61 @ ( sK4_SY253 @ SV41 @ SV26 @ SV10 @ SV52 @ SV61 ) @ ( sK6_SY273 @ SV52 @ SV10 @ SV26 @ SV41 @ SV61 ) )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV61 )
= $true )
| ( ( relati2102071307_hoare @ SV10 @ SV26 @ SV41 @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(775,plain,
! [SV64: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) ) )
= $false )
| ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(776,plain,
! [SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV64: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $false )
| ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(777,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(778,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(779,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(780,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(781,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(782,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(783,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(784,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(785,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(786,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(787,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(788,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(789,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(790,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(791,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(792,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(793,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(794,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(795,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(796,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(797,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(798,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(799,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(800,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(801,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV74: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY276: list_char > int] :
( ~ ( SV23 @ SV74 @ SY276 )
| ( SV7 @ SV74 @ SY276 ) ) )
= $true )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(802,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV75: list_char > int,SV73: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV23 @ SV73 @ SV75 )
| ( SV7 @ SV73 @ SV75 ) )
= $true )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(803,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(804,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(805,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) ) )
= $true )
| ( ( ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(806,plain,
! [SV64: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $true )
| ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) )
| ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(807,plain,
! [SV17: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $false )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(808,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(809,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(810,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(811,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(812,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(813,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(814,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(815,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(816,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[781]) ).
thf(817,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[781]) ).
thf(818,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(819,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(820,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(821,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(822,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(823,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(824,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(825,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(826,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(827,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(828,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(829,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(830,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(831,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(832,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(833,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(834,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(835,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(836,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(837,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(838,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(839,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(840,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(841,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(842,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(843,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(844,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[795]) ).
thf(845,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[795]) ).
thf(846,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(847,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(848,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(849,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(850,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(851,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(852,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(853,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(854,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(855,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[800]) ).
thf(856,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV76: list_char > int,SV74: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV23 @ SV74 @ SV76 )
| ( SV7 @ SV74 @ SV76 ) )
= $true )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(857,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV75: list_char > int,SV73: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV23 @ SV73 @ SV75 ) )
= $true )
| ( ( SV7 @ SV73 @ SV75 )
= $true )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(858,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $true )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(859,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
= $true )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(860,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) )
= $true )
| ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(861,plain,
! [SV17: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) ) )
= $true )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(862,plain,
! [SV17: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $false )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(863,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(864,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(865,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(866,plain,
! [SV2: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(867,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(868,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(869,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(870,plain,
! [SV2: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(871,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(872,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(873,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(874,plain,
! [SV2: $o] :
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(875,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(876,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(877,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(878,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(879,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(880,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(881,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(882,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(883,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(884,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(885,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(886,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(887,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(888,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(889,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(890,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(891,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(892,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(893,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(894,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(895,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(896,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(897,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(898,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(899,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[844]) ).
thf(900,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(901,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(902,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(903,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(904,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(905,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(906,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(907,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(908,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(909,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(910,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(911,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV76: list_char > int,SV74: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV23 @ SV74 @ SV76 ) )
= $true )
| ( ( SV7 @ SV74 @ SV76 )
= $true )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(912,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV75: list_char > int,SV73: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV23 @ SV73 @ SV75 )
= $false )
| ( ( SV7 @ SV73 @ SV75 )
= $true )
| ( ( SV7 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(913,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(914,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(915,plain,
! [SV17: ( list_char > int ) > ( list_char > int ) > $o,SV45: com,SV33: com,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY268: list_char > int,SY269: list_char > int] :
( ~ ( SV68 @ SY268 @ SY269 )
| ( SV56 @ SY268 @ SY269 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(916,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY277: list_char > int] :
( ~ ( SV68 @ ( sK9_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ SY277 )
| ( SV56 @ ( sK9_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ SY277 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $false )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[862]) ).
thf(917,plain,
! [SV7: ( list_char > int ) > ( list_char > int ) > $o,SV76: list_char > int,SV74: list_char > int,SV23: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV23 @ SV74 @ SV76 )
= $false )
| ( ( SV7 @ SV74 @ SV76 )
= $true )
| ( ( SV23 @ ( sK1_SY158 @ SV7 @ SV23 ) @ ( sK2_SY270 @ SV7 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(918,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(919,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(920,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
| ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(921,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ! [SY278: list_char > int] :
( ~ ( SV68 @ ( sK10_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ SY278 )
| ( SV56 @ ( sK10_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ SY278 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[915]) ).
thf(922,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV68 @ ( sK9_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK11_SY277 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) )
| ( SV56 @ ( sK9_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK11_SY277 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $false )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[916]) ).
thf(923,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $true )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(924,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $true )
| ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(925,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[920]) ).
thf(926,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[920]) ).
thf(927,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV68 @ ( sK10_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK12_SY278 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) )
| ( SV56 @ ( sK10_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK12_SY278 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[921]) ).
thf(928,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV68 @ ( sK9_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK11_SY277 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $false )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(929,plain,
! [SV68: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV56 @ ( sK9_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK11_SY277 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $false )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(930,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ SV66 @ SV70 )
= $true )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(931,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) ) )
= $true )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[926]) ).
thf(932,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( SV68 @ ( sK10_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK12_SY278 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(933,plain,
! [SV68: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV56: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV56 @ ( sK10_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK12_SY278 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) )
= $false )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(934,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV68 @ ( sK9_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK11_SY277 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV64 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $false )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(935,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
| ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(936,plain,
! [SV56: ( list_char > int ) > ( list_char > int ) > $o,SV64: ( list_char > int ) > ( list_char > int ) > $o,SV33: com,SV45: com,SV17: ( list_char > int ) > ( list_char > int ) > $o,SV68: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( SV68 @ ( sK10_SY268 @ SV17 @ SV45 @ SV33 @ SV64 @ SV56 @ SV68 ) @ ( sK12_SY278 @ SV56 @ SV64 @ SV33 @ SV45 @ SV17 @ SV68 ) )
= $true )
| ( ( relati2102071307_hoare @ SV64 @ SV33 @ SV45 @ SV68 )
= $true )
| ( ( SV17 @ ( sK7_SY257 @ SV45 @ SV33 @ SV56 @ SV68 @ SV64 @ SV17 ) @ ( sK8_SY274 @ SV64 @ SV68 @ SV56 @ SV33 @ SV45 @ SV17 ) )
= $true )
| ( ( relati2102071307_hoare @ SV17 @ SV33 @ SV45 @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(937,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(938,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( ~ ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(939,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $true )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(940,plain,
! [SV70: ( list_char > int ) > ( list_char > int ) > $o,SV66: com,SV51: com,SV25: ( list_char > int ) > ( list_char > int ) > $o] :
( ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $true )
| ( ( relati775585786_valid @ SV25 @ SV51 @ skip @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) )
= $false )
| ( ( relati775585786_valid @ ( relati1310524937decomp @ SV25 @ SV51 @ SV66 @ SV70 ) @ skip @ SV66 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(941,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[414,940,939,936,934,933,930,929,924,923,917,912,910,909,908,907,906,905,904,903,902,901,900,899,898,897,896,895,894,893,892,891,890,889,888,887,886,885,884,883,882,881,880,879,878,877,876,875,874,873,872,871,870,869,868,867,866,865,864,863,858,774,769,768,767,741,736,732,717,710,694,688,685,684,683,682,681,679,677,675,673,672,671,670,669,667,665,663,661,660,659,658,657,655,653,651,649,648,643,638,598,597,572,549,544,541,521,493,491,488,485,480,479,476,473,470,442,426]) ).
thf(942,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP167^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 11:19:39 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.05/1.61 ..
% 8.05/1.61
% 8.05/1.61 No.of.Axioms: 18
% 8.05/1.61
% 8.05/1.61 Length.of.Defs: 0
% 8.05/1.61
% 8.05/1.61 Contains.Choice.Funs: false
% 8.05/1.61 ..................
% 8.05/1.61
% 8.05/1.61 ********************************
% 8.05/1.61 * All subproblems solved! *
% 8.05/1.61 ********************************
% 8.05/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:18,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:941,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.05/1.61
% 8.05/1.61 %**** Beginning of derivation protocol ****
% 8.05/1.61 % SZS output start CNFRefutation
% See solution above
% 8.05/1.62
% 8.05/1.62 %**** End of derivation protocol ****
% 8.05/1.62 %**** no. of clauses in derivation: 605 ****
% 8.05/1.62 %**** clause counter: 941 ****
% 8.05/1.62
% 8.05/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:18,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:941,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------