%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP011^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:05:11 AM UTC 2026
% Result : Theorem 6.50s 1.33s
% Output : CNFRefutation 6.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 428 ( 113 equ; 0 cnn)
% Maximal formula atoms : 128 ( 6 avg)
% Number of connectives : 5627 ( 161 ~; 228 |; 123 &;5077 @)
% ( 29 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 58 ( 13 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 11 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_23,type,
tyop_2Emin_2Ebool: d ).
thf(decl_24,type,
tyop_2Emin_2Efun: d > d > d ).
thf(decl_25,type,
tyop_2Eoption_2Eoption: d > d ).
thf(decl_26,type,
s: d > u > du ).
thf(decl_27,type,
app_2E2: du > du > u ).
thf(decl_43,type,
c_2Eoption_2EIS__NONE_2E1: du > u ).
thf(decl_45,type,
c_2Eoption_2EIS__SOME_2E1: du > u ).
thf(decl_46,type,
c_2Eoption_2ENONE_2E0: u ).
thf(decl_48,type,
c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
thf(decl_50,type,
c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).
thf(decl_52,type,
c_2Eoption_2EOPTREL_2E3: du > du > du > u ).
thf(decl_53,type,
c_2Eoption_2ESOME_2E0: u ).
thf(decl_54,type,
c_2Eoption_2ESOME_2E1: du > u ).
thf(decl_57,type,
c_2Eoption_2ETHE_2E1: du > u ).
thf(decl_61,type,
c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
thf(decl_68,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(decl_69,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(decl_72,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(decl_75,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(decl_78,type,
esk1_0: d ).
thf(decl_79,type,
esk2_0: u ).
thf(decl_80,type,
esk3_0: u ).
thf(decl_81,type,
esk4_0: u ).
thf(decl_83,type,
esk6_5: d > d > u > u > u > u ).
thf(decl_84,type,
esk7_5: d > d > u > u > u > u ).
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.hT8zQIA68n/E---3.1_522357.p',thm_2Equotient__option_2EOPTION__REL__def) ).
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.hT8zQIA68n/E---3.1_522357.p',thm_2Eoption_2Eoption__CLAUSES) ).
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.hT8zQIA68n/E---3.1_522357.p',thm_2Ebool_2EAND__CLAUSES) ).
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.hT8zQIA68n/E---3.1_522357.p',thm_2Eoption_2EOPTREL__def) ).
thf(thm_2Ebool_2EFALSITY,axiom,
! [X25: $o] :
( mono_2Ec_2Ebool_2EF
=> X25 ),
file('/export/starexec/sandbox2/tmp/tmp.hT8zQIA68n/E---3.1_522357.p',thm_2Ebool_2EFALSITY) ).
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.hT8zQIA68n/E---3.1_522357.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) ).
thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X11: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X11 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.hT8zQIA68n/E---3.1_522357.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X9: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X9 ) ) )
<=> X9 ),
file('/export/starexec/sandbox2/tmp/tmp.hT8zQIA68n/E---3.1_522357.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).
thf(c_0_8,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_9,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_10,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_8])])])])]) ).
thf(c_0_11,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_12,plain,
! [X174: d,X175: d,X176: u,X177: u,X178: u,X181: d,X182: d,X183: u,X184: u,X185: u,X186: u,X187: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
= ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X174 @ ( esk6_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
= ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
= ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X175 @ ( esk7_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
= ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ X174 @ ( esk6_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) @ ( s @ X175 @ ( esk7_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
= ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 )
= ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X174 @ ( esk6_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
= ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
= ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X175 @ ( esk7_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
= ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ X174 @ ( esk6_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) @ ( s @ X175 @ ( esk7_5 @ X174 @ X175 @ X176 @ X177 @ X178 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 )
= ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X174 @ ( tyop_2Emin_2Efun @ X175 @ tyop_2Emin_2Ebool ) ) @ X176 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X174 ) @ X177 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X175 ) @ X178 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ X184 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X181 @ ( tyop_2Emin_2Efun @ X182 @ tyop_2Emin_2Ebool ) ) @ X183 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ X184 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ X184 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X181 @ X186 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X182 @ X187 ) ) ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X182 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X181 @ ( tyop_2Emin_2Efun @ X182 @ tyop_2Emin_2Ebool ) ) @ X183 ) @ ( s @ X181 @ X186 ) ) ) @ ( s @ X182 @ X187 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X181 @ ( tyop_2Emin_2Efun @ X182 @ tyop_2Emin_2Ebool ) ) @ X183 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X181 ) @ X184 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X182 ) @ X185 ) ) ) ) ) ),
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_13,plain,
! [X194: d,X195: d,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,X210: u,X211: u,X212: u,X213: u,X214: u,X215: u,X216: u,X217: u,X218: u,X219: u,X220: u,X221: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X199 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X200 ) ) ) )
| ( ( s @ X194 @ X199 )
= ( s @ X194 @ X200 ) ) )
& ( ( ( s @ X194 @ X199 )
!= ( s @ X194 @ X200 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X199 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X200 ) ) ) ) )
& ( ( s @ X194 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X201 ) ) ) ) )
= ( s @ X194 @ X201 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X202 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X203 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X204 ) ) ) ) ) )
| 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 @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X204 ) ) ) ) ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ 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 @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X205 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X205 )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X205 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X205 ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X206 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X206 )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X206 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X206 ) ) ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X207 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X207 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X207 ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X208 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X208 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X209 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X209 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X209 ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X210 ) ) ) )
| ( ( s @ X195 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X210 ) @ ( s @ X195 @ X198 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X196 ) ) )
= ( s @ X195 @ X198 ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X211 ) ) ) )
| ( ( s @ X195 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X211 ) @ ( s @ X195 @ X198 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X196 ) ) )
= ( s @ X195 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X196 ) @ ( s @ X194 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X211 ) ) ) ) ) ) )
& ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X212 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X212 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X197 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X212 ) ) )
& ( ( s @ X195 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X195 @ X213 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X214 ) ) )
= ( s @ X195 @ X213 ) )
& ( ( s @ X195 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X215 ) ) ) @ ( s @ X195 @ X216 ) @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X217 ) ) )
= ( s @ X195 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X217 ) @ ( s @ X194 @ X215 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X195 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X218 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X194 @ X219 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X195 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X195 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X218 ) @ ( s @ X194 @ X219 ) ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X195 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X194 @ X195 ) @ X220 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X195 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X194 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X221 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X194 ) @ X221 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
thf(c_0_14,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_10]) ).
thf(c_0_15,plain,
! [X223: $o] :
( ( ~ mono_2Ec_2Ebool_2ET
| ~ X223
| X223 )
& ( mono_2Ec_2Ebool_2ET
| ~ X223 )
& ( X223
| ~ X223 )
& ( ~ X223
| ~ mono_2Ec_2Ebool_2ET
| X223 )
& ( X223
| ~ X223 )
& ( mono_2Ec_2Ebool_2ET
| ~ X223 )
& ( ~ mono_2Ec_2Ebool_2EF
| ~ X223
| mono_2Ec_2Ebool_2EF )
& ( mono_2Ec_2Ebool_2EF
| ~ mono_2Ec_2Ebool_2EF )
& ( X223
| ~ mono_2Ec_2Ebool_2EF )
& ( ~ X223
| ~ mono_2Ec_2Ebool_2EF
| mono_2Ec_2Ebool_2EF )
& ( X223
| ~ 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_11])])])]) ).
thf(c_0_16,plain,
! [X222: $o] :
( ~ mono_2Ec_2Ebool_2EF
| X222 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ebool_2EFALSITY])])]) ).
thf(c_0_17,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_12]) ).
thf(c_0_18,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_12]) ).
thf(c_0_19,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_13]) ).
thf(c_0_20,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_13]) ).
thf(c_0_21,plain,
! [X188: d,X189: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X188 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X188 @ X189 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X188 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X188 @ ( tyop_2Eoption_2Eoption @ X188 ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ X188 @ X189 ) ) ) ),
inference(variable_rename,[status(thm)],[arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a]) ).
thf(c_0_22,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_12]) ).
thf(c_0_23,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_14]) ).
thf(c_0_24,plain,
mono_2Ec_2Ebool_2ET,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_15])])]) ).
thf(c_0_25,plain,
~ mono_2Ec_2Ebool_2EF,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_16])])]) ).
thf(c_0_26,plain,
! [X3: u,X4: u,X2: d,X1: 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 ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ),
inference(er,[status(thm)],[c_0_17]) ).
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_18,c_0_19]),c_0_20]) ).
thf(c_0_28,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_21]) ).
thf(c_0_29,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_22,c_0_19]),c_0_20]) ).
thf(c_0_30,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_23,c_0_24])]),c_0_25]) ).
thf(c_0_31,plain,
! [X1: d,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_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ),
inference(er,[status(thm)],[c_0_26]) ).
thf(c_0_32,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_28]),c_0_20]) ).
thf(c_0_33,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_29,c_0_28]),c_0_20]) ).
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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),c_0_32]),c_0_33]) ).
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_12]) ).
thf(c_0_36,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_13]) ).
thf(c_0_37,negated_conjecture,
( ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( 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_22,c_0_34]),c_0_20]) ).
thf(c_0_38,axiom,
! [X11: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X11 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) )
= ( s @ tyop_2Emin_2Ebool @ X11 ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X11 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) )
= ( s @ tyop_2Emin_2Ebool @ X11 ) ) ) ),
inference(fool_unroll,[status(thm)],[ij_2Emono_2Etyop_2Emin_2Ebool]) ).
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_20]) ).
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_36]) ).
thf(c_0_41,negated_conjecture,
( ( ( s @ ( tyop_2Eoption_2Eoption @ esk1_0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( 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_18,c_0_34]),c_0_20]) ).
thf(c_0_42,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_10]) ).
thf(c_0_43,plain,
! [X158: u] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X158 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) )
= ( s @ tyop_2Emin_2Ebool @ X158 ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X158 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) )
= ( s @ tyop_2Emin_2Ebool @ X158 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_38])]) ).
thf(c_0_44,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_45,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_36]) ).
thf(c_0_46,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_42]) ).
thf(c_0_47,plain,
! [X3: u] :
( ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) )
= ( s @ tyop_2Emin_2Ebool @ X3 ) )
| ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_48,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_44,c_0_45]) ).
thf(c_0_49,plain,
! [X159: $o] :
( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X159 ) ) )
| X159 )
& ( ~ X159
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X159 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ji_2Emono_2Etyop_2Emin_2Ebool])])]) ).
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_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_46,c_0_24])]),c_0_25]) ).
thf(c_0_51,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_12]) ).
thf(c_0_52,negated_conjecture,
( ( 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 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_53,plain,
j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_49])])]) ).
thf(c_0_54,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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_31])]),c_0_32]),c_0_33]) ).
thf(c_0_55,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
thf(c_0_56,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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_48])]) ).
thf(c_0_57,plain,
! [X3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ X3 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) )
= ( s @ tyop_2Emin_2Ebool @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_58,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_55]) ).
thf(c_0_59,negated_conjecture,
( ( 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 ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_60,plain,
~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_49])])]) ).
thf(c_0_61,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_58]),c_0_59]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP011^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n018.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 19:28:11 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.33 Running higher-order theorem proving
% 0.25/0.36 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.hT8zQIA68n/E---3.1_522357.p
% 6.50/1.33 % Version: 3.5.1-ho
% 6.50/1.33 % Preprocessing class: HSLSSLSMSSSNSFA.
% 6.50/1.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.50/1.33 % Starting additional_ho_4 with 1500s (5) cores
% 6.50/1.33 % Starting pre_casc_8 with 300s (1) cores
% 6.50/1.33 % Starting pre_casc_5 with 300s (1) cores
% 6.50/1.33 % Starting pre_casc_6 with 300s (1) cores
% 6.50/1.33 % additional_ho_4 with pid 522370 completed with status 0
% 6.50/1.33 % Result found by additional_ho_4
% 6.50/1.33 % Preprocessing class: HSLSSLSMSSSNSFA.
% 6.50/1.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.50/1.33 % Starting additional_ho_4 with 1500s (5) cores
% 6.50/1.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 6.50/1.33 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 6.50/1.33 % Search class: HGHSM-FFLM32-DSFFFFBN
% 6.50/1.33 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 6.50/1.33 % Starting SubtermCWHack with 151s (1) cores
% 6.50/1.33 % Starting lpo8_s with 901s (1) cores
% 6.50/1.33 % Starting pre_casc_8 with 151s (1) cores
% 6.50/1.33 % Starting additional_ho_4 with 151s (1) cores
% 6.50/1.33 % Starting pre_casc_6 with 146s (1) cores
% 6.50/1.33 % additional_ho_4 with pid 522379 completed with status 0
% 6.50/1.33 % Result found by additional_ho_4
% 6.50/1.33 % Preprocessing class: HSLSSLSMSSSNSFA.
% 6.50/1.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.50/1.33 % Starting additional_ho_4 with 1500s (5) cores
% 6.50/1.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 6.50/1.33 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 6.50/1.33 % Search class: HGHSM-FFLM32-DSFFFFBN
% 6.50/1.33 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 6.50/1.33 % Starting SubtermCWHack with 151s (1) cores
% 6.50/1.33 % Starting lpo8_s with 901s (1) cores
% 6.50/1.33 % Starting pre_casc_8 with 151s (1) cores
% 6.50/1.33 % Starting additional_ho_4 with 151s (1) cores
% 6.50/1.33 % Preprocessing time : 0.005 s
% 6.50/1.33 % Presaturation interreduction done
% 6.50/1.33
% 6.50/1.33 % Proof found!
% 6.50/1.33 % SZS status Theorem
% 6.50/1.33 % SZS output start CNFRefutation
% See solution above
% 6.50/1.33 % Parsed axioms : 106
% 6.50/1.33 % Removed by relevancy pruning/SinE : 75
% 6.50/1.33 % Initial clauses : 125
% 6.50/1.33 % Removed in clause preprocessing : 34
% 6.50/1.33 % Initial clauses in saturation : 91
% 6.50/1.33 % Processed clauses : 2829
% 6.50/1.33 % ...of these trivial : 36
% 6.50/1.33 % ...subsumed : 2391
% 6.50/1.33 % ...remaining for further processing : 402
% 6.50/1.33 % Other redundant clauses eliminated : 0
% 6.50/1.33 % Clauses deleted for lack of memory : 0
% 6.50/1.33 % Backward-subsumed : 18
% 6.50/1.33 % Backward-rewritten : 42
% 6.50/1.33 % Generated clauses : 14958
% 6.50/1.33 % ...of the previous two non-redundant : 11012
% 6.50/1.33 % ...aggressively subsumed : 0
% 6.50/1.33 % Contextual simplify-reflections : 2
% 6.50/1.33 % Paramodulations : 14646
% 6.50/1.33 % Factorizations : 57
% 6.50/1.33 % NegExts : 43
% 6.50/1.33 % Equation resolutions : 43
% 6.50/1.33 % Disequality decompositions : 0
% 6.50/1.33 % Total rewrite steps : 4941
% 6.50/1.33 % ...of those cached : 3715
% 6.50/1.33 % Propositional unsat checks : 0
% 6.50/1.33 % Propositional check models : 0
% 6.50/1.33 % Propositional check unsatisfiable : 0
% 6.50/1.33 % Propositional clauses : 0
% 6.50/1.33 % Propositional clauses after purity: 0
% 6.50/1.33 % Propositional unsat core size : 0
% 6.50/1.33 % Propositional preprocessing time : 0.000
% 6.50/1.33 % Propositional encoding time : 0.000
% 6.50/1.33 % Propositional solver time : 0.000
% 6.50/1.33 % Success case prop preproc time : 0.000
% 6.50/1.33 % Success case prop encoding time : 0.000
% 6.50/1.33 % Success case prop solver time : 0.000
% 6.50/1.33 % Current number of processed clauses : 251
% 6.50/1.33 % Positive orientable unit clauses : 41
% 6.50/1.33 % Positive unorientable unit clauses: 3
% 6.50/1.33 % Negative unit clauses : 11
% 6.50/1.33 % Non-unit-clauses : 196
% 6.50/1.33 % Current number of unprocessed clauses: 8109
% 6.50/1.33 % ...number of literals in the above : 32871
% 6.50/1.33 % Current number of archived formulas : 0
% 6.50/1.33 % Current number of archived clauses : 151
% 6.50/1.33 % Clause-clause subsumption calls (NU) : 17869
% 6.50/1.33 % Rec. Clause-clause subsumption calls : 7238
% 6.50/1.33 % Non-unit clause-clause subsumptions : 1494
% 6.50/1.33 % Unit Clause-clause subsumption calls : 133
% 6.50/1.33 % Rewrite failures with RHS unbound : 0
% 6.50/1.33 % BW rewrite match attempts : 291
% 6.50/1.33 % BW rewrite match successes : 21
% 6.50/1.33 % Condensation attempts : 0
% 6.50/1.33 % Condensation successes : 0
% 6.50/1.33 % Termbank termtop insertions : 430299
% 6.50/1.33 % Search garbage collected termcells : 1993
% 6.50/1.33
% 6.50/1.33 % -------------------------------------------------
% 6.50/1.33 % User time : 0.897 s
% 6.50/1.33 % System time : 0.022 s
% 6.50/1.33 % Total time : 0.919 s
% 6.50/1.33 % Maximum resident set size: 4004 pages
% 6.50/1.33
% 6.50/1.33 % -------------------------------------------------
% 6.50/1.33 % User time : 4.472 s
% 6.50/1.33 % System time : 0.119 s
% 6.50/1.33 % Total time : 4.592 s
% 6.50/1.33 % Maximum resident set size: 5120 pages
% 6.50/1.33 % E exiting
%------------------------------------------------------------------------------