TSTP Solution File: ITP011^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP011^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 08:06:21 EDT 2024
% Result : Theorem 1.06s 0.56s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 33
% Syntax : Number of formulae : 80 ( 17 unt; 27 typ; 0 def)
% Number of atoms : 404 ( 109 equ; 0 cnn)
% Maximal formula atoms : 128 ( 7 avg)
% Number of connectives : 5620 ( 154 ~; 225 |; 120 &;5084 @)
% ( 28 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 56 ( 15 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 10 con; 0-5 aty)
% Number of variables : 189 ( 0 ^ 187 !; 2 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
d: $tType ).
thf(decl_sort2,type,
u: $tType ).
thf(decl_sort3,type,
du: $tType ).
thf(decl_22,type,
tyop_2Emin_2Ebool: d ).
thf(decl_23,type,
tyop_2Emin_2Efun: d > d > d ).
thf(decl_24,type,
tyop_2Eoption_2Eoption: d > d ).
thf(decl_25,type,
s: d > u > du ).
thf(decl_26,type,
app_2E2: du > du > u ).
thf(decl_42,type,
c_2Eoption_2EIS__NONE_2E1: du > u ).
thf(decl_44,type,
c_2Eoption_2EIS__SOME_2E1: du > u ).
thf(decl_45,type,
c_2Eoption_2ENONE_2E0: u ).
thf(decl_47,type,
c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
thf(decl_49,type,
c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).
thf(decl_51,type,
c_2Eoption_2EOPTREL_2E3: du > du > du > u ).
thf(decl_52,type,
c_2Eoption_2ESOME_2E0: u ).
thf(decl_53,type,
c_2Eoption_2ESOME_2E1: du > u ).
thf(decl_56,type,
c_2Eoption_2ETHE_2E1: du > u ).
thf(decl_60,type,
c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
thf(decl_67,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(decl_68,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(decl_74,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(decl_77,type,
esk1_0: d ).
thf(decl_78,type,
esk2_0: u ).
thf(decl_79,type,
esk3_0: u ).
thf(decl_80,type,
esk4_0: u ).
thf(decl_82,type,
esk6_5: d > d > u > u > u > u ).
thf(decl_83,type,
esk7_5: d > d > u > u > u > u ).
thf(thm_2Eoption_2Eoption__CLAUSES,axiom,
! [X1: d,X2: d,X3: u,X26: u,X27: u] :
( ! [X28: u,X29: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X28 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X29 ) ) ) )
<=> ( ( s @ X1 @ X28 )
= ( s @ X1 @ X29 ) ) )
& ! [X30: u] :
( ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X30 ) ) ) ) )
= ( s @ X1 @ X30 ) )
& ! [X31: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X31 ) ) ) )
& ! [X32: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X32 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [X33: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X33 ) ) ) ) ) )
<=> mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ! [X34: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X34 ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X34 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [X35: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X35 ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X35 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [X36: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) )
& ! [X37: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X37 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X37 ) )
& ! [X38: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) )
& ! [X39: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X39 ) ) ) )
=> ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X39 ) @ ( s @ X2 @ X27 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) ) )
= ( s @ X2 @ X27 ) ) )
& ! [X40: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) ) ) )
=> ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) @ ( s @ X2 @ X27 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) ) )
= ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) @ ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) ) ) ) ) ) )
& ! [X41: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X26 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) ) )
& ! [X42: u,X43: u] :
( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X2 @ X42 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X43 ) ) )
= ( s @ X2 @ X42 ) )
& ! [X44: u,X45: u,X46: u] :
( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X44 ) ) ) @ ( s @ X2 @ X45 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X46 ) ) )
= ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X46 ) @ ( s @ X1 @ X44 ) ) ) )
& ! [X47: u,X48: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X47 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X48 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X47 ) @ ( s @ X1 @ X48 ) ) ) ) ) )
& ! [X49: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [X50: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X50 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X50 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mohUVITHYN/E---3.1_17235.p',thm_2Eoption_2Eoption__CLAUSES) ).
thf(thm_2Equotient__option_2EOPTION__REL__def,conjecture,
! [X1: d,X55: u,X13: u,X56: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
<=> mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X13 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X55 ) ) ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X13 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X55 ) ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ X1 @ X13 ) ) ) @ ( s @ X1 @ X55 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mohUVITHYN/E---3.1_17235.p',thm_2Equotient__option_2EOPTION__REL__def) ).
thf(thm_2Eoption_2EOPTREL__def,axiom,
! [X1: d,X2: d,X51: u,X13: u,X52: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X51 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X13 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X52 ) ) ) )
<=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X13 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X52 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
| ? [X53: u,X54: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X13 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X53 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X52 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X54 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X51 ) @ ( s @ X1 @ X53 ) ) ) @ ( s @ X2 @ X54 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mohUVITHYN/E---3.1_17235.p',thm_2Eoption_2EOPTREL__def) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [X1: d,X16: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X16 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X1 @ X16 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mohUVITHYN/E---3.1_17235.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) ).
thf(thm_2Ebool_2EAND__CLAUSES,axiom,
! [X25: $o] :
( ( ( mono_2Ec_2Ebool_2ET
& X25 )
<=> X25 )
& ( ( X25
& mono_2Ec_2Ebool_2ET )
<=> X25 )
& ( ( mono_2Ec_2Ebool_2EF
& X25 )
<=> mono_2Ec_2Ebool_2EF )
& ( ( X25
& mono_2Ec_2Ebool_2EF )
<=> mono_2Ec_2Ebool_2EF )
& ( ( X25
& X25 )
<=> X25 ) ),
file('/export/starexec/sandbox2/tmp/tmp.mohUVITHYN/E---3.1_17235.p',thm_2Ebool_2EAND__CLAUSES) ).
thf(thm_2Ebool_2EFALSITY,axiom,
! [X25: $o] :
( mono_2Ec_2Ebool_2EF
=> X25 ),
file('/export/starexec/sandbox2/tmp/tmp.mohUVITHYN/E---3.1_17235.p',thm_2Ebool_2EFALSITY) ).
thf(c_0_6,plain,
! [X1: d,X2: d,X3: u,X26: u,X27: u] :
( ! [X28: u,X29: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X28 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X29 ) ) ) )
<=> ( ( s @ X1 @ X28 )
= ( s @ X1 @ X29 ) ) )
& ! [X30: u] :
( ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X30 ) ) ) ) )
= ( s @ X1 @ X30 ) )
& ! [X31: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X31 ) ) ) )
& ! [X32: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X32 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [X33: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X33 ) ) ) ) ) )
<=> mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ! [X34: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X34 ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X34 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [X35: u] :
( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X35 ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X35 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [X36: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X36 ) ) )
& ! [X37: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X37 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X37 ) )
& ! [X38: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X38 ) )
& ! [X39: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X39 ) ) ) )
=> ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X39 ) @ ( s @ X2 @ X27 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) ) )
= ( s @ X2 @ X27 ) ) )
& ! [X40: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) ) ) )
=> ( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) @ ( s @ X2 @ X27 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) ) )
= ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X3 ) @ ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X40 ) ) ) ) ) ) )
& ! [X41: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X26 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X41 ) ) )
& ! [X42: u,X43: u] :
( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X2 @ X42 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X43 ) ) )
= ( s @ X2 @ X42 ) )
& ! [X44: u,X45: u,X46: u] :
( ( s @ X2 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X44 ) ) ) @ ( s @ X2 @ X45 ) @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X46 ) ) )
= ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X46 ) @ ( s @ X1 @ X44 ) ) ) )
& ! [X47: u,X48: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X47 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X48 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X47 ) @ ( s @ X1 @ X48 ) ) ) ) ) )
& ! [X49: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ X2 ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [X50: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X50 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X50 ) ) ),
inference(fof_simplification,[status(thm)],[thm_2Eoption_2Eoption__CLAUSES]) ).
thf(c_0_7,negated_conjecture,
~ ! [X1: d,X55: u,X13: u,X56: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
<=> mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X13 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X55 ) ) ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X13 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X55 ) ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X56 ) @ ( s @ X1 @ X13 ) ) ) @ ( s @ X1 @ X55 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm_2Equotient__option_2EOPTION__REL__def]) ).
thf(c_0_8,plain,
! [X162: d,X163: d,X164: u,X165: u,X166: u,X169: d,X170: d,X171: u,X172: u,X173: u,X174: u,X175: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 )
= ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X162 @ ( esk6_5 @ X162 @ X163 @ X164 @ X165 @ X166 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 )
= ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X162 @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) ) @ X164 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 )
= ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X163 @ ( esk7_5 @ X162 @ X163 @ X164 @ X165 @ X166 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 )
= ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X162 @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) ) @ X164 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X162 @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) ) @ X164 ) @ ( s @ X162 @ ( esk6_5 @ X162 @ X163 @ X164 @ X165 @ X166 ) ) ) ) @ ( s @ X163 @ ( esk7_5 @ X162 @ X163 @ X164 @ X165 @ X166 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 )
= ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X162 @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) ) @ X164 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 )
= ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X162 @ ( esk6_5 @ X162 @ X163 @ X164 @ X165 @ X166 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 )
= ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X162 @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) ) @ X164 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 )
= ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X163 @ ( esk7_5 @ X162 @ X163 @ X164 @ X165 @ X166 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 )
= ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X162 @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) ) @ X164 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X162 @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) ) @ X164 ) @ ( s @ X162 @ ( esk6_5 @ X162 @ X163 @ X164 @ X165 @ X166 ) ) ) ) @ ( s @ X163 @ ( esk7_5 @ X162 @ X163 @ X164 @ X165 @ X166 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 )
= ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X162 @ ( tyop_2Emin_2Efun @ X163 @ tyop_2Emin_2Ebool ) ) @ X164 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X162 ) @ X165 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X163 ) @ X166 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X169 ) @ X172 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X169 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X170 ) @ X173 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X170 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X169 @ ( tyop_2Emin_2Efun @ X170 @ tyop_2Emin_2Ebool ) ) @ X171 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X169 ) @ X172 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X170 ) @ X173 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X169 ) @ X172 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X169 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X169 @ X174 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X170 ) @ X173 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X170 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X170 @ X175 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X170 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X169 @ ( tyop_2Emin_2Efun @ X170 @ tyop_2Emin_2Ebool ) ) @ X171 ) @ ( s @ X169 @ X174 ) ) ) @ ( s @ X170 @ X175 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X169 @ ( tyop_2Emin_2Efun @ X170 @ tyop_2Emin_2Ebool ) ) @ X171 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X169 ) @ X172 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X170 ) @ X173 ) ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Eoption_2EOPTREL__def])])])])])])]) ).
thf(c_0_9,plain,
! [X176: d,X177: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X176 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X176 @ X177 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X176 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X176 @ ( tyop_2Eoption_2Eoption @ X176 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X176 @ X177 ) ) ) ),
inference(variable_rename,[status(thm)],[arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a]) ).
thf(c_0_10,plain,
! [X182: d,X183: d,X184: u,X185: u,X186: u,X187: u,X188: u,X189: u,X190: u,X191: u,X192: u,X193: u,X194: u,X195: u,X196: u,X197: u,X198: u,X199: u,X200: u,X201: u,X202: u,X203: u,X204: u,X205: u,X206: u,X207: u,X208: u,X209: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X187 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X188 ) ) ) )
| ( ( s @ X182 @ X187 )
= ( s @ X182 @ X188 ) ) )
& ( ( ( s @ X182 @ X187 )
!= ( s @ X182 @ X188 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X187 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X188 ) ) ) ) )
& ( ( s @ X182 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X189 ) ) ) ) )
= ( s @ X182 @ X189 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X190 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X191 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X192 ) ) ) ) ) )
| mono_2Ec_2Ebool_2ET )
& ( ~ mono_2Ec_2Ebool_2ET
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X192 ) ) ) ) ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF )
& ( ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X193 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X193 )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X193 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X193 ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X194 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X194 )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X194 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X194 ) ) ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X195 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X195 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X195 ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X196 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X182 @ ( tyop_2Eoption_2Eoption @ X182 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X196 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X197 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X197 ) @ ( s @ ( tyop_2Emin_2Efun @ X182 @ ( tyop_2Eoption_2Eoption @ X182 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X197 ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X198 ) ) ) )
| ( ( s @ X183 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X198 ) @ ( s @ X183 @ X186 ) @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X184 ) ) )
= ( s @ X183 @ X186 ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X199 ) ) ) )
| ( ( s @ X183 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X199 ) @ ( s @ X183 @ X186 ) @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X184 ) ) )
= ( s @ X183 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X184 ) @ ( s @ X182 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X199 ) ) ) ) ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X200 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X200 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 ) @ ( s @ ( tyop_2Emin_2Efun @ X182 @ ( tyop_2Eoption_2Eoption @ X182 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X200 ) ) )
& ( ( s @ X183 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X183 @ X201 ) @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X202 ) ) )
= ( s @ X183 @ X201 ) )
& ( ( s @ X183 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X203 ) ) ) @ ( s @ X183 @ X204 ) @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X205 ) ) )
= ( s @ X183 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X205 ) @ ( s @ X182 @ X203 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X183 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X206 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X207 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X183 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X183 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X206 ) @ ( s @ X182 @ X207 ) ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X183 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X182 @ X183 ) @ X208 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X183 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X182 ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X182 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X209 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X209 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
thf(c_0_11,negated_conjecture,
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2ET )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2ET )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2ET )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2ET ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
thf(c_0_12,plain,
! [X25: $o] :
( ( ( mono_2Ec_2Ebool_2ET
& X25 )
<=> X25 )
& ( ( X25
& mono_2Ec_2Ebool_2ET )
<=> X25 )
& ( ( mono_2Ec_2Ebool_2EF
& X25 )
<=> mono_2Ec_2Ebool_2EF )
& ( ( X25
& mono_2Ec_2Ebool_2EF )
<=> mono_2Ec_2Ebool_2EF ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EAND__CLAUSES]) ).
thf(c_0_13,plain,
! [X1: d,X2: d,X4: u,X3: u,X5: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( esk6_5 @ X1 @ X2 @ X4 @ X3 @ X5 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
! [X1: d,X3: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X3 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X1 @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,plain,
! [X1: d,X3: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X2: d,X1: d,X5: u,X4: u,X3: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( esk7_5 @ X2 @ X1 @ X4 @ X5 @ X3 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,plain,
! [X211: $o] :
( ( ~ mono_2Ec_2Ebool_2ET
| ~ X211
| X211 )
& ( mono_2Ec_2Ebool_2ET
| ~ X211 )
& ( X211
| ~ X211 )
& ( ~ X211
| ~ mono_2Ec_2Ebool_2ET
| X211 )
& ( X211
| ~ X211 )
& ( mono_2Ec_2Ebool_2ET
| ~ X211 )
& ( ~ mono_2Ec_2Ebool_2EF
| ~ X211
| mono_2Ec_2Ebool_2EF )
& ( mono_2Ec_2Ebool_2EF
| ~ mono_2Ec_2Ebool_2EF )
& ( X211
| ~ mono_2Ec_2Ebool_2EF )
& ( ~ X211
| ~ mono_2Ec_2Ebool_2EF
| mono_2Ec_2Ebool_2EF )
& ( X211
| ~ mono_2Ec_2Ebool_2EF )
& ( mono_2Ec_2Ebool_2EF
| ~ mono_2Ec_2Ebool_2EF ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
thf(c_0_19,plain,
! [X210: $o] :
( ~ mono_2Ec_2Ebool_2EF
| X210 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ebool_2EFALSITY])])]) ).
thf(c_0_20,plain,
! [X1: d,X3: u,X2: d,X4: u,X5: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X1 @ ( esk6_5 @ X1 @ X2 @ X3 @ X4 @ X5 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 ) ) ) ) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_21,plain,
! [X3: u,X2: d,X1: d] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_22,plain,
! [X3: u,X1: d] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X1 @ X3 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
thf(c_0_23,plain,
! [X2: d,X1: d,X4: u,X3: u,X5: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X1 @ ( esk7_5 @ X2 @ X1 @ X3 @ X4 @ X5 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X5 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X5 ) ) ) ) ),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
thf(c_0_24,negated_conjecture,
( mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ mono_2Ec_2Ebool_2ET
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
mono_2Ec_2Ebool_2ET,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_18])])]) ).
thf(c_0_26,plain,
~ mono_2Ec_2Ebool_2EF,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_19])])]) ).
thf(c_0_27,plain,
! [X1: d,X2: d,X4: u,X3: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
thf(c_0_28,plain,
! [X1: d,X4: u,X3: u,X2: d] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_22]) ).
thf(c_0_29,negated_conjecture,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),c_0_26]) ).
thf(c_0_30,plain,
! [X1: d,X5: u,X4: u,X3: u,X2: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_31,plain,
! [X1: d,X2: d,X3: u,X4: u] :
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X4 ) ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_14]),c_0_15]) ).
thf(c_0_32,plain,
! [X1: d,X4: u,X3: u,X2: d] :
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_14]),c_0_15]) ).
thf(c_0_33,plain,
! [X1: d,X3: u] :
( ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X3 ) ) ) ) )
= ( s @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_34,negated_conjecture,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).
thf(c_0_35,plain,
! [X2: d,X1: d,X4: u,X3: u,X5: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ X2 @ ( esk6_5 @ X2 @ X1 @ X3 @ X4 @ X5 ) ) ) ) @ ( s @ X1 @ ( esk7_5 @ X2 @ X1 @ X3 @ X4 @ X5 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X5 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X5 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_36,plain,
! [X1: d,X3: u] :
( ( s @ X1 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Eoption_2Eoption @ X1 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X1 @ X3 ) ) ) ) )
= ( s @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_14]) ).
thf(c_0_37,negated_conjecture,
( ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Eoption_2Eoption @ esk1_0 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ esk1_0 @ ( esk7_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_15]) ).
thf(c_0_38,negated_conjecture,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| mono_2Ec_2Ebool_2EF
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_39,negated_conjecture,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ ( esk6_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ) @ ( s @ esk1_0 @ ( esk7_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_15]) ).
thf(c_0_40,negated_conjecture,
( ( ( s @ esk1_0 @ ( esk7_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) )
= ( s @ esk1_0 @ esk2_0 ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33]) ).
thf(c_0_41,negated_conjecture,
( ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Eoption_2Eoption @ esk1_0 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ esk1_0 @ ( esk6_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_34]),c_0_15]) ).
thf(c_0_42,negated_conjecture,
( mono_2Ec_2Ebool_2EF
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ mono_2Ec_2Ebool_2ET
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ) ),
inference(cn,[status(thm)],[c_0_38]) ).
thf(c_0_43,negated_conjecture,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ ( esk6_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_44,negated_conjecture,
( ( ( s @ esk1_0 @ ( esk6_5 @ esk1_0 @ esk1_0 @ esk4_0 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) )
= ( s @ esk1_0 @ esk3_0 ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_41]),c_0_33]) ).
thf(c_0_45,negated_conjecture,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_25])]),c_0_26]) ).
thf(c_0_46,plain,
! [X1: d,X2: d,X5: u,X4: u,X3: u,X7: u,X6: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X7 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X4 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X5 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X1 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X7 ) @ ( s @ X1 @ X4 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_47,negated_conjecture,
j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_48,negated_conjecture,
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
thf(c_0_49,negated_conjecture,
! [X4: u,X3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X4 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X4 )
!= ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_50,negated_conjecture,
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_47])]),c_0_32]),c_0_31]) ).
thf(c_0_51,negated_conjecture,
! [X3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ esk1_0 @ ( tyop_2Emin_2Efun @ esk1_0 @ tyop_2Emin_2Ebool ) ) @ esk4_0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk2_0 ) ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ esk1_0 @ esk3_0 ) ) ) ) ),
inference(er,[status(thm)],[c_0_49]) ).
thf(c_0_52,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_50,c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ITP011^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.11/0.30 % Computer : n003.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Fri May 3 12:54:06 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.15/0.41 Running higher-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.mohUVITHYN/E---3.1_17235.p
% 1.06/0.56 # Version: 3.1.0-ho
% 1.06/0.56 # Preprocessing class: HSLSSLSMSSSNSFA.
% 1.06/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.56 # Starting additional_ho_4 with 1500s (5) cores
% 1.06/0.56 # Starting pre_casc_8 with 300s (1) cores
% 1.06/0.56 # Starting pre_casc_5 with 300s (1) cores
% 1.06/0.56 # Starting pre_casc_6 with 300s (1) cores
% 1.06/0.56 # pre_casc_5 with pid 17315 completed with status 0
% 1.06/0.56 # Result found by pre_casc_5
% 1.06/0.56 # Preprocessing class: HSLSSLSMSSSNSFA.
% 1.06/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.56 # Starting additional_ho_4 with 1500s (5) cores
% 1.06/0.56 # Starting pre_casc_8 with 300s (1) cores
% 1.06/0.56 # Starting pre_casc_5 with 300s (1) cores
% 1.06/0.56 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 1.06/0.56 # Search class: HGHSM-FFLM32-DSFFFFNN
% 1.06/0.56 # partial match(1): HGHSM-FFLM32-DSFFFFBN
% 1.06/0.56 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.06/0.56 # Starting lpo8_s with 181s (1) cores
% 1.06/0.56 # lpo8_s with pid 17320 completed with status 0
% 1.06/0.56 # Result found by lpo8_s
% 1.06/0.56 # Preprocessing class: HSLSSLSMSSSNSFA.
% 1.06/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.06/0.56 # Starting additional_ho_4 with 1500s (5) cores
% 1.06/0.56 # Starting pre_casc_8 with 300s (1) cores
% 1.06/0.56 # Starting pre_casc_5 with 300s (1) cores
% 1.06/0.56 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 1.06/0.56 # Search class: HGHSM-FFLM32-DSFFFFNN
% 1.06/0.56 # partial match(1): HGHSM-FFLM32-DSFFFFBN
% 1.06/0.56 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.06/0.56 # Starting lpo8_s with 181s (1) cores
% 1.06/0.56 # Preprocessing time : 0.003 s
% 1.06/0.56 # Presaturation interreduction done
% 1.06/0.56
% 1.06/0.56 # Proof found!
% 1.06/0.56 # SZS status Theorem
% 1.06/0.56 # SZS output start CNFRefutation
% See solution above
% 1.06/0.56 # Parsed axioms : 106
% 1.06/0.56 # Removed by relevancy pruning/SinE : 83
% 1.06/0.56 # Initial clauses : 114
% 1.06/0.56 # Removed in clause preprocessing : 34
% 1.06/0.56 # Initial clauses in saturation : 80
% 1.06/0.56 # Processed clauses : 973
% 1.06/0.56 # ...of these trivial : 42
% 1.06/0.56 # ...subsumed : 790
% 1.06/0.56 # ...remaining for further processing : 141
% 1.06/0.56 # Other redundant clauses eliminated : 0
% 1.06/0.56 # Clauses deleted for lack of memory : 0
% 1.06/0.56 # Backward-subsumed : 8
% 1.06/0.56 # Backward-rewritten : 9
% 1.06/0.56 # Generated clauses : 3409
% 1.06/0.56 # ...of the previous two non-redundant : 2833
% 1.06/0.56 # ...aggressively subsumed : 0
% 1.06/0.56 # Contextual simplify-reflections : 0
% 1.06/0.56 # Paramodulations : 3406
% 1.06/0.56 # Factorizations : 0
% 1.06/0.56 # NegExts : 0
% 1.06/0.56 # Equation resolutions : 3
% 1.06/0.56 # Disequality decompositions : 0
% 1.06/0.56 # Total rewrite steps : 908
% 1.06/0.56 # ...of those cached : 538
% 1.06/0.56 # Propositional unsat checks : 0
% 1.06/0.56 # Propositional check models : 0
% 1.06/0.56 # Propositional check unsatisfiable : 0
% 1.06/0.56 # Propositional clauses : 0
% 1.06/0.56 # Propositional clauses after purity: 0
% 1.06/0.56 # Propositional unsat core size : 0
% 1.06/0.56 # Propositional preprocessing time : 0.000
% 1.06/0.56 # Propositional encoding time : 0.000
% 1.06/0.56 # Propositional solver time : 0.000
% 1.28/0.56 # Success case prop preproc time : 0.000
% 1.28/0.56 # Success case prop encoding time : 0.000
% 1.28/0.56 # Success case prop solver time : 0.000
% 1.28/0.56 # Current number of processed clauses : 79
% 1.28/0.56 # Positive orientable unit clauses : 20
% 1.28/0.56 # Positive unorientable unit clauses: 5
% 1.28/0.56 # Negative unit clauses : 16
% 1.28/0.56 # Non-unit-clauses : 38
% 1.28/0.56 # Current number of unprocessed clauses: 1943
% 1.28/0.56 # ...number of literals in the above : 4351
% 1.28/0.56 # Current number of archived formulas : 0
% 1.28/0.56 # Current number of archived clauses : 62
% 1.28/0.56 # Clause-clause subsumption calls (NU) : 1196
% 1.28/0.56 # Rec. Clause-clause subsumption calls : 898
% 1.28/0.56 # Non-unit clause-clause subsumptions : 322
% 1.28/0.56 # Unit Clause-clause subsumption calls : 62
% 1.28/0.56 # Rewrite failures with RHS unbound : 0
% 1.28/0.56 # BW rewrite match attempts : 165
% 1.28/0.56 # BW rewrite match successes : 28
% 1.28/0.56 # Condensation attempts : 973
% 1.28/0.56 # Condensation successes : 7
% 1.28/0.56 # Termbank termtop insertions : 130931
% 1.28/0.56 # Search garbage collected termcells : 1940
% 1.28/0.56
% 1.28/0.56 # -------------------------------------------------
% 1.28/0.56 # User time : 0.122 s
% 1.28/0.56 # System time : 0.008 s
% 1.28/0.56 # Total time : 0.130 s
% 1.28/0.56 # Maximum resident set size: 2368 pages
% 1.28/0.56
% 1.28/0.56 # -------------------------------------------------
% 1.28/0.56 # User time : 0.127 s
% 1.28/0.56 # System time : 0.010 s
% 1.28/0.56 # Total time : 0.137 s
% 1.28/0.56 # Maximum resident set size: 2168 pages
% 1.28/0.56 % E---3.1 exiting
% 1.28/0.56 % E exiting
%------------------------------------------------------------------------------