TSTP Solution File: SWW469+5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:50:18 EDT 2022
% Result : Theorem 2.31s 2.54s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 100
% Syntax : Number of formulae : 637 ( 410 unt; 37 typ; 0 def)
% Number of atoms : 3127 (1363 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 34825 ( 899 ~; 869 |; 34 &;32931 @)
% ( 20 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 11 con; 0-7 aty)
% Number of variables : 2168 ( 0 ^2164 !; 4 ?;2168 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bool,type,
bool: $i ).
thf(tp_cl_HOL_Oequal,type,
cl_HOL_Oequal: $i > $o ).
thf(tp_collect,type,
collect: $i > $i ).
thf(tp_com,type,
com: $i ).
thf(tp_enum,type,
enum: $i > $o ).
thf(tp_equal_equal,type,
equal_equal: $i > $i ).
thf(tp_fequal,type,
fequal: $i > $i ).
thf(tp_fun,type,
fun: $i > $i > $i ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_hoare_1580379338ep_set,type,
hoare_1580379338ep_set: $i > $i ).
thf(tp_hoare_1883395792gleton,type,
hoare_1883395792gleton: $i ).
thf(tp_hoare_2037801986triple,type,
hoare_2037801986triple: $i > $i ).
thf(tp_hoare_244953527triple,type,
hoare_244953527triple: $i > $i ).
thf(tp_hoare_509422987triple,type,
hoare_509422987triple: $i > $i ).
thf(tp_induct_equal,type,
induct_equal: $i > $i ).
thf(tp_induct_false,type,
induct_false: $i ).
thf(tp_induct_true,type,
induct_true: $i ).
thf(tp_member,type,
member: $i > $i ).
thf(tp_node,type,
node: $i > $i > $i ).
thf(tp_sK10_X_2,type,
sK10_X_2: $i > $i > $i > $i ).
thf(tp_sK11_S,type,
sK11_S: $i ).
thf(tp_sK12_SY158,type,
sK12_SY158: $i ).
thf(tp_sK1_T,type,
sK1_T: $i ).
thf(tp_sK2_X_2,type,
sK2_X_2: $i > $i > $i > $i > $i ).
thf(tp_sK3_X_2,type,
sK3_X_2: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK4_Y_2,type,
sK4_Y_2: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK5_Y_2,type,
sK5_Y_2: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK6_X_2,type,
sK6_X_2: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_Y_2,type,
sK7_Y_2: $i > $i > $i ).
thf(tp_sK8_Y_2,type,
sK8_Y_2: $i > $i > $i > $i ).
thf(tp_sK9_X_2,type,
sK9_X_2: $i > $i > $i ).
thf(tp_state,type,
state: $i ).
thf(tp_sum_sum,type,
sum_sum: $i > $i > $i ).
thf(tp_ti,type,
ti: $i > $i > $i ).
thf(tp_type_definition,type,
type_definition: $i > $i > $i ).
thf(tp_undefined,type,
undefined: $i > $i ).
thf(1,axiom,
! [X_a: $i,X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(2,axiom,
! [X_a: $i,X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(3,axiom,
! [T_1: $i,A: $i] :
( ( ti @ T_1 @ ( ti @ T_1 @ A ) )
= ( ti @ T_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
thf(4,axiom,
! [T_1_1: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ T_1_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal) ).
thf(5,axiom,
! [T_2: $i,T_1_1: $i] : ( cl_HOL_Oequal @ ( sum_sum @ T_2 @ T_1_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___HOL_Oequal) ).
thf(6,axiom,
cl_HOL_Oequal @ state,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ostate___HOL_Oequal) ).
thf(7,axiom,
cl_HOL_Oequal @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
thf(8,axiom,
cl_HOL_Oequal @ com,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ocom___HOL_Oequal) ).
thf(9,axiom,
! [T_2: $i,T_1_1: $i] :
( ( ( cl_HOL_Oequal @ T_1_1 )
& ( enum @ T_2 ) )
=> ( cl_HOL_Oequal @ ( fun @ T_2 @ T_1_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
thf(10,axiom,
! [T_2: $i,T_1_1: $i] :
( ( ( enum @ T_1_1 )
& ( enum @ T_2 ) )
=> ( enum @ ( fun @ T_2 @ T_1_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(11,axiom,
enum @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(12,axiom,
! [T_2: $i,T_1_1: $i] :
( ( ( enum @ T_1_1 )
& ( enum @ T_2 ) )
=> ( enum @ ( sum_sum @ T_2 @ T_1_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___Enum_Oenum) ).
thf(13,axiom,
! [X_a: $i,P: $i] :
( ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ P )
= ( ti @ ( fun @ X_a @ bool ) @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Collect__def) ).
thf(14,axiom,
! [X_a: $i,X_1: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
<=> ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_mem__def) ).
thf(15,axiom,
! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ! [X_2: $i] :
( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ G @ X_2 ) )
=> ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_ext) ).
thf(16,axiom,
! [X_a: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) )
<=> ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_induct__equal__def) ).
thf(17,axiom,
hBOOL @ induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_induct__true__def) ).
thf(18,axiom,
hBOOL @ induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_induct__trueI) ).
thf(19,axiom,
! [X_b: $i,X_a: $i,P: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
=> ( ! [X_2: $i] : ( hBOOL @ ( hAPP @ X_b @ bool @ P @ ( hAPP @ X_a @ X_b @ Rep @ X_2 ) ) )
=> ( hBOOL @ ( hAPP @ X_b @ bool @ P @ Y_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_type__definition_ORep__induct) ).
thf(20,axiom,
! [X_b: $i,X_a: $i,X_1: $i,P: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ! [Y_2: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_2 ) @ A_1 ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ P @ ( hAPP @ X_b @ X_a @ Abs @ Y_2 ) ) ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ P @ X_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_type__definition_OAbs__induct) ).
thf(21,axiom,
! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ~ ! [Y_2: $i] :
( ( ( ti @ X_a @ X_1 )
= ( hAPP @ X_b @ X_a @ Abs @ Y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_2 ) @ A_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_type__definition_OAbs__cases) ).
thf(22,axiom,
! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
=> ~ ! [X_2: $i] :
( ( ti @ X_b @ Y_1 )
!= ( hAPP @ X_a @ X_b @ Rep @ X_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_type__definition_ORep__cases) ).
thf(23,axiom,
~ ( hBOOL @ induct_false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_induct__false__def) ).
thf(24,axiom,
! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) ) @ A_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_type__definition_ORep) ).
thf(25,axiom,
! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hAPP @ X_b @ X_a @ Abs @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) )
= ( ti @ X_a @ X_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_type__definition_ORep__inverse) ).
thf(26,axiom,
! [X_b: $i,X_a: $i,X_1: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
= ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) )
<=> ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_type__definition_ORep__inject) ).
thf(27,axiom,
! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
=> ( ( hAPP @ X_a @ X_b @ Rep @ ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
= ( ti @ X_b @ Y_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_type__definition_OAbs__inverse) ).
thf(28,axiom,
! [X_b: $i,X_a: $i,Y_1: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
=> ( ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
= ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
<=> ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ Y_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_type__definition_OAbs__inject) ).
thf(29,axiom,
! [X_a: $i,X_1: $i] :
~ ! [Y_2: $i] :
( ( X_1
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Abs__triple__cases) ).
thf(30,axiom,
! [X_a: $i,X_1: $i,P: $i] :
( ! [Y_2: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_2 ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ X_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Abs__triple__induct) ).
thf(31,axiom,
! [X_a: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Abs__triple__inject) ).
thf(32,axiom,
! [X_a: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_type__definition__triple) ).
thf(33,axiom,
! [X_a: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
= Y_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Abs__triple__inverse) ).
thf(34,axiom,
! [X_a: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ~ ! [X_2: $i] :
( Y_1
!= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Rep__triple__cases) ).
thf(35,axiom,
! [X_a: $i,P: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( ! [X_2: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ Y_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Rep__triple__induct) ).
thf(36,axiom,
! [X_a: $i,X_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Rep__triple) ).
thf(37,axiom,
! [X_a: $i,X_1: $i] :
( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) )
= X_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Rep__triple__inverse) ).
thf(38,axiom,
! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ( ( fequal @ X_a )
= ( equal_equal @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_eq__equal) ).
thf(39,axiom,
! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) )
<=> ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_equal__eq) ).
thf(40,axiom,
! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ! [X: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X ) @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_equal__refl) ).
thf(41,axiom,
! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ( ( equal_equal @ X_a )
= ( fequal @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_equal) ).
thf(42,axiom,
! [X_a: $i,X_1: $i,Y_1: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Rep__triple__inject) ).
thf(43,axiom,
! [X_a: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_equal__triple__def) ).
thf(44,axiom,
( ( hBOOL @ hoare_1883395792gleton )
<=> ? [S: $i,T: $i] :
( ( ti @ state @ S )
!= ( ti @ state @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
thf(45,axiom,
! [X_b: $i] :
( ( ti @ ( fun @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( member @ X_b ) )
= ( member @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(46,axiom,
! [X_a: $i,X_b: $i,B_1: $i,B_2: $i] :
( ( ti @ X_a @ ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(47,axiom,
! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
( ( hAPP @ X_b @ X_a @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(48,axiom,
! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
( ( hAPP @ X_b @ X_a @ ( ti @ ( fun @ X_b @ X_a ) @ B_1 ) @ B_2 )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(49,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fequal @ X_a ) )
= ( fequal @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
thf(50,axiom,
! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) ) @ ( type_definition @ X_a @ X_b ) )
= ( type_definition @ X_a @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Typedef_Otype__definition_res) ).
thf(51,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) ) @ ( collect @ X_a ) )
= ( collect @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
thf(52,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ X_a ) )
= ( hoare_1580379338ep_set @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res) ).
thf(53,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) )
= ( hoare_2037801986triple @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res) ).
thf(54,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) )
= ( hoare_244953527triple @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res) ).
thf(55,axiom,
! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(56,axiom,
( ( ti @ bool @ induct_true )
= induct_true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__true_res) ).
thf(57,axiom,
( ( ti @ bool @ induct_false )
= induct_false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__false_res) ).
thf(58,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( induct_equal @ X_a ) )
= ( induct_equal @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__equal_res) ).
thf(59,axiom,
! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( equal_equal @ X_a ) )
= ( equal_equal @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oequal__class_Oequal_res) ).
thf(60,axiom,
hBOOL @ hoare_1883395792gleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(61,axiom,
! [B_1: $i] :
( ( hBOOL @ ( ti @ bool @ B_1 ) )
<=> ( hBOOL @ B_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(62,axiom,
( ( ti @ bool @ hoare_1883395792gleton )
= hoare_1883395792gleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res) ).
thf(63,conjecture,
! [T: $i] :
~ ! [S: $i] :
( ( ti @ state @ S )
= ( ti @ state @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(64,negated_conjecture,
( ( ! [T: $i] :
~ ! [S: $i] :
( ( ti @ state @ S )
= ( ti @ state @ T ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[63]) ).
thf(65,plain,
( ( ! [T: $i] :
~ ! [S: $i] :
( ( ti @ state @ S )
= ( ti @ state @ T ) ) )
= $false ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(67,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(68,plain,
( ( ! [T_1: $i,A: $i] :
( ( ti @ T_1 @ ( ti @ T_1 @ A ) )
= ( ti @ T_1 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [T_1_1: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ T_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(70,plain,
( ( ! [T_2: $i,T_1_1: $i] : ( cl_HOL_Oequal @ ( sum_sum @ T_2 @ T_1_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(71,plain,
( ( cl_HOL_Oequal @ state )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(72,plain,
( ( cl_HOL_Oequal @ bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(73,plain,
( ( cl_HOL_Oequal @ com )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(74,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ( ( cl_HOL_Oequal @ T_1_1 )
& ( enum @ T_2 ) )
=> ( cl_HOL_Oequal @ ( fun @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(75,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ( ( enum @ T_1_1 )
& ( enum @ T_2 ) )
=> ( enum @ ( fun @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(76,plain,
( ( enum @ bool )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(77,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ( ( enum @ T_1_1 )
& ( enum @ T_2 ) )
=> ( enum @ ( sum_sum @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(78,plain,
( ( ! [X_a: $i,P: $i] :
( ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ P )
= ( ti @ ( fun @ X_a @ bool ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(79,plain,
( ( ! [X_a: $i,X_1: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
<=> ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(80,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ! [X_2: $i] :
( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ G @ X_2 ) )
=> ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(81,plain,
( ( ! [X_a: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) )
<=> ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(82,plain,
( ( hBOOL @ induct_true )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(83,plain,
( ( hBOOL @ induct_true )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(84,plain,
( ( ! [X_b: $i,X_a: $i,P: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
=> ( ! [X_2: $i] : ( hBOOL @ ( hAPP @ X_b @ bool @ P @ ( hAPP @ X_a @ X_b @ Rep @ X_2 ) ) )
=> ( hBOOL @ ( hAPP @ X_b @ bool @ P @ Y_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(85,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,P: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ! [Y_2: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_2 ) @ A_1 ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ P @ ( hAPP @ X_b @ X_a @ Abs @ Y_2 ) ) ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ P @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(86,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ~ ! [Y_2: $i] :
( ( ( ti @ X_a @ X_1 )
= ( hAPP @ X_b @ X_a @ Abs @ Y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_2 ) @ A_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(87,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
=> ~ ! [X_2: $i] :
( ( ti @ X_b @ Y_1 )
!= ( hAPP @ X_a @ X_b @ Rep @ X_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(88,plain,
( ( ~ ( hBOOL @ induct_false ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(89,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) ) @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(90,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hAPP @ X_b @ X_a @ Abs @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) )
= ( ti @ X_a @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(91,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
= ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) )
<=> ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(92,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
=> ( ( hAPP @ X_a @ X_b @ Rep @ ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
= ( ti @ X_b @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(93,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
=> ( ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
= ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
<=> ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ Y_1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(94,plain,
( ( ! [X_a: $i,X_1: $i] :
~ ! [Y_2: $i] :
( ( X_1
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_2 ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(95,plain,
( ( ! [X_a: $i,X_1: $i,P: $i] :
( ! [Y_2: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_2 ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(96,plain,
( ( ! [X_a: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(97,plain,
( ( ! [X_a: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(98,plain,
( ( ! [X_a: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
= Y_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(99,plain,
( ( ! [X_a: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ~ ! [X_2: $i] :
( Y_1
!= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(100,plain,
( ( ! [X_a: $i,P: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
=> ( ! [X_2: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(101,plain,
( ( ! [X_a: $i,X_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(102,plain,
( ( ! [X_a: $i,X_1: $i] :
( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) )
= X_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(103,plain,
( ( ! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ( ( fequal @ X_a )
= ( equal_equal @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(104,plain,
( ( ! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) )
<=> ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(105,plain,
( ( ! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ! [X: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X ) @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(106,plain,
( ( ! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ( ( equal_equal @ X_a )
= ( fequal @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(107,plain,
( ( ! [X_a: $i,X_1: $i,Y_1: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(108,plain,
( ( ! [X_a: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(109,plain,
( ( ( hBOOL @ hoare_1883395792gleton )
<=> ? [S: $i,T: $i] :
( ( ti @ state @ S )
!= ( ti @ state @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(110,plain,
( ( ! [X_b: $i] :
( ( ti @ ( fun @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( member @ X_b ) )
= ( member @ X_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(111,plain,
( ( ! [X_a: $i,X_b: $i,B_1: $i,B_2: $i] :
( ( ti @ X_a @ ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(112,plain,
( ( ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
( ( hAPP @ X_b @ X_a @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(113,plain,
( ( ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
( ( hAPP @ X_b @ X_a @ ( ti @ ( fun @ X_b @ X_a ) @ B_1 ) @ B_2 )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(114,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fequal @ X_a ) )
= ( fequal @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(115,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) ) @ ( type_definition @ X_a @ X_b ) )
= ( type_definition @ X_a @ X_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(116,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) ) @ ( collect @ X_a ) )
= ( collect @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(117,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ X_a ) )
= ( hoare_1580379338ep_set @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(118,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) )
= ( hoare_2037801986triple @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(119,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) )
= ( hoare_244953527triple @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(120,plain,
( ( ! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(121,plain,
( ( ( ti @ bool @ induct_true )
= induct_true )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(122,plain,
( ( ( ti @ bool @ induct_false )
= induct_false )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(123,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( induct_equal @ X_a ) )
= ( induct_equal @ X_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(124,plain,
( ( ! [X_a: $i] :
( ( cl_HOL_Oequal @ X_a )
=> ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( equal_equal @ X_a ) )
= ( equal_equal @ X_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(125,plain,
( ( hBOOL @ hoare_1883395792gleton )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(126,plain,
( ( ! [B_1: $i] :
( ( hBOOL @ ( ti @ bool @ B_1 ) )
<=> ( hBOOL @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(127,plain,
( ( ( ti @ bool @ hoare_1883395792gleton )
= hoare_1883395792gleton )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(128,plain,
( ( ~ ! [SY157: $i] :
( ( ti @ state @ SY157 )
= ( ti @ state @ sK1_T ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(129,plain,
( ( ! [SY157: $i] :
( ( ti @ state @ SY157 )
= ( ti @ state @ sK1_T ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[128]) ).
thf(130,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(131,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ~ ( cl_HOL_Oequal @ T_1_1 )
| ~ ( enum @ T_2 )
| ( cl_HOL_Oequal @ ( fun @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(132,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ~ ( enum @ T_1_1 )
| ~ ( enum @ T_2 )
| ( enum @ ( fun @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(133,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ~ ( enum @ T_1_1 )
| ~ ( enum @ T_2 )
| ( enum @ ( sum_sum @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(134,plain,
( ( ! [X_a: $i] :
( ! [X_1: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) ) )
& ! [X_1: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(135,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ( ( hAPP @ X_a @ X_b @ F @ ( sK2_X_2 @ G @ F @ X_b @ X_a ) )
!= ( hAPP @ X_a @ X_b @ G @ ( sK2_X_2 @ G @ F @ X_b @ X_a ) ) )
| ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(136,plain,
( ( ! [X_a: $i] :
( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( ti @ X_a @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(137,plain,
( ( ! [X_b: $i,X_a: $i,P: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ X_b @ bool @ P @ ( hAPP @ X_a @ X_b @ Rep @ ( sK3_X_2 @ A_1 @ Abs @ Rep @ Y_1 @ P @ X_a @ X_b ) ) ) )
| ( hBOOL @ ( hAPP @ X_b @ bool @ P @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(138,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,P: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( sK4_Y_2 @ A_1 @ Abs @ Rep @ P @ X_1 @ X_a @ X_b ) ) @ A_1 ) )
& ~ ( hBOOL @ ( hAPP @ X_a @ bool @ P @ ( hAPP @ X_b @ X_a @ Abs @ ( sK4_Y_2 @ A_1 @ Abs @ Rep @ P @ X_1 @ X_a @ X_b ) ) ) ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ P @ X_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(139,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( ( ti @ X_a @ X_1 )
= ( hAPP @ X_b @ X_a @ Abs @ ( sK5_Y_2 @ A_1 @ Abs @ Rep @ X_1 @ X_a @ X_b ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( sK5_Y_2 @ A_1 @ Abs @ Rep @ X_1 @ X_a @ X_b ) ) @ A_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(140,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ( ( ti @ X_b @ Y_1 )
= ( hAPP @ X_a @ X_b @ Rep @ ( sK6_X_2 @ A_1 @ Abs @ Rep @ Y_1 @ X_a @ X_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(141,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) ) @ A_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(142,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i] :
( ! [A_1: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( hAPP @ X_b @ X_a @ Abs @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) )
= ( ti @ X_a @ X_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(143,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Y_1: $i,Rep: $i] :
( ( ! [Abs: $i,A_1: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
!= ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) )
| ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) )
& ( ! [Abs: $i,A_1: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( ti @ X_a @ X_1 )
!= ( ti @ X_a @ Y_1 ) )
| ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
= ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(144,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ Rep @ ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
= ( ti @ X_b @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(145,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,X_1: $i,Rep: $i] :
( ! [Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
!= ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
| ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ Y_1 ) ) )
& ! [Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ( ( ti @ X_b @ X_1 )
!= ( ti @ X_b @ Y_1 ) )
| ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
= ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(146,plain,
( ( ! [X_a: $i,X_1: $i] :
( ( X_1
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( sK7_Y_2 @ X_1 @ X_a ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( sK7_Y_2 @ X_1 @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(147,plain,
( ( ! [X_a: $i,X_1: $i,P: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( sK8_Y_2 @ P @ X_1 @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( sK8_Y_2 @ P @ X_1 @ X_a ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ X_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(148,plain,
( ( ! [X_a: $i] :
( ! [Y_1: $i,X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
| ( X_1 = Y_1 ) )
& ! [Y_1: $i,X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ( X_1 != Y_1 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(149,plain,
( ( ! [X_a: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
= Y_1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(150,plain,
( ( ! [X_a: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ( Y_1
= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( sK9_X_2 @ Y_1 @ X_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(151,plain,
( ( ! [X_a: $i,P: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( sK10_X_2 @ Y_1 @ P @ X_a ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(152,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ( ( fequal @ X_a )
= ( equal_equal @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(153,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( ti @ X_a @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(154,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ! [X: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(155,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ( ( equal_equal @ X_a )
= ( fequal @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(156,plain,
( ( ! [X_a: $i] :
( ! [X_1: $i,Y_1: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
!= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) )
| ( X_1 = Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ( X_1 != Y_1 )
| ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(157,plain,
( ( ! [X_a: $i] :
( ! [X_1: $i,Y_1: $i] :
( ( X_1 != Y_1 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) )
| ( X_1 = Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(158,plain,
( ( ( ! [S: $i,T: $i] :
( ( ti @ state @ S )
= ( ti @ state @ T ) )
| ( hBOOL @ hoare_1883395792gleton ) )
& ( ~ ( hBOOL @ hoare_1883395792gleton )
| ( ( ti @ state @ sK11_S )
!= ( ti @ state @ sK12_SY158 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(159,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( equal_equal @ X_a ) )
= ( equal_equal @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(160,plain,
( ( ! [B_1: $i] :
( ~ ( hBOOL @ ( ti @ bool @ B_1 ) )
| ( hBOOL @ B_1 ) )
& ! [B_1: $i] :
( ~ ( hBOOL @ B_1 )
| ( hBOOL @ ( ti @ bool @ B_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(161,plain,
( ( ( ti @ bool @ hoare_1883395792gleton )
= hoare_1883395792gleton )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(162,plain,
( ( ! [B_1: $i] :
( ~ ( hBOOL @ ( ti @ bool @ B_1 ) )
| ( hBOOL @ B_1 ) )
& ! [B_1: $i] :
( ~ ( hBOOL @ B_1 )
| ( hBOOL @ ( ti @ bool @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(163,plain,
( ( hBOOL @ hoare_1883395792gleton )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(164,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( equal_equal @ X_a ) )
= ( equal_equal @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(165,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( induct_equal @ X_a ) )
= ( induct_equal @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(166,plain,
( ( ( ti @ bool @ induct_false )
= induct_false )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(167,plain,
( ( ( ti @ bool @ induct_true )
= induct_true )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(168,plain,
( ( ! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(169,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) )
= ( hoare_244953527triple @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(170,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) )
= ( hoare_2037801986triple @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(171,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ X_a ) )
= ( hoare_1580379338ep_set @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(172,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) ) @ ( collect @ X_a ) )
= ( collect @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(173,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) ) @ ( type_definition @ X_a @ X_b ) )
= ( type_definition @ X_a @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(174,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fequal @ X_a ) )
= ( fequal @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(175,plain,
( ( ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
( ( hAPP @ X_b @ X_a @ ( ti @ ( fun @ X_b @ X_a ) @ B_1 ) @ B_2 )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(176,plain,
( ( ! [X_b: $i,X_a: $i,B_1: $i,B_2: $i] :
( ( hAPP @ X_b @ X_a @ B_1 @ ( ti @ X_b @ B_2 ) )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(177,plain,
( ( ! [X_a: $i,X_b: $i,B_1: $i,B_2: $i] :
( ( ti @ X_a @ ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) )
= ( hAPP @ X_b @ X_a @ B_1 @ B_2 ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(178,plain,
( ( ! [X_b: $i] :
( ( ti @ ( fun @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( member @ X_b ) )
= ( member @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(179,plain,
( ( ( ! [S: $i,T: $i] :
( ( ti @ state @ S )
= ( ti @ state @ T ) )
| ( hBOOL @ hoare_1883395792gleton ) )
& ( ~ ( hBOOL @ hoare_1883395792gleton )
| ( ( ti @ state @ sK11_S )
!= ( ti @ state @ sK12_SY158 ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(180,plain,
( ( ! [X_a: $i] :
( ! [X_1: $i,Y_1: $i] :
( ( X_1 != Y_1 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( hoare_509422987triple @ X_a ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ X_a ) ) @ X_1 ) @ Y_1 ) )
| ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(181,plain,
( ( ! [X_a: $i] :
( ! [X_1: $i,Y_1: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
!= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) )
| ( X_1 = Y_1 ) )
& ! [X_1: $i,Y_1: $i] :
( ( X_1 != Y_1 )
| ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 )
= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(182,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ( ( equal_equal @ X_a )
= ( fequal @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(183,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ! [X: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(184,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( ti @ X_a @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( equal_equal @ X_a ) @ X_1 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(185,plain,
( ( ! [X_a: $i] :
( ~ ( cl_HOL_Oequal @ X_a )
| ( ( fequal @ X_a )
= ( equal_equal @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(186,plain,
( ( ! [X_a: $i,X_1: $i] :
( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) )
= X_1 ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(187,plain,
( ( ! [X_a: $i,X_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ X_1 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(188,plain,
( ( ! [X_a: $i,P: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( sK10_X_2 @ Y_1 @ P @ X_a ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool @ P @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(189,plain,
( ( ! [X_a: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ( Y_1
= ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( sK9_X_2 @ Y_1 @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(190,plain,
( ( ! [X_a: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ( ( hAPP @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_2037801986triple @ X_a ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
= Y_1 ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(191,plain,
( ( ! [X_a: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ X_a ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_2037801986triple @ X_a ) ) @ ( hoare_244953527triple @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(192,plain,
( ( ! [X_a: $i] :
( ! [Y_1: $i,X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) )
| ( X_1 = Y_1 ) )
& ! [Y_1: $i,X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ X_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ Y_1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
| ( X_1 != Y_1 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ X_1 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(193,plain,
( ( ! [X_a: $i,X_1: $i,P: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( sK8_Y_2 @ P @ X_1 @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) )
& ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( sK8_Y_2 @ P @ X_1 @ X_a ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ X_a ) @ bool @ P @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(194,plain,
( ( ! [X_a: $i,X_1: $i] :
( ( X_1
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( hoare_509422987triple @ X_a ) @ ( hoare_244953527triple @ X_a ) @ ( sK7_Y_2 @ X_1 @ X_a ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( sK7_Y_2 @ X_1 @ X_a ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ X_a @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ X_a ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(195,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,X_1: $i,Rep: $i] :
( ! [Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
!= ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
| ( ( ti @ X_b @ X_1 )
= ( ti @ X_b @ Y_1 ) ) )
& ! [Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ X_1 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ( ( ti @ X_b @ X_1 )
!= ( ti @ X_b @ Y_1 ) )
| ( ( hAPP @ X_b @ X_a @ Abs @ X_1 )
= ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(196,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ Rep @ ( hAPP @ X_b @ X_a @ Abs @ Y_1 ) )
= ( ti @ X_b @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(197,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Y_1: $i,Rep: $i] :
( ( ! [Abs: $i,A_1: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
!= ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) )
| ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) )
& ( ! [Abs: $i,A_1: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( ti @ X_a @ X_1 )
!= ( ti @ X_a @ Y_1 ) )
| ( ( hAPP @ X_a @ X_b @ Rep @ X_1 )
= ( hAPP @ X_a @ X_b @ Rep @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(198,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i] :
( ! [A_1: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( hAPP @ X_b @ X_a @ Abs @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) )
= ( ti @ X_a @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(199,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ Rep @ X_1 ) ) @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(200,plain,
( ( ~ ( hBOOL @ induct_false ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(201,plain,
( ( ! [X_b: $i,X_a: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ( ( ti @ X_b @ Y_1 )
= ( hAPP @ X_a @ X_b @ Rep @ ( sK6_X_2 @ A_1 @ Abs @ Rep @ Y_1 @ X_a @ X_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(202,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( ( ti @ X_a @ X_1 )
= ( hAPP @ X_b @ X_a @ Abs @ ( sK5_Y_2 @ A_1 @ Abs @ Rep @ X_1 @ X_a @ X_b ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( sK5_Y_2 @ A_1 @ Abs @ Rep @ X_1 @ X_a @ X_b ) ) @ A_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(203,plain,
( ( ! [X_b: $i,X_a: $i,X_1: $i,P: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ( ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( sK4_Y_2 @ A_1 @ Abs @ Rep @ P @ X_1 @ X_a @ X_b ) ) @ A_1 ) )
& ~ ( hBOOL @ ( hAPP @ X_a @ bool @ P @ ( hAPP @ X_b @ X_a @ Abs @ ( sK4_Y_2 @ A_1 @ Abs @ Rep @ P @ X_1 @ X_a @ X_b ) ) ) ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ P @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(204,plain,
( ( ! [X_b: $i,X_a: $i,P: $i,Y_1: $i,Rep: $i,Abs: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_b @ X_a ) @ ( fun @ ( fun @ X_b @ bool ) @ bool ) ) @ ( type_definition @ X_a @ X_b ) @ Rep ) @ Abs ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ Y_1 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ X_b @ bool @ P @ ( hAPP @ X_a @ X_b @ Rep @ ( sK3_X_2 @ A_1 @ Abs @ Rep @ Y_1 @ P @ X_a @ X_b ) ) ) )
| ( hBOOL @ ( hAPP @ X_b @ bool @ P @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(205,plain,
( ( hBOOL @ induct_true )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(206,plain,
( ( hBOOL @ induct_true )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(207,plain,
( ( ! [X_a: $i] :
( ! [X_1: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_1 )
!= ( ti @ X_a @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) ) )
& ! [X_1: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( induct_equal @ X_a ) @ X_1 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(208,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ( ( hAPP @ X_a @ X_b @ F @ ( sK2_X_2 @ G @ F @ X_b @ X_a ) )
!= ( hAPP @ X_a @ X_b @ G @ ( sK2_X_2 @ G @ F @ X_b @ X_a ) ) )
| ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(209,plain,
( ( ! [X_a: $i] :
( ! [X_1: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) ) )
& ! [X_1: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(210,plain,
( ( ! [X_a: $i,P: $i] :
( ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ P )
= ( ti @ ( fun @ X_a @ bool ) @ P ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(211,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ~ ( enum @ T_1_1 )
| ~ ( enum @ T_2 )
| ( enum @ ( sum_sum @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(212,plain,
( ( enum @ bool )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(213,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ~ ( enum @ T_1_1 )
| ~ ( enum @ T_2 )
| ( enum @ ( fun @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(214,plain,
( ( ! [T_2: $i,T_1_1: $i] :
( ~ ( cl_HOL_Oequal @ T_1_1 )
| ~ ( enum @ T_2 )
| ( cl_HOL_Oequal @ ( fun @ T_2 @ T_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(215,plain,
( ( cl_HOL_Oequal @ com )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(216,plain,
( ( cl_HOL_Oequal @ bool )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(217,plain,
( ( cl_HOL_Oequal @ state )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(218,plain,
( ( ! [T_2: $i,T_1_1: $i] : ( cl_HOL_Oequal @ ( sum_sum @ T_2 @ T_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(219,plain,
( ( ! [T_1_1: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ T_1_1 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(220,plain,
( ( ! [T_1: $i,A: $i] :
( ( ti @ T_1 @ ( ti @ T_1 @ A ) )
= ( ti @ T_1 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(221,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(222,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(223,plain,
( ( ! [SY157: $i] :
( ( ti @ state @ SY157 )
= ( ti @ state @ sK1_T ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(224,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( sK8_Y_2 @ SX2 @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ bool @ SX2 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ ( sK8_Y_2 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ bool @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(225,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX3 ) @ SX4 ) @ SX5 ) )
| ~ ( ( ( ti @ SX1 @ SX2 )
!= ( hAPP @ SX0 @ SX1 @ SX4 @ ( sK5_Y_2 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ ( sK5_Y_2 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(226,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ! [SX5: $i,SX6: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
| ( ( hAPP @ SX1 @ SX0 @ SX4 @ SX2 )
!= ( hAPP @ SX1 @ SX0 @ SX4 @ SX3 ) )
| ( ( ti @ SX1 @ SX2 )
= ( ti @ SX1 @ SX3 ) ) )
| ~ ( ! [SX5: $i,SX6: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
| ( ( ti @ SX1 @ SX2 )
!= ( ti @ SX1 @ SX3 ) )
| ( ( hAPP @ SX1 @ SX0 @ SX4 @ SX2 )
= ( hAPP @ SX1 @ SX0 @ SX4 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(227,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ ( sK4_Y_2 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX6 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SX1 @ bool @ SX3 @ ( hAPP @ SX0 @ SX1 @ SX5 @ ( sK4_Y_2 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SX1 @ bool @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(228,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ SX2 @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(229,plain,
( ( ~ ( ~ ( ! [SX0: $i,SX1: $i] :
( ( ti @ state @ SX0 )
= ( ti @ state @ SX1 ) )
| ( hBOOL @ hoare_1883395792gleton ) )
| ~ ( ~ ( hBOOL @ hoare_1883395792gleton )
| ( ( ti @ state @ sK11_S )
!= ( ti @ state @ sK12_SY158 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(230,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( ti @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( induct_equal @ SX0 ) @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( induct_equal @ SX0 ) @ SX1 ) @ SX2 ) )
| ( ( ti @ SX0 @ SX1 )
= ( ti @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(231,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(232,plain,
( ( ! [SX0: $i] :
( ~ ( cl_HOL_Oequal @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( ti @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( equal_equal @ SX0 ) @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( equal_equal @ SX0 ) @ SX1 ) @ SX2 ) )
| ( ( ti @ SX0 @ SX1 )
= ( ti @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(233,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ( SX1
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ ( sK7_Y_2 @ SX1 @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( sK7_Y_2 @ SX1 @ SX0 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(234,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ SX2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ SX1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ SX2 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ SX1 ) )
| ( SX2 = SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ SX2 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ SX1 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SX0 ) ) ) )
| ( SX2 != SX1 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ SX2 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_509422987triple @ SX0 ) @ ( hoare_244953527triple @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(235,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_2037801986triple @ SX0 ) @ SX1 )
!= ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_2037801986triple @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_2037801986triple @ SX0 ) @ SX1 )
= ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SX0 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SX0 ) ) @ bool ) @ ( hoare_2037801986triple @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(236,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ! [SX5: $i,SX6: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX3 ) @ SX6 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX2 ) @ SX6 ) )
| ( ( hAPP @ SX0 @ SX1 @ SX5 @ SX3 )
!= ( hAPP @ SX0 @ SX1 @ SX5 @ SX2 ) )
| ( ( ti @ SX0 @ SX3 )
= ( ti @ SX0 @ SX2 ) ) )
| ~ ! [SX5: $i,SX6: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SX1 @ SX0 ) @ ( fun @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) ) @ ( type_definition @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) @ SX6 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX3 ) @ SX6 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX2 ) @ SX6 ) )
| ( ( ti @ SX0 @ SX3 )
!= ( ti @ SX0 @ SX2 ) )
| ( ( hAPP @ SX0 @ SX1 @ SX5 @ SX3 )
= ( hAPP @ SX0 @ SX1 @ SX5 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(237,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( hoare_509422987triple @ SX0 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SX0 ) ) @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SX0 ) @ ( fun @ ( hoare_509422987triple @ SX0 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SX0 ) ) @ SX1 ) @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(238,plain,
! [SV1: $i] :
( ( ~ ( cl_HOL_Oequal @ SV1 )
| ( ( ti @ ( fun @ SV1 @ ( fun @ SV1 @ bool ) ) @ ( equal_equal @ SV1 ) )
= ( equal_equal @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(239,plain,
! [SV2: $i] :
( ( ( ti @ ( fun @ SV2 @ ( fun @ SV2 @ bool ) ) @ ( induct_equal @ SV2 ) )
= ( induct_equal @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(240,plain,
! [SV3: $i] :
( ( ( ti @ SV3 @ ( undefined @ SV3 ) )
= ( undefined @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(241,plain,
! [SV4: $i] :
( ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV4 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV4 ) ) @ bool ) @ ( hoare_509422987triple @ SV4 ) ) @ ( hoare_244953527triple @ SV4 ) )
= ( hoare_244953527triple @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(242,plain,
! [SV5: $i] :
( ( ( ti @ ( fun @ ( hoare_509422987triple @ SV5 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV5 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV5 ) ) @ bool ) ) @ ( hoare_2037801986triple @ SV5 ) )
= ( hoare_2037801986triple @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(243,plain,
! [SV6: $i] :
( ( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV6 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV6 ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ SV6 ) )
= ( hoare_1580379338ep_set @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(244,plain,
! [SV7: $i] :
( ( ( ti @ ( fun @ ( fun @ SV7 @ bool ) @ ( fun @ SV7 @ bool ) ) @ ( collect @ SV7 ) )
= ( collect @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(245,plain,
! [SV8: $i] :
( ( ! [SY159: $i] :
( ( ti @ ( fun @ ( fun @ SV8 @ SY159 ) @ ( fun @ ( fun @ SY159 @ SV8 ) @ ( fun @ ( fun @ SY159 @ bool ) @ bool ) ) ) @ ( type_definition @ SV8 @ SY159 ) )
= ( type_definition @ SV8 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(246,plain,
! [SV9: $i] :
( ( ( ti @ ( fun @ SV9 @ ( fun @ SV9 @ bool ) ) @ ( fequal @ SV9 ) )
= ( fequal @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(247,plain,
! [SV10: $i] :
( ( ! [SY160: $i,SY161: $i,SY162: $i] :
( ( hAPP @ SV10 @ SY160 @ ( ti @ ( fun @ SV10 @ SY160 ) @ SY161 ) @ SY162 )
= ( hAPP @ SV10 @ SY160 @ SY161 @ SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(248,plain,
! [SV11: $i] :
( ( ! [SY163: $i,SY164: $i,SY165: $i] :
( ( hAPP @ SV11 @ SY163 @ SY164 @ ( ti @ SV11 @ SY165 ) )
= ( hAPP @ SV11 @ SY163 @ SY164 @ SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(249,plain,
! [SV12: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i] :
( ( ti @ SV12 @ ( hAPP @ SY166 @ SV12 @ SY167 @ SY168 ) )
= ( hAPP @ SY166 @ SV12 @ SY167 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(250,plain,
! [SV13: $i] :
( ( ( ti @ ( fun @ SV13 @ ( fun @ ( fun @ SV13 @ bool ) @ bool ) ) @ ( member @ SV13 ) )
= ( member @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(251,plain,
! [SV14: $i] :
( ( ~ ( cl_HOL_Oequal @ SV14 )
| ( ( equal_equal @ SV14 )
= ( fequal @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(252,plain,
! [SV15: $i] :
( ( ~ ( cl_HOL_Oequal @ SV15 )
| ! [SY169: $i] : ( hBOOL @ ( hAPP @ SV15 @ bool @ ( hAPP @ SV15 @ ( fun @ SV15 @ bool ) @ ( equal_equal @ SV15 ) @ SY169 ) @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(253,plain,
! [SV16: $i] :
( ( ~ ( cl_HOL_Oequal @ SV16 )
| ( ( fequal @ SV16 )
= ( equal_equal @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(254,plain,
! [SV17: $i] :
( ( ! [SY170: $i] :
( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV17 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV17 ) ) @ bool ) @ ( hoare_509422987triple @ SV17 ) @ ( hoare_244953527triple @ SV17 ) @ ( hAPP @ ( hoare_509422987triple @ SV17 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV17 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV17 ) ) @ bool ) @ ( hoare_2037801986triple @ SV17 ) @ SY170 ) )
= SY170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(255,plain,
! [SV18: $i] :
( ( ! [SY171: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ SV18 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ ( hoare_2037801986triple @ SV18 ) @ SY171 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(256,plain,
! [SV19: $i] :
( ( ! [SY172: $i,SY173: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SY173 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SY172 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SY173 @ SY172 @ SV19 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SY172 @ SY173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(257,plain,
! [SV20: $i] :
( ( ! [SY174: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ SY174 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV20 ) ) ) )
| ( SY174
= ( hAPP @ ( hoare_509422987triple @ SV20 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( hoare_2037801986triple @ SV20 ) @ ( sK9_X_2 @ SY174 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(258,plain,
! [SV21: $i] :
( ( ! [SY175: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ SY175 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV21 ) ) ) )
| ( ( hAPP @ ( hoare_509422987triple @ SV21 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_2037801986triple @ SV21 ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_509422987triple @ SV21 ) @ ( hoare_244953527triple @ SV21 ) @ SY175 ) )
= SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(259,plain,
! [SV22: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ ( hoare_509422987triple @ SV22 ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ SV22 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ ( hoare_509422987triple @ SV22 ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ SV22 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) ) @ ( hoare_2037801986triple @ SV22 ) ) @ ( hoare_244953527triple @ SV22 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV22 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV22 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(260,plain,
! [SV23: $i] :
( ( ! [SY176: $i,SY177: $i,SY178: $i,SY179: $i,SY180: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SY176 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY176 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SY176 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SY176 @ SV23 ) @ SY178 ) @ SY179 ) @ SY180 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SY177 ) @ SY180 ) )
| ( ( hAPP @ SY176 @ SV23 @ SY178 @ ( hAPP @ SV23 @ SY176 @ SY179 @ SY177 ) )
= ( ti @ SV23 @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(261,plain,
! [SV24: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i,SY184: $i] :
( ! [SY185: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SY181 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY181 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SY181 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SY181 @ SV24 ) @ SY183 ) @ SY184 ) @ SY185 ) )
| ( ( hAPP @ SV24 @ SY181 @ SY184 @ ( hAPP @ SY181 @ SV24 @ SY183 @ SY182 ) )
= ( ti @ SY181 @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(262,plain,
! [SV25: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i,SY189: $i,SY190: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SY186 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY186 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SY186 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SY186 @ SV25 ) @ SY188 ) @ SY189 ) @ SY190 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SY186 @ SV25 @ SY188 @ SY187 ) ) @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(263,plain,
( ( hBOOL @ induct_false )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(264,plain,
! [SV26: $i] :
( ( ! [SY191: $i,SY192: $i,SY193: $i,SY194: $i,SY195: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SY191 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY191 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SY191 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SY191 @ SV26 ) @ SY193 ) @ SY194 ) @ SY195 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SY192 ) @ SY195 ) )
| ( ( ti @ SV26 @ SY192 )
= ( hAPP @ SY191 @ SV26 @ SY193 @ ( sK6_X_2 @ SY195 @ SY194 @ SY193 @ SY192 @ SY191 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(265,plain,
! [SV27: $i] :
( ( ! [SY196: $i,SY197: $i,SY198: $i,SY199: $i,SY200: $i,SY201: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SY196 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY196 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SY196 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SY196 @ SV27 ) @ SY199 ) @ SY200 ) @ SY201 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SY198 ) @ SY201 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SY197 @ ( hAPP @ SY196 @ SV27 @ SY199 @ ( sK3_X_2 @ SY201 @ SY200 @ SY199 @ SY198 @ SY197 @ SY196 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SY197 @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(266,plain,
! [SV28: $i] :
( ( ! [SY202: $i,SY203: $i,SY204: $i] :
( ( ( hAPP @ SV28 @ SY202 @ SY203 @ ( sK2_X_2 @ SY204 @ SY203 @ SY202 @ SV28 ) )
!= ( hAPP @ SV28 @ SY202 @ SY204 @ ( sK2_X_2 @ SY204 @ SY203 @ SY202 @ SV28 ) ) )
| ( ( ti @ ( fun @ SV28 @ SY202 ) @ SY203 )
= ( ti @ ( fun @ SV28 @ SY202 ) @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(267,plain,
! [SV29: $i] :
( ( ! [SY205: $i] :
( ( hAPP @ ( fun @ SV29 @ bool ) @ ( fun @ SV29 @ bool ) @ ( collect @ SV29 ) @ SY205 )
= ( ti @ ( fun @ SV29 @ bool ) @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(268,plain,
! [SV30: $i] :
( ( ! [SY206: $i] :
( ~ ( enum @ SY206 )
| ~ ( enum @ SV30 )
| ( enum @ ( sum_sum @ SV30 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(269,plain,
! [SV31: $i] :
( ( ! [SY207: $i] :
( ~ ( enum @ SY207 )
| ~ ( enum @ SV31 )
| ( enum @ ( fun @ SV31 @ SY207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(270,plain,
! [SV32: $i] :
( ( ! [SY208: $i] :
( ~ ( cl_HOL_Oequal @ SY208 )
| ~ ( enum @ SV32 )
| ( cl_HOL_Oequal @ ( fun @ SV32 @ SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(271,plain,
! [SV33: $i] :
( ( ! [SY209: $i] : ( cl_HOL_Oequal @ ( sum_sum @ SV33 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(272,plain,
! [SV34: $i] :
( ( cl_HOL_Oequal @ ( hoare_509422987triple @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(273,plain,
! [SV35: $i] :
( ( ! [SY210: $i] :
( ( ti @ SV35 @ ( ti @ SV35 @ SY210 ) )
= ( ti @ SV35 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(274,plain,
! [SV36: $i] :
( ( ! [SY211: $i,SY212: $i] :
( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SY211 ) @ SY212 ) )
| ( ( ti @ SV36 @ SY211 )
= ( ti @ SV36 @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(275,plain,
! [SV37: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ( ( ti @ SV37 @ SY213 )
!= ( ti @ SV37 @ SY214 ) )
| ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SY213 ) @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(276,plain,
! [SV38: $i] :
( ( ( ti @ state @ SV38 )
= ( ti @ state @ sK1_T ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(277,plain,
! [SV39: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SY216 @ SY215 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SY216 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SY216 @ SY215 @ SV39 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SY216 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(278,plain,
! [SV40: $i] :
( ( ! [SY217: $i,SY218: $i,SY219: $i,SY220: $i,SY221: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SY217 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY217 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SY217 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SY217 @ SV40 ) @ SY219 ) @ SY220 ) @ SY221 ) )
| ~ ( ( ( ti @ SY217 @ SY218 )
!= ( hAPP @ SV40 @ SY217 @ SY220 @ ( sK5_Y_2 @ SY221 @ SY220 @ SY219 @ SY218 @ SY217 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY221 @ SY220 @ SY219 @ SY218 @ SY217 @ SV40 ) ) @ SY221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(279,plain,
! [SV41: $i] :
( ( ! [SY222: $i,SY223: $i,SY224: $i,SY225: $i] :
~ ( ~ ( ! [SY226: $i,SY227: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SY222 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY222 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SY222 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SY222 @ SV41 ) @ SY225 ) @ SY226 ) @ SY227 ) )
| ( ( hAPP @ SY222 @ SV41 @ SY225 @ SY223 )
!= ( hAPP @ SY222 @ SV41 @ SY225 @ SY224 ) )
| ( ( ti @ SY222 @ SY223 )
= ( ti @ SY222 @ SY224 ) ) )
| ~ ( ! [SY228: $i,SY229: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SY222 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY222 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SY222 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SY222 @ SV41 ) @ SY225 ) @ SY228 ) @ SY229 ) )
| ( ( ti @ SY222 @ SY223 )
!= ( ti @ SY222 @ SY224 ) )
| ( ( hAPP @ SY222 @ SV41 @ SY225 @ SY223 )
= ( hAPP @ SY222 @ SV41 @ SY225 @ SY224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(280,plain,
! [SV42: $i] :
( ( ! [SY230: $i,SY231: $i,SY232: $i,SY233: $i,SY234: $i,SY235: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SY230 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY230 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SY230 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SY230 @ SV42 ) @ SY233 ) @ SY234 ) @ SY235 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY235 @ SY234 @ SY233 @ SY232 @ SY231 @ SY230 @ SV42 ) ) @ SY235 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SY230 @ bool @ SY232 @ ( hAPP @ SV42 @ SY230 @ SY234 @ ( sK4_Y_2 @ SY235 @ SY234 @ SY233 @ SY232 @ SY231 @ SY230 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SY230 @ bool @ SY232 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(281,plain,
! [SV43: $i] :
( ( ~ ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY236 ) @ SY237 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ SY237 @ SY236 ) ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY239 @ SY238 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY238 ) @ SY239 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(282,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ( ti @ state @ SX0 )
= ( ti @ state @ SX1 ) )
| ( hBOOL @ hoare_1883395792gleton ) )
| ~ ( ~ ( hBOOL @ hoare_1883395792gleton )
| ( ( ti @ state @ sK11_S )
!= ( ti @ state @ sK12_SY158 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(283,plain,
! [SV44: $i] :
( ( ~ ( ~ ! [SY240: $i,SY241: $i] :
( ( ( ti @ SV44 @ SY240 )
!= ( ti @ SV44 @ SY241 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY240 ) @ SY241 ) ) )
| ~ ! [SY242: $i,SY243: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY242 ) @ SY243 ) )
| ( ( ti @ SV44 @ SY242 )
= ( ti @ SV44 @ SY243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(284,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(285,plain,
! [SV45: $i] :
( ( ~ ( cl_HOL_Oequal @ SV45 )
| ~ ( ~ ! [SY244: $i,SY245: $i] :
( ( ( ti @ SV45 @ SY244 )
!= ( ti @ SV45 @ SY245 ) )
| ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
| ( ( ti @ SV45 @ SY246 )
= ( ti @ SV45 @ SY247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(286,plain,
! [SV46: $i] :
( ( ! [SY248: $i] :
~ ( ( SY248
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SY248 @ SV46 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SY248 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(287,plain,
! [SV47: $i] :
( ( ~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY250 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY249 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY250 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY249 ) )
| ( SY250 = SY249 ) )
| ~ ! [SY251: $i,SY252: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY252 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY251 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( SY252 != SY251 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY252 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(288,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY253: $i,SY254: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY253 )
!= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY254 ) )
| ( SY253 = SY254 ) )
| ~ ! [SY255: $i,SY256: $i] :
( ( SY255 != SY256 )
| ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY255 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(289,plain,
! [SV49: $i] :
( ( ! [SY257: $i,SY258: $i,SY259: $i,SY260: $i] :
~ ( ~ ! [SY261: $i,SY262: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SY257 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY257 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SY257 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SY257 @ SV49 ) @ SY260 ) @ SY261 ) @ SY262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY259 ) @ SY262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY258 ) @ SY262 ) )
| ( ( hAPP @ SV49 @ SY257 @ SY261 @ SY259 )
!= ( hAPP @ SV49 @ SY257 @ SY261 @ SY258 ) )
| ( ( ti @ SV49 @ SY259 )
= ( ti @ SV49 @ SY258 ) ) )
| ~ ! [SY263: $i,SY264: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SY257 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SY257 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SY257 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SY257 @ SV49 ) @ SY260 ) @ SY263 ) @ SY264 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY259 ) @ SY264 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY258 ) @ SY264 ) )
| ( ( ti @ SV49 @ SY259 )
!= ( ti @ SV49 @ SY258 ) )
| ( ( hAPP @ SV49 @ SY257 @ SY263 @ SY259 )
= ( hAPP @ SV49 @ SY257 @ SY263 @ SY258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(290,plain,
! [SV50: $i] :
( ( ~ ( ~ ! [SY265: $i,SY266: $i] :
( ( SY265 != SY266 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY265 ) @ SY266 ) ) )
| ~ ! [SY267: $i,SY268: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY267 ) @ SY268 ) )
| ( SY267 = SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(291,plain,
! [SV1: $i] :
( ( ( ~ ( cl_HOL_Oequal @ SV1 ) )
= $true )
| ( ( ( ti @ ( fun @ SV1 @ ( fun @ SV1 @ bool ) ) @ ( equal_equal @ SV1 ) )
= ( equal_equal @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(292,plain,
! [SV51: $i,SV8: $i] :
( ( ( ti @ ( fun @ ( fun @ SV8 @ SV51 ) @ ( fun @ ( fun @ SV51 @ SV8 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) ) ) @ ( type_definition @ SV8 @ SV51 ) )
= ( type_definition @ SV8 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(293,plain,
! [SV52: $i,SV10: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ( hAPP @ SV10 @ SV52 @ ( ti @ ( fun @ SV10 @ SV52 ) @ SY269 ) @ SY270 )
= ( hAPP @ SV10 @ SV52 @ SY269 @ SY270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(294,plain,
! [SV53: $i,SV11: $i] :
( ( ! [SY271: $i,SY272: $i] :
( ( hAPP @ SV11 @ SV53 @ SY271 @ ( ti @ SV11 @ SY272 ) )
= ( hAPP @ SV11 @ SV53 @ SY271 @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(295,plain,
! [SV54: $i,SV12: $i] :
( ( ! [SY273: $i,SY274: $i] :
( ( ti @ SV12 @ ( hAPP @ SV54 @ SV12 @ SY273 @ SY274 ) )
= ( hAPP @ SV54 @ SV12 @ SY273 @ SY274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(296,plain,
! [SV14: $i] :
( ( ( ~ ( cl_HOL_Oequal @ SV14 ) )
= $true )
| ( ( ( equal_equal @ SV14 )
= ( fequal @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(297,plain,
! [SV15: $i] :
( ( ( ~ ( cl_HOL_Oequal @ SV15 ) )
= $true )
| ( ( ! [SY169: $i] : ( hBOOL @ ( hAPP @ SV15 @ bool @ ( hAPP @ SV15 @ ( fun @ SV15 @ bool ) @ ( equal_equal @ SV15 ) @ SY169 ) @ SY169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(298,plain,
! [SV16: $i] :
( ( ( ~ ( cl_HOL_Oequal @ SV16 ) )
= $true )
| ( ( ( fequal @ SV16 )
= ( equal_equal @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(299,plain,
! [SV55: $i,SV17: $i] :
( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV17 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV17 ) ) @ bool ) @ ( hoare_509422987triple @ SV17 ) @ ( hoare_244953527triple @ SV17 ) @ ( hAPP @ ( hoare_509422987triple @ SV17 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV17 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV17 ) ) @ bool ) @ ( hoare_2037801986triple @ SV17 ) @ SV55 ) )
= SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(300,plain,
! [SV56: $i,SV18: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ SV18 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ ( hoare_2037801986triple @ SV18 ) @ SV56 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV18 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV18 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(301,plain,
! [SV57: $i,SV19: $i] :
( ( ! [SY275: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SY275 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SY275 @ SV57 @ SV19 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SY275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(302,plain,
! [SV58: $i,SV20: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ SV58 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV20 ) ) ) )
| ( SV58
= ( hAPP @ ( hoare_509422987triple @ SV20 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( hoare_2037801986triple @ SV20 ) @ ( sK9_X_2 @ SV58 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(303,plain,
! [SV59: $i,SV21: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ SV59 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV21 ) ) ) )
| ( ( hAPP @ ( hoare_509422987triple @ SV21 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_2037801986triple @ SV21 ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_509422987triple @ SV21 ) @ ( hoare_244953527triple @ SV21 ) @ SV59 ) )
= SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(304,plain,
! [SV60: $i,SV23: $i] :
( ( ! [SY276: $i,SY277: $i,SY278: $i,SY279: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SY277 ) @ SY278 ) @ SY279 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SY276 ) @ SY279 ) )
| ( ( hAPP @ SV60 @ SV23 @ SY277 @ ( hAPP @ SV23 @ SV60 @ SY278 @ SY276 ) )
= ( ti @ SV23 @ SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(305,plain,
! [SV61: $i,SV24: $i] :
( ( ! [SY280: $i,SY281: $i,SY282: $i] :
( ! [SY283: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SY281 ) @ SY282 ) @ SY283 ) )
| ( ( hAPP @ SV24 @ SV61 @ SY282 @ ( hAPP @ SV61 @ SV24 @ SY281 @ SY280 ) )
= ( ti @ SV61 @ SY280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(306,plain,
! [SV62: $i,SV25: $i] :
( ( ! [SY284: $i,SY285: $i,SY286: $i,SY287: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SY285 ) @ SY286 ) @ SY287 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SY285 @ SY284 ) ) @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(307,plain,
! [SV63: $i,SV26: $i] :
( ( ! [SY288: $i,SY289: $i,SY290: $i,SY291: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SY289 ) @ SY290 ) @ SY291 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SY288 ) @ SY291 ) )
| ( ( ti @ SV26 @ SY288 )
= ( hAPP @ SV63 @ SV26 @ SY289 @ ( sK6_X_2 @ SY291 @ SY290 @ SY289 @ SY288 @ SV63 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(308,plain,
! [SV64: $i,SV27: $i] :
( ( ! [SY292: $i,SY293: $i,SY294: $i,SY295: $i,SY296: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SY294 ) @ SY295 ) @ SY296 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SY293 ) @ SY296 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SY292 @ ( hAPP @ SV64 @ SV27 @ SY294 @ ( sK3_X_2 @ SY296 @ SY295 @ SY294 @ SY293 @ SY292 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SY292 @ SY293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(309,plain,
! [SV65: $i,SV28: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ( ( hAPP @ SV28 @ SV65 @ SY297 @ ( sK2_X_2 @ SY298 @ SY297 @ SV65 @ SV28 ) )
!= ( hAPP @ SV28 @ SV65 @ SY298 @ ( sK2_X_2 @ SY298 @ SY297 @ SV65 @ SV28 ) ) )
| ( ( ti @ ( fun @ SV28 @ SV65 ) @ SY297 )
= ( ti @ ( fun @ SV28 @ SV65 ) @ SY298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(310,plain,
! [SV66: $i,SV29: $i] :
( ( ( hAPP @ ( fun @ SV29 @ bool ) @ ( fun @ SV29 @ bool ) @ ( collect @ SV29 ) @ SV66 )
= ( ti @ ( fun @ SV29 @ bool ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(311,plain,
! [SV30: $i,SV67: $i] :
( ( ~ ( enum @ SV67 )
| ~ ( enum @ SV30 )
| ( enum @ ( sum_sum @ SV30 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(312,plain,
! [SV31: $i,SV68: $i] :
( ( ~ ( enum @ SV68 )
| ~ ( enum @ SV31 )
| ( enum @ ( fun @ SV31 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(313,plain,
! [SV32: $i,SV69: $i] :
( ( ~ ( cl_HOL_Oequal @ SV69 )
| ~ ( enum @ SV32 )
| ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(314,plain,
! [SV70: $i,SV33: $i] :
( ( cl_HOL_Oequal @ ( sum_sum @ SV33 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(315,plain,
! [SV71: $i,SV35: $i] :
( ( ( ti @ SV35 @ ( ti @ SV35 @ SV71 ) )
= ( ti @ SV35 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(316,plain,
! [SV72: $i,SV36: $i] :
( ( ! [SY299: $i] :
( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SV72 ) @ SY299 ) )
| ( ( ti @ SV36 @ SV72 )
= ( ti @ SV36 @ SY299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(317,plain,
! [SV73: $i,SV37: $i] :
( ( ! [SY300: $i] :
( ( ( ti @ SV37 @ SV73 )
!= ( ti @ SV37 @ SY300 ) )
| ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SV73 ) @ SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(318,plain,
! [SV74: $i,SV39: $i] :
( ( ! [SY301: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SY301 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SY301 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SY301 @ SV74 @ SV39 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SY301 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(319,plain,
! [SV75: $i,SV40: $i] :
( ( ! [SY302: $i,SY303: $i,SY304: $i,SY305: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SY303 ) @ SY304 ) @ SY305 ) )
| ~ ( ( ( ti @ SV75 @ SY302 )
!= ( hAPP @ SV40 @ SV75 @ SY304 @ ( sK5_Y_2 @ SY305 @ SY304 @ SY303 @ SY302 @ SV75 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY305 @ SY304 @ SY303 @ SY302 @ SV75 @ SV40 ) ) @ SY305 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(320,plain,
! [SV76: $i,SV41: $i] :
( ( ! [SY306: $i,SY307: $i,SY308: $i] :
~ ( ~ ( ! [SY309: $i,SY310: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY308 ) @ SY309 ) @ SY310 ) )
| ( ( hAPP @ SV76 @ SV41 @ SY308 @ SY306 )
!= ( hAPP @ SV76 @ SV41 @ SY308 @ SY307 ) )
| ( ( ti @ SV76 @ SY306 )
= ( ti @ SV76 @ SY307 ) ) )
| ~ ( ! [SY311: $i,SY312: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY308 ) @ SY311 ) @ SY312 ) )
| ( ( ti @ SV76 @ SY306 )
!= ( ti @ SV76 @ SY307 ) )
| ( ( hAPP @ SV76 @ SV41 @ SY308 @ SY306 )
= ( hAPP @ SV76 @ SV41 @ SY308 @ SY307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(321,plain,
! [SV77: $i,SV42: $i] :
( ( ! [SY313: $i,SY314: $i,SY315: $i,SY316: $i,SY317: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SY315 ) @ SY316 ) @ SY317 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY317 @ SY316 @ SY315 @ SY314 @ SY313 @ SV77 @ SV42 ) ) @ SY317 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SY314 @ ( hAPP @ SV42 @ SV77 @ SY316 @ ( sK4_Y_2 @ SY317 @ SY316 @ SY315 @ SY314 @ SY313 @ SV77 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ bool @ SY314 @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(322,plain,
! [SV43: $i] :
( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY236 ) @ SY237 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ SY237 @ SY236 ) ) )
| ~ ! [SY238: $i,SY239: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY239 @ SY238 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY238 ) @ SY239 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(323,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
( ( ti @ state @ SX0 )
= ( ti @ state @ SX1 ) )
| ( hBOOL @ hoare_1883395792gleton ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(324,plain,
( ( ~ ( ~ ( hBOOL @ hoare_1883395792gleton )
| ( ( ti @ state @ sK11_S )
!= ( ti @ state @ sK12_SY158 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(325,plain,
! [SV44: $i] :
( ( ~ ! [SY240: $i,SY241: $i] :
( ( ( ti @ SV44 @ SY240 )
!= ( ti @ SV44 @ SY241 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY240 ) @ SY241 ) ) )
| ~ ! [SY242: $i,SY243: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY242 ) @ SY243 ) )
| ( ( ti @ SV44 @ SY242 )
= ( ti @ SV44 @ SY243 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(326,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(327,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(328,plain,
! [SV45: $i] :
( ( ( ~ ( cl_HOL_Oequal @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY244: $i,SY245: $i] :
( ( ( ti @ SV45 @ SY244 )
!= ( ti @ SV45 @ SY245 ) )
| ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
| ( ( ti @ SV45 @ SY246 )
= ( ti @ SV45 @ SY247 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(329,plain,
! [SV46: $i,SV78: $i] :
( ( ~ ( ( SV78
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(330,plain,
! [SV47: $i] :
( ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY250 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY249 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY250 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY249 ) )
| ( SY250 = SY249 ) )
| ~ ! [SY251: $i,SY252: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY252 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY251 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( SY252 != SY251 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY252 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY251 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(331,plain,
! [SV48: $i] :
( ( ~ ! [SY253: $i,SY254: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY253 )
!= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY254 ) )
| ( SY253 = SY254 ) )
| ~ ! [SY255: $i,SY256: $i] :
( ( SY255 != SY256 )
| ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY255 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY256 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(332,plain,
! [SV79: $i,SV49: $i] :
( ( ! [SY318: $i,SY319: $i,SY320: $i] :
~ ( ~ ! [SY321: $i,SY322: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY320 ) @ SY321 ) @ SY322 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY319 ) @ SY322 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY318 ) @ SY322 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY321 @ SY319 )
!= ( hAPP @ SV49 @ SV79 @ SY321 @ SY318 ) )
| ( ( ti @ SV49 @ SY319 )
= ( ti @ SV49 @ SY318 ) ) )
| ~ ! [SY323: $i,SY324: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY320 ) @ SY323 ) @ SY324 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY319 ) @ SY324 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY318 ) @ SY324 ) )
| ( ( ti @ SV49 @ SY319 )
!= ( ti @ SV49 @ SY318 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY323 @ SY319 )
= ( hAPP @ SV49 @ SV79 @ SY323 @ SY318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(333,plain,
! [SV50: $i] :
( ( ~ ! [SY265: $i,SY266: $i] :
( ( SY265 != SY266 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY265 ) @ SY266 ) ) )
| ~ ! [SY267: $i,SY268: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY267 ) @ SY268 ) )
| ( SY267 = SY268 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(334,plain,
! [SV1: $i] :
( ( ( cl_HOL_Oequal @ SV1 )
= $false )
| ( ( ( ti @ ( fun @ SV1 @ ( fun @ SV1 @ bool ) ) @ ( equal_equal @ SV1 ) )
= ( equal_equal @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(335,plain,
! [SV80: $i,SV52: $i,SV10: $i] :
( ( ! [SY325: $i] :
( ( hAPP @ SV10 @ SV52 @ ( ti @ ( fun @ SV10 @ SV52 ) @ SV80 ) @ SY325 )
= ( hAPP @ SV10 @ SV52 @ SV80 @ SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(336,plain,
! [SV81: $i,SV53: $i,SV11: $i] :
( ( ! [SY326: $i] :
( ( hAPP @ SV11 @ SV53 @ SV81 @ ( ti @ SV11 @ SY326 ) )
= ( hAPP @ SV11 @ SV53 @ SV81 @ SY326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(337,plain,
! [SV82: $i,SV54: $i,SV12: $i] :
( ( ! [SY327: $i] :
( ( ti @ SV12 @ ( hAPP @ SV54 @ SV12 @ SV82 @ SY327 ) )
= ( hAPP @ SV54 @ SV12 @ SV82 @ SY327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(338,plain,
! [SV14: $i] :
( ( ( cl_HOL_Oequal @ SV14 )
= $false )
| ( ( ( equal_equal @ SV14 )
= ( fequal @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(339,plain,
! [SV15: $i] :
( ( ( cl_HOL_Oequal @ SV15 )
= $false )
| ( ( ! [SY169: $i] : ( hBOOL @ ( hAPP @ SV15 @ bool @ ( hAPP @ SV15 @ ( fun @ SV15 @ bool ) @ ( equal_equal @ SV15 ) @ SY169 ) @ SY169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(340,plain,
! [SV16: $i] :
( ( ( cl_HOL_Oequal @ SV16 )
= $false )
| ( ( ( fequal @ SV16 )
= ( equal_equal @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(341,plain,
! [SV57: $i,SV83: $i,SV19: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(342,plain,
! [SV58: $i,SV20: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ SV58 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV20 ) ) ) ) )
= $true )
| ( ( SV58
= ( hAPP @ ( hoare_509422987triple @ SV20 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( hoare_2037801986triple @ SV20 ) @ ( sK9_X_2 @ SV58 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(343,plain,
! [SV59: $i,SV21: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ SV59 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV21 ) ) ) ) )
= $true )
| ( ( ( hAPP @ ( hoare_509422987triple @ SV21 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_2037801986triple @ SV21 ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_509422987triple @ SV21 ) @ ( hoare_244953527triple @ SV21 ) @ SV59 ) )
= SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(344,plain,
! [SV84: $i,SV60: $i,SV23: $i] :
( ( ! [SY328: $i,SY329: $i,SY330: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SY328 ) @ SY329 ) @ SY330 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SY330 ) )
| ( ( hAPP @ SV60 @ SV23 @ SY328 @ ( hAPP @ SV23 @ SV60 @ SY329 @ SV84 ) )
= ( ti @ SV23 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(345,plain,
! [SV85: $i,SV61: $i,SV24: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ! [SY283: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SY331 ) @ SY332 ) @ SY283 ) )
| ( ( hAPP @ SV24 @ SV61 @ SY332 @ ( hAPP @ SV61 @ SV24 @ SY331 @ SV85 ) )
= ( ti @ SV61 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(346,plain,
! [SV86: $i,SV62: $i,SV25: $i] :
( ( ! [SY334: $i,SY335: $i,SY336: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SY334 ) @ SY335 ) @ SY336 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SY334 @ SV86 ) ) @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(347,plain,
! [SV87: $i,SV63: $i,SV26: $i] :
( ( ! [SY337: $i,SY338: $i,SY339: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SY337 ) @ SY338 ) @ SY339 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SY339 ) )
| ( ( ti @ SV26 @ SV87 )
= ( hAPP @ SV63 @ SV26 @ SY337 @ ( sK6_X_2 @ SY339 @ SY338 @ SY337 @ SV87 @ SV63 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(348,plain,
! [SV88: $i,SV64: $i,SV27: $i] :
( ( ! [SY340: $i,SY341: $i,SY342: $i,SY343: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SY341 ) @ SY342 ) @ SY343 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SY340 ) @ SY343 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SY341 @ ( sK3_X_2 @ SY343 @ SY342 @ SY341 @ SY340 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SY340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(349,plain,
! [SV89: $i,SV65: $i,SV28: $i] :
( ( ! [SY344: $i] :
( ( ( hAPP @ SV28 @ SV65 @ SV89 @ ( sK2_X_2 @ SY344 @ SV89 @ SV65 @ SV28 ) )
!= ( hAPP @ SV28 @ SV65 @ SY344 @ ( sK2_X_2 @ SY344 @ SV89 @ SV65 @ SV28 ) ) )
| ( ( ti @ ( fun @ SV28 @ SV65 ) @ SV89 )
= ( ti @ ( fun @ SV28 @ SV65 ) @ SY344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(350,plain,
! [SV30: $i,SV67: $i] :
( ( ( ~ ( enum @ SV67 )
| ~ ( enum @ SV30 ) )
= $true )
| ( ( enum @ ( sum_sum @ SV30 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(351,plain,
! [SV31: $i,SV68: $i] :
( ( ( ~ ( enum @ SV68 )
| ~ ( enum @ SV31 ) )
= $true )
| ( ( enum @ ( fun @ SV31 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(352,plain,
! [SV32: $i,SV69: $i] :
( ( ( ~ ( cl_HOL_Oequal @ SV69 )
| ~ ( enum @ SV32 ) )
= $true )
| ( ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(353,plain,
! [SV90: $i,SV72: $i,SV36: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SV72 ) @ SV90 ) )
| ( ( ti @ SV36 @ SV72 )
= ( ti @ SV36 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(354,plain,
! [SV91: $i,SV73: $i,SV37: $i] :
( ( ( ( ti @ SV37 @ SV73 )
!= ( ti @ SV37 @ SV91 ) )
| ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SV73 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(355,plain,
! [SV74: $i,SV92: $i,SV39: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(356,plain,
! [SV93: $i,SV75: $i,SV40: $i] :
( ( ! [SY345: $i,SY346: $i,SY347: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SY345 ) @ SY346 ) @ SY347 ) )
| ~ ( ( ( ti @ SV75 @ SV93 )
!= ( hAPP @ SV40 @ SV75 @ SY346 @ ( sK5_Y_2 @ SY347 @ SY346 @ SY345 @ SV93 @ SV75 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY347 @ SY346 @ SY345 @ SV93 @ SV75 @ SV40 ) ) @ SY347 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(357,plain,
! [SV94: $i,SV76: $i,SV41: $i] :
( ( ! [SY348: $i,SY349: $i] :
~ ( ~ ( ! [SY309: $i,SY310: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY349 ) @ SY309 ) @ SY310 ) )
| ( ( hAPP @ SV76 @ SV41 @ SY349 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SY349 @ SY348 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SY348 ) ) )
| ~ ( ! [SY311: $i,SY312: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY349 ) @ SY311 ) @ SY312 ) )
| ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SY348 ) )
| ( ( hAPP @ SV76 @ SV41 @ SY349 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SY349 @ SY348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(358,plain,
! [SV95: $i,SV77: $i,SV42: $i] :
( ( ! [SY354: $i,SY355: $i,SY356: $i,SY357: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SY355 ) @ SY356 ) @ SY357 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY357 @ SY356 @ SY355 @ SY354 @ SV95 @ SV77 @ SV42 ) ) @ SY357 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SY354 @ ( hAPP @ SV42 @ SV77 @ SY356 @ ( sK4_Y_2 @ SY357 @ SY356 @ SY355 @ SY354 @ SV95 @ SV77 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ bool @ SY354 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(359,plain,
! [SV43: $i] :
( ( ~ ! [SY236: $i,SY237: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY236 ) @ SY237 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ SY237 @ SY236 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(360,plain,
! [SV43: $i] :
( ( ~ ! [SY238: $i,SY239: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY239 @ SY238 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY238 ) @ SY239 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(361,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ti @ state @ SX0 )
= ( ti @ state @ SX1 ) )
| ( hBOOL @ hoare_1883395792gleton ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(362,plain,
( ( ~ ( hBOOL @ hoare_1883395792gleton )
| ( ( ti @ state @ sK11_S )
!= ( ti @ state @ sK12_SY158 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(363,plain,
! [SV44: $i] :
( ( ~ ! [SY240: $i,SY241: $i] :
( ( ( ti @ SV44 @ SY240 )
!= ( ti @ SV44 @ SY241 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY240 ) @ SY241 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(364,plain,
! [SV44: $i] :
( ( ~ ! [SY242: $i,SY243: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY242 ) @ SY243 ) )
| ( ( ti @ SV44 @ SY242 )
= ( ti @ SV44 @ SY243 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(365,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(366,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(367,plain,
! [SV45: $i] :
( ( ( cl_HOL_Oequal @ SV45 )
= $false )
| ( ( ~ ( ~ ! [SY244: $i,SY245: $i] :
( ( ( ti @ SV45 @ SY244 )
!= ( ti @ SV45 @ SY245 ) )
| ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
| ( ( ti @ SV45 @ SY246 )
= ( ti @ SV45 @ SY247 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(368,plain,
! [SV46: $i,SV78: $i] :
( ( ( SV78
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(369,plain,
! [SV47: $i] :
( ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY250 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY249 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY250 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY249 ) )
| ( SY250 = SY249 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(370,plain,
! [SV47: $i] :
( ( ~ ! [SY251: $i,SY252: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY252 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY251 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( SY252 != SY251 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY252 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY251 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(371,plain,
! [SV48: $i] :
( ( ~ ! [SY253: $i,SY254: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY253 )
!= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY254 ) )
| ( SY253 = SY254 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(372,plain,
! [SV48: $i] :
( ( ~ ! [SY255: $i,SY256: $i] :
( ( SY255 != SY256 )
| ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY255 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY256 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(373,plain,
! [SV96: $i,SV79: $i,SV49: $i] :
( ( ! [SY358: $i,SY359: $i] :
~ ( ~ ! [SY360: $i,SY361: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY359 ) @ SY360 ) @ SY361 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY358 ) @ SY361 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY361 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY360 @ SY358 )
!= ( hAPP @ SV49 @ SV79 @ SY360 @ SV96 ) )
| ( ( ti @ SV49 @ SY358 )
= ( ti @ SV49 @ SV96 ) ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY359 ) @ SY362 ) @ SY363 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SY358 ) @ SY363 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY363 ) )
| ( ( ti @ SV49 @ SY358 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY362 @ SY358 )
= ( hAPP @ SV49 @ SV79 @ SY362 @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(374,plain,
! [SV50: $i] :
( ( ~ ! [SY265: $i,SY266: $i] :
( ( SY265 != SY266 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY265 ) @ SY266 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(375,plain,
! [SV50: $i] :
( ( ~ ! [SY267: $i,SY268: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY267 ) @ SY268 ) )
| ( SY267 = SY268 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(376,plain,
! [SV97: $i,SV80: $i,SV52: $i,SV10: $i] :
( ( ( hAPP @ SV10 @ SV52 @ ( ti @ ( fun @ SV10 @ SV52 ) @ SV80 ) @ SV97 )
= ( hAPP @ SV10 @ SV52 @ SV80 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(377,plain,
! [SV98: $i,SV81: $i,SV53: $i,SV11: $i] :
( ( ( hAPP @ SV11 @ SV53 @ SV81 @ ( ti @ SV11 @ SV98 ) )
= ( hAPP @ SV11 @ SV53 @ SV81 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(378,plain,
! [SV99: $i,SV82: $i,SV54: $i,SV12: $i] :
( ( ( ti @ SV12 @ ( hAPP @ SV54 @ SV12 @ SV82 @ SV99 ) )
= ( hAPP @ SV54 @ SV12 @ SV82 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(379,plain,
! [SV100: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ SV15 @ bool @ ( hAPP @ SV15 @ ( fun @ SV15 @ bool ) @ ( equal_equal @ SV15 ) @ SV100 ) @ SV100 ) )
= $true )
| ( ( cl_HOL_Oequal @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(380,plain,
! [SV57: $i,SV83: $i,SV19: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(381,plain,
! [SV58: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ SV58 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV20 ) ) ) )
= $false )
| ( ( SV58
= ( hAPP @ ( hoare_509422987triple @ SV20 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV20 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV20 ) ) @ bool ) @ ( hoare_2037801986triple @ SV20 ) @ ( sK9_X_2 @ SV58 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(382,plain,
! [SV59: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ SV59 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV21 ) ) ) )
= $false )
| ( ( ( hAPP @ ( hoare_509422987triple @ SV21 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_2037801986triple @ SV21 ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV21 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV21 ) ) @ bool ) @ ( hoare_509422987triple @ SV21 ) @ ( hoare_244953527triple @ SV21 ) @ SV59 ) )
= SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(383,plain,
! [SV84: $i,SV101: $i,SV60: $i,SV23: $i] :
( ( ! [SY364: $i,SY365: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SY364 ) @ SY365 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SY365 ) )
| ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SY364 @ SV84 ) )
= ( ti @ SV23 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(384,plain,
! [SV85: $i,SV102: $i,SV61: $i,SV24: $i] :
( ( ! [SY366: $i] :
( ! [SY367: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SY366 ) @ SY367 ) )
| ( ( hAPP @ SV24 @ SV61 @ SY366 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
= ( ti @ SV61 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(385,plain,
! [SV86: $i,SV103: $i,SV62: $i,SV25: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SY368 ) @ SY369 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SY369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(386,plain,
! [SV87: $i,SV104: $i,SV63: $i,SV26: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SY370 ) @ SY371 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SY371 ) )
| ( ( ti @ SV26 @ SV87 )
= ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SY371 @ SY370 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(387,plain,
! [SV88: $i,SV105: $i,SV64: $i,SV27: $i] :
( ( ! [SY372: $i,SY373: $i,SY374: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SY372 ) @ SY373 ) @ SY374 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SY374 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SY372 @ ( sK3_X_2 @ SY374 @ SY373 @ SY372 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(388,plain,
! [SV106: $i,SV89: $i,SV65: $i,SV28: $i] :
( ( ( ( hAPP @ SV28 @ SV65 @ SV89 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) )
!= ( hAPP @ SV28 @ SV65 @ SV106 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) ) )
| ( ( ti @ ( fun @ SV28 @ SV65 ) @ SV89 )
= ( ti @ ( fun @ SV28 @ SV65 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(389,plain,
! [SV30: $i,SV67: $i] :
( ( ( ~ ( enum @ SV67 ) )
= $true )
| ( ( ~ ( enum @ SV30 ) )
= $true )
| ( ( enum @ ( sum_sum @ SV30 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(390,plain,
! [SV31: $i,SV68: $i] :
( ( ( ~ ( enum @ SV68 ) )
= $true )
| ( ( ~ ( enum @ SV31 ) )
= $true )
| ( ( enum @ ( fun @ SV31 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(391,plain,
! [SV32: $i,SV69: $i] :
( ( ( ~ ( cl_HOL_Oequal @ SV69 ) )
= $true )
| ( ( ~ ( enum @ SV32 ) )
= $true )
| ( ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(392,plain,
! [SV90: $i,SV72: $i,SV36: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SV72 ) @ SV90 ) ) )
= $true )
| ( ( ( ti @ SV36 @ SV72 )
= ( ti @ SV36 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(393,plain,
! [SV91: $i,SV73: $i,SV37: $i] :
( ( ( ( ( ti @ SV37 @ SV73 )
!= ( ti @ SV37 @ SV91 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SV73 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(394,plain,
! [SV74: $i,SV92: $i,SV39: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(395,plain,
! [SV93: $i,SV107: $i,SV75: $i,SV40: $i] :
( ( ! [SY375: $i,SY376: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SY375 ) @ SY376 ) )
| ~ ( ( ( ti @ SV75 @ SV93 )
!= ( hAPP @ SV40 @ SV75 @ SY375 @ ( sK5_Y_2 @ SY376 @ SY375 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY376 @ SY375 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SY376 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(396,plain,
! [SV108: $i,SV94: $i,SV76: $i,SV41: $i] :
( ( ! [SY377: $i] :
~ ( ~ ( ! [SY309: $i,SY310: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY377 ) @ SY309 ) @ SY310 ) )
| ( ( hAPP @ SV76 @ SV41 @ SY377 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SY377 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) )
| ~ ( ! [SY311: $i,SY312: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SY377 ) @ SY311 ) @ SY312 ) )
| ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SY377 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SY377 @ SV108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(397,plain,
! [SV95: $i,SV109: $i,SV77: $i,SV42: $i] :
( ( ! [SY382: $i,SY383: $i,SY384: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SY382 ) @ SY383 ) @ SY384 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY384 @ SY383 @ SY382 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SY384 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SY383 @ ( sK4_Y_2 @ SY384 @ SY383 @ SY382 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(398,plain,
! [SV43: $i] :
( ( ! [SY236: $i,SY237: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY236 ) @ SY237 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ SY237 @ SY236 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(399,plain,
! [SV43: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY239 @ SY238 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SY238 ) @ SY239 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(400,plain,
( ( ( ! [SX0: $i,SX1: $i] :
( ( ti @ state @ SX0 )
= ( ti @ state @ SX1 ) ) )
= $true )
| ( ( hBOOL @ hoare_1883395792gleton )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(401,plain,
( ( ( ~ ( hBOOL @ hoare_1883395792gleton ) )
= $true )
| ( ( ( ( ti @ state @ sK11_S )
!= ( ti @ state @ sK12_SY158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(402,plain,
! [SV44: $i] :
( ( ! [SY240: $i,SY241: $i] :
( ( ( ti @ SV44 @ SY240 )
!= ( ti @ SV44 @ SY241 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY240 ) @ SY241 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(403,plain,
! [SV44: $i] :
( ( ! [SY242: $i,SY243: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SY242 ) @ SY243 ) )
| ( ( ti @ SV44 @ SY242 )
= ( ti @ SV44 @ SY243 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(404,plain,
! [SV110: $i] :
( ( ~ ( hBOOL @ ( ti @ bool @ SV110 ) )
| ( hBOOL @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(405,plain,
! [SV111: $i] :
( ( ~ ( hBOOL @ SV111 )
| ( hBOOL @ ( ti @ bool @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(406,plain,
! [SV45: $i] :
( ( ( ~ ! [SY244: $i,SY245: $i] :
( ( ( ti @ SV45 @ SY244 )
!= ( ti @ SV45 @ SY245 ) )
| ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
| ( ( ti @ SV45 @ SY246 )
= ( ti @ SV45 @ SY247 ) ) ) )
= $false )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(407,plain,
! [SV46: $i,SV78: $i] :
( ( ( SV78
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(408,plain,
! [SV78: $i,SV46: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(409,plain,
! [SV47: $i] :
( ( ! [SY249: $i,SY250: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY250 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY249 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY250 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY249 ) )
| ( SY250 = SY249 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(410,plain,
! [SV47: $i] :
( ( ! [SY251: $i,SY252: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY252 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY251 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( SY252 != SY251 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY252 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY251 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(411,plain,
! [SV48: $i] :
( ( ! [SY253: $i,SY254: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY253 )
!= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY254 ) )
| ( SY253 = SY254 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(412,plain,
! [SV48: $i] :
( ( ! [SY255: $i,SY256: $i] :
( ( SY255 != SY256 )
| ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY255 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY256 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(413,plain,
! [SV96: $i,SV112: $i,SV79: $i,SV49: $i] :
( ( ! [SY385: $i] :
~ ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY385 ) @ SY386 ) @ SY387 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY387 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY387 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY386 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SY386 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SY385 ) @ SY388 ) @ SY389 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY389 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY389 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY388 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SY388 @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(414,plain,
! [SV50: $i] :
( ( ! [SY265: $i,SY266: $i] :
( ( SY265 != SY266 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY265 ) @ SY266 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(415,plain,
! [SV50: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SY267 ) @ SY268 ) )
| ( SY267 = SY268 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(416,plain,
! [SV57: $i,SV83: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(417,plain,
! [SV84: $i,SV113: $i,SV101: $i,SV60: $i,SV23: $i] :
( ( ! [SY390: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SY390 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SY390 ) )
| ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
= ( ti @ SV23 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(418,plain,
! [SV85: $i,SV114: $i,SV102: $i,SV61: $i,SV24: $i] :
( ( ! [SY391: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SV114 ) @ SY391 ) )
| ( ( hAPP @ SV24 @ SV61 @ SV114 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
= ( ti @ SV61 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(419,plain,
! [SV86: $i,SV115: $i,SV103: $i,SV62: $i,SV25: $i] :
( ( ! [SY392: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SV115 ) @ SY392 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SY392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(420,plain,
! [SV87: $i,SV116: $i,SV104: $i,SV63: $i,SV26: $i] :
( ( ! [SY393: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SY393 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SY393 ) )
| ( ( ti @ SV26 @ SV87 )
= ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SY393 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(421,plain,
! [SV88: $i,SV105: $i,SV117: $i,SV64: $i,SV27: $i] :
( ( ! [SY394: $i,SY395: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SY394 ) @ SY395 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SY395 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SY395 @ SY394 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(422,plain,
! [SV106: $i,SV89: $i,SV65: $i,SV28: $i] :
( ( ( ( ( hAPP @ SV28 @ SV65 @ SV89 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) )
!= ( hAPP @ SV28 @ SV65 @ SV106 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ SV28 @ SV65 ) @ SV89 )
= ( ti @ ( fun @ SV28 @ SV65 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(423,plain,
! [SV30: $i,SV67: $i] :
( ( ( enum @ SV67 )
= $false )
| ( ( ~ ( enum @ SV30 ) )
= $true )
| ( ( enum @ ( sum_sum @ SV30 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(424,plain,
! [SV31: $i,SV68: $i] :
( ( ( enum @ SV68 )
= $false )
| ( ( ~ ( enum @ SV31 ) )
= $true )
| ( ( enum @ ( fun @ SV31 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(425,plain,
! [SV32: $i,SV69: $i] :
( ( ( cl_HOL_Oequal @ SV69 )
= $false )
| ( ( ~ ( enum @ SV32 ) )
= $true )
| ( ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(426,plain,
! [SV90: $i,SV72: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( fequal @ SV36 ) @ SV72 ) @ SV90 ) )
= $false )
| ( ( ( ti @ SV36 @ SV72 )
= ( ti @ SV36 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(427,plain,
! [SV91: $i,SV73: $i,SV37: $i] :
( ( ( ( ti @ SV37 @ SV73 )
= ( ti @ SV37 @ SV91 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( fequal @ SV37 ) @ SV73 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(428,plain,
! [SV74: $i,SV92: $i,SV39: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(429,plain,
! [SV93: $i,SV118: $i,SV107: $i,SV75: $i,SV40: $i] :
( ( ! [SY396: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SY396 ) )
| ~ ( ( ( ti @ SV75 @ SV93 )
!= ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SY396 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SY396 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SY396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(430,plain,
! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ~ ( ~ ( ! [SY397: $i,SY398: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) )
| ~ ( ! [SY399: $i,SY400: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) )
| ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(431,plain,
! [SV95: $i,SV109: $i,SV120: $i,SV77: $i,SV42: $i] :
( ( ! [SY401: $i,SY402: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SY401 ) @ SY402 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY402 @ SY401 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SY402 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SY401 @ ( sK4_Y_2 @ SY402 @ SY401 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(432,plain,
! [SV121: $i,SV43: $i] :
( ( ! [SY403: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV121 ) @ SY403 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ SY403 @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(433,plain,
! [SV122: $i,SV43: $i] :
( ( ! [SY404: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SY404 @ SV122 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV122 ) @ SY404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(434,plain,
! [SV123: $i] :
( ( ( ! [SY405: $i] :
( ( ti @ state @ SV123 )
= ( ti @ state @ SY405 ) ) )
= $true )
| ( ( hBOOL @ hoare_1883395792gleton )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(435,plain,
( ( ( hBOOL @ hoare_1883395792gleton )
= $false )
| ( ( ( ( ti @ state @ sK11_S )
!= ( ti @ state @ sK12_SY158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(436,plain,
! [SV124: $i,SV44: $i] :
( ( ! [SY406: $i] :
( ( ( ti @ SV44 @ SV124 )
!= ( ti @ SV44 @ SY406 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV124 ) @ SY406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(437,plain,
! [SV125: $i,SV44: $i] :
( ( ! [SY407: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV125 ) @ SY407 ) )
| ( ( ti @ SV44 @ SV125 )
= ( ti @ SV44 @ SY407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(438,plain,
! [SV110: $i] :
( ( ( ~ ( hBOOL @ ( ti @ bool @ SV110 ) ) )
= $true )
| ( ( hBOOL @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(439,plain,
! [SV111: $i] :
( ( ( ~ ( hBOOL @ SV111 ) )
= $true )
| ( ( hBOOL @ ( ti @ bool @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(440,plain,
! [SV45: $i] :
( ( ( ~ ! [SY244: $i,SY245: $i] :
( ( ( ti @ SV45 @ SY244 )
!= ( ti @ SV45 @ SY245 ) )
| ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) ) )
= $false )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(441,plain,
! [SV45: $i] :
( ( ( ~ ! [SY246: $i,SY247: $i] :
( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
| ( ( ti @ SV45 @ SY246 )
= ( ti @ SV45 @ SY247 ) ) ) )
= $false )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(442,plain,
! [SV46: $i,SV78: $i] :
( ( SV78
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( hoare_509422987triple @ SV46 ) @ ( hoare_244953527triple @ SV46 ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(443,plain,
! [SV78: $i,SV46: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( sK7_Y_2 @ SV78 @ SV46 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV46 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV46 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV46 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(444,plain,
! [SV126: $i,SV47: $i] :
( ( ! [SY408: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY408 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY408 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
| ( SY408 = SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(445,plain,
! [SV127: $i,SV47: $i] :
( ( ! [SY409: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SY409 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( SY409 != SV127 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SY409 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(446,plain,
! [SV128: $i,SV48: $i] :
( ( ! [SY410: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV128 )
!= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY410 ) )
| ( SV128 = SY410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(447,plain,
! [SV48: $i,SV129: $i] :
( ( ! [SY411: $i] :
( ( SV129 != SY411 )
| ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV129 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SY411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(448,plain,
! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ~ ( ~ ! [SY412: $i,SY413: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY412 ) @ SY413 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY413 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY413 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY412 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SY412 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
| ~ ! [SY414: $i,SY415: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY414 ) @ SY415 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY415 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY415 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY414 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SY414 @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(449,plain,
! [SV50: $i,SV131: $i] :
( ( ! [SY416: $i] :
( ( SV131 != SY416 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV131 ) @ SY416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(450,plain,
! [SV132: $i,SV50: $i] :
( ( ! [SY417: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV132 ) @ SY417 ) )
| ( SV132 = SY417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(451,plain,
! [SV83: $i,SV57: $i,SV19: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(452,plain,
! [SV84: $i,SV133: $i,SV113: $i,SV101: $i,SV60: $i,SV23: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) )
| ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
= ( ti @ SV23 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(453,plain,
! [SV85: $i,SV114: $i,SV102: $i,SV61: $i,SV24: $i] :
( ( ( ! [SY391: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SV114 ) @ SY391 ) ) )
= $true )
| ( ( ( hAPP @ SV24 @ SV61 @ SV114 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
= ( ti @ SV61 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(454,plain,
! [SV86: $i,SV134: $i,SV115: $i,SV103: $i,SV62: $i,SV25: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SV115 ) @ SV134 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(455,plain,
! [SV87: $i,SV135: $i,SV116: $i,SV104: $i,SV63: $i,SV26: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) )
| ( ( ti @ SV26 @ SV87 )
= ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(456,plain,
! [SV88: $i,SV105: $i,SV136: $i,SV117: $i,SV64: $i,SV27: $i] :
( ( ! [SY418: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SY418 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SY418 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SY418 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(457,plain,
! [SV106: $i,SV89: $i,SV65: $i,SV28: $i] :
( ( ( ( hAPP @ SV28 @ SV65 @ SV89 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) )
= ( hAPP @ SV28 @ SV65 @ SV106 @ ( sK2_X_2 @ SV106 @ SV89 @ SV65 @ SV28 ) ) )
= $false )
| ( ( ( ti @ ( fun @ SV28 @ SV65 ) @ SV89 )
= ( ti @ ( fun @ SV28 @ SV65 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(458,plain,
! [SV67: $i,SV30: $i] :
( ( ( enum @ SV30 )
= $false )
| ( ( enum @ SV67 )
= $false )
| ( ( enum @ ( sum_sum @ SV30 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(459,plain,
! [SV68: $i,SV31: $i] :
( ( ( enum @ SV31 )
= $false )
| ( ( enum @ SV68 )
= $false )
| ( ( enum @ ( fun @ SV31 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(460,plain,
! [SV69: $i,SV32: $i] :
( ( ( enum @ SV32 )
= $false )
| ( ( cl_HOL_Oequal @ SV69 )
= $false )
| ( ( cl_HOL_Oequal @ ( fun @ SV32 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(461,plain,
! [SV74: $i,SV92: $i,SV39: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(462,plain,
! [SV74: $i,SV92: $i,SV39: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(463,plain,
! [SV93: $i,SV137: $i,SV118: $i,SV107: $i,SV75: $i,SV40: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
| ~ ( ( ( ti @ SV75 @ SV93 )
!= ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(464,plain,
! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ~ ( ! [SY397: $i,SY398: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) )
| ~ ( ! [SY399: $i,SY400: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) )
| ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(465,plain,
! [SV95: $i,SV109: $i,SV138: $i,SV120: $i,SV77: $i,SV42: $i] :
( ( ! [SY419: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SY419 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SY419 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SY419 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SY419 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(466,plain,
! [SV139: $i,SV121: $i,SV43: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV121 ) @ SV139 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ SV139 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(467,plain,
! [SV122: $i,SV140: $i,SV43: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SV140 @ SV122 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV122 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(468,plain,
! [SV141: $i,SV123: $i] :
( ( ( ( ti @ state @ SV123 )
= ( ti @ state @ SV141 ) )
= $true )
| ( ( hBOOL @ hoare_1883395792gleton )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(469,plain,
( ( ( ( ti @ state @ sK11_S )
= ( ti @ state @ sK12_SY158 ) )
= $false )
| ( ( hBOOL @ hoare_1883395792gleton )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(470,plain,
! [SV142: $i,SV124: $i,SV44: $i] :
( ( ( ( ti @ SV44 @ SV124 )
!= ( ti @ SV44 @ SV142 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV124 ) @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(471,plain,
! [SV143: $i,SV125: $i,SV44: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV125 ) @ SV143 ) )
| ( ( ti @ SV44 @ SV125 )
= ( ti @ SV44 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(472,plain,
! [SV110: $i] :
( ( ( hBOOL @ ( ti @ bool @ SV110 ) )
= $false )
| ( ( hBOOL @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(473,plain,
! [SV111: $i] :
( ( ( hBOOL @ SV111 )
= $false )
| ( ( hBOOL @ ( ti @ bool @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(474,plain,
! [SV45: $i] :
( ( ( ! [SY244: $i,SY245: $i] :
( ( ( ti @ SV45 @ SY244 )
!= ( ti @ SV45 @ SY245 ) )
| ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY244 ) @ SY245 ) ) ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(475,plain,
! [SV45: $i] :
( ( ( ! [SY246: $i,SY247: $i] :
( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SY246 ) @ SY247 ) )
| ( ( ti @ SV45 @ SY246 )
= ( ti @ SV45 @ SY247 ) ) ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(476,plain,
! [SV126: $i,SV144: $i,SV47: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
| ( SV144 = SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(477,plain,
! [SV127: $i,SV145: $i,SV47: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( SV145 != SV127 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(478,plain,
! [SV146: $i,SV128: $i,SV48: $i] :
( ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV128 )
!= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV146 ) )
| ( SV128 = SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(479,plain,
! [SV48: $i,SV147: $i,SV129: $i] :
( ( ( SV129 != SV147 )
| ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV129 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(480,plain,
! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ~ ! [SY412: $i,SY413: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY412 ) @ SY413 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY413 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY413 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY412 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SY412 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
| ~ ! [SY414: $i,SY415: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY414 ) @ SY415 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY415 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY415 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY414 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SY414 @ SV96 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(481,plain,
! [SV50: $i,SV148: $i,SV131: $i] :
( ( ( SV131 != SV148 )
| ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV131 ) @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(482,plain,
! [SV149: $i,SV132: $i,SV50: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV132 ) @ SV149 ) )
| ( SV132 = SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(483,plain,
! [SV83: $i,SV57: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ ( hAPP @ ( hoare_509422987triple @ SV19 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( hoare_2037801986triple @ SV19 ) @ ( sK10_X_2 @ SV83 @ SV57 @ SV19 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool @ SV57 @ SV83 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ SV83 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV19 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV19 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV19 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(484,plain,
! [SV84: $i,SV133: $i,SV113: $i,SV101: $i,SV60: $i,SV23: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) )
| ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
= ( ti @ SV23 @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(485,plain,
! [SV85: $i,SV150: $i,SV114: $i,SV102: $i,SV61: $i,SV24: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SV114 ) @ SV150 ) ) )
= $true )
| ( ( ( hAPP @ SV24 @ SV61 @ SV114 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
= ( ti @ SV61 @ SV85 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(486,plain,
! [SV86: $i,SV134: $i,SV115: $i,SV103: $i,SV62: $i,SV25: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SV115 ) @ SV134 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(487,plain,
! [SV87: $i,SV135: $i,SV116: $i,SV104: $i,SV63: $i,SV26: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) )
| ( ( ti @ SV26 @ SV87 )
= ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(488,plain,
! [SV88: $i,SV105: $i,SV151: $i,SV136: $i,SV117: $i,SV64: $i,SV27: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(489,plain,
! [SV74: $i,SV92: $i,SV39: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV39 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(490,plain,
! [SV74: $i,SV92: $i,SV39: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(491,plain,
! [SV93: $i,SV137: $i,SV118: $i,SV107: $i,SV75: $i,SV40: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) ) )
= $true )
| ( ( ~ ( ( ( ti @ SV75 @ SV93 )
!= ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(492,plain,
! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ~ ( ! [SY397: $i,SY398: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(493,plain,
! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ~ ( ! [SY399: $i,SY400: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) )
| ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(494,plain,
! [SV95: $i,SV109: $i,SV152: $i,SV138: $i,SV120: $i,SV77: $i,SV42: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(495,plain,
! [SV139: $i,SV121: $i,SV43: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV121 ) @ SV139 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV43 @ bool @ SV139 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(496,plain,
! [SV122: $i,SV140: $i,SV43: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV43 @ bool @ SV140 @ SV122 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV122 ) @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(497,plain,
! [SV142: $i,SV124: $i,SV44: $i] :
( ( ( ( ( ti @ SV44 @ SV124 )
!= ( ti @ SV44 @ SV142 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV124 ) @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(498,plain,
! [SV143: $i,SV125: $i,SV44: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV125 ) @ SV143 ) ) )
= $true )
| ( ( ( ti @ SV44 @ SV125 )
= ( ti @ SV44 @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(499,plain,
! [SV153: $i,SV45: $i] :
( ( ( ! [SY420: $i] :
( ( ( ti @ SV45 @ SV153 )
!= ( ti @ SV45 @ SY420 ) )
| ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV153 ) @ SY420 ) ) ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(500,plain,
! [SV154: $i,SV45: $i] :
( ( ( ! [SY421: $i] :
( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV154 ) @ SY421 ) )
| ( ( ti @ SV45 @ SV154 )
= ( ti @ SV45 @ SY421 ) ) ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(501,plain,
! [SV126: $i,SV144: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
| ( SV144 = SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(502,plain,
! [SV127: $i,SV145: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( SV145 != SV127 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(503,plain,
! [SV146: $i,SV128: $i,SV48: $i] :
( ( ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV128 )
!= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV146 ) ) )
= $true )
| ( ( SV128 = SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(504,plain,
! [SV48: $i,SV147: $i,SV129: $i] :
( ( ( ( SV129 != SV147 ) )
= $true )
| ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV129 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(505,plain,
! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ~ ! [SY412: $i,SY413: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY412 ) @ SY413 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY413 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY413 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY412 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SY412 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(506,plain,
! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ~ ! [SY414: $i,SY415: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY414 ) @ SY415 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY415 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY415 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY414 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SY414 @ SV96 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(507,plain,
! [SV50: $i,SV148: $i,SV131: $i] :
( ( ( ( SV131 != SV148 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV131 ) @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(508,plain,
! [SV149: $i,SV132: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV132 ) @ SV149 ) ) )
= $true )
| ( ( SV132 = SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(509,plain,
! [SV84: $i,SV133: $i,SV113: $i,SV101: $i,SV60: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) )
| ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
= ( ti @ SV23 @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(510,plain,
! [SV85: $i,SV150: $i,SV114: $i,SV102: $i,SV61: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV24 @ bool ) @ bool @ ( hAPP @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV61 @ SV24 ) @ ( fun @ ( fun @ SV24 @ SV61 ) @ ( fun @ ( fun @ SV24 @ bool ) @ bool ) ) @ ( type_definition @ SV61 @ SV24 ) @ SV102 ) @ SV114 ) @ SV150 ) )
= $false )
| ( ( ( hAPP @ SV24 @ SV61 @ SV114 @ ( hAPP @ SV61 @ SV24 @ SV102 @ SV85 ) )
= ( ti @ SV61 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(511,plain,
! [SV86: $i,SV134: $i,SV115: $i,SV103: $i,SV62: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV62 @ SV25 ) @ ( fun @ ( fun @ SV25 @ SV62 ) @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) ) @ ( type_definition @ SV62 @ SV25 ) @ SV103 ) @ SV115 ) @ SV134 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV25 @ bool ) @ bool @ ( hAPP @ SV25 @ ( fun @ ( fun @ SV25 @ bool ) @ bool ) @ ( member @ SV25 ) @ ( hAPP @ SV62 @ SV25 @ SV103 @ SV86 ) ) @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(512,plain,
! [SV87: $i,SV135: $i,SV116: $i,SV104: $i,SV63: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) )
| ( ( ti @ SV26 @ SV87 )
= ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(513,plain,
! [SV88: $i,SV105: $i,SV151: $i,SV136: $i,SV117: $i,SV64: $i,SV27: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(514,plain,
! [SV74: $i,SV92: $i,SV39: $i] :
( ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV39 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV39 ) ) @ bool ) @ ( hoare_509422987triple @ SV39 ) @ ( hoare_244953527triple @ SV39 ) @ ( sK8_Y_2 @ SV92 @ SV74 @ SV39 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV39 ) @ bool @ SV92 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(515,plain,
! [SV93: $i,SV137: $i,SV118: $i,SV107: $i,SV75: $i,SV40: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
= $false )
| ( ( ~ ( ( ( ti @ SV75 @ SV93 )
!= ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(516,plain,
! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ! [SY397: $i,SY398: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(517,plain,
! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ! [SY399: $i,SY400: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) )
| ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(518,plain,
! [SV95: $i,SV109: $i,SV152: $i,SV138: $i,SV120: $i,SV77: $i,SV42: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(519,plain,
! [SV139: $i,SV121: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV121 ) @ SV139 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV43 @ bool @ SV139 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(520,plain,
! [SV122: $i,SV140: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ SV43 @ bool @ SV140 @ SV122 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV43 @ bool ) @ bool @ ( hAPP @ SV43 @ ( fun @ ( fun @ SV43 @ bool ) @ bool ) @ ( member @ SV43 ) @ SV122 ) @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(521,plain,
! [SV142: $i,SV124: $i,SV44: $i] :
( ( ( ( ti @ SV44 @ SV124 )
= ( ti @ SV44 @ SV142 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV124 ) @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(522,plain,
! [SV143: $i,SV125: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( induct_equal @ SV44 ) @ SV125 ) @ SV143 ) )
= $false )
| ( ( ( ti @ SV44 @ SV125 )
= ( ti @ SV44 @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(523,plain,
! [SV155: $i,SV153: $i,SV45: $i] :
( ( ( ( ( ti @ SV45 @ SV153 )
!= ( ti @ SV45 @ SV155 ) )
| ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV153 ) @ SV155 ) ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(524,plain,
! [SV156: $i,SV154: $i,SV45: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV154 ) @ SV156 ) )
| ( ( ti @ SV45 @ SV154 )
= ( ti @ SV45 @ SV156 ) ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(525,plain,
! [SV126: $i,SV144: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
| ( SV144 = SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(526,plain,
! [SV127: $i,SV145: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
| ( SV145 != SV127 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(527,plain,
! [SV146: $i,SV128: $i,SV48: $i] :
( ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV128 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV146 ) )
= $false )
| ( ( SV128 = SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(528,plain,
! [SV48: $i,SV147: $i,SV129: $i] :
( ( ( SV129 = SV147 )
= $false )
| ( ( ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV129 )
= ( hAPP @ ( hoare_509422987triple @ SV48 ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV48 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV48 ) ) @ bool ) @ ( hoare_2037801986triple @ SV48 ) @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(529,plain,
! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ! [SY412: $i,SY413: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY412 ) @ SY413 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY413 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY413 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY412 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SY412 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(530,plain,
! [SV96: $i,SV112: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ! [SY414: $i,SY415: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SY414 ) @ SY415 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY415 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY415 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SY414 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SY414 @ SV96 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(531,plain,
! [SV50: $i,SV148: $i,SV131: $i] :
( ( ( SV131 = SV148 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV131 ) @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(532,plain,
! [SV149: $i,SV132: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ bool @ ( hAPP @ ( hoare_509422987triple @ SV50 ) @ ( fun @ ( hoare_509422987triple @ SV50 ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ SV50 ) ) @ SV132 ) @ SV149 ) )
= $false )
| ( ( SV132 = SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(533,plain,
! [SV113: $i,SV101: $i,SV60: $i,SV133: $i,SV84: $i,SV23: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) ) )
= $true )
| ( ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
= ( ti @ SV23 @ SV84 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(534,plain,
! [SV116: $i,SV104: $i,SV63: $i,SV135: $i,SV87: $i,SV26: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) ) )
= $true )
| ( ( ( ti @ SV26 @ SV87 )
= ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(535,plain,
! [SV88: $i,SV105: $i,SV151: $i,SV136: $i,SV117: $i,SV64: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
| ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(536,plain,
! [SV107: $i,SV137: $i,SV118: $i,SV40: $i,SV93: $i,SV75: $i] :
( ( ( ( ( ti @ SV75 @ SV93 )
!= ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(537,plain,
! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ( ! [SY397: $i,SY398: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY397 ) @ SY398 ) ) )
= $true )
| ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(538,plain,
! [SV108: $i,SV94: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ( ! [SY399: $i,SY400: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SY399 ) @ SY400 ) ) )
= $true )
| ( ( ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(539,plain,
! [SV95: $i,SV109: $i,SV152: $i,SV138: $i,SV120: $i,SV77: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
| ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(540,plain,
! [SV155: $i,SV153: $i,SV45: $i] :
( ( ( ( ( ti @ SV45 @ SV153 )
!= ( ti @ SV45 @ SV155 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV153 ) @ SV155 ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(541,plain,
! [SV156: $i,SV154: $i,SV45: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV154 ) @ SV156 ) ) )
= $true )
| ( ( ( ti @ SV45 @ SV154 )
= ( ti @ SV45 @ SV156 ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(542,plain,
! [SV144: $i,SV126: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) ) )
= $true )
| ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
| ( SV144 = SV126 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(543,plain,
! [SV145: $i,SV127: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) ) )
= $true )
| ( ( ( SV145 != SV127 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(544,plain,
! [SV96: $i,SV112: $i,SV157: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ! [SY422: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SY422 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY422 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY422 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(545,plain,
! [SV96: $i,SV112: $i,SV158: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ! [SY423: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SY423 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SY423 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SY423 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(546,plain,
! [SV113: $i,SV101: $i,SV60: $i,SV133: $i,SV84: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV84 ) @ SV133 ) )
= $false )
| ( ( ( hAPP @ SV60 @ SV23 @ SV101 @ ( hAPP @ SV23 @ SV60 @ SV113 @ SV84 ) )
= ( ti @ SV23 @ SV84 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV60 @ SV23 ) @ ( fun @ ( fun @ SV23 @ SV60 ) @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) ) @ ( type_definition @ SV60 @ SV23 ) @ SV101 ) @ SV113 ) @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(547,plain,
! [SV116: $i,SV104: $i,SV63: $i,SV135: $i,SV87: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ SV26 @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( member @ SV26 ) @ SV87 ) @ SV135 ) )
= $false )
| ( ( ( ti @ SV26 @ SV87 )
= ( hAPP @ SV63 @ SV26 @ SV104 @ ( sK6_X_2 @ SV135 @ SV116 @ SV104 @ SV87 @ SV63 @ SV26 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV26 @ bool ) @ bool @ ( hAPP @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV63 @ SV26 ) @ ( fun @ ( fun @ SV26 @ SV63 ) @ ( fun @ ( fun @ SV26 @ bool ) @ bool ) ) @ ( type_definition @ SV63 @ SV26 ) @ SV104 ) @ SV116 ) @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(548,plain,
! [SV136: $i,SV117: $i,SV64: $i,SV88: $i,SV151: $i,SV105: $i,SV27: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(549,plain,
! [SV107: $i,SV137: $i,SV118: $i,SV40: $i,SV93: $i,SV75: $i] :
( ( ( ( ( ti @ SV75 @ SV93 )
!= ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(550,plain,
! [SV75: $i,SV93: $i,SV107: $i,SV118: $i,SV137: $i,SV40: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(551,plain,
! [SV108: $i,SV94: $i,SV159: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ( ! [SY424: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SY424 ) ) )
= $true )
| ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(552,plain,
! [SV108: $i,SV94: $i,SV160: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ( ! [SY425: $i] :
~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SY425 ) ) )
= $true )
| ( ( ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(553,plain,
! [SV77: $i,SV95: $i,SV109: $i,SV120: $i,SV138: $i,SV152: $i,SV42: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(554,plain,
! [SV155: $i,SV153: $i,SV45: $i] :
( ( ( ( ti @ SV45 @ SV153 )
= ( ti @ SV45 @ SV155 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV153 ) @ SV155 ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(555,plain,
! [SV156: $i,SV154: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( equal_equal @ SV45 ) @ SV154 ) @ SV156 ) )
= $false )
| ( ( ( ti @ SV45 @ SV154 )
= ( ti @ SV45 @ SV156 ) )
= $true )
| ( ( cl_HOL_Oequal @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(556,plain,
! [SV144: $i,SV126: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false )
| ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
| ( SV144 = SV126 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(557,plain,
! [SV145: $i,SV127: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false )
| ( ( ( SV145 != SV127 )
| ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(558,plain,
! [SV96: $i,SV112: $i,SV161: $i,SV157: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(559,plain,
! [SV96: $i,SV112: $i,SV162: $i,SV158: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(560,plain,
! [SV136: $i,SV117: $i,SV64: $i,SV88: $i,SV151: $i,SV105: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(561,plain,
! [SV107: $i,SV137: $i,SV118: $i,SV40: $i,SV93: $i,SV75: $i] :
( ( ( ( ti @ SV75 @ SV93 )
= ( hAPP @ SV40 @ SV75 @ SV118 @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(562,plain,
! [SV75: $i,SV93: $i,SV107: $i,SV118: $i,SV137: $i,SV40: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ SV40 @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( member @ SV40 ) @ ( sK5_Y_2 @ SV137 @ SV118 @ SV107 @ SV93 @ SV75 @ SV40 ) ) @ SV137 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV40 @ bool ) @ bool @ ( hAPP @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV75 @ SV40 ) @ ( fun @ ( fun @ SV40 @ SV75 ) @ ( fun @ ( fun @ SV40 @ bool ) @ bool ) ) @ ( type_definition @ SV75 @ SV40 ) @ SV107 ) @ SV118 ) @ SV137 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(563,plain,
! [SV108: $i,SV94: $i,SV163: $i,SV159: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SV163 ) ) )
= $true )
| ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(564,plain,
! [SV108: $i,SV94: $i,SV164: $i,SV160: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SV164 ) ) )
= $true )
| ( ( ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(565,plain,
! [SV77: $i,SV95: $i,SV109: $i,SV120: $i,SV138: $i,SV152: $i,SV42: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
| ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(566,plain,
! [SV126: $i,SV144: $i,SV47: $i] :
( ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
!= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) ) )
= $true )
| ( ( SV144 = SV126 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(567,plain,
! [SV47: $i,SV127: $i,SV145: $i] :
( ( ( ( SV145 != SV127 ) )
= $true )
| ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(568,plain,
! [SV96: $i,SV112: $i,SV161: $i,SV157: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(569,plain,
! [SV96: $i,SV112: $i,SV162: $i,SV158: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(570,plain,
! [SV105: $i,SV136: $i,SV151: $i,SV117: $i,SV64: $i,SV88: $i,SV27: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(571,plain,
! [SV108: $i,SV94: $i,SV163: $i,SV159: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SV163 ) )
= $false )
| ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
| ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(572,plain,
! [SV108: $i,SV94: $i,SV164: $i,SV160: $i,SV119: $i,SV76: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SV164 ) )
= $false )
| ( ( ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) )
| ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(573,plain,
! [SV77: $i,SV95: $i,SV109: $i,SV120: $i,SV138: $i,SV152: $i,SV42: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[565]) ).
thf(574,plain,
! [SV95: $i,SV120: $i,SV152: $i,SV138: $i,SV42: $i,SV109: $i,SV77: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[565]) ).
thf(575,plain,
! [SV126: $i,SV144: $i,SV47: $i] :
( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV144 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV126 ) )
= $false )
| ( ( SV144 = SV126 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV126 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV144 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(576,plain,
! [SV47: $i,SV127: $i,SV145: $i] :
( ( ( SV145 = SV127 )
= $false )
| ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV145 )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( hoare_509422987triple @ SV47 ) @ ( hoare_244953527triple @ SV47 ) @ SV127 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV127 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ SV145 ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ SV47 @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ SV47 ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ SV47 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(577,plain,
! [SV96: $i,SV112: $i,SV161: $i,SV157: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(578,plain,
! [SV96: $i,SV112: $i,SV162: $i,SV158: $i,SV130: $i,SV79: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(579,plain,
! [SV105: $i,SV136: $i,SV151: $i,SV117: $i,SV64: $i,SV88: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ ( hAPP @ SV64 @ SV27 @ SV117 @ ( sK3_X_2 @ SV151 @ SV136 @ SV117 @ SV105 @ SV88 @ SV64 @ SV27 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV27 @ bool @ SV88 @ SV105 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ SV27 @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( member @ SV27 ) @ SV105 ) @ SV151 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV27 @ bool ) @ bool @ ( hAPP @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ SV27 ) @ ( fun @ ( fun @ SV27 @ SV64 ) @ ( fun @ ( fun @ SV27 @ bool ) @ bool ) ) @ ( type_definition @ SV64 @ SV27 ) @ SV117 ) @ SV136 ) @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(580,plain,
! [SV163: $i,SV159: $i,SV108: $i,SV94: $i,SV119: $i,SV41: $i,SV76: $i] :
( ( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
!= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) ) )
= $true )
| ( ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(581,plain,
! [SV164: $i,SV160: $i,SV119: $i,SV41: $i,SV108: $i,SV94: $i,SV76: $i] :
( ( ( ( ( ti @ SV76 @ SV94 )
!= ( ti @ SV76 @ SV108 ) ) )
= $true )
| ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SV164 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(582,plain,
! [SV77: $i,SV95: $i,SV109: $i,SV120: $i,SV138: $i,SV152: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ SV42 @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( member @ SV42 ) @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) @ SV152 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(583,plain,
! [SV95: $i,SV120: $i,SV152: $i,SV138: $i,SV42: $i,SV109: $i,SV77: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(584,plain,
! [SV130: $i,SV157: $i,SV79: $i,SV96: $i,SV161: $i,SV112: $i,SV49: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(585,plain,
! [SV130: $i,SV158: $i,SV79: $i,SV96: $i,SV162: $i,SV112: $i,SV49: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(586,plain,
! [SV163: $i,SV159: $i,SV108: $i,SV94: $i,SV119: $i,SV41: $i,SV76: $i] :
( ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
= $false )
| ( ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV159 ) @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(587,plain,
! [SV164: $i,SV160: $i,SV119: $i,SV41: $i,SV108: $i,SV94: $i,SV76: $i] :
( ( ( ( ti @ SV76 @ SV94 )
= ( ti @ SV76 @ SV108 ) )
= $false )
| ( ( ( hAPP @ SV76 @ SV41 @ SV119 @ SV94 )
= ( hAPP @ SV76 @ SV41 @ SV119 @ SV108 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV41 @ bool ) @ bool @ ( hAPP @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV76 @ SV41 ) @ ( fun @ ( fun @ SV41 @ SV76 ) @ ( fun @ ( fun @ SV41 @ bool ) @ bool ) ) @ ( type_definition @ SV76 @ SV41 ) @ SV119 ) @ SV160 ) @ SV164 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(588,plain,
! [SV95: $i,SV120: $i,SV152: $i,SV138: $i,SV42: $i,SV109: $i,SV77: $i] :
( ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ ( hAPP @ SV42 @ SV77 @ SV138 @ ( sK4_Y_2 @ SV152 @ SV138 @ SV120 @ SV109 @ SV95 @ SV77 @ SV42 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV77 @ bool @ SV109 @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV42 @ bool ) @ bool @ ( hAPP @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV77 @ SV42 ) @ ( fun @ ( fun @ SV42 @ SV77 ) @ ( fun @ ( fun @ SV42 @ bool ) @ bool ) ) @ ( type_definition @ SV77 @ SV42 ) @ SV120 ) @ SV138 ) @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(589,plain,
! [SV130: $i,SV157: $i,SV79: $i,SV96: $i,SV161: $i,SV112: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(590,plain,
! [SV130: $i,SV158: $i,SV79: $i,SV96: $i,SV162: $i,SV112: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
| ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(591,plain,
! [SV130: $i,SV112: $i,SV157: $i,SV79: $i,SV161: $i,SV96: $i,SV49: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) ) )
= $true )
| ( ( ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(592,plain,
! [SV130: $i,SV158: $i,SV79: $i,SV112: $i,SV162: $i,SV96: $i,SV49: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) ) )
= $true )
| ( ( ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(593,plain,
! [SV130: $i,SV112: $i,SV157: $i,SV79: $i,SV161: $i,SV96: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
= $false )
| ( ( ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
| ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(594,plain,
! [SV130: $i,SV158: $i,SV79: $i,SV112: $i,SV162: $i,SV96: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
= $false )
| ( ( ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) )
| ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(595,plain,
! [SV130: $i,SV161: $i,SV96: $i,SV112: $i,SV157: $i,SV79: $i,SV49: $i] :
( ( ( ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
!= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) ) )
= $true )
| ( ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(596,plain,
! [SV130: $i,SV162: $i,SV158: $i,SV79: $i,SV96: $i,SV112: $i,SV49: $i] :
( ( ( ( ( ti @ SV49 @ SV112 )
!= ( ti @ SV49 @ SV96 ) ) )
= $true )
| ( ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(597,plain,
! [SV130: $i,SV161: $i,SV96: $i,SV112: $i,SV157: $i,SV79: $i,SV49: $i] :
( ( ( ( hAPP @ SV49 @ SV79 @ SV157 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV157 @ SV96 ) )
= $false )
| ( ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV157 ) @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(598,plain,
! [SV130: $i,SV162: $i,SV158: $i,SV79: $i,SV96: $i,SV112: $i,SV49: $i] :
( ( ( ( ti @ SV49 @ SV112 )
= ( ti @ SV49 @ SV96 ) )
= $false )
| ( ( ( hAPP @ SV49 @ SV79 @ SV158 @ SV112 )
= ( hAPP @ SV49 @ SV79 @ SV158 @ SV96 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV96 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ SV49 @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( member @ SV49 ) @ SV112 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV49 @ bool ) @ bool @ ( hAPP @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) @ ( hAPP @ ( fun @ SV79 @ SV49 ) @ ( fun @ ( fun @ SV49 @ SV79 ) @ ( fun @ ( fun @ SV49 @ bool ) @ bool ) ) @ ( type_definition @ SV79 @ SV49 ) @ SV130 ) @ SV158 ) @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(599,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[161,598,597,588,587,586,582,579,576,575,562,561,555,554,547,546,532,531,528,527,522,521,520,519,514,511,510,489,483,473,472,469,468,460,459,458,457,443,442,427,426,382,381,379,378,377,376,340,338,334,315,314,310,300,299,292,276,272,263,259,250,246,244,243,242,241,240,239,217,216,215,212,206,205,167,166,163]) ).
thf(600,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 4 21:24:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.40 .
% 0.47/0.67
% 0.47/0.67 No.of.Axioms: 62
% 0.47/0.67
% 0.47/0.67 Length.of.Defs: 0
% 0.47/0.67
% 0.47/0.67 Contains.Choice.Funs: false
% 0.52/0.72 ..
% 0.69/0.92 (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:0,translation:fof_full)...................................................................................
% 2.31/2.54
% 2.31/2.54 ********************************
% 2.31/2.54 * All subproblems solved! *
% 2.31/2.54 ********************************
% 2.31/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:599,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.49/2.71
% 2.49/2.71 %**** Beginning of derivation protocol ****
% 2.49/2.71 % SZS output start CNFRefutation
% See solution above
% 2.49/2.72
% 2.49/2.72 %**** End of derivation protocol ****
% 2.49/2.72 %**** no. of clauses in derivation: 600 ****
% 2.49/2.72 %**** clause counter: 599 ****
% 2.49/2.72
% 2.49/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:62,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:599,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------