%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP011^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:53:24 AM UTC 2026
% Result : Theorem 22.66s 4.27s
% Output : Refutation 22.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 132 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 1092 ( 497 equ; 0 cnn)
% Maximal formula atoms : 33 ( 8 avg)
% Number of connectives : 7137 ( 254 ~; 249 |; 191 &;6391 @)
% ( 38 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 67 usr; 35 con; 0-5 aty)
% Number of variables : 348 ( 0 ^; 326 !; 22 ?; 348 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_4,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_5,type,
tyop_2Eoption_2Eoption: d > d ).
thf(func_def_6,type,
s: d > u > du ).
thf(func_def_7,type,
app_2E2: du > du > u ).
thf(func_def_8,type,
combin_i_2E0: u ).
thf(func_def_9,type,
combin_k_2E0: u ).
thf(func_def_10,type,
combin_s_2E0: u ).
thf(func_def_11,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_12,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_13,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_14,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_15,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_16,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_18,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_19,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_20,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_21,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_22,type,
c_2Eoption_2EIS__NONE_2E0: u ).
thf(func_def_23,type,
c_2Eoption_2EIS__NONE_2E1: du > u ).
thf(func_def_24,type,
c_2Eoption_2EIS__SOME_2E0: u ).
thf(func_def_25,type,
c_2Eoption_2EIS__SOME_2E1: du > u ).
thf(func_def_26,type,
c_2Eoption_2ENONE_2E0: u ).
thf(func_def_27,type,
c_2Eoption_2EOPTION__JOIN_2E0: u ).
thf(func_def_28,type,
c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
thf(func_def_29,type,
c_2Eoption_2EOPTION__MAP_2E0: u ).
thf(func_def_30,type,
c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).
thf(func_def_31,type,
c_2Eoption_2EOPTREL_2E0: u ).
thf(func_def_32,type,
c_2Eoption_2EOPTREL_2E3: du > du > du > u ).
thf(func_def_33,type,
c_2Eoption_2ESOME_2E0: u ).
thf(func_def_34,type,
c_2Eoption_2ESOME_2E1: du > u ).
thf(func_def_35,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_36,type,
c_2Eoption_2ETHE_2E0: u ).
thf(func_def_37,type,
c_2Eoption_2ETHE_2E1: du > u ).
thf(func_def_38,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_39,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_40,type,
c_2Eoption_2Eoption__CASE_2E0: u ).
thf(func_def_41,type,
c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
thf(func_def_42,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_43,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_44,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_45,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_46,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_47,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_50,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_51,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_52,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_53,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_54,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(func_def_55,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_56,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_57,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(func_def_63,type,
sK0: u > u > d > u > d > u ).
thf(func_def_64,type,
sK1: u > u > d > u > d > u ).
thf(func_def_65,type,
sK2: d > u > d > u > u ).
thf(func_def_66,type,
sK3: u ).
thf(func_def_67,type,
sK4: u ).
thf(func_def_68,type,
sK5: d ).
thf(func_def_69,type,
sK6: u ).
thf(f1022,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f383,f581,f613,f759,f774,f832,f1021]) ).
thf(f1021,plain,
( ~ spl7_3
| spl7_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f1020]) ).
thf(f1020,plain,
( $false
| ~ spl7_3
| spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1011]) ).
thf(f1011,plain,
( ( $true = $false )
| ~ spl7_3
| spl7_7 ),
inference(backward_demodulation,[status(thm)],[f366,f1006]) ).
thf(f1006,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ~ spl7_3
| spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ( $true = $false )
| ~ spl7_3
| spl7_7 ),
inference(forward_demodulation,[status(thm)],[f1004,f834]) ).
thf(f834,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $false )
| spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f833]) ).
thf(f833,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $false )
| ( $true != $true )
| spl7_7 ),
inference(superposition,[status(thm)],[f381,f305]) ).
thf(f305,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
inference(not_proxy_clausification,[status(thm)],[f304]) ).
thf(f304,plain,
! [X0: $o] :
( ( ( ~ X0 ) != $true )
| ( $false = X0 ) ),
inference(boolean_simplification,[status(thm)],[f238]) ).
thf(f238,plain,
! [X0: $o] :
( ( ( ~ X0 ) != $true )
| ( ( ~ $true ) = X0 ) ),
inference(definition_unfolding,[status(thm)],[f161,f227]) ).
thf(f227,plain,
( mono_2Ec_2Ebool_2EF = ( ~ $true ) ),
inference(definition_unfolding,[status(thm)],[f172,f170]) ).
thf(f170,plain,
mono_2Ec_2Ebool_2ET = $true,
inference(cnf_transformation,[status(thm)],[f62]) ).
thf(f62,plain,
mono_2Ec_2Ebool_2ET = $true,
inference(fool_elimination,[status(thm)],[f61]) ).
thf(f61,plain,
mono_2Ec_2Ebool_2ET,
inference(rectify,[status(thm)],[f37]) ).
thf(f37,axiom,
mono_2Ec_2Ebool_2ET,
file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Ebool_2ETRUTH) ).
thf(f172,plain,
( mono_2Ec_2Ebool_2EF = ( ~ mono_2Ec_2Ebool_2ET ) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
( ! [X0: $o] :
( ( ~ ~ X0 )
= X0 )
& ( mono_2Ec_2Ebool_2EF = ( ~ mono_2Ec_2Ebool_2ET ) )
& ( mono_2Ec_2Ebool_2ET = ( ~ mono_2Ec_2Ebool_2EF ) ) ),
inference(fool_elimination,[status(thm)],[f51]) ).
thf(f51,plain,
( ! [X0: $o] :
( X0
<=> ~ ~ X0 )
& ( mono_2Ec_2Ebool_2EF
<=> ~ mono_2Ec_2Ebool_2ET )
& ( ~ mono_2Ec_2Ebool_2EF
<=> mono_2Ec_2Ebool_2ET ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,axiom,
( ! [X18: $o] :
( X18
<=> ~ ~ X18 )
& ( mono_2Ec_2Ebool_2EF
<=> ~ mono_2Ec_2Ebool_2ET )
& ( ~ mono_2Ec_2Ebool_2EF
<=> mono_2Ec_2Ebool_2ET ) ),
file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(f161,plain,
! [X0: $o] :
( ( mono_2Ec_2Ebool_2EF = X0 )
| ( ( ~ X0 ) != $true ) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
thf(f115,plain,
! [X0: $o] :
( ( ( mono_2Ec_2Ebool_2EF = X0 )
| ( ( ~ X0 ) != $true ) )
& ( ( ( ~ X0 ) = $true )
| ( mono_2Ec_2Ebool_2EF != X0 ) )
& ( ( mono_2Ec_2Ebool_2EF = X0 )
| ( ( ~ X0 ) != $true ) )
& ( ( ( ~ X0 ) = $true )
| ( mono_2Ec_2Ebool_2EF != X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( mono_2Ec_2Ebool_2ET != X0 ) )
& ( ( $true = X0 )
| ( mono_2Ec_2Ebool_2ET != X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
| ( $true != X0 ) ) ),
inference(flattening,[status(thm)],[f114]) ).
thf(f114,plain,
! [X0: $o] :
( ( ( mono_2Ec_2Ebool_2EF = X0 )
| ( ( ~ X0 ) != $true ) )
& ( ( ( ~ X0 ) = $true )
| ( mono_2Ec_2Ebool_2EF != X0 ) )
& ( ( mono_2Ec_2Ebool_2EF = X0 )
| ( ( ~ X0 ) != $true ) )
& ( ( ( ~ X0 ) = $true )
| ( mono_2Ec_2Ebool_2EF != X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( mono_2Ec_2Ebool_2ET != X0 ) )
& ( ( $true = X0 )
| ( mono_2Ec_2Ebool_2ET != X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
| ( $true != X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f82]) ).
thf(f82,plain,
! [X0: $o] :
( ( ( mono_2Ec_2Ebool_2EF = X0 )
<=> ( ( ~ X0 ) = $true ) )
& ( ( mono_2Ec_2Ebool_2EF = X0 )
<=> ( ( ~ X0 ) = $true ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
<=> ( $true = X0 ) )
& ( ( $true = X0 )
<=> ( mono_2Ec_2Ebool_2ET = X0 ) ) ),
inference(fool_elimination,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $o] :
( ( ( mono_2Ec_2Ebool_2ET = X0 )
<=> X0 )
& ( ( mono_2Ec_2Ebool_2EF = X0 )
<=> ~ X0 )
& ( X0
<=> ( mono_2Ec_2Ebool_2ET = X0 ) )
& ( ~ X0
<=> ( mono_2Ec_2Ebool_2EF = X0 ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,axiom,
! [X18: $o] :
( ( ( mono_2Ec_2Ebool_2ET = X18 )
<=> X18 )
& ( ( mono_2Ec_2Ebool_2EF = X18 )
<=> ~ X18 )
& ( X18
<=> ( mono_2Ec_2Ebool_2ET = X18 ) )
& ( ~ X18
<=> ( mono_2Ec_2Ebool_2EF = X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(f381,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
!= $true )
| spl7_7 ),
inference(avatar_component_clause,[status(thm)],[f380]) ).
thf(f380,definition,
( spl7_7
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_7])],[avatar_definition]) ).
thf(f1004,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ~ spl7_3 ),
inference(forward_demodulation,[status(thm)],[f1003,f924]) ).
thf(f924,plain,
( ( ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) )
= ( s @ sK5 @ sK3 ) )
| ~ spl7_3 ),
inference(forward_demodulation,[status(thm)],[f882,f192]) ).
thf(f192,plain,
! [X2: d,X18: u] :
( ( s @ X2 @ X18 )
= ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X18 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
thf(f123,plain,
! [X0: u,X1: u,X2: d,X3: u,X4: d] :
( ! [X5: u,X6: u,X7: u] :
( ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ X2 @ X6 ) ) )
= ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) @ ( s @ X4 @ X7 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) ) ) )
& ! [X8: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X8 ) ) ) )
= $true )
& ! [X9: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X9 ) ) ) )
!= $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X9 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X9 ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
& ! [X10: u] :
( $true
= ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X10 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [X11: u] :
( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X11 ) ) ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X12: u,X13: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X13 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X12 ) ) ) )
| ( ( s @ X2 @ X12 )
!= ( s @ X2 @ X13 ) ) )
& ( ( ( s @ X2 @ X12 )
= ( s @ X2 @ X13 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X13 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X12 ) ) ) ) ) )
& ! [X14: u,X15: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X14 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X15 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X14 ) @ ( s @ X2 @ X15 ) ) ) ) ) )
& ! [X16: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X16 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X17: u] :
( ( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X17 ) ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X17 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X17 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X17 ) ) ) ) ) ) ) )
& ! [X18: u] :
( ( s @ X2 @ X18 )
= ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X18 ) ) ) ) ) )
& ! [X19: u] :
( ( ( s @ X4 @ X3 )
= ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X19 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X19 ) ) ) ) ) )
& ! [X20: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X20 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X20 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) ) )
& ! [X21: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) )
& ! [X22: u,X23: u] :
( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X4 @ X22 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X23 ) ) )
= ( s @ X4 @ X22 ) )
& ! [X24: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X24 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X24 ) ) ) ) ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X24 ) ) ) ) ) )
& ! [X25: u] :
( ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 ) ) ) ) ) ) )
& ! [X26: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) ) ) ) ) )
& ! [X27: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) ) ) ) )
| ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f122]) ).
thf(f122,plain,
! [X0: u,X1: u,X2: d,X3: u,X4: d] :
( ! [X7: u,X8: u,X9: u] :
( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X8 ) ) ) @ ( s @ X4 @ X9 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X7 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X7 ) @ ( s @ X2 @ X8 ) ) ) )
& ! [X15: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X15 ) ) ) )
= $true )
& ! [X21: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
& ! [X23: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X23 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
= $true )
& ! [X19: u] :
( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X19 ) ) ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X12: u,X13: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X13 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X12 ) ) ) )
| ( ( s @ X2 @ X12 )
!= ( s @ X2 @ X13 ) ) )
& ( ( ( s @ X2 @ X12 )
= ( s @ X2 @ X13 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X13 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X12 ) ) ) ) ) )
& ! [X5: u,X6: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ X2 @ X6 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) ) ) )
& ! [X20: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X20 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X25: u] :
( ( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 ) ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( $true
!= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 ) ) ) ) ) ) ) )
& ! [X24: u] :
( ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X24 ) ) ) ) )
= ( s @ X2 @ X24 ) )
& ! [X26: u] :
( ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ X3 ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) ) ) )
!= $true ) )
& ! [X14: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) ) )
& ! [X27: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) )
& ! [X17: u,X18: u] :
( ( s @ X4 @ X17 )
= ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X4 @ X17 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X18 ) ) ) )
& ! [X16: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) ) ) ) )
& ! [X22: u] :
( ( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) ) ) ) ) ) )
& ! [X10: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X10 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X10 ) )
& ! [X11: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) ) ) ) )
| ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f109]) ).
thf(f109,plain,
! [X0: u,X1: u,X2: d,X3: u,X4: d] :
( ! [X7: u,X8: u,X9: u] :
( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X8 ) ) ) @ ( s @ X4 @ X9 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X7 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X7 ) @ ( s @ X2 @ X8 ) ) ) )
& ! [X15: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X15 ) ) ) )
= $true )
& ! [X21: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
& ! [X23: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X23 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
= $true )
& ! [X19: u] :
( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X19 ) ) ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X12: u,X13: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X13 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X12 ) ) ) )
<=> ( ( s @ X2 @ X12 )
= ( s @ X2 @ X13 ) ) )
& ! [X5: u,X6: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ X2 @ X6 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) ) ) )
& ! [X20: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X20 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X25: u] :
( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 ) ) ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [X24: u] :
( ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X24 ) ) ) ) )
= ( s @ X2 @ X24 ) )
& ! [X26: u] :
( ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ X3 ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) ) ) )
!= $true ) )
& ! [X14: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) ) )
& ! [X27: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) )
& ! [X17: u,X18: u] :
( ( s @ X4 @ X17 )
= ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X4 @ X17 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X18 ) ) ) )
& ! [X16: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) )
| ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) ) ) ) )
& ! [X22: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) ) )
& ! [X10: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X10 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X10 ) )
& ! [X11: u] :
( ( $true
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) ) ) ) )
| ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f66]) ).
thf(f66,plain,
! [X0: u,X1: u,X2: d,X3: u,X4: d] :
( ! [X25: u] :
( ( $true
= ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 ) ) ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [X19: u] :
( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X19 ) ) ) ) ) ) )
& ! [X21: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) ) )
& ! [X22: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) ) )
& ! [X16: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) )
& ! [X10: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X10 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X10 ) )
& ! [X26: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) ) ) )
= $true )
=> ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ X3 ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X12: u,X13: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X13 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X12 ) ) ) )
<=> ( ( s @ X2 @ X12 )
= ( s @ X2 @ X13 ) ) )
& ! [X14: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) ) )
& ! [X11: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) ) ) ) )
=> ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) ) ) ) ) ) )
& ! [X7: u,X8: u,X9: u] :
( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X8 ) ) ) @ ( s @ X4 @ X9 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X7 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X7 ) @ ( s @ X2 @ X8 ) ) ) )
& ! [X17: u,X18: u] :
( ( s @ X4 @ X17 )
= ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X4 @ X17 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X18 ) ) ) )
& ! [X23: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X23 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
= $true )
& ! [X5: u,X6: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ X2 @ X6 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) ) ) )
& ! [X24: u] :
( ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X24 ) ) ) ) )
= ( s @ X2 @ X24 ) )
& ! [X15: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X15 ) ) ) )
= $true )
& ! [X20: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X20 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X27: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) )
& ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f65]) ).
thf(f65,plain,
! [X0: u,X1: u,X2: d,X3: u,X4: d] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X5: u,X6: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ X2 @ X6 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) ) ) )
& ! [X7: u,X8: u,X9: u] :
( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X8 ) ) ) @ ( s @ X4 @ X9 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X7 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X7 ) @ ( s @ X2 @ X8 ) ) ) )
& ! [X10: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X10 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X10 ) )
& ! [X11: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) ) ) )
=> ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X11 ) ) ) ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
& ! [X12: u,X13: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X13 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X12 ) ) ) )
<=> ( ( s @ X2 @ X12 )
= ( s @ X2 @ X13 ) ) )
& ! [X14: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X14 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) ) )
& ! [X15: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X15 ) ) ) )
& ! [X16: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X16 ) ) )
& ! [X17: u,X18: u] :
( ( s @ X4 @ X17 )
= ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X4 @ X17 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X18 ) ) ) )
& ! [X19: u] :
( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X19 ) ) ) ) ) ) )
& ! [X20: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X4 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X20 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X21: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X21 ) ) )
& ! [X22: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X22 ) ) ) ) )
& ! [X23: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X23 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [X24: u] :
( ( s @ X2 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X24 ) ) ) ) )
= ( s @ X2 @ X24 ) )
& ! [X25: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
<=> ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X25 ) ) ) ) )
& ! [X26: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) ) ) )
=> ( ( s @ X4 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X26 ) @ ( s @ X4 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ X4 ) @ X1 ) ) )
= ( s @ X4 @ X3 ) ) )
& ! [X27: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Eoption_2Eoption @ X2 ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X27 ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,axiom,
! [X19: u,X2: u,X0: d,X20: u,X1: d] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X0 ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [X40: u,X41: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X40 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X41 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X40 ) @ ( s @ X0 @ X41 ) ) ) ) ) )
& ! [X39: u,X37: u,X38: u] :
( ( s @ X1 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X37 ) ) ) @ ( s @ X1 @ X38 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X39 ) ) )
= ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X39 ) @ ( s @ X0 @ X37 ) ) ) )
& ! [X43: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X43 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ X0 ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X43 ) ) ) ) ) )
& ! [X33: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X33 ) ) ) )
=> ( ( s @ X1 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X33 ) @ ( s @ X1 @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X2 ) ) )
= ( s @ X1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X2 ) @ ( s @ X0 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X33 ) ) ) ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
& ! [X21: u,X22: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X21 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X22 ) ) ) )
<=> ( ( s @ X0 @ X21 )
= ( s @ X0 @ X22 ) ) )
& ! [X31: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X31 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X31 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X31 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Eoption_2Eoption @ X0 ) ) @ c_2Eoption_2ESOME_2E0 ) ) ) )
& ! [X24: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X24 ) ) ) )
& ! [X29: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X29 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X29 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X29 ) ) ) ) ) ) )
& ! [X35: u,X36: u] :
( ( s @ X1 @ X35 )
= ( s @ X1 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ X1 @ X35 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X36 ) ) ) )
& ! [X26: u] :
( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X26 ) ) ) ) ) ) )
& ! [X42: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X42 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [X34: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X34 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X34 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X34 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X19 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Eoption_2Eoption @ X0 ) ) @ c_2Eoption_2ESOME_2E0 ) ) ) ) )
& ! [X27: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X27 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X27 ) ) ) ) )
& ! [X25: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X25 ) ) ) )
& ! [X23: u] :
( ( s @ X0 @ X23 )
= ( s @ X0 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X23 ) ) ) ) ) )
& ! [X28: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X28 ) )
<=> ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X28 ) ) ) ) )
& ! [X32: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X32 ) ) ) )
=> ( ( s @ X1 @ X20 )
= ( s @ X1 @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X32 ) @ ( s @ X1 @ X20 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ X1 ) @ X2 ) ) ) ) )
& ! [X30: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X30 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X30 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Eoption_2Eoption @ X0 ) ) @ c_2Eoption_2ESOME_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Eoption_2Eoption__CLAUSES) ).
thf(f882,plain,
( ( ( s @ sK5 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) )
= ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) )
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f192,f811]) ).
thf(f811,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ~ spl7_3 ),
inference(subsumption_resolution,[status(thm)],[f804,f338]) ).
thf(f338,plain,
! [X2: d,X10: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X10 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f337]) ).
thf(f337,plain,
! [X2: d,X10: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X10 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f336]) ).
thf(f336,plain,
! [X2: d,X10: u] :
( ( $true = $false )
| ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X10 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f333]) ).
thf(f333,plain,
! [X2: d,X10: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X10 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
= $false )
| ( $true = ( ~ $true ) ) ),
inference(cases_simplifying,[status(thm)],[f201]) ).
thf(f201,plain,
! [X2: d,X10: u] :
( $true
= ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X10 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
thf(f804,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ~ spl7_3 ),
inference(trivial_inequality_removal,[status(thm)],[f789]) ).
thf(f789,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ( $true != $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f179,f366]) ).
thf(f179,plain,
! [X2: d,X3: u,X0: d,X1: u,X4: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
!= $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( sK1 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
thf(f121,plain,
! [X0: d,X1: u,X2: d,X3: u,X4: u] :
( ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
= $true )
| ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
& ! [X5: u,X6: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
| ( $true
!= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) ) ) ) )
& ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
| ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( sK1 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
& ( ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ ( sK0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) @ ( s @ X2 @ ( sK1 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
= $true )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ ( sK0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f119,f120]) ).
thf(f120,plain,
! [X0: d,X1: u,X2: d,X3: u,X4: u] :
( ? [X7: u,X8: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X8 ) ) ) )
& ( ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X7 ) ) ) @ ( s @ X2 @ X8 ) ) ) )
= $true )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X7 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
=> ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( sK1 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
& ( ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ ( sK0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) @ ( s @ X2 @ ( sK1 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
= $true )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ ( sK0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f119,plain,
! [X0: d,X1: u,X2: d,X3: u,X4: u] :
( ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
= $true )
| ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
& ! [X5: u,X6: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
| ( $true
!= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) ) ) ) )
& ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
| ? [X7: u,X8: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X8 ) ) ) )
& ( ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X7 ) ) ) @ ( s @ X2 @ X8 ) ) ) )
= $true )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X7 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f118]) ).
thf(f118,plain,
! [X0: d,X1: u,X2: d,X3: u,X4: u] :
( ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
= $true )
| ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
& ! [X5: u,X6: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
| ( $true
!= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) ) ) ) )
& ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
| ? [X5: u,X6: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
& ( $true
= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f117]) ).
thf(f117,plain,
! [X0: d,X1: u,X2: d,X3: u,X4: u] :
( ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
= $true )
| ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
& ! [X5: u,X6: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
| ( $true
!= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) ) ) ) )
& ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
| ? [X5: u,X6: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
& ( $true
= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: d,X1: u,X2: d,X3: u,X4: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
= $true )
<=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) )
| ? [X5: u,X6: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
& ( $true
= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: d,X1: u,X2: d,X3: u,X4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
<=> ( ? [X5: u,X6: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) ) )
| ( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,axiom,
! [X0: d,X45: u,X1: d,X12: u,X44: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X44 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X45 ) ) ) )
<=> ( ? [X46: u,X47: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X45 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ X47 ) ) ) )
& ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X44 ) @ ( s @ X0 @ X46 ) ) ) @ ( s @ X1 @ X47 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X12 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X46 ) ) ) ) )
| ( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X12 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X45 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Eoption_2EOPTREL__def) ).
thf(f1003,plain,
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ~ spl7_3 ),
inference(subsumption_resolution,[status(thm)],[f996,f338]) ).
thf(f996,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) ) ) )
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f477,f984]) ).
thf(f984,plain,
( ( ( s @ sK5 @ sK4 )
= ( s @ sK5 @ ( sK0 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) )
| ~ spl7_3 ),
inference(forward_demodulation,[status(thm)],[f946,f192]) ).
thf(f946,plain,
( ( ( s @ sK5 @ ( sK0 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) )
= ( s @ sK5 @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) ) ) )
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f192,f813]) ).
thf(f813,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK0 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) ) )
| ~ spl7_3 ),
inference(subsumption_resolution,[status(thm)],[f802,f338]) ).
thf(f802,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK0 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) ) )
| ~ spl7_3 ),
inference(trivial_inequality_removal,[status(thm)],[f787]) ).
thf(f787,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK0 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) ) )
| ( $true != $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ~ spl7_3 ),
inference(superposition,[status(thm)],[f177,f366]) ).
thf(f177,plain,
! [X2: d,X3: u,X0: d,X1: u,X4: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
!= $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ ( sK0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
thf(f477,plain,
! [X2: u,X3: u,X0: d,X1: d,X4: 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 @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ X0 @ ( sK0 @ X2 @ X3 @ X1 @ X4 @ X0 ) ) ) ) @ ( s @ X1 @ ( sK1 @ X2 @ X3 @ X1 @ X4 @ X0 ) ) ) ) )
= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) ) ) )
= $false )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f476]) ).
thf(f476,plain,
! [X2: u,X3: u,X0: d,X1: d,X4: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) )
| ( $true != $true )
| ( ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ X0 @ ( sK0 @ X2 @ X3 @ X1 @ X4 @ X0 ) ) ) ) @ ( s @ X1 @ ( sK1 @ X2 @ X3 @ X1 @ X4 @ X0 ) ) ) ) )
= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f175,f305]) ).
thf(f175,plain,
! [X2: d,X3: u,X0: d,X1: u,X4: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
!= $true )
| ( ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ ( sK0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) @ ( s @ X2 @ ( sK1 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
= $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
thf(f366,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $true )
| ~ spl7_3 ),
inference(avatar_component_clause,[status(thm)],[f364]) ).
thf(f364,definition,
( spl7_3
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition]) ).
thf(f832,plain,
( ~ spl7_3
| ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f831]) ).
thf(f831,plain,
( $false
| ~ spl7_3
| ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f822]) ).
thf(f822,plain,
( ( $true = $false )
| ~ spl7_3
| ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(backward_demodulation,[status(thm)],[f366,f779]) ).
thf(f779,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f778]) ).
thf(f778,plain,
( ( $true = $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(forward_demodulation,[status(thm)],[f777,f382]) ).
thf(f382,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $true )
| ~ spl7_7 ),
inference(avatar_component_clause,[status(thm)],[f380]) ).
thf(f777,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ~ spl7_4
| ~ spl7_6 ),
inference(subsumption_resolution,[status(thm)],[f776,f493]) ).
thf(f493,plain,
! [X2: u,X0: d,X1: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= $true ),
inference(equality_resolution,[status(thm)],[f401]) ).
thf(f401,plain,
! [X2: d,X3: u,X0: d,X1: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X1 ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X1 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f181]) ).
thf(f181,plain,
! [X2: d,X3: u,X0: d,X1: u,X4: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
thf(f776,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ~ spl7_4
| ~ spl7_6 ),
inference(subsumption_resolution,[status(thm)],[f775,f369]) ).
thf(f369,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ~ spl7_4 ),
inference(avatar_component_clause,[status(thm)],[f368]) ).
thf(f368,definition,
( spl7_4
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition]) ).
thf(f775,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
!= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $true )
| ~ spl7_6 ),
inference(subsumption_resolution,[status(thm)],[f320,f377]) ).
thf(f377,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= $false )
| ~ spl7_6 ),
inference(avatar_component_clause,[status(thm)],[f376]) ).
thf(f376,definition,
( spl7_6
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition]) ).
thf(f320,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
!= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f318]) ).
thf(f318,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
!= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f317]) ).
thf(f317,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
!= ( ~ $true ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $false ) ),
inference(boolean_simplification,[status(thm)],[f262]) ).
thf(f262,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= ( ~ $true ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
!= ( ~ $true ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f226,f227,f170,f227]) ).
thf(f226,plain,
( ( mono_2Ec_2Ebool_2EF
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) )
| ( mono_2Ec_2Ebool_2ET
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ 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 @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
thf(f129,plain,
( ( mono_2Ec_2Ebool_2EF
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) )
| ( mono_2Ec_2Ebool_2ET
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ 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 @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f111,f128]) ).
thf(f128,plain,
( ? [X0: u,X1: u,X2: d,X3: u] :
( ( mono_2Ec_2Ebool_2EF
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X1 ) ) ) @ ( 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 @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X1 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X0 ) ) ) ) ) )
!= ( 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 @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ X2 @ X1 ) ) ) @ ( s @ X2 @ X0 ) ) ) ) )
| ( mono_2Ec_2Ebool_2ET
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ 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 @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X0 ) ) ) ) ) ) ) )
=> ( ( mono_2Ec_2Ebool_2EF
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) )
| ( mono_2Ec_2Ebool_2ET
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ 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 @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f111,plain,
? [X0: u,X1: u,X2: d,X3: u] :
( ( mono_2Ec_2Ebool_2EF
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X1 ) ) ) @ ( 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 @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X1 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X0 ) ) ) ) ) )
!= ( 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 @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ X2 @ X1 ) ) ) @ ( s @ X2 @ X0 ) ) ) ) )
| ( mono_2Ec_2Ebool_2ET
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ 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 @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X0 ) ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f89]) ).
thf(f89,plain,
~ ! [X0: u,X1: u,X2: d,X3: u] :
( ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X1 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ 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 @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X0 ) ) ) ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X1 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X0 ) ) ) ) ) )
= ( 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 @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ X2 @ X1 ) ) ) @ ( s @ X2 @ X0 ) ) ) ) )
& ( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f49]) ).
thf(f49,negated_conjecture,
~ ! [X48: u,X12: u,X0: d,X49: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X12 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X48 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ X0 @ X12 ) ) ) @ ( s @ X0 @ X48 ) ) ) ) )
& ( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ 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 @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X48 ) ) ) ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X12 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
thf(f48,conjecture,
! [X48: u,X12: u,X0: d,X49: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X12 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X48 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ X0 @ X12 ) ) ) @ ( s @ X0 @ X48 ) ) ) ) )
& ( mono_2Ec_2Ebool_2ET
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ 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 @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X48 ) ) ) ) ) ) )
& ( mono_2Ec_2Ebool_2EF
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) ) @ X49 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X12 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Equotient__option_2EOPTION__REL__def) ).
thf(f774,plain,
( spl7_3
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f773]) ).
thf(f773,plain,
( $false
| spl7_3
| ~ spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f772]) ).
thf(f772,plain,
( ( $true = $false )
| spl7_3
| ~ spl7_7 ),
inference(forward_demodulation,[status(thm)],[f771,f394]) ).
thf(f394,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| spl7_3 ),
inference(trivial_inequality_removal,[status(thm)],[f393]) ).
thf(f393,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $false )
| ( $true != $true )
| spl7_3 ),
inference(superposition,[status(thm)],[f365,f305]) ).
thf(f365,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
!= $true )
| spl7_3 ),
inference(avatar_component_clause,[status(thm)],[f364]) ).
thf(f771,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $true )
| ~ spl7_7 ),
inference(equality_resolution,[status(thm)],[f766]) ).
thf(f766,plain,
( ! [X0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X0 ) ) ) ) ) )
| ~ spl7_7 ),
inference(equality_resolution,[status(thm)],[f761]) ).
thf(f761,plain,
( ! [X0: u,X1: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X1 ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X1 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X0 ) ) ) )
= $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) )
| ~ spl7_7 ),
inference(trivial_inequality_removal,[status(thm)],[f760]) ).
thf(f760,plain,
( ! [X0: u,X1: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X1 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X0 ) ) ) )
= $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X1 ) )
| ( $true != $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ X0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) )
| ~ spl7_7 ),
inference(superposition,[status(thm)],[f180,f382]) ).
thf(f180,plain,
! [X2: d,X3: u,X0: d,X1: u,X6: u,X4: u,X5: u] :
( ( $true
!= ( 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 @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ X0 @ X5 ) ) ) @ ( s @ X2 @ X6 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ X6 ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
!= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ X5 ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
thf(f759,plain,
spl7_5,
inference(avatar_contradiction_clause,[status(thm)],[f758]) ).
thf(f758,plain,
( $false
| spl7_5 ),
inference(trivial_inequality_removal,[status(thm)],[f740]) ).
thf(f740,plain,
( ( $true = $false )
| spl7_5 ),
inference(superposition,[status(thm)],[f493,f385]) ).
thf(f385,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= $false )
| spl7_5 ),
inference(trivial_inequality_removal,[status(thm)],[f384]) ).
thf(f384,plain,
( ( $true != $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= $false )
| spl7_5 ),
inference(superposition,[status(thm)],[f374,f305]) ).
thf(f374,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $true )
| spl7_5 ),
inference(avatar_component_clause,[status(thm)],[f372]) ).
thf(f372,definition,
( spl7_5
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition]) ).
thf(f613,plain,
spl7_4,
inference(avatar_contradiction_clause,[status(thm)],[f612]) ).
thf(f612,plain,
( $false
| spl7_4 ),
inference(subsumption_resolution,[status(thm)],[f611,f338]) ).
thf(f611,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| spl7_4 ),
inference(subsumption_resolution,[status(thm)],[f607,f338]) ).
thf(f607,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK0 @ sK6 @ c_2Eoption_2ENONE_2E0 @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| spl7_4 ),
inference(trivial_inequality_removal,[status(thm)],[f597]) ).
thf(f597,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) )
| ( $false != $false )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK0 @ sK6 @ c_2Eoption_2ENONE_2E0 @ sK5 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) @ sK5 ) ) ) ) )
| spl7_4 ),
inference(superposition,[status(thm)],[f370,f441]) ).
thf(f441,plain,
! [X2: u,X3: u,X0: d,X1: d,X4: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) ) ) )
= $false )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ ( sK0 @ X2 @ X3 @ X1 @ X4 @ X0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f440]) ).
thf(f440,plain,
! [X2: u,X3: u,X0: d,X1: d,X4: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X0 @ ( sK0 @ X2 @ X3 @ X1 @ X4 @ X0 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) ) ) )
= $false )
| ( $true != $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) ) ),
inference(superposition,[status(thm)],[f177,f305]) ).
thf(f370,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
!= $false )
| spl7_4 ),
inference(avatar_component_clause,[status(thm)],[f368]) ).
thf(f581,plain,
spl7_6,
inference(avatar_contradiction_clause,[status(thm)],[f580]) ).
thf(f580,plain,
( $false
| spl7_6 ),
inference(subsumption_resolution,[status(thm)],[f579,f338]) ).
thf(f579,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) )
| spl7_6 ),
inference(subsumption_resolution,[status(thm)],[f574,f338]) ).
thf(f574,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ c_2Eoption_2ENONE_2E0 @ sK5 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) )
| spl7_6 ),
inference(trivial_inequality_removal,[status(thm)],[f565]) ).
thf(f565,plain,
( ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ ( sK1 @ sK6 @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) @ sK5 @ c_2Eoption_2ENONE_2E0 @ sK5 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) )
| ( $false != $false )
| spl7_6 ),
inference(superposition,[status(thm)],[f378,f418]) ).
thf(f418,plain,
! [X2: u,X3: u,X0: d,X1: d,X4: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) ) ) )
= $false )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( sK1 @ X2 @ X3 @ X1 @ X4 @ X0 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f417]) ).
thf(f417,plain,
! [X2: u,X3: u,X0: d,X1: d,X4: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool ) ) @ X2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) ) ) )
= $false )
| ( $true != $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X1 @ ( sK1 @ X2 @ X3 @ X1 @ X4 @ X0 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ X1 ) @ X4 ) ) ),
inference(superposition,[status(thm)],[f176,f305]) ).
thf(f176,plain,
! [X2: d,X3: u,X0: d,X1: u,X4: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) ) @ X4 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) @ ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 ) ) ) )
!= $true )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ X1 )
= ( s @ ( tyop_2Eoption_2Eoption @ X2 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ X2 @ ( sK1 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
| ( ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ X0 ) @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
thf(f378,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $false )
| spl7_6 ),
inference(avatar_component_clause,[status(thm)],[f376]) ).
thf(f383,plain,
( spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6
| spl7_7 ),
inference(avatar_split_clause,[status(thm)],[f319,f380,f376,f372,f368,f364]) ).
thf(f319,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK3 ) ) ) ) ) )
!= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sK5 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK5 @ ( tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool ) ) @ sK6 ) @ ( s @ sK5 @ sK4 ) ) ) @ ( s @ sK5 @ sK3 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP011^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 08:19:30 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 ---- Original DTF file ---
% 0.15/0.34 thf(spec,logic,$$dhol).
% 0.15/0.34 %------------------------------------------------------------------------------
% 0.15/0.34 % File : ITP011^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.15/0.34 % Domain : Interactive Theorem Proving
% 0.15/0.34 % Problem : HOL4 syntactic export of thm_2Equotient__option_2EOPTION__REL__def.p, bushy mode
% 0.15/0.34 % Version : [BG+19] axioms.
% 0.15/0.34 % English :
% 0.15/0.34
% 0.15/0.34 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.15/0.34 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.15/0.34 % Source : [BG+19]
% 0.15/0.34 % Names : thm_2Equotient__option_2EOPTION__REL__def.p [Gau19]
% 0.15/0.34 % : HL405001^1.p [TPAP]
% 0.15/0.34
% 0.15/0.34 % Status : Theorem
% 0.15/0.34 % Rating : 0.56 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.45 v7.5.0
% 0.15/0.34 % Syntax : Number of formulae : 106 ( 33 unt; 58 typ; 0 def)
% 0.15/0.34 % Number of atoms : 147 ( 66 equ; 10 cnn)
% 0.15/0.34 % Maximal formula atoms : 30 ( 3 avg)
% 0.15/0.34 % Number of connectives : 1446 ( 10 ~; 7 |; 44 &;1343 @)
% 0.15/0.34 % ( 31 <=>; 11 =>; 0 <=; 0 <~>)
% 0.15/0.34 % Maximal formula depth : 28 ( 6 avg)
% 0.15/0.34 % Number of types : 4 ( 3 usr)
% 0.15/0.34 % Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% 0.15/0.34 % Number of symbols : 57 ( 55 usr; 25 con; 0-3 aty)
% 0.15/0.34 % Number of variables : 141 ( 0 ^; 137 !; 4 ?; 141 :)
% 0.15/0.34 % SPC : TH0_THM_EQU_NAR
% 0.15/0.34
% 0.15/0.34 % Comments :
% 0.15/0.34 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.15/0.34 %------------------------------------------------------------------------------
% 0.15/0.34 thf(u,type,
% 0.15/0.34 u: $tType ).
% 0.15/0.34
% 0.15/0.34 thf(d,type,
% 0.15/0.34 d: $tType ).
% 0.15/0.34
% 0.15/0.34 thf(du,type,
% 0.15/0.34 du: $tType ).
% 0.15/0.34
% 0.15/0.34 thf(tyop_2Emin_2Ebool,type,
% 0.15/0.34 tyop_2Emin_2Ebool: d ).
% 0.15/0.34
% 0.15/0.34 thf(tyop_2Emin_2Efun,type,
% 0.15/0.34 tyop_2Emin_2Efun: d > d > d ).
% 0.15/0.34
% 0.15/0.34 thf(tyop_2Eoption_2Eoption,type,
% 0.15/0.34 tyop_2Eoption_2Eoption: d > d ).
% 0.15/0.34
% 0.15/0.34 thf(s,type,
% 0.15/0.34 s: d > u > du ).
% 0.15/0.34
% 0.15/0.34 thf(app_2E2,type,
% 0.15/0.34 app_2E2: du > du > u ).
% 0.15/0.34
% 0.15/0.34 thf(combin_i_2E0,type,
% 0.15/0.34 combin_i_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(combin_k_2E0,type,
% 0.15/0.34 combin_k_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(combin_s_2E0,type,
% 0.15/0.34 combin_s_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_21_2E0,type,
% 0.15/0.34 c_2Ebool_2E_21_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_21_2E1,type,
% 0.15/0.34 c_2Ebool_2E_21_2E1: du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.15/0.34 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.15/0.34 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Emin_2E_3D_2E0,type,
% 0.15/0.34 c_2Emin_2E_3D_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Emin_2E_3D_2E2,type,
% 0.15/0.34 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.15/0.34 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.15/0.34 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_3F_2E0,type,
% 0.15/0.34 c_2Ebool_2E_3F_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_3F_2E1,type,
% 0.15/0.34 c_2Ebool_2E_3F_2E1: du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2EF_2E0,type,
% 0.15/0.34 c_2Ebool_2EF_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EIS__NONE_2E0,type,
% 0.15/0.34 c_2Eoption_2EIS__NONE_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EIS__NONE_2E1,type,
% 0.15/0.34 c_2Eoption_2EIS__NONE_2E1: du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EIS__SOME_2E0,type,
% 0.15/0.34 c_2Eoption_2EIS__SOME_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EIS__SOME_2E1,type,
% 0.15/0.34 c_2Eoption_2EIS__SOME_2E1: du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2ENONE_2E0,type,
% 0.15/0.34 c_2Eoption_2ENONE_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EOPTION__JOIN_2E0,type,
% 0.15/0.34 c_2Eoption_2EOPTION__JOIN_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EOPTION__JOIN_2E1,type,
% 0.15/0.34 c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EOPTION__MAP_2E0,type,
% 0.15/0.34 c_2Eoption_2EOPTION__MAP_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EOPTION__MAP_2E2,type,
% 0.15/0.34 c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EOPTREL_2E0,type,
% 0.15/0.34 c_2Eoption_2EOPTREL_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2EOPTREL_2E3,type,
% 0.15/0.34 c_2Eoption_2EOPTREL_2E3: du > du > du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2ESOME_2E0,type,
% 0.15/0.34 c_2Eoption_2ESOME_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2ESOME_2E1,type,
% 0.15/0.34 c_2Eoption_2ESOME_2E1: du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2ET_2E0,type,
% 0.15/0.34 c_2Ebool_2ET_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2ETHE_2E0,type,
% 0.15/0.34 c_2Eoption_2ETHE_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2ETHE_2E1,type,
% 0.15/0.34 c_2Eoption_2ETHE_2E1: du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.15/0.34 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.15/0.34 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2Eoption__CASE_2E0,type,
% 0.15/0.34 c_2Eoption_2Eoption__CASE_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Eoption_2Eoption__CASE_2E3,type,
% 0.15/0.34 c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_7E_2E0,type,
% 0.15/0.34 c_2Ebool_2E_7E_2E0: u ).
% 0.15/0.34
% 0.15/0.34 thf(c_2Ebool_2E_7E_2E1,type,
% 0.15/0.34 c_2Ebool_2E_7E_2E1: du > u ).
% 0.15/0.34
% 0.15/0.34 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.15/0.34 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.15/0.34
% 0.15/0.34 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.15/0.34 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.15/0.34
% 0.15/0.34 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.15/0.34 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.15/0.34
% 0.15/0.34 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.15/0.34 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.15/0.34
% 0.15/0.34 thf(mono_2Ec_2Ebool_2EF,type,
% 0.15/0.34 mono_2Ec_2Ebool_2EF: $o ).
% 0.15/0.34
% 0.15/0.34 thf(mono_2Ec_2Ebool_2ET,type,
% 0.15/0.34 mono_2Ec_2Ebool_2ET: $o ).
% 0.15/0.34
% 0.15/0.34 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.15/0.34 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.15/0.34
% 0.15/0.34 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.15/0.34 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.15/0.34
% 0.15/0.34 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.15/0.34 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.15/0.34
% 0.15/0.34 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.15/0.34 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.15/0.34
% 0.15/0.34 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.15/0.34 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.15/0.34
% 0.15/0.34 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.15/0.34 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.15/0.34
% 0.15/0.34 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.15/0.34 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.15/0.34
% 0.15/0.34 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.15/0.34 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.15/0.34 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.15/0.34 ( ! [V2x_2E0: u] :
% 0.15/0.34 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.15/0.34 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.15/0.34 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.15/0.34 ! [A_27a: d,V0x_2E0: u] :
% 0.15/0.34 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.15/0.34 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.15/0.34 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Eho_2Es__thm,axiom,
% 0.15/0.34 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.15/0.34 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.15/0.34 ! [V0: $o,V1: $o] :
% 0.15/0.34 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.15/0.34 <=> ( V0
% 0.15/0.34 & V1 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.15/0.34 ! [V0: $o,V1: $o] :
% 0.15/0.34 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.15/0.34 <=> ( V0
% 0.15/0.34 | V1 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Elogic_2E_7E,axiom,
% 0.15/0.34 ! [V0: $o] :
% 0.15/0.34 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.15/0.34 <=> ( (~) @ V0 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.15/0.34 ! [V0: $o,V1: $o] :
% 0.15/0.34 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.15/0.34 <=> ( V0
% 0.15/0.34 => V1 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Elogic_2E_3D,axiom,
% 0.15/0.34 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.15/0.34 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.15/0.34 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Equant_2E_21,axiom,
% 0.15/0.34 ! [A_27a: d,V0f_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.15/0.34 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(reserved_2Equant_2E_3F,axiom,
% 0.15/0.34 ! [A_27a: d,V0f_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.15/0.34 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.15/0.34 ! [V0_2E0: u] :
% 0.15/0.34 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.15/0.34 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.15/0.34 ! [V0_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.15/0.34 ! [V0_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.15/0.34 ! [V0: $o] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.15/0.34 = V0 ) ).
% 0.15/0.34
% 0.15/0.34 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.15/0.34 ! [V0: $o > $o] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.15/0.34 = V0 ) ).
% 0.15/0.34
% 0.15/0.34 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.15/0.34 ! [V0: $o > $o > $o] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.15/0.34 = V0 ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.15/0.34 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.15/0.34 ( ( ( s @ A_27a @ X0_2E0 )
% 0.15/0.34 = ( s @ A_27a @ X1_2E0 ) )
% 0.15/0.34 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.15/0.34 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) )
% 0.15/0.34 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__NONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) )
% 0.15/0.34 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.15/0.34 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) )
% 0.15/0.34 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.15/0.34 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) )
% 0.15/0.34 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
% 0.15/0.34 ! [A_27b: d,X0_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u] :
% 0.15/0.34 ( ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ A_27a ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.15/0.34 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 0.15/0.34 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
% 0.15/0.34 ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.15/0.34 ! [V0: $o > $o,V1: $o] :
% 0.15/0.34 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.15/0.34 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.15/0.34 ! [V0: $o > $o > $o,V1: $o] :
% 0.15/0.34 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.15/0.34 ! [V0: $o > $o,V1: $o] :
% 0.15/0.34 ( ( V0 @ V1 )
% 0.15/0.34 = ( V0 @ V1 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.15/0.34 ! [V0: $o > $o > $o,V1: $o] :
% 0.15/0.34 ( ( V0 @ V1 )
% 0.15/0.34 = ( V0 @ V1 ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.15/0.34 mono_2Ec_2Ebool_2ET ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.15/0.34 ! [V0t1: $o,V1t2: $o] :
% 0.15/0.34 ( ( V0t1
% 0.15/0.34 => V1t2 )
% 0.15/0.34 => ( ( V1t2
% 0.15/0.34 => V0t1 )
% 0.15/0.34 => ( V0t1 = V1t2 ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2EFALSITY,axiom,
% 0.15/0.34 ! [V0t: $o] :
% 0.15/0.34 ( mono_2Ec_2Ebool_2EF
% 0.15/0.34 => V0t ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2EEXISTS__SIMP,axiom,
% 0.15/0.34 ! [A_27a: d,V0t: $o] :
% 0.15/0.34 ( ? [V1x_2E0: u] : V0t
% 0.15/0.34 <=> V0t ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2EAND__CLAUSES,axiom,
% 0.15/0.34 ! [V0t: $o] :
% 0.15/0.34 ( ( ( mono_2Ec_2Ebool_2ET
% 0.15/0.34 & V0t )
% 0.15/0.34 <=> V0t )
% 0.15/0.34 & ( ( V0t
% 0.15/0.34 & mono_2Ec_2Ebool_2ET )
% 0.15/0.34 <=> V0t )
% 0.15/0.34 & ( ( mono_2Ec_2Ebool_2EF
% 0.15/0.34 & V0t )
% 0.15/0.34 <=> mono_2Ec_2Ebool_2EF )
% 0.15/0.34 & ( ( V0t
% 0.15/0.34 & mono_2Ec_2Ebool_2EF )
% 0.15/0.34 <=> mono_2Ec_2Ebool_2EF )
% 0.15/0.34 & ( ( V0t
% 0.15/0.34 & V0t )
% 0.15/0.34 <=> V0t ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2EOR__CLAUSES,axiom,
% 0.15/0.34 ! [V0t: $o] :
% 0.15/0.34 ( ( ( mono_2Ec_2Ebool_2ET
% 0.15/0.34 | V0t )
% 0.15/0.34 <=> mono_2Ec_2Ebool_2ET )
% 0.15/0.34 & ( ( V0t
% 0.15/0.34 | mono_2Ec_2Ebool_2ET )
% 0.15/0.34 <=> mono_2Ec_2Ebool_2ET )
% 0.15/0.34 & ( ( mono_2Ec_2Ebool_2EF
% 0.15/0.34 | V0t )
% 0.15/0.34 <=> V0t )
% 0.15/0.34 & ( ( V0t
% 0.15/0.34 | mono_2Ec_2Ebool_2EF )
% 0.15/0.34 <=> V0t )
% 0.15/0.34 & ( ( V0t
% 0.15/0.34 | V0t )
% 0.15/0.34 <=> V0t ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.15/0.34 ( ! [V0t: $o] :
% 0.15/0.34 ( ( (~) @ ( (~) @ V0t ) )
% 0.15/0.34 <=> V0t )
% 0.15/0.34 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 0.15/0.34 <=> mono_2Ec_2Ebool_2EF )
% 0.15/0.34 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 0.15/0.34 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.15/0.34 ! [A_27a: d,V0x_2E0: u] :
% 0.15/0.34 ( ( ( s @ A_27a @ V0x_2E0 )
% 0.15/0.34 = ( s @ A_27a @ V0x_2E0 ) )
% 0.15/0.34 <=> mono_2Ec_2Ebool_2ET ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.15/0.34 ! [V0t: $o] :
% 0.15/0.34 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 0.15/0.34 <=> V0t )
% 0.15/0.34 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 0.15/0.34 <=> V0t )
% 0.15/0.34 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 0.15/0.34 <=> ( (~) @ V0t ) )
% 0.15/0.34 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 0.15/0.34 <=> ( (~) @ V0t ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Eoption_2Eoption__CLAUSES,axiom,
% 0.15/0.34 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1e_2E0: u,V2e_2E0: u] :
% 0.15/0.34 ( ! [V3x_2E0: u,V4y_2E0: u] :
% 0.15/0.34 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4y_2E0 ) ) ) )
% 0.15/0.34 <=> ( ( s @ A_27a @ V3x_2E0 )
% 0.15/0.34 = ( s @ A_27a @ V4y_2E0 ) ) )
% 0.15/0.34 & ! [V5x_2E0: u] :
% 0.15/0.34 ( ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) ) )
% 0.15/0.34 = ( s @ A_27a @ V5x_2E0 ) )
% 0.15/0.34 & ! [V6x_2E0: u] :
% 0.15/0.34 ( (~)
% 0.15/0.34 @ ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6x_2E0 ) ) ) ) )
% 0.15/0.34 & ! [V7x_2E0: u] :
% 0.15/0.34 ( (~)
% 0.15/0.34 @ ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7x_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.15/0.34 & ! [V8x_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V8x_2E0 ) ) ) ) ) )
% 0.15/0.34 = mono_2Ec_2Ebool_2ET )
% 0.15/0.34 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 0.15/0.34 = mono_2Ec_2Ebool_2EF )
% 0.15/0.34 & ! [V9x_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 ) ) ) )
% 0.15/0.34 <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.15/0.34 & ! [V10x_2E0: u] :
% 0.15/0.34 ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 ) ) ) ) )
% 0.15/0.34 <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.15/0.34 & ! [V11x_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) )
% 0.15/0.34 => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) )
% 0.15/0.34 & ! [V12x_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) )
% 0.15/0.34 & ! [V13x_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) )
% 0.15/0.34 & ! [V14x_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) ) ) )
% 0.15/0.34 => ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) @ ( s @ A_27b @ V2e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27b @ V2e_2E0 ) ) )
% 0.15/0.34 & ! [V15x_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) )
% 0.15/0.34 => ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) @ ( s @ A_27b @ V2e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) ) ) ) )
% 0.15/0.34 & ! [V16x_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) ) )
% 0.15/0.34 => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) )
% 0.15/0.34 & ! [V17v_2E0: u,V18f_2E0: u] :
% 0.15/0.34 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ A_27b @ V17v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V18f_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27b @ V17v_2E0 ) )
% 0.15/0.34 & ! [V19x_2E0: u,V20v_2E0: u,V21f_2E0: u] :
% 0.15/0.34 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V19x_2E0 ) ) ) @ ( s @ A_27b @ V20v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) ) )
% 0.15/0.34 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) @ ( s @ A_27a @ V19x_2E0 ) ) ) )
% 0.15/0.34 & ! [V22f_2E0: u,V23x_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V23x_2E0 ) ) ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ ( s @ A_27a @ V23x_2E0 ) ) ) ) ) )
% 0.15/0.34 & ! [V24f_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V24f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) )
% 0.15/0.34 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
% 0.15/0.34 & ! [V25x_2E0: u] :
% 0.15/0.34 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) ) )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Eoption_2EOPTREL__def,axiom,
% 0.15/0.34 ! [A_27a: d,A_27b: d,V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
% 0.15/0.34 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) ) ) )
% 0.15/0.34 <=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
% 0.15/0.34 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 0.15/0.34 | ? [V3x0_2E0: u,V4y0_2E0: u] :
% 0.15/0.34 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x0_2E0 ) ) ) )
% 0.15/0.34 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 )
% 0.15/0.34 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V4y0_2E0 ) ) ) )
% 0.15/0.34 & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) @ ( s @ A_27b @ V4y0_2E0 ) ) ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 thf(thm_2Equotient__option_2EOPTION__REL__def,conjecture,
% 0.15/0.34 ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2R_2E0: u] :
% 0.15/0.34 ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 0.15/0.34 = mono_2Ec_2Ebool_2ET )
% 0.15/0.34 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 0.15/0.34 = mono_2Ec_2Ebool_2EF )
% 0.15/0.34 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) )
% 0.15/0.34 = mono_2Ec_2Ebool_2EF )
% 0.15/0.34 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) )
% 0.15/0.34 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) ).
% 0.15/0.34
% 0.15/0.34 %------------------------------------------------------------------------------
% 0.15/0.34 ------------------------
% 1.45/1.10 ---- Embedded in THF ---
% 1.45/1.10 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.10 %%% Generated on Tue Feb 24 08:19:31 EST 2026
% 1.45/1.10 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.10 %%% Logic specification used:
% 1.45/1.10 %%% thf(spec, logic, $$dhol).
% 1.45/1.10
% 1.45/1.10 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2DTF17206.p
% See solution above
% 1.45/1.10 ------------------------
% 1.64/1.12 ---- Cleaned THF ---
% 1.64/1.12 thf(u,type,
% 1.64/1.12 u: $tType ).
% 1.64/1.12
% 1.64/1.12 thf(d,type,
% 1.64/1.12 d: $tType ).
% 1.64/1.12
% 1.64/1.12 thf(du,type,
% 1.64/1.12 du: $tType ).
% 1.64/1.12
% 1.64/1.12 thf(tyop_2Emin_2Ebool,type,
% 1.64/1.12 tyop_2Emin_2Ebool: d ).
% 1.64/1.12
% 1.64/1.12 thf(tyop_2Emin_2Efun,type,
% 1.64/1.12 tyop_2Emin_2Efun: d > d > d ).
% 1.64/1.12
% 1.64/1.12 thf(tyop_2Eoption_2Eoption,type,
% 1.64/1.12 tyop_2Eoption_2Eoption: d > d ).
% 1.64/1.12
% 1.64/1.12 thf(s,type,
% 1.64/1.12 s: d > u > du ).
% 1.64/1.12
% 1.64/1.12 thf(app_2E2,type,
% 1.64/1.12 app_2E2: du > du > u ).
% 1.64/1.12
% 1.64/1.12 thf(combin_i_2E0,type,
% 1.64/1.12 combin_i_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(combin_k_2E0,type,
% 1.64/1.12 combin_k_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(combin_s_2E0,type,
% 1.64/1.12 combin_s_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_21_2E0,type,
% 1.64/1.12 c_2Ebool_2E_21_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_21_2E1,type,
% 1.64/1.12 c_2Ebool_2E_21_2E1: du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 1.64/1.12 c_2Ebool_2E_2F_5C_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 1.64/1.12 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Emin_2E_3D_2E0,type,
% 1.64/1.12 c_2Emin_2E_3D_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Emin_2E_3D_2E2,type,
% 1.64/1.12 c_2Emin_2E_3D_2E2: du > du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 1.64/1.12 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 1.64/1.12 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_3F_2E0,type,
% 1.64/1.12 c_2Ebool_2E_3F_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_3F_2E1,type,
% 1.64/1.12 c_2Ebool_2E_3F_2E1: du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2EF_2E0,type,
% 1.64/1.12 c_2Ebool_2EF_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EIS__NONE_2E0,type,
% 1.64/1.12 c_2Eoption_2EIS__NONE_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EIS__NONE_2E1,type,
% 1.64/1.12 c_2Eoption_2EIS__NONE_2E1: du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EIS__SOME_2E0,type,
% 1.64/1.12 c_2Eoption_2EIS__SOME_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EIS__SOME_2E1,type,
% 1.64/1.12 c_2Eoption_2EIS__SOME_2E1: du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2ENONE_2E0,type,
% 1.64/1.12 c_2Eoption_2ENONE_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EOPTION__JOIN_2E0,type,
% 1.64/1.12 c_2Eoption_2EOPTION__JOIN_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EOPTION__JOIN_2E1,type,
% 1.64/1.12 c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EOPTION__MAP_2E0,type,
% 1.64/1.12 c_2Eoption_2EOPTION__MAP_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EOPTION__MAP_2E2,type,
% 1.64/1.12 c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EOPTREL_2E0,type,
% 1.64/1.12 c_2Eoption_2EOPTREL_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2EOPTREL_2E3,type,
% 1.64/1.12 c_2Eoption_2EOPTREL_2E3: du > du > du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2ESOME_2E0,type,
% 1.64/1.12 c_2Eoption_2ESOME_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2ESOME_2E1,type,
% 1.64/1.12 c_2Eoption_2ESOME_2E1: du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2ET_2E0,type,
% 1.64/1.12 c_2Ebool_2ET_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2ETHE_2E0,type,
% 1.64/1.12 c_2Eoption_2ETHE_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2ETHE_2E1,type,
% 1.64/1.12 c_2Eoption_2ETHE_2E1: du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 1.64/1.12 c_2Ebool_2E_5C_2F_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 1.64/1.12 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2Eoption__CASE_2E0,type,
% 1.64/1.12 c_2Eoption_2Eoption__CASE_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Eoption_2Eoption__CASE_2E3,type,
% 1.64/1.12 c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_7E_2E0,type,
% 1.64/1.12 c_2Ebool_2E_7E_2E0: u ).
% 1.64/1.12
% 1.64/1.12 thf(c_2Ebool_2E_7E_2E1,type,
% 1.64/1.12 c_2Ebool_2E_7E_2E1: du > u ).
% 1.64/1.12
% 1.64/1.12 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 1.64/1.12 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 1.64/1.12
% 1.64/1.12 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 1.64/1.12 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 1.64/1.12
% 1.64/1.12 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 1.64/1.12 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 1.64/1.12
% 1.64/1.12 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 1.64/1.12 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 1.64/1.12
% 1.64/1.12 thf(mono_2Ec_2Ebool_2EF,type,
% 1.64/1.12 mono_2Ec_2Ebool_2EF: $o ).
% 1.64/1.12
% 1.64/1.12 thf(mono_2Ec_2Ebool_2ET,type,
% 1.64/1.12 mono_2Ec_2Ebool_2ET: $o ).
% 1.64/1.12
% 1.64/1.12 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 1.64/1.12 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 1.64/1.12
% 1.64/1.12 thf(mono_2Ec_2Ebool_2E_7E,type,
% 1.64/1.12 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 1.64/1.12
% 1.64/1.12 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 1.64/1.12 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 1.64/1.12
% 1.64/1.12 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 1.64/1.12 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 1.64/1.12
% 1.64/1.12 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 1.64/1.12 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 1.64/1.12
% 1.64/1.12 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 1.64/1.12 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 1.64/1.12
% 1.64/1.12 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 1.64/1.12 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 1.64/1.12
% 1.64/1.12 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 1.64/1.12 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Eho_2Eeq__ext,axiom,
% 1.64/1.12 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 1.64/1.12 ( ! [V2x_2E0: u] :
% 1.64/1.12 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 1.64/1.12 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 1.64/1.12 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Eho_2Ei__thm,axiom,
% 1.64/1.12 ! [A_27a: d,V0x_2E0: u] :
% 1.64/1.12 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Eho_2Ek__thm,axiom,
% 1.64/1.12 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 1.64/1.12 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Eho_2Es__thm,axiom,
% 1.64/1.12 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 1.64/1.12 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 1.64/1.12 ! [V0: $o,V1: $o] :
% 1.64/1.12 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 1.64/1.12 <=> ( V0
% 1.64/1.12 & V1 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 1.64/1.12 ! [V0: $o,V1: $o] :
% 1.64/1.12 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 1.64/1.12 <=> ( V0
% 1.64/1.12 | V1 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Elogic_2E_7E,axiom,
% 1.64/1.12 ! [V0: $o] :
% 1.64/1.12 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 1.64/1.12 <=> ( (~) @ V0 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 1.64/1.12 ! [V0: $o,V1: $o] :
% 1.64/1.12 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 1.64/1.12 <=> ( V0
% 1.64/1.12 => V1 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Elogic_2E_3D,axiom,
% 1.64/1.12 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 1.64/1.12 <=> ( ( s @ A_27a @ V0_2E0 )
% 1.64/1.12 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Equant_2E_21,axiom,
% 1.64/1.12 ! [A_27a: d,V0f_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 1.64/1.12 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(reserved_2Equant_2E_3F,axiom,
% 1.64/1.12 ! [A_27a: d,V0f_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 1.64/1.12 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 1.64/1.12 ! [V0_2E0: u] :
% 1.64/1.12 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 1.64/1.12 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 1.64/1.12 ! [V0_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 1.64/1.12 ! [V0_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 1.64/1.12 ! [V0: $o] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 1.64/1.12 = V0 ) ).
% 1.64/1.12
% 1.64/1.12 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 1.64/1.12 ! [V0: $o > $o] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 1.64/1.12 = V0 ) ).
% 1.64/1.12
% 1.64/1.12 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 1.64/1.12 ! [V0: $o > $o > $o] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 1.64/1.12 = V0 ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 1.64/1.12 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 1.64/1.12 ( ( ( s @ A_27a @ X0_2E0 )
% 1.64/1.12 = ( s @ A_27a @ X1_2E0 ) )
% 1.64/1.12 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 1.64/1.12 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) )
% 1.64/1.12 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__NONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) )
% 1.64/1.12 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 1.64/1.12 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) )
% 1.64/1.12 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 1.64/1.12 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) )
% 1.64/1.12 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
% 1.64/1.12 ! [A_27b: d,X0_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u] :
% 1.64/1.12 ( ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ A_27a ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 1.64/1.12 ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 1.64/1.12 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ A_27b ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
% 1.64/1.12 ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 1.64/1.12 ! [V0: $o > $o,V1: $o] :
% 1.64/1.12 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 1.64/1.12 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 1.64/1.12 ! [V0: $o > $o > $o,V1: $o] :
% 1.64/1.12 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 1.64/1.12 ! [V0: $o > $o,V1: $o] :
% 1.64/1.12 ( ( V0 @ V1 )
% 1.64/1.12 = ( V0 @ V1 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 1.64/1.12 ! [V0: $o > $o > $o,V1: $o] :
% 1.64/1.12 ( ( V0 @ V1 )
% 1.64/1.12 = ( V0 @ V1 ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2ETRUTH,axiom,
% 1.64/1.12 mono_2Ec_2Ebool_2ET ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 1.64/1.12 ! [V0t1: $o,V1t2: $o] :
% 1.64/1.12 ( ( V0t1
% 1.64/1.12 => V1t2 )
% 1.64/1.12 => ( ( V1t2
% 1.64/1.12 => V0t1 )
% 1.64/1.12 => ( V0t1 = V1t2 ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2EFALSITY,axiom,
% 1.64/1.12 ! [V0t: $o] :
% 1.64/1.12 ( mono_2Ec_2Ebool_2EF
% 1.64/1.12 => V0t ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2EEXISTS__SIMP,axiom,
% 1.64/1.12 ! [A_27a: d,V0t: $o] :
% 1.64/1.12 ( ? [V1x_2E0: u] : V0t
% 1.64/1.12 <=> V0t ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2EAND__CLAUSES,axiom,
% 1.64/1.12 ! [V0t: $o] :
% 1.64/1.12 ( ( ( mono_2Ec_2Ebool_2ET
% 1.64/1.12 & V0t )
% 1.64/1.12 <=> V0t )
% 1.64/1.12 & ( ( V0t
% 1.64/1.12 & mono_2Ec_2Ebool_2ET )
% 1.64/1.12 <=> V0t )
% 1.64/1.12 & ( ( mono_2Ec_2Ebool_2EF
% 1.64/1.12 & V0t )
% 1.64/1.12 <=> mono_2Ec_2Ebool_2EF )
% 1.64/1.12 & ( ( V0t
% 1.64/1.12 & mono_2Ec_2Ebool_2EF )
% 1.64/1.12 <=> mono_2Ec_2Ebool_2EF )
% 1.64/1.12 & ( ( V0t
% 1.64/1.12 & V0t )
% 1.64/1.12 <=> V0t ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2EOR__CLAUSES,axiom,
% 1.64/1.12 ! [V0t: $o] :
% 1.64/1.12 ( ( ( mono_2Ec_2Ebool_2ET
% 1.64/1.12 | V0t )
% 1.64/1.12 <=> mono_2Ec_2Ebool_2ET )
% 1.64/1.12 & ( ( V0t
% 1.64/1.12 | mono_2Ec_2Ebool_2ET )
% 1.64/1.12 <=> mono_2Ec_2Ebool_2ET )
% 1.64/1.12 & ( ( mono_2Ec_2Ebool_2EF
% 1.64/1.12 | V0t )
% 1.64/1.12 <=> V0t )
% 1.64/1.12 & ( ( V0t
% 1.64/1.12 | mono_2Ec_2Ebool_2EF )
% 1.64/1.12 <=> V0t )
% 1.64/1.12 & ( ( V0t
% 1.64/1.12 | V0t )
% 1.64/1.12 <=> V0t ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 1.64/1.12 ( ! [V0t: $o] :
% 1.64/1.12 ( ( (~) @ ( (~) @ V0t ) )
% 1.64/1.12 <=> V0t )
% 1.64/1.12 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 1.64/1.12 <=> mono_2Ec_2Ebool_2EF )
% 1.64/1.12 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 1.64/1.12 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 1.64/1.12 ! [A_27a: d,V0x_2E0: u] :
% 1.64/1.12 ( ( ( s @ A_27a @ V0x_2E0 )
% 1.64/1.12 = ( s @ A_27a @ V0x_2E0 ) )
% 1.64/1.12 <=> mono_2Ec_2Ebool_2ET ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 1.64/1.12 ! [V0t: $o] :
% 1.64/1.12 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 1.64/1.12 <=> V0t )
% 1.64/1.12 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 1.64/1.12 <=> V0t )
% 1.64/1.12 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 1.64/1.12 <=> ( (~) @ V0t ) )
% 1.64/1.12 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 1.64/1.12 <=> ( (~) @ V0t ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Eoption_2Eoption__CLAUSES,axiom,
% 1.64/1.12 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1e_2E0: u,V2e_2E0: u] :
% 1.64/1.12 ( ! [V3x_2E0: u,V4y_2E0: u] :
% 1.64/1.12 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4y_2E0 ) ) ) )
% 1.64/1.12 <=> ( ( s @ A_27a @ V3x_2E0 )
% 1.64/1.12 = ( s @ A_27a @ V4y_2E0 ) ) )
% 1.64/1.12 & ! [V5x_2E0: u] :
% 1.64/1.12 ( ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) ) )
% 1.64/1.12 = ( s @ A_27a @ V5x_2E0 ) )
% 1.64/1.12 & ! [V6x_2E0: u] :
% 1.64/1.12 ( (~)
% 1.64/1.12 @ ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6x_2E0 ) ) ) ) )
% 1.64/1.12 & ! [V7x_2E0: u] :
% 1.64/1.12 ( (~)
% 1.64/1.12 @ ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V7x_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 1.64/1.12 & ! [V8x_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V8x_2E0 ) ) ) ) ) )
% 1.64/1.12 = mono_2Ec_2Ebool_2ET )
% 1.64/1.12 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 1.64/1.12 = mono_2Ec_2Ebool_2EF )
% 1.64/1.12 & ! [V9x_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 ) ) ) )
% 1.64/1.12 <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V9x_2E0 )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 1.64/1.12 & ! [V10x_2E0: u] :
% 1.64/1.12 ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 ) ) ) ) )
% 1.64/1.12 <=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V10x_2E0 )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 1.64/1.12 & ! [V11x_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) )
% 1.64/1.12 => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V11x_2E0 ) ) )
% 1.64/1.12 & ! [V12x_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V12x_2E0 ) )
% 1.64/1.12 & ! [V13x_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V13x_2E0 ) )
% 1.64/1.12 & ! [V14x_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) ) ) )
% 1.64/1.12 => ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V14x_2E0 ) @ ( s @ A_27b @ V2e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27b @ V2e_2E0 ) ) )
% 1.64/1.12 & ! [V15x_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) )
% 1.64/1.12 => ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) @ ( s @ A_27b @ V2e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V15x_2E0 ) ) ) ) ) ) )
% 1.64/1.12 & ! [V16x_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) ) )
% 1.64/1.12 => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1e_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V16x_2E0 ) ) )
% 1.64/1.12 & ! [V17v_2E0: u,V18f_2E0: u] :
% 1.64/1.12 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ A_27b @ V17v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V18f_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27b @ V17v_2E0 ) )
% 1.64/1.12 & ! [V19x_2E0: u,V20v_2E0: u,V21f_2E0: u] :
% 1.64/1.12 ( ( s @ A_27b @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V19x_2E0 ) ) ) @ ( s @ A_27b @ V20v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) ) )
% 1.64/1.12 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V21f_2E0 ) @ ( s @ A_27a @ V19x_2E0 ) ) ) )
% 1.64/1.12 & ! [V22f_2E0: u,V23x_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V23x_2E0 ) ) ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V22f_2E0 ) @ ( s @ A_27a @ V23x_2E0 ) ) ) ) ) )
% 1.64/1.12 & ! [V24f_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V24f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) )
% 1.64/1.12 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
% 1.64/1.12 & ! [V25x_2E0: u] :
% 1.64/1.12 ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) ) )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V25x_2E0 ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Eoption_2EOPTREL__def,axiom,
% 1.64/1.12 ! [A_27a: d,A_27b: d,V0R_2E0: u,V1x_2E0: u,V2y_2E0: u] :
% 1.64/1.12 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 ) ) ) )
% 1.64/1.12 <=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
% 1.64/1.12 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) )
% 1.64/1.12 | ? [V3x0_2E0: u,V4y0_2E0: u] :
% 1.64/1.12 ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1x_2E0 )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x0_2E0 ) ) ) )
% 1.64/1.12 & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ V2y_2E0 )
% 1.64/1.12 = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V4y0_2E0 ) ) ) )
% 1.64/1.12 & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) @ ( s @ A_27b @ V4y0_2E0 ) ) ) ) ) ) ) ).
% 1.64/1.12
% 1.64/1.12 thf(thm_2Equotient__option_2EOPTION__REL__def,conjecture,
% 1.64/1.12 ! [A_27a: d,V0y_2E0: u,V1x_2E0: u,V2R_2E0: u] :
% 1.64/1.12 ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 1.64/1.12 = mono_2Ec_2Ebool_2ET )
% 1.64/1.12 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
% 1.64/1.12 = mono_2Ec_2Ebool_2EF )
% 1.64/1.12 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) )
% 1.64/1.12 = mono_2Ec_2Ebool_2EF )
% 1.64/1.12 & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) )
% 1.64/1.12 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V0y_2E0 ) ) ) ) ) ) ).
% 1.64/1.12 ------------------------
% 1.64/1.13 % (17518)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/183Mi)
% 1.64/1.13 % (17519)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/4Mi)
% 1.64/1.13 % (17520)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/27Mi)
% 1.64/1.13 % (17521)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/2Mi)
% 1.64/1.13 % (17522)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/2Mi)
% 1.64/1.13 % (17523)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/275Mi)
% 1.64/1.13 % (17524)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/18Mi)
% 1.64/1.14 % (17521)Instruction limit reached!
% 1.64/1.14 % (17521)------------------------------
% 1.64/1.14 % (17521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.14 % (17521)Termination reason: Unknown
% 1.64/1.14 % (17521)Termination phase: shuffling
% 1.64/1.14
% 1.64/1.14 % (17521)Memory used [KB]: 1151
% 1.64/1.14 % (17521)Time elapsed: 0.002 s
% 1.64/1.14 % (17521)Instructions burned: 3 (million)
% 1.64/1.14 % (17521)------------------------------
% 1.64/1.14 % (17521)------------------------------
% 1.64/1.14 % (17522)Instruction limit reached!
% 1.64/1.14 % (17522)------------------------------
% 1.64/1.14 % (17522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.14 % (17522)Termination reason: Unknown
% 1.64/1.14 % (17522)Termination phase: shuffling
% 1.64/1.14
% 1.64/1.14 % (17522)Memory used [KB]: 1151
% 1.64/1.14 % (17522)Time elapsed: 0.002 s
% 1.64/1.14 % (17522)Instructions burned: 3 (million)
% 1.64/1.14 % (17522)------------------------------
% 1.64/1.14 % (17522)------------------------------
% 1.64/1.14 % (17519)Instruction limit reached!
% 1.64/1.14 % (17519)------------------------------
% 1.64/1.14 % (17519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.14 % (17519)Termination reason: Unknown
% 1.64/1.14 % (17519)Termination phase: shuffling
% 1.64/1.14
% 1.64/1.14 % (17519)Memory used [KB]: 1151
% 1.64/1.14 % (17519)Time elapsed: 0.003 s
% 1.64/1.14 % (17519)Instructions burned: 6 (million)
% 1.64/1.14 % (17519)------------------------------
% 1.64/1.14 % (17519)------------------------------
% 1.64/1.14 % (17524)Instruction limit reached!
% 1.64/1.14 % (17524)------------------------------
% 1.64/1.14 % (17524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.14 % (17524)Termination reason: Unknown
% 1.64/1.14 % (17524)Termination phase: Property scanning
% 1.64/1.14
% 1.64/1.14 % (17524)Memory used [KB]: 1279
% 1.64/1.14 % (17524)Time elapsed: 0.007 s
% 1.64/1.14 % (17524)Instructions burned: 20 (million)
% 1.64/1.14 % (17524)------------------------------
% 1.64/1.14 % (17524)------------------------------
% 1.64/1.14 % (17520)Instruction limit reached!
% 1.64/1.14 % (17520)------------------------------
% 1.64/1.14 % (17520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.14 % (17520)Termination reason: Unknown
% 1.64/1.14 % (17520)Termination phase: Property scanning
% 1.64/1.14
% 1.64/1.14 % (17520)Memory used [KB]: 1279
% 1.64/1.14 % (17520)Time elapsed: 0.009 s
% 1.64/1.14 % (17520)Instructions burned: 28 (million)
% 1.64/1.14 % (17520)------------------------------
% 1.64/1.14 % (17520)------------------------------
% 1.64/1.15 % (17530)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/3Mi)
% 1.64/1.15 % (17531)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/37Mi)
% 1.64/1.15 % (17530)Instruction limit reached!
% 1.64/1.15 % (17530)------------------------------
% 1.64/1.15 % (17530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.15 % (17530)Termination reason: Unknown
% 1.64/1.15 % (17530)Termination phase: shuffling
% 1.64/1.15
% 1.64/1.15 % (17530)Memory used [KB]: 1023
% 1.64/1.15 % (17530)Time elapsed: 0.002 s
% 1.64/1.15 % (17530)Instructions burned: 3 (million)
% 1.64/1.15 % (17530)------------------------------
% 1.64/1.15 % (17530)------------------------------
% 1.64/1.15 % (17532)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/15Mi)
% 1.64/1.15 % (17536)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/3Mi)
% 1.64/1.15 % (17532)Instruction limit reached!
% 1.64/1.15 % (17532)------------------------------
% 1.64/1.15 % (17532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.15 % (17532)Termination reason: Unknown
% 1.64/1.15 % (17532)Termination phase: Naming
% 1.64/1.15
% 1.64/1.15 % (17532)Memory used [KB]: 1151
% 1.64/1.15 % (17532)Time elapsed: 0.006 s
% 1.64/1.15 % (17532)Instructions burned: 17 (million)
% 1.64/1.15 % (17532)------------------------------
% 1.64/1.15 % (17532)------------------------------
% 1.64/1.15 % (17536)Instruction limit reached!
% 1.64/1.15 % (17536)------------------------------
% 1.64/1.15 % (17536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.15 % (17536)Termination reason: Unknown
% 1.64/1.15 % (17536)Termination phase: shuffling
% 1.64/1.15
% 1.64/1.15 % (17536)Memory used [KB]: 1023
% 1.64/1.15 % (17536)Time elapsed: 0.002 s
% 1.64/1.15 % (17536)Instructions burned: 3 (million)
% 1.64/1.15 % (17536)------------------------------
% 1.64/1.15 % (17536)------------------------------
% 1.64/1.15 % (17538)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/1041Mi)
% 1.64/1.16 % (17531)Instruction limit reached!
% 1.64/1.16 % (17531)------------------------------
% 1.64/1.16 % (17531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.16 % (17531)Termination reason: Unknown
% 1.64/1.16 % (17531)Termination phase: Function definition elimination
% 1.64/1.16
% 1.64/1.16 % (17531)Memory used [KB]: 1407
% 1.64/1.16 % (17531)Time elapsed: 0.011 s
% 1.64/1.16 % (17531)Instructions burned: 39 (million)
% 1.64/1.16 % (17531)------------------------------
% 1.64/1.16 % (17531)------------------------------
% 1.64/1.16 % (17541)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/7Mi)
% 1.64/1.16 % (17541)Instruction limit reached!
% 1.64/1.16 % (17541)------------------------------
% 1.64/1.16 % (17541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.16 % (17541)Termination reason: Unknown
% 1.64/1.16 % (17541)Termination phase: shuffling
% 1.64/1.16
% 1.64/1.16 % (17541)Memory used [KB]: 1151
% 1.64/1.16 % (17541)Time elapsed: 0.003 s
% 1.64/1.16 % (17541)Instructions burned: 7 (million)
% 1.64/1.16 % (17541)------------------------------
% 1.64/1.16 % (17541)------------------------------
% 1.64/1.16 % (17544)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/16Mi)
% 1.64/1.16 % (17545)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/3Mi)
% 1.64/1.16 % (17545)Instruction limit reached!
% 1.64/1.16 % (17545)------------------------------
% 1.64/1.16 % (17545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.16 % (17545)Termination reason: Unknown
% 1.64/1.16 % (17545)Termination phase: shuffling
% 1.64/1.16
% 1.64/1.16 % (17545)Memory used [KB]: 1151
% 1.64/1.16 % (17545)Time elapsed: 0.002 s
% 1.64/1.16 % (17545)Instructions burned: 4 (million)
% 1.64/1.16 % (17545)------------------------------
% 1.64/1.16 % (17545)------------------------------
% 1.64/1.16 % (17547)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/3Mi)
% 1.64/1.17 % (17544)Instruction limit reached!
% 1.64/1.17 % (17544)------------------------------
% 1.64/1.17 % (17544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.17 % (17544)Termination reason: Unknown
% 1.64/1.17 % (17544)Termination phase: Preprocessing 3
% 1.64/1.17
% 1.64/1.17 % (17544)Memory used [KB]: 1279
% 1.64/1.17 % (17544)Time elapsed: 0.006 s
% 1.64/1.17 % (17544)Instructions burned: 18 (million)
% 1.64/1.17 % (17544)------------------------------
% 1.64/1.17 % (17544)------------------------------
% 1.64/1.17 % (17547)Instruction limit reached!
% 1.64/1.17 % (17547)------------------------------
% 1.64/1.17 % (17547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.17 % (17547)Termination reason: Unknown
% 1.64/1.17 % (17547)Termination phase: shuffling
% 1.64/1.17
% 1.64/1.17 % (17547)Memory used [KB]: 1151
% 1.64/1.17 % (17547)Time elapsed: 0.002 s
% 1.64/1.17 % (17547)Instructions burned: 4 (million)
% 1.64/1.17 % (17547)------------------------------
% 1.64/1.17 % (17547)------------------------------
% 1.64/1.17 % (17548)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/7Mi)
% 1.64/1.17 % (17548)Instruction limit reached!
% 1.64/1.17 % (17548)------------------------------
% 1.64/1.17 % (17548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.17 % (17548)Termination reason: Unknown
% 1.64/1.17 % (17548)Termination phase: shuffling
% 1.64/1.17
% 1.64/1.17 % (17548)Memory used [KB]: 1151
% 1.64/1.17 % (17548)Time elapsed: 0.003 s
% 1.64/1.17 % (17548)Instructions burned: 7 (million)
% 1.64/1.17 % (17548)------------------------------
% 1.64/1.17 % (17548)------------------------------
% 1.64/1.17 % (17552)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/3Mi)
% 1.64/1.17 % (17552)Instruction limit reached!
% 1.64/1.17 % (17552)------------------------------
% 1.64/1.17 % (17552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.17 % (17552)Termination reason: Unknown
% 1.64/1.17 % (17552)Termination phase: shuffling
% 1.64/1.17
% 1.64/1.17 % (17552)Memory used [KB]: 1151
% 1.64/1.17 % (17552)Time elapsed: 0.002 s
% 1.64/1.17 % (17552)Instructions burned: 4 (million)
% 1.64/1.17 % (17552)------------------------------
% 1.64/1.17 % (17552)------------------------------
% 1.64/1.17 % (17554)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/4Mi)
% 1.64/1.17 % (17556)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/18Mi)
% 1.64/1.18 % (17554)Instruction limit reached!
% 1.64/1.18 % (17554)------------------------------
% 1.64/1.18 % (17554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.18 % (17554)Termination reason: Unknown
% 1.64/1.18 % (17554)Termination phase: shuffling
% 1.64/1.18
% 1.64/1.18 % (17554)Memory used [KB]: 1151
% 1.64/1.18 % (17554)Time elapsed: 0.003 s
% 1.64/1.18 % (17554)Instructions burned: 6 (million)
% 1.64/1.18 % (17554)------------------------------
% 1.64/1.18 % (17554)------------------------------
% 1.64/1.18 % (17558)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/710Mi)
% 1.64/1.18 % (17556)Instruction limit reached!
% 1.64/1.18 % (17556)------------------------------
% 1.64/1.18 % (17556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.18 % (17556)Termination reason: Unknown
% 1.64/1.18 % (17556)Termination phase: Property scanning
% 1.64/1.18
% 1.64/1.18 % (17556)Memory used [KB]: 1279
% 1.64/1.18 % (17556)Time elapsed: 0.007 s
% 1.64/1.18 % (17556)Instructions burned: 21 (million)
% 1.64/1.18 % (17556)------------------------------
% 1.64/1.18 % (17556)------------------------------
% 1.64/1.18 % (17561)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/6Mi)
% 1.64/1.18 % (17561)Instruction limit reached!
% 1.64/1.18 % (17561)------------------------------
% 1.64/1.18 % (17561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.18 % (17561)Termination reason: Unknown
% 1.64/1.18 % (17561)Termination phase: shuffling
% 1.64/1.18
% 1.64/1.18 % (17561)Memory used [KB]: 1151
% 1.64/1.18 % (17561)Time elapsed: 0.003 s
% 1.64/1.18 % (17561)Instructions burned: 6 (million)
% 1.64/1.18 % (17561)------------------------------
% 1.64/1.18 % (17561)------------------------------
% 1.64/1.19 % (17563)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/902Mi)
% 1.64/1.19 % (17565)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/21Mi)
% 1.64/1.19 % (17518)Instruction limit reached!
% 1.64/1.19 % (17518)------------------------------
% 1.64/1.19 % (17518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.19 % (17518)Termination reason: Unknown
% 1.64/1.19 % (17518)Termination phase: Saturation
% 1.64/1.19
% 1.64/1.19 % (17518)Memory used [KB]: 6524
% 1.64/1.19 % (17518)Time elapsed: 0.057 s
% 1.64/1.19 % (17518)Instructions burned: 184 (million)
% 1.64/1.19 % (17518)------------------------------
% 1.64/1.19 % (17518)------------------------------
% 1.64/1.19 % (17566)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/5Mi)
% 1.64/1.19 % (17566)Instruction limit reached!
% 1.64/1.19 % (17566)------------------------------
% 1.64/1.19 % (17566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.19 % (17566)Termination reason: Unknown
% 1.64/1.19 % (17566)Termination phase: shuffling
% 1.64/1.19
% 1.64/1.19 % (17566)Memory used [KB]: 1151
% 1.64/1.19 % (17566)Time elapsed: 0.003 s
% 1.64/1.19 % (17566)Instructions burned: 7 (million)
% 1.64/1.19 % (17566)------------------------------
% 1.64/1.19 % (17566)------------------------------
% 1.65/1.20 % (17565)Instruction limit reached!
% 1.65/1.20 % (17565)------------------------------
% 1.65/1.20 % (17565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.20 % (17565)Termination reason: Unknown
% 1.65/1.20 % (17565)Termination phase: SInE selection
% 1.65/1.20
% 1.65/1.20 % (17565)Memory used [KB]: 1279
% 1.65/1.20 % (17565)Time elapsed: 0.008 s
% 1.65/1.20 % (17565)Instructions burned: 23 (million)
% 1.65/1.20 % (17565)------------------------------
% 1.65/1.20 % (17565)------------------------------
% 1.65/1.20 % (17569)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/6Mi)
% 1.65/1.20 % (17569)Instruction limit reached!
% 1.65/1.20 % (17569)------------------------------
% 1.65/1.20 % (17569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.20 % (17569)Termination reason: Unknown
% 1.65/1.20 % (17569)Termination phase: shuffling
% 1.65/1.20
% 1.65/1.20 % (17569)Memory used [KB]: 1151
% 1.65/1.20 % (17569)Time elapsed: 0.003 s
% 1.65/1.20 % (17569)Instructions burned: 7 (million)
% 1.65/1.20 % (17569)------------------------------
% 1.65/1.20 % (17569)------------------------------
% 1.65/1.20 % (17570)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/377Mi)
% 1.65/1.21 % (17572)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/779Mi)
% 1.65/1.21 % (17575)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/19Mi)
% 1.65/1.22 % (17523)Instruction limit reached!
% 1.65/1.22 % (17523)------------------------------
% 1.65/1.22 % (17523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.22 % (17523)Termination reason: Unknown
% 1.65/1.22 % (17523)Termination phase: Saturation
% 1.65/1.22
% 1.65/1.22 % (17523)Memory used [KB]: 6268
% 1.65/1.22 % (17523)Time elapsed: 0.082 s
% 1.65/1.22 % (17523)Instructions burned: 275 (million)
% 1.65/1.22 % (17523)------------------------------
% 1.65/1.22 % (17523)------------------------------
% 1.65/1.22 % (17575)Instruction limit reached!
% 1.65/1.22 % (17575)------------------------------
% 1.65/1.22 % (17575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.22 % (17575)Termination reason: Unknown
% 1.65/1.22 % (17575)Termination phase: Property scanning
% 1.65/1.22
% 1.65/1.22 % (17575)Memory used [KB]: 1407
% 1.65/1.22 % (17575)Time elapsed: 0.006 s
% 1.65/1.22 % (17575)Instructions burned: 19 (million)
% 1.65/1.22 % (17575)------------------------------
% 1.65/1.22 % (17575)------------------------------
% 1.65/1.23 % (17585)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/879Mi)
% 1.65/1.23 % (17586)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/17Mi)
% 1.65/1.23 % (17586)Instruction limit reached!
% 1.65/1.23 % (17586)------------------------------
% 1.65/1.23 % (17586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.23 % (17586)Termination reason: Unknown
% 1.65/1.23 % (17586)Termination phase: Preprocessing 3
% 1.65/1.23
% 1.65/1.23 % (17586)Memory used [KB]: 1279
% 1.65/1.23 % (17586)Time elapsed: 0.006 s
% 1.65/1.23 % (17586)Instructions burned: 18 (million)
% 1.65/1.23 % (17586)------------------------------
% 1.65/1.23 % (17586)------------------------------
% 1.65/1.24 % (17593)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17206 for (2999ds/3Mi)
% 1.65/1.24 % (17593)Instruction limit reached!
% 1.65/1.24 % (17593)------------------------------
% 1.65/1.24 % (17593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.24 % (17593)Termination reason: Unknown
% 1.65/1.24 % (17593)Termination phase: shuffling
% 1.65/1.24
% 1.65/1.24 % (17593)Memory used [KB]: 1151
% 1.65/1.24 % (17593)Time elapsed: 0.002 s
% 1.65/1.24 % (17593)Instructions burned: 4 (million)
% 1.65/1.24 % (17593)------------------------------
% 1.65/1.24 % (17593)------------------------------
% 1.65/1.25 % (17597)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17206 for (2998ds/30Mi)
% 1.65/1.26 % (17597)Instruction limit reached!
% 1.65/1.26 % (17597)------------------------------
% 1.65/1.26 % (17597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.26 % (17597)Termination reason: Unknown
% 1.65/1.26 % (17597)Termination phase: Property scanning
% 1.65/1.26
% 1.65/1.26 % (17597)Memory used [KB]: 1279
% 1.65/1.26 % (17597)Time elapsed: 0.010 s
% 1.65/1.26 % (17597)Instructions burned: 31 (million)
% 1.65/1.26 % (17597)------------------------------
% 1.65/1.26 % (17597)------------------------------
% 1.65/1.27 % (17612)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17206 for (2998ds/127Mi)
% 1.65/1.31 % (17612)Instruction limit reached!
% 1.65/1.31 % (17612)------------------------------
% 1.65/1.31 % (17612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (17612)Termination reason: Unknown
% 1.65/1.31 % (17612)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (17612)Memory used [KB]: 6268
% 1.65/1.31 % (17612)Time elapsed: 0.063 s
% 1.65/1.31 % (17612)Instructions burned: 128 (million)
% 1.65/1.31 % (17612)------------------------------
% 1.65/1.31 % (17612)------------------------------
% 1.65/1.31 % (17570)Instruction limit reached!
% 1.65/1.31 % (17570)------------------------------
% 1.65/1.31 % (17570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (17570)Termination reason: Unknown
% 1.65/1.31 % (17570)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (17570)Memory used [KB]: 6524
% 1.65/1.31 % (17570)Time elapsed: 0.112 s
% 1.65/1.31 % (17570)Instructions burned: 378 (million)
% 1.65/1.31 % (17570)------------------------------
% 1.65/1.31 % (17570)------------------------------
% 1.65/1.32 % (17669)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17206 for (2998ds/100Mi)
% 1.65/1.32 % (17673)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_17206 for (2998ds/3Mi)
% 1.65/1.32 % (17673)Instruction limit reached!
% 1.65/1.32 % (17673)------------------------------
% 1.65/1.32 % (17673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (17673)Termination reason: Unknown
% 1.65/1.32 % (17673)Termination phase: shuffling
% 1.65/1.32
% 1.65/1.32 % (17673)Memory used [KB]: 1151
% 1.65/1.32 % (17673)Time elapsed: 0.002 s
% 1.65/1.32 % (17673)Instructions burned: 3 (million)
% 1.65/1.32 % (17673)------------------------------
% 1.65/1.32 % (17673)------------------------------
% 1.65/1.33 % (17675)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_17206 for (2997ds/20Mi)
% 1.65/1.34 % (17675)Instruction limit reached!
% 1.65/1.34 % (17675)------------------------------
% 1.65/1.34 % (17675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (17675)Termination reason: Unknown
% 1.65/1.34 % (17675)Termination phase: Preprocessing 3
% 1.65/1.34
% 1.65/1.34 % (17675)Memory used [KB]: 1151
% 1.65/1.34 % (17675)Time elapsed: 0.007 s
% 1.65/1.34 % (17675)Instructions burned: 20 (million)
% 1.65/1.34 % (17675)------------------------------
% 1.65/1.34 % (17675)------------------------------
% 1.65/1.35 % (17669)Instruction limit reached!
% 1.65/1.35 % (17669)------------------------------
% 1.65/1.35 % (17669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (17669)Termination reason: Unknown
% 1.65/1.35 % (17669)Termination phase: Saturation
% 1.65/1.35
% 1.65/1.35 % (17669)Memory used [KB]: 6268
% 1.65/1.35 % (17669)Time elapsed: 0.030 s
% 1.65/1.35 % (17669)Instructions burned: 102 (million)
% 1.65/1.35 % (17669)------------------------------
% 1.65/1.35 % (17669)------------------------------
% 1.65/1.35 % (17676)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_17206 for (2997ds/86Mi)
% 1.65/1.36 % (17677)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_17206 for (2997ds/107Mi)
% 1.65/1.38 % (17676)Instruction limit reached!
% 1.65/1.38 % (17676)------------------------------
% 1.65/1.38 % (17676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (17676)Termination reason: Unknown
% 1.65/1.38 % (17676)Termination phase: Saturation
% 1.65/1.38
% 1.65/1.38 % (17676)Memory used [KB]: 6140
% 1.65/1.38 % (17676)Time elapsed: 0.028 s
% 1.65/1.38 % (17676)Instructions burned: 87 (million)
% 1.65/1.38 % (17676)------------------------------
% 1.65/1.38 % (17676)------------------------------
% 1.65/1.39 % (17678)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_17206 for (2997ds/39Mi)
% 1.65/1.39 % (17558)Instruction limit reached!
% 1.65/1.39 % (17558)------------------------------
% 1.65/1.39 % (17558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (17558)Termination reason: Unknown
% 1.65/1.39 % (17558)Termination phase: Saturation
% 1.65/1.39
% 1.65/1.39 % (17558)Memory used [KB]: 7419
% 1.65/1.39 % (17558)Time elapsed: 0.212 s
% 1.65/1.39 % (17558)Instructions burned: 712 (million)
% 1.65/1.39 % (17558)------------------------------
% 1.65/1.39 % (17558)------------------------------
% 1.65/1.39 % (17677)Instruction limit reached!
% 1.65/1.39 % (17677)------------------------------
% 1.65/1.39 % (17677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (17677)Termination reason: Unknown
% 1.65/1.39 % (17677)Termination phase: Saturation
% 1.65/1.39
% 1.65/1.39 % (17677)Memory used [KB]: 6268
% 1.65/1.39 % (17677)Time elapsed: 0.034 s
% 1.65/1.39 % (17677)Instructions burned: 108 (million)
% 1.65/1.39 % (17677)------------------------------
% 1.65/1.39 % (17677)------------------------------
% 1.65/1.40 % (17678)Instruction limit reached!
% 1.65/1.40 % (17678)------------------------------
% 1.65/1.40 % (17678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (17678)Termination reason: Unknown
% 1.65/1.40 % (17678)Termination phase: Property scanning
% 1.65/1.40
% 1.65/1.40 % (17678)Memory used [KB]: 1407
% 1.65/1.40 % (17678)Time elapsed: 0.011 s
% 1.65/1.40 % (17678)Instructions burned: 40 (million)
% 1.65/1.40 % (17678)------------------------------
% 1.65/1.40 % (17678)------------------------------
% 1.65/1.40 % (17679)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_17206 for (2997ds/448Mi)
% 1.65/1.40 % (17680)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_17206 for (2997ds/46Mi)
% 1.65/1.41 % (17681)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_17206 for (2997ds/98Mi)
% 1.65/1.41 % (17680)Instruction limit reached!
% 1.65/1.41 % (17680)------------------------------
% 1.65/1.41 % (17680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (17680)Termination reason: Unknown
% 1.65/1.41 % (17680)Termination phase: Saturation
% 1.65/1.41
% 1.65/1.41 % (17680)Memory used [KB]: 5884
% 1.65/1.41 % (17680)Time elapsed: 0.015 s
% 1.65/1.41 % (17680)Instructions burned: 48 (million)
% 1.65/1.41 % (17680)------------------------------
% 1.65/1.41 % (17680)------------------------------
% 1.65/1.42 % (17692)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_17206 for (2997ds/507Mi)
% 1.65/1.43 % (17572)Instruction limit reached!
% 1.65/1.43 % (17572)------------------------------
% 1.65/1.43 % (17572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.43 % (17572)Termination reason: Unknown
% 1.65/1.43 % (17572)Termination phase: Saturation
% 1.65/1.43
% 1.65/1.43 % (17572)Memory used [KB]: 7547
% 1.65/1.43 % (17572)Time elapsed: 0.222 s
% 1.65/1.43 % (17572)Instructions burned: 781 (million)
% 1.65/1.43 % (17572)------------------------------
% 1.65/1.43 % (17572)------------------------------
% 1.65/1.43 % (17681)Instruction limit reached!
% 1.65/1.43 % (17681)------------------------------
% 1.65/1.43 % (17681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.43 % (17681)Termination reason: Unknown
% 1.65/1.43 % (17681)Termination phase: Saturation
% 1.65/1.43
% 1.65/1.43 % (17681)Memory used [KB]: 1791
% 1.65/1.43 % (17681)Time elapsed: 0.030 s
% 1.65/1.43 % (17681)Instructions burned: 101 (million)
% 1.65/1.43 % (17681)------------------------------
% 1.65/1.43 % (17681)------------------------------
% 1.65/1.44 % (17701)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/149Mi)
% 1.65/1.44 % (17704)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/39Mi)
% 1.65/1.45 % (17704)Instruction limit reached!
% 1.65/1.45 % (17704)------------------------------
% 1.65/1.45 % (17704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.45 % (17704)Termination reason: Unknown
% 1.65/1.45 % (17704)Termination phase: Saturation
% 1.65/1.45
% 1.65/1.45 % (17704)Memory used [KB]: 1279
% 1.65/1.45 % (17704)Time elapsed: 0.011 s
% 1.65/1.45 % (17704)Instructions burned: 39 (million)
% 1.65/1.45 % (17704)------------------------------
% 1.65/1.45 % (17704)------------------------------
% 1.65/1.46 % (17563)Instruction limit reached!
% 1.65/1.46 % (17563)------------------------------
% 1.65/1.46 % (17563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (17563)Termination reason: Unknown
% 1.65/1.46 % (17563)Termination phase: Saturation
% 1.65/1.46
% 1.65/1.46 % (17563)Memory used [KB]: 7931
% 1.65/1.46 % (17563)Time elapsed: 0.271 s
% 1.65/1.46 % (17563)Instructions burned: 903 (million)
% 1.65/1.46 % (17563)------------------------------
% 1.65/1.46 % (17563)------------------------------
% 1.65/1.46 % (17719)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/6Mi)
% 1.65/1.46 % (17538)Instruction limit reached!
% 1.65/1.46 % (17538)------------------------------
% 1.65/1.46 % (17538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (17538)Termination reason: Unknown
% 1.65/1.46 % (17538)Termination phase: Saturation
% 1.65/1.46
% 1.65/1.46 % (17538)Memory used [KB]: 9210
% 1.65/1.46 % (17538)Time elapsed: 0.313 s
% 1.65/1.46 % (17538)Instructions burned: 1043 (million)
% 1.65/1.46 % (17538)------------------------------
% 1.65/1.46 % (17538)------------------------------
% 1.65/1.46 % (17719)Instruction limit reached!
% 1.65/1.46 % (17719)------------------------------
% 1.65/1.46 % (17719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.46 % (17719)Termination reason: Unknown
% 1.65/1.46 % (17719)Termination phase: shuffling
% 1.65/1.46
% 1.65/1.46 % (17719)Memory used [KB]: 1151
% 1.65/1.46 % (17719)Time elapsed: 0.003 s
% 1.65/1.46 % (17719)Instructions burned: 8 (million)
% 1.65/1.46 % (17719)------------------------------
% 1.65/1.46 % (17719)------------------------------
% 1.65/1.47 % (17721)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/1087Mi)
% 1.65/1.47 % (17727)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/47Mi)
% 1.65/1.47 % (17728)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/44Mi)
% 1.65/1.48 % (17701)Instruction limit reached!
% 1.65/1.48 % (17701)------------------------------
% 1.65/1.48 % (17701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.48 % (17701)Termination reason: Unknown
% 1.65/1.48 % (17701)Termination phase: Saturation
% 1.65/1.48
% 1.65/1.48 % (17701)Memory used [KB]: 6268
% 1.65/1.48 % (17701)Time elapsed: 0.049 s
% 1.65/1.48 % (17701)Instructions burned: 149 (million)
% 1.65/1.48 % (17701)------------------------------
% 1.65/1.48 % (17701)------------------------------
% 1.65/1.49 % (17728)Instruction limit reached!
% 1.65/1.49 % (17728)------------------------------
% 1.65/1.49 % (17728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (17728)Termination reason: Unknown
% 1.65/1.49 % (17728)Termination phase: Saturation
% 1.65/1.49
% 1.65/1.49 % (17728)Memory used [KB]: 1407
% 1.65/1.49 % (17728)Time elapsed: 0.013 s
% 1.65/1.49 % (17728)Instructions burned: 46 (million)
% 1.65/1.49 % (17728)------------------------------
% 1.65/1.49 % (17728)------------------------------
% 1.65/1.49 % (17727)Instruction limit reached!
% 1.65/1.49 % (17727)------------------------------
% 1.65/1.49 % (17727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.49 % (17727)Termination reason: Unknown
% 1.65/1.49 % (17727)Termination phase: Saturation
% 1.65/1.49
% 1.65/1.49 % (17727)Memory used [KB]: 5884
% 1.65/1.49 % (17727)Time elapsed: 0.014 s
% 1.65/1.49 % (17727)Instructions burned: 47 (million)
% 1.65/1.49 % (17727)------------------------------
% 1.65/1.49 % (17727)------------------------------
% 1.65/1.49 % (17735)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/432Mi)
% 1.65/1.50 % (17737)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/62Mi)
% 1.65/1.50 % (17738)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/31Mi)
% 1.65/1.50 % (17738)Instruction limit reached!
% 1.65/1.50 % (17738)------------------------------
% 1.65/1.50 % (17738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.50 % (17738)Termination reason: Unknown
% 1.65/1.50 % (17738)Termination phase: Property scanning
% 1.65/1.50
% 1.65/1.50 % (17738)Memory used [KB]: 1279
% 1.65/1.50 % (17738)Time elapsed: 0.010 s
% 1.65/1.50 % (17738)Instructions burned: 33 (million)
% 1.65/1.50 % (17738)------------------------------
% 1.65/1.50 % (17738)------------------------------
% 1.65/1.51 % (17737)Instruction limit reached!
% 1.65/1.51 % (17737)------------------------------
% 1.65/1.51 % (17737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.51 % (17737)Termination reason: Unknown
% 1.65/1.51 % (17737)Termination phase: Saturation
% 1.65/1.51
% 1.65/1.51 % (17737)Memory used [KB]: 6012
% 1.65/1.51 % (17737)Time elapsed: 0.018 s
% 1.65/1.51 % (17737)Instructions burned: 64 (million)
% 1.65/1.51 % (17737)------------------------------
% 1.65/1.51 % (17737)------------------------------
% 1.65/1.51 % (17585)Instruction limit reached!
% 1.65/1.51 % (17585)------------------------------
% 1.65/1.51 % (17585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.51 % (17585)Termination reason: Unknown
% 1.65/1.51 % (17585)Termination phase: Saturation
% 1.65/1.51
% 1.65/1.51 % (17585)Memory used [KB]: 7164
% 1.65/1.51 % (17585)Time elapsed: 0.310 s
% 1.65/1.51 % (17585)Instructions burned: 881 (million)
% 1.65/1.51 % (17585)------------------------------
% 1.65/1.51 % (17585)------------------------------
% 1.65/1.51 % (17746)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/96Mi)
% 1.65/1.52 % (17750)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/453Mi)
% 1.65/1.52 % (17751)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_17206 for (2996ds/71Mi)
% 1.65/1.53 % (17679)Instruction limit reached!
% 1.65/1.53 % (17679)------------------------------
% 1.65/1.53 % (17679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.53 % (17679)Termination reason: Unknown
% 1.65/1.53 % (17679)Termination phase: Saturation
% 1.65/1.53
% 1.65/1.53 % (17679)Memory used [KB]: 7036
% 1.65/1.53 % (17679)Time elapsed: 0.130 s
% 1.65/1.53 % (17679)Instructions burned: 449 (million)
% 1.65/1.53 % (17679)------------------------------
% 1.65/1.53 % (17679)------------------------------
% 1.65/1.54 % (17761)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/83Mi)
% 1.65/1.54 % (17746)Instruction limit reached!
% 1.65/1.54 % (17746)------------------------------
% 1.65/1.54 % (17746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.54 % (17746)Termination reason: Unknown
% 1.65/1.54 % (17746)Termination phase: Saturation
% 1.65/1.54
% 1.65/1.54 % (17746)Memory used [KB]: 6140
% 1.65/1.54 % (17746)Time elapsed: 0.030 s
% 1.65/1.54 % (17746)Instructions burned: 96 (million)
% 1.65/1.54 % (17746)------------------------------
% 1.65/1.54 % (17746)------------------------------
% 1.65/1.54 % (17751)Instruction limit reached!
% 1.65/1.54 % (17751)------------------------------
% 1.65/1.54 % (17751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.54 % (17751)Termination reason: Unknown
% 1.65/1.54 % (17751)Termination phase: Saturation
% 1.65/1.54
% 1.65/1.54 % (17751)Memory used [KB]: 6140
% 1.65/1.54 % (17751)Time elapsed: 0.022 s
% 1.65/1.54 % (17751)Instructions burned: 73 (million)
% 1.65/1.54 % (17751)------------------------------
% 1.65/1.54 % (17751)------------------------------
% 1.65/1.55 % (17780)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/11Mi)
% 1.65/1.55 % (17783)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/41Mi)
% 1.65/1.56 % (17780)Instruction limit reached!
% 1.65/1.56 % (17780)------------------------------
% 1.65/1.56 % (17780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.56 % (17780)Termination reason: Unknown
% 1.65/1.56 % (17780)Termination phase: shuffling
% 1.65/1.56
% 1.65/1.56 % (17780)Memory used [KB]: 1279
% 1.65/1.56 % (17780)Time elapsed: 0.005 s
% 1.65/1.56 % (17780)Instructions burned: 13 (million)
% 1.65/1.56 % (17780)------------------------------
% 1.65/1.56 % (17780)------------------------------
% 1.65/1.56 % (17761)Instruction limit reached!
% 1.65/1.56 % (17761)------------------------------
% 1.65/1.56 % (17761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.56 % (17761)Termination reason: Unknown
% 1.65/1.56 % (17761)Termination phase: Saturation
% 1.65/1.56
% 1.65/1.56 % (17761)Memory used [KB]: 5884
% 1.65/1.56 % (17761)Time elapsed: 0.026 s
% 1.65/1.56 % (17761)Instructions burned: 83 (million)
% 1.65/1.56 % (17761)------------------------------
% 1.65/1.56 % (17761)------------------------------
% 1.65/1.56 % (17783)Instruction limit reached!
% 1.65/1.56 % (17783)------------------------------
% 1.65/1.56 % (17783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.56 % (17783)Termination reason: Unknown
% 1.65/1.56 % (17783)Termination phase: Property scanning
% 1.65/1.56
% 1.65/1.56 % (17783)Memory used [KB]: 1407
% 1.65/1.56 % (17783)Time elapsed: 0.012 s
% 1.65/1.56 % (17783)Instructions burned: 42 (million)
% 1.65/1.56 % (17783)------------------------------
% 1.65/1.56 % (17783)------------------------------
% 1.65/1.57 % (17793)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/6Mi)
% 1.65/1.57 % (17793)Instruction limit reached!
% 1.65/1.57 % (17793)------------------------------
% 1.65/1.57 % (17793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.57 % (17793)Termination reason: Unknown
% 1.65/1.57 % (17793)Termination phase: shuffling
% 1.65/1.57
% 1.65/1.57 % (17793)Memory used [KB]: 1151
% 1.65/1.57 % (17793)Time elapsed: 0.003 s
% 1.65/1.57 % (17793)Instructions burned: 6 (million)
% 1.65/1.57 % (17793)------------------------------
% 1.65/1.57 % (17793)------------------------------
% 1.65/1.57 % (17801)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/150Mi)
% 1.65/1.57 % (17803)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/343Mi)
% 1.65/1.58 % (17692)Instruction limit reached!
% 1.65/1.58 % (17692)------------------------------
% 1.65/1.58 % (17692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.58 % (17692)Termination reason: Unknown
% 1.65/1.58 % (17692)Termination phase: Saturation
% 1.65/1.58
% 1.65/1.58 % (17692)Memory used [KB]: 7419
% 1.65/1.58 % (17692)Time elapsed: 0.154 s
% 1.65/1.58 % (17692)Instructions burned: 508 (million)
% 1.65/1.58 % (17692)------------------------------
% 1.65/1.58 % (17692)------------------------------
% 1.65/1.58 % (17809)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/109Mi)
% 1.65/1.59 % (17812)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/253Mi)
% 1.65/1.61 % (17809)Instruction limit reached!
% 1.65/1.61 % (17809)------------------------------
% 1.65/1.61 % (17809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.61 % (17809)Termination reason: Unknown
% 1.65/1.61 % (17809)Termination phase: Saturation
% 1.65/1.61
% 1.65/1.61 % (17809)Memory used [KB]: 6268
% 1.65/1.61 % (17809)Time elapsed: 0.035 s
% 1.65/1.61 % (17809)Instructions burned: 111 (million)
% 1.65/1.61 % (17809)------------------------------
% 1.65/1.61 % (17809)------------------------------
% 1.65/1.62 % (17801)Instruction limit reached!
% 1.65/1.62 % (17801)------------------------------
% 1.65/1.62 % (17801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.62 % (17801)Termination reason: Unknown
% 1.65/1.62 % (17801)Termination phase: Saturation
% 1.65/1.62
% 1.65/1.62 % (17801)Memory used [KB]: 6140
% 1.65/1.62 % (17801)Time elapsed: 0.047 s
% 1.65/1.62 % (17801)Instructions burned: 152 (million)
% 1.65/1.62 % (17801)------------------------------
% 1.65/1.62 % (17801)------------------------------
% 1.65/1.62 % (17844)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/140Mi)
% 1.65/1.62 % (17735)Instruction limit reached!
% 1.65/1.62 % (17735)------------------------------
% 1.65/1.62 % (17735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.62 % (17735)Termination reason: Unknown
% 1.65/1.62 % (17735)Termination phase: Saturation
% 1.65/1.62
% 1.65/1.62 % (17735)Memory used [KB]: 2814
% 1.65/1.62 % (17735)Time elapsed: 0.131 s
% 1.65/1.62 % (17735)Instructions burned: 432 (million)
% 1.65/1.62 % (17735)------------------------------
% 1.65/1.62 % (17735)------------------------------
% 1.65/1.63 % (17849)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/614Mi)
% 1.65/1.63 % (17853)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_17206 for (2995ds/202Mi)
% 1.65/1.65 % (17750)Instruction limit reached!
% 1.65/1.65 % (17750)------------------------------
% 1.65/1.65 % (17750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.65 % (17750)Termination reason: Unknown
% 1.65/1.65 % (17750)Termination phase: Saturation
% 1.65/1.65
% 1.65/1.65 % (17750)Memory used [KB]: 6524
% 1.65/1.65 % (17750)Time elapsed: 0.131 s
% 1.65/1.65 % (17750)Instructions burned: 453 (million)
% 1.65/1.65 % (17750)------------------------------
% 1.65/1.65 % (17750)------------------------------
% 1.65/1.66 % (17812)Instruction limit reached!
% 1.65/1.66 % (17812)------------------------------
% 1.65/1.66 % (17812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.66 % (17812)Termination reason: Unknown
% 1.65/1.66 % (17812)Termination phase: Saturation
% 1.65/1.66
% 1.65/1.66 % (17812)Memory used [KB]: 6524
% 1.65/1.66 % (17812)Time elapsed: 0.075 s
% 1.65/1.66 % (17812)Instructions burned: 254 (million)
% 1.65/1.66 % (17812)------------------------------
% 1.65/1.66 % (17812)------------------------------
% 1.65/1.66 % (17867)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_17206 for (2994ds/339Mi)
% 1.65/1.66 % (17844)Instruction limit reached!
% 1.65/1.66 % (17844)------------------------------
% 1.65/1.66 % (17844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.66 % (17844)Termination reason: Unknown
% 1.65/1.66 % (17844)Termination phase: Saturation
% 1.65/1.66
% 1.65/1.66 % (17844)Memory used [KB]: 6396
% 1.65/1.66 % (17844)Time elapsed: 0.044 s
% 1.65/1.66 % (17844)Instructions burned: 142 (million)
% 1.65/1.66 % (17844)------------------------------
% 1.65/1.66 % (17844)------------------------------
% 1.65/1.67 % (17874)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_17206 for (2994ds/283Mi)
% 1.65/1.67 % (17875)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17206 for (2994ds/134Mi)
% 1.65/1.67 % (17803)Instruction limit reached!
% 1.65/1.67 % (17803)------------------------------
% 1.65/1.67 % (17803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.67 % (17803)Termination reason: Unknown
% 1.65/1.67 % (17803)Termination phase: Saturation
% 1.65/1.67
% 1.65/1.67 % (17803)Memory used [KB]: 6524
% 1.65/1.67 % (17803)Time elapsed: 0.102 s
% 1.65/1.67 % (17803)Instructions burned: 343 (million)
% 1.65/1.67 % (17803)------------------------------
% 1.65/1.67 % (17803)------------------------------
% 1.65/1.68 % (17880)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17206 for (2994ds/298Mi)
% 1.65/1.69 % (17853)Instruction limit reached!
% 1.65/1.69 % (17853)------------------------------
% 1.65/1.69 % (17853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.69 % (17853)Termination reason: Unknown
% 1.65/1.69 % (17853)Termination phase: Saturation
% 1.65/1.69
% 1.65/1.69 % (17853)Memory used [KB]: 6396
% 1.65/1.69 % (17853)Time elapsed: 0.061 s
% 1.65/1.69 % (17853)Instructions burned: 204 (million)
% 1.65/1.69 % (17853)------------------------------
% 1.65/1.69 % (17853)------------------------------
% 1.65/1.70 % (17892)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17206 for (2994ds/192Mi)
% 1.65/1.71 % (17875)Instruction limit reached!
% 1.65/1.71 % (17875)------------------------------
% 1.65/1.71 % (17875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.71 % (17875)Termination reason: Unknown
% 1.65/1.71 % (17875)Termination phase: Saturation
% 1.65/1.71
% 1.65/1.71 % (17875)Memory used [KB]: 6268
% 1.65/1.71 % (17875)Time elapsed: 0.042 s
% 1.65/1.71 % (17875)Instructions burned: 134 (million)
% 1.65/1.71 % (17875)------------------------------
% 1.65/1.71 % (17875)------------------------------
% 1.65/1.72 % (17902)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_17206 for (2994ds/258Mi)
% 1.65/1.75 % (17874)Instruction limit reached!
% 1.65/1.75 % (17874)------------------------------
% 1.65/1.75 % (17874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.75 % (17874)Termination reason: Unknown
% 1.65/1.75 % (17874)Termination phase: Saturation
% 1.65/1.75
% 1.65/1.75 % (17874)Memory used [KB]: 6780
% 1.65/1.75 % (17874)Time elapsed: 0.084 s
% 1.65/1.75 % (17874)Instructions burned: 284 (million)
% 1.65/1.75 % (17874)------------------------------
% 1.65/1.75 % (17874)------------------------------
% 1.65/1.76 % (17867)Instruction limit reached!
% 1.65/1.76 % (17867)------------------------------
% 1.65/1.76 % (17867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.76 % (17867)Termination reason: Unknown
% 1.65/1.76 % (17867)Termination phase: Saturation
% 1.65/1.76
% 1.65/1.76 % (17867)Memory used [KB]: 7036
% 1.65/1.76 % (17867)Time elapsed: 0.100 s
% 1.65/1.76 % (17867)Instructions burned: 340 (million)
% 1.65/1.76 % (17867)------------------------------
% 1.65/1.76 % (17867)------------------------------
% 1.65/1.76 % (17892)Instruction limit reached!
% 1.65/1.76 % (17892)------------------------------
% 1.65/1.76 % (17892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.76 % (17892)Termination reason: Unknown
% 1.65/1.76 % (17892)Termination phase: Saturation
% 1.65/1.76
% 1.65/1.76 % (17892)Memory used [KB]: 6780
% 1.65/1.76 % (17892)Time elapsed: 0.059 s
% 1.65/1.76 % (17892)Instructions burned: 193 (million)
% 1.65/1.76 % (17892)------------------------------
% 1.65/1.76 % (17892)------------------------------
% 1.65/1.76 % (17933)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/90Mi)
% 1.65/1.77 % (17939)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/231Mi)
% 1.65/1.77 % (17940)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/458Mi)
% 1.65/1.77 % (17880)Instruction limit reached!
% 1.65/1.77 % (17880)------------------------------
% 1.65/1.77 % (17880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.77 % (17880)Termination reason: Unknown
% 1.65/1.77 % (17880)Termination phase: Saturation
% 1.65/1.77
% 1.65/1.77 % (17880)Memory used [KB]: 6652
% 1.65/1.77 % (17880)Time elapsed: 0.089 s
% 1.65/1.77 % (17880)Instructions burned: 299 (million)
% 1.65/1.77 % (17880)------------------------------
% 1.65/1.77 % (17880)------------------------------
% 1.65/1.78 % (17945)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/31Mi)
% 1.65/1.78 % (17721)Instruction limit reached!
% 1.65/1.78 % (17721)------------------------------
% 1.65/1.78 % (17721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.78 % (17721)Termination reason: Unknown
% 1.65/1.78 % (17721)Termination phase: Saturation
% 1.65/1.78
% 1.65/1.78 % (17721)Memory used [KB]: 7675
% 1.65/1.78 % (17721)Time elapsed: 0.318 s
% 1.65/1.78 % (17721)Instructions burned: 1087 (million)
% 1.65/1.78 % (17721)------------------------------
% 1.65/1.78 % (17721)------------------------------
% 1.65/1.79 % (17933)Instruction limit reached!
% 1.65/1.79 % (17933)------------------------------
% 1.65/1.79 % (17933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.79 % (17933)Termination reason: Unknown
% 1.65/1.79 % (17933)Termination phase: Saturation
% 1.65/1.79
% 1.65/1.79 % (17933)Memory used [KB]: 6268
% 1.65/1.79 % (17933)Time elapsed: 0.028 s
% 1.65/1.79 % (17933)Instructions burned: 90 (million)
% 1.65/1.79 % (17933)------------------------------
% 1.65/1.79 % (17933)------------------------------
% 1.65/1.79 % (17945)Instruction limit reached!
% 1.65/1.79 % (17945)------------------------------
% 1.65/1.79 % (17945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.79 % (17945)Termination reason: Unknown
% 1.65/1.79 % (17945)Termination phase: Property scanning
% 1.65/1.79
% 1.65/1.79 % (17945)Memory used [KB]: 1279
% 1.65/1.79 % (17945)Time elapsed: 0.010 s
% 1.65/1.79 % (17945)Instructions burned: 32 (million)
% 1.65/1.79 % (17945)------------------------------
% 1.65/1.79 % (17945)------------------------------
% 1.65/1.79 % (17946)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/297Mi)
% 1.65/1.80 % (17947)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/987Mi)
% 1.65/1.80 % (17948)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/182Mi)
% 1.65/1.80 % (17902)Instruction limit reached!
% 1.65/1.80 % (17902)------------------------------
% 1.65/1.80 % (17902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.80 % (17902)Termination reason: Unknown
% 1.65/1.80 % (17902)Termination phase: Saturation
% 1.65/1.80
% 1.65/1.80 % (17902)Memory used [KB]: 6780
% 1.65/1.80 % (17902)Time elapsed: 0.082 s
% 1.65/1.80 % (17902)Instructions burned: 261 (million)
% 1.65/1.80 % (17902)------------------------------
% 1.65/1.80 % (17902)------------------------------
% 1.65/1.81 % (17849)Instruction limit reached!
% 1.65/1.81 % (17849)------------------------------
% 1.65/1.81 % (17849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.81 % (17849)Termination reason: Unknown
% 1.65/1.81 % (17849)Termination phase: Saturation
% 1.65/1.81
% 1.65/1.81 % (17849)Memory used [KB]: 7419
% 1.65/1.81 % (17849)Time elapsed: 0.186 s
% 1.65/1.81 % (17849)Instructions burned: 616 (million)
% 1.65/1.81 % (17849)------------------------------
% 1.65/1.81 % (17849)------------------------------
% 1.65/1.81 % (17949)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/182Mi)
% 1.65/1.82 % (17950)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_17206 for (2993ds/154Mi)
% 1.65/1.84 % (17939)Instruction limit reached!
% 1.65/1.84 % (17939)------------------------------
% 1.65/1.84 % (17939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.84 % (17939)Termination reason: Unknown
% 1.65/1.84 % (17939)Termination phase: Saturation
% 1.65/1.84
% 1.65/1.84 % (17939)Memory used [KB]: 6652
% 1.65/1.84 % (17939)Time elapsed: 0.073 s
% 1.65/1.84 % (17939)Instructions burned: 231 (million)
% 1.65/1.84 % (17939)------------------------------
% 1.65/1.84 % (17939)------------------------------
% 1.65/1.85 % (17950)Refutation not found, incomplete strategy
% 1.65/1.85 % (17950)------------------------------
% 1.65/1.85 % (17950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.85 % (17950)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.85
% 1.65/1.85
% 1.65/1.85 % (17950)Memory used [KB]: 6268
% 1.65/1.85 % (17950)Time elapsed: 0.029 s
% 1.65/1.85 % (17950)Instructions burned: 98 (million)
% 1.65/1.85 % (17950)------------------------------
% 1.65/1.85 % (17950)------------------------------
% 1.65/1.85 % (17951)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/79Mi)
% 1.65/1.86 % (17948)Instruction limit reached!
% 1.65/1.86 % (17948)------------------------------
% 1.65/1.86 % (17948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.86 % (17948)Termination reason: Unknown
% 1.65/1.86 % (17948)Termination phase: Saturation
% 1.65/1.86
% 1.65/1.86 % (17948)Memory used [KB]: 6268
% 1.65/1.86 % (17948)Time elapsed: 0.057 s
% 1.65/1.86 % (17948)Instructions burned: 182 (million)
% 1.65/1.86 % (17948)------------------------------
% 1.65/1.86 % (17948)------------------------------
% 1.65/1.86 % (17952)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/216Mi)
% 1.65/1.86 % (17953)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/114Mi)
% 1.65/1.87 % (17949)Instruction limit reached!
% 1.65/1.87 % (17949)------------------------------
% 1.65/1.87 % (17949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.87 % (17949)Termination reason: Unknown
% 1.65/1.87 % (17949)Termination phase: Saturation
% 1.65/1.87
% 1.65/1.87 % (17949)Memory used [KB]: 6396
% 1.65/1.87 % (17949)Time elapsed: 0.057 s
% 1.65/1.87 % (17949)Instructions burned: 183 (million)
% 1.65/1.87 % (17949)------------------------------
% 1.65/1.87 % (17949)------------------------------
% 1.65/1.87 % (17951)Instruction limit reached!
% 1.65/1.87 % (17951)------------------------------
% 1.65/1.87 % (17951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.87 % (17951)Termination reason: Unknown
% 1.65/1.87 % (17951)Termination phase: Saturation
% 1.65/1.87
% 1.65/1.87 % (17951)Memory used [KB]: 6140
% 1.65/1.87 % (17951)Time elapsed: 0.025 s
% 1.65/1.87 % (17951)Instructions burned: 81 (million)
% 1.65/1.87 % (17951)------------------------------
% 1.65/1.87 % (17951)------------------------------
% 1.65/1.88 % (17954)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/922Mi)
% 1.65/1.88 % (17946)Instruction limit reached!
% 1.65/1.88 % (17946)------------------------------
% 1.65/1.88 % (17946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.88 % (17946)Termination reason: Unknown
% 1.65/1.88 % (17946)Termination phase: Saturation
% 1.65/1.88
% 1.65/1.88 % (17946)Memory used [KB]: 6396
% 1.65/1.88 % (17946)Time elapsed: 0.090 s
% 1.65/1.88 % (17946)Instructions burned: 298 (million)
% 1.65/1.88 % (17946)------------------------------
% 1.65/1.88 % (17946)------------------------------
% 1.65/1.88 % (17955)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/182Mi)
% 1.65/1.89 % (17956)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/164Mi)
% 1.65/1.90 % (17953)Instruction limit reached!
% 1.65/1.90 % (17953)------------------------------
% 1.65/1.90 % (17953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.90 % (17953)Termination reason: Unknown
% 1.65/1.90 % (17953)Termination phase: Saturation
% 1.65/1.90
% 1.65/1.90 % (17953)Memory used [KB]: 6268
% 1.65/1.90 % (17953)Time elapsed: 0.036 s
% 1.65/1.90 % (17953)Instructions burned: 115 (million)
% 1.65/1.90 % (17953)------------------------------
% 1.65/1.90 % (17953)------------------------------
% 1.65/1.90 % (17956)Refutation not found, incomplete strategy
% 1.65/1.90 % (17956)------------------------------
% 1.65/1.90 % (17956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.90 % (17956)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.90
% 1.65/1.90
% 1.65/1.90 % (17956)Memory used [KB]: 1535
% 1.65/1.90 % (17956)Time elapsed: 0.015 s
% 1.65/1.90 % (17956)Instructions burned: 49 (million)
% 1.65/1.90 % (17956)------------------------------
% 1.65/1.90 % (17956)------------------------------
% 1.65/1.91 % (17957)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/50Mi)
% 1.65/1.91 % (17940)Instruction limit reached!
% 1.65/1.91 % (17940)------------------------------
% 1.65/1.91 % (17940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.91 % (17940)Termination reason: Unknown
% 1.65/1.91 % (17940)Termination phase: Saturation
% 1.65/1.91
% 1.65/1.91 % (17940)Memory used [KB]: 7036
% 1.65/1.91 % (17940)Time elapsed: 0.141 s
% 1.65/1.91 % (17940)Instructions burned: 459 (million)
% 1.65/1.91 % (17940)------------------------------
% 1.65/1.91 % (17940)------------------------------
% 1.65/1.91 % (17958)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/368Mi)
% 1.65/1.92 % (17959)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/1021Mi)
% 1.65/1.92 % (17952)Instruction limit reached!
% 1.65/1.92 % (17952)------------------------------
% 1.65/1.92 % (17952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.92 % (17952)Termination reason: Unknown
% 1.65/1.92 % (17952)Termination phase: Saturation
% 1.65/1.92
% 1.65/1.92 % (17952)Memory used [KB]: 6268
% 1.65/1.92 % (17952)Time elapsed: 0.064 s
% 1.65/1.92 % (17952)Instructions burned: 216 (million)
% 1.65/1.92 % (17952)------------------------------
% 1.65/1.92 % (17952)------------------------------
% 1.65/1.92 % (17957)Instruction limit reached!
% 1.65/1.92 % (17957)------------------------------
% 1.65/1.92 % (17957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.92 % (17957)Termination reason: Unknown
% 1.65/1.92 % (17957)Termination phase: Saturation
% 1.65/1.92
% 1.65/1.92 % (17957)Memory used [KB]: 10362
% 1.65/1.92 % (17957)Time elapsed: 0.014 s
% 1.65/1.92 % (17957)Instructions burned: 50 (million)
% 1.65/1.92 % (17957)------------------------------
% 1.65/1.92 % (17957)------------------------------
% 1.65/1.93 % (17960)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/267Mi)
% 1.65/1.93 % (17961)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_17206 for (2992ds/204Mi)
% 1.65/1.94 % (17955)Instruction limit reached!
% 1.65/1.94 % (17955)------------------------------
% 1.65/1.94 % (17955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.94 % (17955)Termination reason: Unknown
% 1.65/1.94 % (17955)Termination phase: Saturation
% 1.65/1.94
% 1.65/1.94 % (17955)Memory used [KB]: 6268
% 1.65/1.94 % (17955)Time elapsed: 0.052 s
% 1.65/1.94 % (17955)Instructions burned: 183 (million)
% 1.65/1.94 % (17955)------------------------------
% 1.65/1.94 % (17955)------------------------------
% 1.65/1.94 % (17962)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17206 for (2991ds/26Mi)
% 1.65/1.95 % (17962)Instruction limit reached!
% 1.65/1.95 % (17962)------------------------------
% 1.65/1.95 % (17962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.95 % (17962)Termination reason: Unknown
% 1.65/1.95 % (17962)Termination phase: Property scanning
% 1.65/1.95
% 1.65/1.95 % (17962)Memory used [KB]: 1407
% 1.65/1.95 % (17962)Time elapsed: 0.008 s
% 1.65/1.95 % (17962)Instructions burned: 28 (million)
% 1.65/1.95 % (17962)------------------------------
% 1.65/1.95 % (17962)------------------------------
% 1.65/1.96 % (17963)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_17206 for (2991ds/53Mi)
% 1.65/1.97 % (17963)Instruction limit reached!
% 1.65/1.97 % (17963)------------------------------
% 1.65/1.97 % (17963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.97 % (17963)Termination reason: Unknown
% 1.65/1.97 % (17963)Termination phase: Saturation
% 1.65/1.97
% 1.65/1.97 % (17963)Memory used [KB]: 5884
% 1.65/1.97 % (17963)Time elapsed: 0.014 s
% 1.65/1.97 % (17963)Instructions burned: 53 (million)
% 1.65/1.97 % (17963)------------------------------
% 1.65/1.97 % (17963)------------------------------
% 1.65/1.98 % (17964)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_17206 for (2991ds/4436Mi)
% 1.65/1.99 % (17961)Instruction limit reached!
% 1.65/1.99 % (17961)------------------------------
% 1.65/1.99 % (17961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.99 % (17961)Termination reason: Unknown
% 1.65/1.99 % (17961)Termination phase: Saturation
% 1.65/1.99
% 1.65/1.99 % (17961)Memory used [KB]: 6140
% 1.65/1.99 % (17961)Time elapsed: 0.062 s
% 1.65/1.99 % (17961)Instructions burned: 206 (million)
% 1.65/1.99 % (17961)------------------------------
% 1.65/1.99 % (17961)------------------------------
% 1.65/2.00 % (17965)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_17206 for (2991ds/1539Mi)
% 1.65/2.01 % (17960)Instruction limit reached!
% 1.65/2.01 % (17960)------------------------------
% 1.65/2.01 % (17960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/2.01 % (17960)Termination reason: Unknown
% 1.65/2.01 % (17960)Termination phase: Saturation
% 1.65/2.01
% 1.65/2.01 % (17960)Memory used [KB]: 6652
% 1.65/2.01 % (17960)Time elapsed: 0.079 s
% 1.65/2.01 % (17960)Instructions burned: 267 (million)
% 1.65/2.01 % (17960)------------------------------
% 1.65/2.01 % (17960)------------------------------
% 7.80/2.02 % (17966)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_17206 for (2991ds/408Mi)
% 7.80/2.02 % (17958)Instruction limit reached!
% 7.80/2.02 % (17958)------------------------------
% 7.80/2.02 % (17958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.80/2.02 % (17958)Termination reason: Unknown
% 7.80/2.02 % (17958)Termination phase: Saturation
% 7.80/2.02
% 7.80/2.02 % (17958)Memory used [KB]: 6908
% 7.80/2.02 % (17958)Time elapsed: 0.110 s
% 7.80/2.02 % (17958)Instructions burned: 369 (million)
% 7.80/2.02 % (17958)------------------------------
% 7.80/2.02 % (17958)------------------------------
% 7.80/2.03 % (17967)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_17206 for (2990ds/5205Mi)
% 7.80/2.09 % (17947)Instruction limit reached!
% 7.80/2.09 % (17947)------------------------------
% 7.80/2.09 % (17947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.80/2.09 % (17947)Termination reason: Unknown
% 7.80/2.09 % (17947)Termination phase: Saturation
% 7.80/2.09
% 7.80/2.09 % (17947)Memory used [KB]: 7803
% 7.80/2.09 % (17947)Time elapsed: 0.297 s
% 7.80/2.09 % (17947)Instructions burned: 988 (million)
% 7.80/2.09 % (17947)------------------------------
% 7.80/2.09 % (17947)------------------------------
% 7.80/2.10 % (17968)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_17206 for (2990ds/1913Mi)
% 8.32/2.13 % (17966)Instruction limit reached!
% 8.32/2.13 % (17966)------------------------------
% 8.32/2.13 % (17966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.13 % (17966)Termination reason: Unknown
% 8.32/2.13 % (17966)Termination phase: Saturation
% 8.32/2.13
% 8.32/2.13 % (17966)Memory used [KB]: 6780
% 8.32/2.13 % (17966)Time elapsed: 0.140 s
% 8.32/2.13 % (17966)Instructions burned: 410 (million)
% 8.32/2.13 % (17966)------------------------------
% 8.32/2.13 % (17966)------------------------------
% 8.32/2.14 % (17969)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_17206 for (2989ds/4350Mi)
% 8.32/2.14 % (17954)Instruction limit reached!
% 8.32/2.14 % (17954)------------------------------
% 8.32/2.14 % (17954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.14 % (17954)Termination reason: Unknown
% 8.32/2.14 % (17954)Termination phase: Saturation
% 8.32/2.14
% 8.32/2.14 % (17954)Memory used [KB]: 7291
% 8.32/2.14 % (17954)Time elapsed: 0.267 s
% 8.32/2.14 % (17954)Instructions burned: 923 (million)
% 8.32/2.14 % (17954)------------------------------
% 8.32/2.14 % (17954)------------------------------
% 8.32/2.15 % (17970)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_17206 for (2989ds/68Mi)
% 8.32/2.17 % (17970)Instruction limit reached!
% 8.32/2.17 % (17970)------------------------------
% 8.32/2.17 % (17970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.17 % (17970)Termination reason: Unknown
% 8.32/2.17 % (17970)Termination phase: Saturation
% 8.32/2.17
% 8.32/2.17 % (17970)Memory used [KB]: 6140
% 8.32/2.17 % (17970)Time elapsed: 0.020 s
% 8.32/2.17 % (17970)Instructions burned: 68 (million)
% 8.32/2.17 % (17970)------------------------------
% 8.32/2.17 % (17970)------------------------------
% 8.32/2.18 % (17971)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_17206 for (2989ds/358Mi)
% 8.77/2.22 % (17959)Instruction limit reached!
% 8.77/2.22 % (17959)------------------------------
% 8.77/2.22 % (17959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.22 % (17959)Termination reason: Unknown
% 8.77/2.22 % (17959)Termination phase: Saturation
% 8.77/2.22
% 8.77/2.22 % (17959)Memory used [KB]: 7803
% 8.77/2.22 % (17959)Time elapsed: 0.301 s
% 8.77/2.22 % (17959)Instructions burned: 1021 (million)
% 8.77/2.22 % (17959)------------------------------
% 8.77/2.22 % (17959)------------------------------
% 8.77/2.23 % (17972)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17206 for (2988ds/31Mi)
% 8.77/2.24 % (17972)Instruction limit reached!
% 8.77/2.24 % (17972)------------------------------
% 8.77/2.24 % (17972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.24 % (17972)Termination reason: Unknown
% 8.77/2.24 % (17972)Termination phase: Property scanning
% 8.77/2.24
% 8.77/2.24 % (17972)Memory used [KB]: 1279
% 8.77/2.24 % (17972)Time elapsed: 0.010 s
% 8.77/2.24 % (17972)Instructions burned: 34 (million)
% 8.77/2.24 % (17972)------------------------------
% 8.77/2.24 % (17972)------------------------------
% 8.77/2.25 % (17973)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_17206 for (2988ds/279Mi)
% 8.77/2.27 % (17973)Refutation not found, incomplete strategy
% 8.77/2.27 % (17973)------------------------------
% 8.77/2.27 % (17973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.27 % (17973)Termination reason: Refutation not found, incomplete strategy
% 8.77/2.27
% 8.77/2.27
% 8.77/2.27 % (17973)Memory used [KB]: 6012
% 8.77/2.27 % (17973)Time elapsed: 0.020 s
% 8.77/2.27 % (17973)Instructions burned: 74 (million)
% 8.77/2.27 % (17973)------------------------------
% 8.77/2.27 % (17973)------------------------------
% 8.77/2.28 % (17974)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_17206 for (2988ds/258Mi)
% 8.77/2.29 % (17971)Instruction limit reached!
% 8.77/2.29 % (17971)------------------------------
% 8.77/2.29 % (17971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.29 % (17971)Termination reason: Unknown
% 8.77/2.29 % (17971)Termination phase: Saturation
% 8.77/2.29
% 8.77/2.29 % (17971)Memory used [KB]: 6268
% 8.77/2.29 % (17971)Time elapsed: 0.105 s
% 8.77/2.29 % (17971)Instructions burned: 360 (million)
% 8.77/2.29 % (17971)------------------------------
% 8.77/2.29 % (17971)------------------------------
% 8.77/2.30 % (17975)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17206 for (2988ds/26Mi)
% 9.16/2.30 % (17975)Instruction limit reached!
% 9.16/2.30 % (17975)------------------------------
% 9.16/2.30 % (17975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.30 % (17975)Termination reason: Unknown
% 9.16/2.30 % (17975)Termination phase: Property scanning
% 9.16/2.30
% 9.16/2.30 % (17975)Memory used [KB]: 1407
% 9.16/2.30 % (17975)Time elapsed: 0.008 s
% 9.16/2.30 % (17975)Instructions burned: 28 (million)
% 9.16/2.30 % (17975)------------------------------
% 9.16/2.30 % (17975)------------------------------
% 9.16/2.31 % (17976)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_17206 for (2988ds/995Mi)
% 9.16/2.35 % (17974)Instruction limit reached!
% 9.16/2.35 % (17974)------------------------------
% 9.16/2.35 % (17974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.35 % (17974)Termination reason: Unknown
% 9.16/2.35 % (17974)Termination phase: Saturation
% 9.16/2.35
% 9.16/2.35 % (17974)Memory used [KB]: 6652
% 9.16/2.35 % (17974)Time elapsed: 0.076 s
% 9.16/2.35 % (17974)Instructions burned: 258 (million)
% 9.16/2.35 % (17974)------------------------------
% 9.16/2.35 % (17974)------------------------------
% 9.16/2.36 % (17977)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_17206 for (2987ds/373Mi)
% 9.46/2.45 % (17965)Instruction limit reached!
% 9.46/2.45 % (17965)------------------------------
% 9.46/2.45 % (17965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.45 % (17965)Termination reason: Unknown
% 9.46/2.45 % (17965)Termination phase: Saturation
% 9.46/2.45
% 9.46/2.45 % (17965)Memory used [KB]: 7547
% 9.46/2.45 % (17965)Time elapsed: 0.446 s
% 9.46/2.45 % (17965)Instructions burned: 1539 (million)
% 9.46/2.45 % (17965)------------------------------
% 9.46/2.45 % (17965)------------------------------
% 9.46/2.46 % (17978)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_17206 for (2986ds/253Mi)
% 9.46/2.47 % (17977)Instruction limit reached!
% 9.46/2.47 % (17977)------------------------------
% 9.46/2.47 % (17977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.47 % (17977)Termination reason: Unknown
% 9.46/2.47 % (17977)Termination phase: Saturation
% 9.46/2.47
% 9.46/2.47 % (17977)Memory used [KB]: 6268
% 9.46/2.47 % (17977)Time elapsed: 0.109 s
% 9.46/2.47 % (17977)Instructions burned: 373 (million)
% 9.46/2.47 % (17977)------------------------------
% 9.46/2.47 % (17977)------------------------------
% 9.46/2.48 % (17979)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_17206 for (2986ds/832Mi)
% 9.73/2.53 % (17978)Instruction limit reached!
% 9.73/2.53 % (17978)------------------------------
% 9.73/2.53 % (17978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.73/2.53 % (17978)Termination reason: Unknown
% 9.73/2.53 % (17978)Termination phase: Saturation
% 9.73/2.53
% 9.73/2.53 % (17978)Memory used [KB]: 6524
% 9.73/2.53 % (17978)Time elapsed: 0.074 s
% 9.73/2.53 % (17978)Instructions burned: 255 (million)
% 9.73/2.53 % (17978)------------------------------
% 9.73/2.53 % (17978)------------------------------
% 9.73/2.54 % (17980)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_17206 for (2985ds/668Mi)
% 9.73/2.59 % (17976)Instruction limit reached!
% 9.73/2.59 % (17976)------------------------------
% 9.73/2.59 % (17976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.73/2.59 % (17976)Termination reason: Unknown
% 9.73/2.59 % (17976)Termination phase: Saturation
% 9.73/2.59
% 9.73/2.59 % (17976)Memory used [KB]: 8955
% 9.73/2.59 % (17976)Time elapsed: 0.279 s
% 9.73/2.59 % (17976)Instructions burned: 997 (million)
% 9.73/2.59 % (17976)------------------------------
% 9.73/2.59 % (17976)------------------------------
% 10.20/2.60 % (17981)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_17206 for (2985ds/40Mi)
% 10.20/2.61 % (17981)Instruction limit reached!
% 10.20/2.61 % (17981)------------------------------
% 10.20/2.61 % (17981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.61 % (17981)Termination reason: Unknown
% 10.20/2.61 % (17981)Termination phase: Property scanning
% 10.20/2.61
% 10.20/2.61 % (17981)Memory used [KB]: 1407
% 10.20/2.61 % (17981)Time elapsed: 0.011 s
% 10.20/2.61 % (17981)Instructions burned: 41 (million)
% 10.20/2.61 % (17981)------------------------------
% 10.20/2.61 % (17981)------------------------------
% 10.20/2.62 % (17982)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_17206 for (2985ds/294Mi)
% 10.20/2.65 % (17968)Instruction limit reached!
% 10.20/2.65 % (17968)------------------------------
% 10.20/2.65 % (17968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.65 % (17968)Termination reason: Unknown
% 10.20/2.65 % (17968)Termination phase: Saturation
% 10.20/2.65
% 10.20/2.65 % (17968)Memory used [KB]: 3070
% 10.20/2.65 % (17968)Time elapsed: 0.548 s
% 10.20/2.65 % (17968)Instructions burned: 1914 (million)
% 10.20/2.65 % (17968)------------------------------
% 10.20/2.65 % (17968)------------------------------
% 10.20/2.66 % (17983)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_17206 for (2984ds/187Mi)
% 10.20/2.69 % (17982)Instruction limit reached!
% 10.20/2.69 % (17982)------------------------------
% 10.20/2.69 % (17982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.69 % (17982)Termination reason: Unknown
% 10.20/2.69 % (17982)Termination phase: Saturation
% 10.20/2.69
% 10.20/2.69 % (17982)Memory used [KB]: 6140
% 10.20/2.69 % (17982)Time elapsed: 0.076 s
% 10.20/2.69 % (17982)Instructions burned: 297 (million)
% 10.20/2.69 % (17982)------------------------------
% 10.20/2.69 % (17982)------------------------------
% 10.96/2.70 % (17984)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_17206 for (2984ds/371Mi)
% 10.96/2.72 % (17983)Instruction limit reached!
% 10.96/2.72 % (17983)------------------------------
% 10.96/2.72 % (17983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.72 % (17983)Termination reason: Unknown
% 10.96/2.72 % (17983)Termination phase: Saturation
% 10.96/2.72
% 10.96/2.72 % (17983)Memory used [KB]: 6268
% 10.96/2.72 % (17983)Time elapsed: 0.057 s
% 10.96/2.72 % (17983)Instructions burned: 189 (million)
% 10.96/2.72 % (17983)------------------------------
% 10.96/2.72 % (17983)------------------------------
% 10.96/2.72 % (17979)Instruction limit reached!
% 10.96/2.72 % (17979)------------------------------
% 10.96/2.72 % (17979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.72 % (17979)Termination reason: Unknown
% 10.96/2.72 % (17979)Termination phase: Saturation
% 10.96/2.72
% 10.96/2.72 % (17979)Memory used [KB]: 7291
% 10.96/2.72 % (17979)Time elapsed: 0.242 s
% 10.96/2.72 % (17979)Instructions burned: 832 (million)
% 10.96/2.72 % (17979)------------------------------
% 10.96/2.72 % (17979)------------------------------
% 10.96/2.72 % (17980)Instruction limit reached!
% 10.96/2.72 % (17980)------------------------------
% 10.96/2.72 % (17980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.72 % (17980)Termination reason: Unknown
% 10.96/2.72 % (17980)Termination phase: Saturation
% 10.96/2.72
% 10.96/2.72 % (17980)Memory used [KB]: 12025
% 10.96/2.72 % (17980)Time elapsed: 0.187 s
% 10.96/2.72 % (17980)Instructions burned: 670 (million)
% 10.96/2.72 % (17980)------------------------------
% 10.96/2.72 % (17980)------------------------------
% 10.96/2.73 % (17985)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_17206 for (2984ds/1827Mi)
% 10.96/2.73 % (17986)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_17206 for (2984ds/70Mi)
% 10.96/2.73 % (17987)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_17206 for (2983ds/316Mi)
% 10.96/2.75 % (17986)Instruction limit reached!
% 10.96/2.75 % (17986)------------------------------
% 10.96/2.75 % (17986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.75 % (17986)Termination reason: Unknown
% 10.96/2.75 % (17986)Termination phase: Saturation
% 10.96/2.75
% 10.96/2.75 % (17986)Memory used [KB]: 1535
% 10.96/2.75 % (17986)Time elapsed: 0.020 s
% 10.96/2.75 % (17986)Instructions burned: 72 (million)
% 10.96/2.75 % (17986)------------------------------
% 10.96/2.75 % (17986)------------------------------
% 10.96/2.75 % (17987)Refutation not found, incomplete strategy
% 10.96/2.75 % (17987)------------------------------
% 10.96/2.75 % (17987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.75 % (17987)Termination reason: Refutation not found, incomplete strategy
% 10.96/2.75
% 10.96/2.75
% 10.96/2.75 % (17987)Memory used [KB]: 6012
% 10.96/2.75 % (17987)Time elapsed: 0.018 s
% 10.96/2.75 % (17987)Instructions burned: 67 (million)
% 10.96/2.75 % (17987)------------------------------
% 10.96/2.75 % (17987)------------------------------
% 10.96/2.76 % (17988)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_17206 for (2983ds/932Mi)
% 10.96/2.76 % (17989)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_17206 for (2983ds/4714Mi)
% 10.96/2.78 % (17989)Refutation not found, incomplete strategy
% 10.96/2.78 % (17989)------------------------------
% 10.96/2.78 % (17989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.78 % (17989)Termination reason: Refutation not found, incomplete strategy
% 10.96/2.78
% 10.96/2.78
% 10.96/2.78 % (17989)Memory used [KB]: 6012
% 10.96/2.78 % (17989)Time elapsed: 0.021 s
% 10.96/2.78 % (17989)Instructions burned: 78 (million)
% 10.96/2.78 % (17989)------------------------------
% 10.96/2.78 % (17989)------------------------------
% 10.96/2.79 % (17990)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_17206 for (2983ds/8250Mi)
% 11.65/2.81 % (17984)Instruction limit reached!
% 11.65/2.81 % (17984)------------------------------
% 11.65/2.81 % (17984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.65/2.81 % (17984)Termination reason: Unknown
% 11.65/2.81 % (17984)Termination phase: Saturation
% 11.65/2.81
% 11.65/2.81 % (17984)Memory used [KB]: 6908
% 11.65/2.81 % (17984)Time elapsed: 0.110 s
% 11.65/2.81 % (17984)Instructions burned: 374 (million)
% 11.65/2.81 % (17984)------------------------------
% 11.65/2.81 % (17984)------------------------------
% 11.65/2.82 % (17991)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_17206 for (2983ds/770Mi)
% 11.65/2.83 % (17991)Refutation not found, incomplete strategy
% 11.65/2.83 % (17991)------------------------------
% 11.65/2.83 % (17991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.65/2.83 % (17991)Termination reason: Refutation not found, incomplete strategy
% 11.65/2.83
% 11.65/2.83
% 11.65/2.83 % (17991)Memory used [KB]: 5884
% 11.65/2.83 % (17991)Time elapsed: 0.013 s
% 11.65/2.83 % (17991)Instructions burned: 39 (million)
% 11.65/2.83 % (17991)------------------------------
% 11.65/2.83 % (17991)------------------------------
% 11.65/2.84 % (17992)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_17206 for (2982ds/794Mi)
% 11.91/3.01 % (17988)Instruction limit reached!
% 11.91/3.01 % (17988)------------------------------
% 11.91/3.01 % (17988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.91/3.01 % (17988)Termination reason: Unknown
% 11.91/3.01 % (17988)Termination phase: Saturation
% 11.91/3.01
% 11.91/3.01 % (17988)Memory used [KB]: 7036
% 11.91/3.01 % (17988)Time elapsed: 0.253 s
% 11.91/3.01 % (17988)Instructions burned: 934 (million)
% 11.91/3.01 % (17988)------------------------------
% 11.91/3.01 % (17988)------------------------------
% 14.81/3.02 % (17993)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_17206 for (2981ds/464Mi)
% 14.81/3.08 % (17992)Instruction limit reached!
% 14.81/3.08 % (17992)------------------------------
% 14.81/3.08 % (17992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.81/3.08 % (17992)Termination reason: Unknown
% 14.81/3.08 % (17992)Termination phase: Saturation
% 14.81/3.08
% 14.81/3.08 % (17992)Memory used [KB]: 3582
% 14.81/3.08 % (17992)Time elapsed: 0.233 s
% 14.81/3.08 % (17992)Instructions burned: 794 (million)
% 14.81/3.08 % (17992)------------------------------
% 14.81/3.08 % (17992)------------------------------
% 14.81/3.09 % (17994)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_17206 for (2980ds/1376Mi)
% 15.39/3.16 % (17993)Instruction limit reached!
% 15.39/3.16 % (17993)------------------------------
% 15.39/3.16 % (17993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.16 % (17993)Termination reason: Unknown
% 15.39/3.16 % (17993)Termination phase: Saturation
% 15.39/3.16
% 15.39/3.16 % (17993)Memory used [KB]: 6524
% 15.39/3.16 % (17993)Time elapsed: 0.143 s
% 15.39/3.16 % (17993)Instructions burned: 464 (million)
% 15.39/3.16 % (17993)------------------------------
% 15.39/3.16 % (17993)------------------------------
% 15.39/3.17 % (17995)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_17206 for (2979ds/906Mi)
% 15.97/3.25 % (17985)Instruction limit reached!
% 15.97/3.25 % (17985)------------------------------
% 15.97/3.25 % (17985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/3.25 % (17985)Termination reason: Unknown
% 15.97/3.25 % (17985)Termination phase: Saturation
% 15.97/3.25
% 15.97/3.25 % (17985)Memory used [KB]: 9338
% 15.97/3.25 % (17985)Time elapsed: 0.529 s
% 15.97/3.25 % (17985)Instructions burned: 1827 (million)
% 15.97/3.25 % (17985)------------------------------
% 15.97/3.25 % (17985)------------------------------
% 15.97/3.26 % (17964)Instruction limit reached!
% 15.97/3.26 % (17964)------------------------------
% 15.97/3.26 % (17964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/3.26 % (17964)Termination reason: Unknown
% 15.97/3.26 % (17964)Termination phase: Saturation
% 15.97/3.26
% 15.97/3.26 % (17964)Memory used [KB]: 9978
% 15.97/3.26 % (17964)Time elapsed: 1.279 s
% 15.97/3.26 % (17964)Instructions burned: 4436 (million)
% 15.97/3.26 % (17964)------------------------------
% 15.97/3.26 % (17964)------------------------------
% 15.97/3.26 % (17996)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_17206 for (2978ds/434Mi)
% 15.97/3.27 % (17997)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_17206 for (2978ds/865Mi)
% 16.40/3.39 % (17996)Instruction limit reached!
% 16.40/3.39 % (17996)------------------------------
% 16.40/3.39 % (17996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.39 % (17996)Termination reason: Unknown
% 16.40/3.39 % (17996)Termination phase: Saturation
% 16.40/3.39
% 16.40/3.39 % (17996)Memory used [KB]: 6524
% 16.40/3.39 % (17996)Time elapsed: 0.129 s
% 16.40/3.39 % (17996)Instructions burned: 434 (million)
% 16.40/3.39 % (17996)------------------------------
% 16.40/3.39 % (17996)------------------------------
% 16.85/3.40 % (17998)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_17206 for (2977ds/593Mi)
% 16.85/3.43 % (17969)Instruction limit reached!
% 16.85/3.43 % (17969)------------------------------
% 16.85/3.43 % (17969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/3.43 % (17969)Termination reason: Unknown
% 16.85/3.43 % (17969)Termination phase: Saturation
% 16.85/3.43
% 16.85/3.43 % (17969)Memory used [KB]: 9210
% 16.85/3.43 % (17969)Time elapsed: 1.287 s
% 16.85/3.43 % (17969)Instructions burned: 4351 (million)
% 16.85/3.43 % (17969)------------------------------
% 16.85/3.43 % (17969)------------------------------
% 16.85/3.44 % (17999)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_17206 for (2976ds/443Mi)
% 16.85/3.45 % (17995)Instruction limit reached!
% 16.85/3.45 % (17995)------------------------------
% 16.85/3.45 % (17995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/3.45 % (17995)Termination reason: Unknown
% 16.85/3.45 % (17995)Termination phase: Saturation
% 16.85/3.45
% 16.85/3.45 % (17995)Memory used [KB]: 9850
% 16.85/3.45 % (17995)Time elapsed: 0.282 s
% 16.85/3.45 % (17995)Instructions burned: 909 (million)
% 16.85/3.45 % (17995)------------------------------
% 16.85/3.45 % (17995)------------------------------
% 16.85/3.46 % (18000)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_17206 for (2976ds/594Mi)
% 17.38/3.50 % (17994)Instruction limit reached!
% 17.38/3.50 % (17994)------------------------------
% 17.38/3.50 % (17994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.38/3.50 % (17994)Termination reason: Unknown
% 17.38/3.50 % (17994)Termination phase: Saturation
% 17.38/3.50
% 17.38/3.50 % (17994)Memory used [KB]: 10746
% 17.38/3.50 % (17994)Time elapsed: 0.419 s
% 17.38/3.50 % (17994)Instructions burned: 1378 (million)
% 17.38/3.50 % (17994)------------------------------
% 17.38/3.50 % (17994)------------------------------
% 17.38/3.51 % (18001)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_17206 for (2976ds/327Mi)
% 17.38/3.52 % (17967)Instruction limit reached!
% 17.38/3.52 % (17967)------------------------------
% 17.38/3.52 % (17967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.38/3.52 % (17967)Termination reason: Unknown
% 17.38/3.52 % (17967)Termination phase: Saturation
% 17.38/3.52
% 17.38/3.52 % (17967)Memory used [KB]: 18549
% 17.38/3.52 % (17967)Time elapsed: 1.492 s
% 17.38/3.52 % (17967)Instructions burned: 5205 (million)
% 17.38/3.52 % (17967)------------------------------
% 17.38/3.52 % (17967)------------------------------
% 17.38/3.52 % (17997)Instruction limit reached!
% 17.38/3.52 % (17997)------------------------------
% 17.38/3.52 % (17997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.38/3.52 % (17997)Termination reason: Unknown
% 17.38/3.52 % (17997)Termination phase: Saturation
% 17.38/3.52
% 17.38/3.52 % (17997)Memory used [KB]: 9338
% 17.38/3.52 % (17997)Time elapsed: 0.255 s
% 17.38/3.52 % (17997)Instructions burned: 865 (million)
% 17.38/3.52 % (17997)------------------------------
% 17.38/3.52 % (17997)------------------------------
% 17.38/3.53 % (18002)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_17206 for (2976ds/5411Mi)
% 17.38/3.53 % (18003)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_17206 for (2976ds/1762Mi)
% 17.38/3.57 % (17998)Instruction limit reached!
% 17.38/3.57 % (17998)------------------------------
% 17.38/3.57 % (17998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.38/3.57 % (17998)Termination reason: Unknown
% 17.38/3.57 % (17998)Termination phase: Saturation
% 17.38/3.57
% 17.38/3.57 % (17998)Memory used [KB]: 8187
% 17.38/3.57 % (17998)Time elapsed: 0.172 s
% 17.38/3.57 % (17998)Instructions burned: 594 (million)
% 17.38/3.57 % (17998)------------------------------
% 17.38/3.57 % (17998)------------------------------
% 17.38/3.57 % (17999)Instruction limit reached!
% 17.38/3.57 % (17999)------------------------------
% 17.38/3.57 % (17999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.38/3.57 % (17999)Termination reason: Unknown
% 17.38/3.57 % (17999)Termination phase: Saturation
% 17.38/3.57
% 17.38/3.57 % (17999)Memory used [KB]: 6908
% 17.38/3.57 % (17999)Time elapsed: 0.135 s
% 17.38/3.57 % (17999)Instructions burned: 443 (million)
% 17.38/3.57 % (17999)------------------------------
% 17.38/3.57 % (17999)------------------------------
% 17.38/3.58 % (18004)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_17206 for (2975ds/96Mi)
% 17.38/3.58 % (18005)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_17206 for (2975ds/503Mi)
% 18.53/3.61 % (18004)Instruction limit reached!
% 18.53/3.61 % (18004)------------------------------
% 18.53/3.61 % (18004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.53/3.61 % (18004)Termination reason: Unknown
% 18.53/3.61 % (18004)Termination phase: Saturation
% 18.53/3.61
% 18.53/3.61 % (18004)Memory used [KB]: 6012
% 18.53/3.61 % (18004)Time elapsed: 0.029 s
% 18.53/3.61 % (18004)Instructions burned: 98 (million)
% 18.53/3.61 % (18004)------------------------------
% 18.53/3.61 % (18004)------------------------------
% 18.53/3.61 % (18001)Instruction limit reached!
% 18.53/3.61 % (18001)------------------------------
% 18.53/3.61 % (18001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.53/3.61 % (18001)Termination reason: Unknown
% 18.53/3.61 % (18001)Termination phase: Saturation
% 18.53/3.61
% 18.53/3.61 % (18001)Memory used [KB]: 6396
% 18.53/3.61 % (18001)Time elapsed: 0.101 s
% 18.53/3.61 % (18001)Instructions burned: 329 (million)
% 18.53/3.61 % (18001)------------------------------
% 18.53/3.61 % (18001)------------------------------
% 18.53/3.62 % (18006)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_17206 for (2975ds/90Mi)
% 18.53/3.62 % (18007)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_17206 for (2975ds/593Mi)
% 18.53/3.64 % (18000)Instruction limit reached!
% 18.53/3.64 % (18000)------------------------------
% 18.53/3.64 % (18000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.53/3.64 % (18000)Termination reason: Unknown
% 18.53/3.64 % (18000)Termination phase: Saturation
% 18.53/3.64
% 18.53/3.64 % (18000)Memory used [KB]: 6524
% 18.53/3.64 % (18000)Time elapsed: 0.175 s
% 18.53/3.64 % (18000)Instructions burned: 594 (million)
% 18.53/3.64 % (18000)------------------------------
% 18.53/3.64 % (18000)------------------------------
% 18.53/3.64 % (18006)Instruction limit reached!
% 18.53/3.64 % (18006)------------------------------
% 18.53/3.64 % (18006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.53/3.64 % (18006)Termination reason: Unknown
% 18.53/3.64 % (18006)Termination phase: Saturation
% 18.53/3.64
% 18.53/3.64 % (18006)Memory used [KB]: 6268
% 18.53/3.64 % (18006)Time elapsed: 0.027 s
% 18.53/3.64 % (18006)Instructions burned: 90 (million)
% 18.53/3.64 % (18006)------------------------------
% 18.53/3.64 % (18006)------------------------------
% 18.53/3.65 % (18008)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_17206 for (2974ds/1512Mi)
% 18.53/3.65 % (18009)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_17206 for (2974ds/569Mi)
% 19.00/3.73 % (18005)Instruction limit reached!
% 19.00/3.73 % (18005)------------------------------
% 19.00/3.73 % (18005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.00/3.73 % (18005)Termination reason: Unknown
% 19.00/3.73 % (18005)Termination phase: Saturation
% 19.00/3.73
% 19.00/3.73 % (18005)Memory used [KB]: 6780
% 19.00/3.73 % (18005)Time elapsed: 0.146 s
% 19.00/3.73 % (18005)Instructions burned: 506 (million)
% 19.00/3.73 % (18005)------------------------------
% 19.00/3.73 % (18005)------------------------------
% 19.00/3.74 % (18010)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_17206 for (2974ds/501Mi)
% 19.26/3.80 % (18007)Instruction limit reached!
% 19.26/3.80 % (18007)------------------------------
% 19.26/3.80 % (18007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.26/3.80 % (18007)Termination reason: Unknown
% 19.26/3.80 % (18007)Termination phase: Saturation
% 19.26/3.80
% 19.26/3.80 % (18007)Memory used [KB]: 6780
% 19.26/3.80 % (18007)Time elapsed: 0.180 s
% 19.26/3.80 % (18007)Instructions burned: 596 (million)
% 19.26/3.80 % (18007)------------------------------
% 19.26/3.80 % (18007)------------------------------
% 19.26/3.81 % (18011)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_17206 for (2973ds/562Mi)
% 19.26/3.82 % (18009)Instruction limit reached!
% 19.26/3.82 % (18009)------------------------------
% 19.26/3.82 % (18009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.26/3.82 % (18009)Termination reason: Unknown
% 19.26/3.82 % (18009)Termination phase: Saturation
% 19.26/3.82
% 19.26/3.82 % (18009)Memory used [KB]: 7164
% 19.26/3.82 % (18009)Time elapsed: 0.167 s
% 19.26/3.82 % (18009)Instructions burned: 570 (million)
% 19.26/3.82 % (18009)------------------------------
% 19.26/3.82 % (18009)------------------------------
% 19.26/3.83 % (18012)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_17206 for (2973ds/406Mi)
% 19.26/3.88 % (18010)Instruction limit reached!
% 19.26/3.88 % (18010)------------------------------
% 19.26/3.88 % (18010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.26/3.88 % (18010)Termination reason: Unknown
% 19.26/3.88 % (18010)Termination phase: Saturation
% 19.26/3.88
% 19.26/3.88 % (18010)Memory used [KB]: 7036
% 19.26/3.88 % (18010)Time elapsed: 0.165 s
% 19.26/3.88 % (18010)Instructions burned: 503 (million)
% 19.26/3.88 % (18010)------------------------------
% 19.26/3.88 % (18010)------------------------------
% 19.26/3.89 % (18013)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_17206 for (2972ds/582Mi)
% 19.88/3.95 % (18012)Instruction limit reached!
% 19.88/3.95 % (18012)------------------------------
% 19.88/3.95 % (18012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/3.95 % (18012)Termination reason: Unknown
% 19.88/3.95 % (18012)Termination phase: Saturation
% 19.88/3.95
% 19.88/3.95 % (18012)Memory used [KB]: 6780
% 19.88/3.95 % (18012)Time elapsed: 0.147 s
% 19.88/3.95 % (18012)Instructions burned: 406 (million)
% 19.88/3.95 % (18012)------------------------------
% 19.88/3.95 % (18012)------------------------------
% 19.88/3.96 % (18014)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_17206 for (2971ds/456Mi)
% 19.88/3.97 % (18011)Instruction limit reached!
% 19.88/3.97 % (18011)------------------------------
% 19.88/3.97 % (18011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/3.97 % (18011)Termination reason: Unknown
% 19.88/3.97 % (18011)Termination phase: Saturation
% 19.88/3.97
% 19.88/3.97 % (18011)Memory used [KB]: 8059
% 19.88/3.97 % (18011)Time elapsed: 0.179 s
% 19.88/3.97 % (18011)Instructions burned: 562 (million)
% 19.88/3.97 % (18011)------------------------------
% 19.88/3.97 % (18011)------------------------------
% 19.88/3.98 % (18015)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_17206 for (2971ds/393Mi)
% 21.82/4.05 % (18003)Instruction limit reached!
% 21.82/4.05 % (18003)------------------------------
% 21.82/4.05 % (18003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.82/4.05 % (18003)Termination reason: Unknown
% 21.82/4.05 % (18003)Termination phase: Saturation
% 21.82/4.05
% 21.82/4.05 % (18003)Memory used [KB]: 7164
% 21.82/4.05 % (18003)Time elapsed: 0.520 s
% 21.82/4.05 % (18003)Instructions burned: 1762 (million)
% 21.82/4.05 % (18003)------------------------------
% 21.82/4.05 % (18003)------------------------------
% 21.82/4.06 % (18013)Instruction limit reached!
% 21.82/4.06 % (18013)------------------------------
% 21.82/4.06 % (18013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.82/4.06 % (18013)Termination reason: Unknown
% 21.82/4.06 % (18013)Termination phase: Saturation
% 21.82/4.06
% 21.82/4.06 % (18013)Memory used [KB]: 6268
% 21.82/4.06 % (18013)Time elapsed: 0.195 s
% 21.82/4.06 % (18013)Instructions burned: 584 (million)
% 21.82/4.06 % (18013)------------------------------
% 21.82/4.06 % (18013)------------------------------
% 21.82/4.06 % (18016)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_17206 for (2970ds/1335Mi)
% 21.82/4.07 % (18017)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_17206 for (2970ds/3373Mi)
% 21.82/4.09 % (18015)Instruction limit reached!
% 21.82/4.09 % (18015)------------------------------
% 21.82/4.09 % (18015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.82/4.09 % (18015)Termination reason: Unknown
% 21.82/4.09 % (18015)Termination phase: Saturation
% 21.82/4.09
% 21.82/4.09 % (18015)Memory used [KB]: 7036
% 21.82/4.09 % (18015)Time elapsed: 0.113 s
% 21.82/4.09 % (18015)Instructions burned: 394 (million)
% 21.82/4.09 % (18015)------------------------------
% 21.82/4.09 % (18015)------------------------------
% 21.82/4.10 % (18008)Instruction limit reached!
% 21.82/4.10 % (18008)------------------------------
% 21.82/4.10 % (18008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.82/4.10 % (18008)Termination reason: Unknown
% 21.82/4.10 % (18008)Termination phase: Saturation
% 21.82/4.10
% 21.82/4.10 % (18008)Memory used [KB]: 9722
% 21.82/4.10 % (18008)Time elapsed: 0.452 s
% 21.82/4.10 % (18008)Instructions burned: 1514 (million)
% 21.82/4.10 % (18008)------------------------------
% 21.82/4.10 % (18008)------------------------------
% 21.82/4.10 % (18014)Instruction limit reached!
% 21.82/4.10 % (18014)------------------------------
% 21.82/4.10 % (18014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.82/4.10 % (18014)Termination reason: Unknown
% 21.82/4.10 % (18014)Termination phase: Saturation
% 21.82/4.10
% 21.82/4.10 % (18014)Memory used [KB]: 7036
% 21.82/4.10 % (18014)Time elapsed: 0.137 s
% 21.82/4.10 % (18014)Instructions burned: 456 (million)
% 21.82/4.10 % (18014)------------------------------
% 21.82/4.10 % (18014)------------------------------
% 21.82/4.10 % (18018)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_17206 for (2970ds/474Mi)
% 21.82/4.11 % (18019)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_17206 for (2970ds/157Mi)
% 21.82/4.11 % (18020)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_17206 for (2970ds/590Mi)
% 22.40/4.15 % (18019)Instruction limit reached!
% 22.40/4.15 % (18019)------------------------------
% 22.40/4.15 % (18019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.40/4.15 % (18019)Termination reason: Unknown
% 22.40/4.15 % (18019)Termination phase: Saturation
% 22.40/4.15
% 22.40/4.15 % (18019)Memory used [KB]: 6524
% 22.40/4.15 % (18019)Time elapsed: 0.046 s
% 22.40/4.15 % (18019)Instructions burned: 157 (million)
% 22.40/4.15 % (18019)------------------------------
% 22.40/4.15 % (18019)------------------------------
% 22.40/4.16 % (18021)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_17206 for (2969ds/104Mi)
% 22.40/4.19 % (18021)Instruction limit reached!
% 22.40/4.19 % (18021)------------------------------
% 22.40/4.19 % (18021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.40/4.19 % (18021)Termination reason: Unknown
% 22.40/4.19 % (18021)Termination phase: Saturation
% 22.40/4.19
% 22.40/4.19 % (18021)Memory used [KB]: 6396
% 22.40/4.19 % (18021)Time elapsed: 0.030 s
% 22.40/4.19 % (18021)Instructions burned: 104 (million)
% 22.40/4.19 % (18021)------------------------------
% 22.40/4.19 % (18021)------------------------------
% 22.66/4.20 % (18022)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_17206 for (2969ds/414Mi)
% 22.66/4.24 % (18018)Instruction limit reached!
% 22.66/4.24 % (18018)------------------------------
% 22.66/4.24 % (18018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.66/4.24 % (18018)Termination reason: Unknown
% 22.66/4.24 % (18018)Termination phase: Saturation
% 22.66/4.24
% 22.66/4.24 % (18018)Memory used [KB]: 7164
% 22.66/4.24 % (18018)Time elapsed: 0.142 s
% 22.66/4.24 % (18018)Instructions burned: 475 (million)
% 22.66/4.24 % (18018)------------------------------
% 22.66/4.24 % (18018)------------------------------
% 22.66/4.25 % (18023)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_17206 for (2968ds/715Mi)
% 22.66/4.26 % (18020)First to succeed.
% 22.66/4.27 % (18020)Refutation found. Thanks to Tanya!
% 22.66/4.27 % SZS status Theorem for DTF2THF_17206
% 22.66/4.27 % SZS output start Proof for DTF2THF_17206
% 22.66/4.27 thf(type_def_5, type, d: $tType).
% 22.66/4.27 thf(type_def_7, type, u: $tType).
% 22.66/4.27 thf(type_def_8, type, du: $tType).
% 22.66/4.27 thf(func_def_0, type, u: $tType).
% 22.66/4.27 thf(func_def_1, type, d: $tType).
% 22.66/4.27 thf(func_def_2, type, du: $tType).
% 22.66/4.27 thf(func_def_3, type, tyop_2Emin_2Ebool: d).
% 22.66/4.27 thf(func_def_4, type, tyop_2Emin_2Efun: d > d > d).
% 22.66/4.27 thf(func_def_5, type, tyop_2Eoption_2Eoption: d > d).
% 22.66/4.27 thf(func_def_6, type, s: d > u > du).
% 22.66/4.27 thf(func_def_7, type, app_2E2: du > du > u).
% 22.66/4.27 thf(func_def_8, type, combin_i_2E0: u).
% 22.66/4.27 thf(func_def_9, type, combin_k_2E0: u).
% 22.66/4.27 thf(func_def_10, type, combin_s_2E0: u).
% 22.66/4.27 thf(func_def_11, type, c_2Ebool_2E_21_2E0: u).
% 22.66/4.27 thf(func_def_12, type, c_2Ebool_2E_21_2E1: du > u).
% 22.66/4.27 thf(func_def_13, type, c_2Ebool_2E_2F_5C_2E0: u).
% 22.66/4.27 thf(func_def_14, type, c_2Ebool_2E_2F_5C_2E2: du > du > u).
% 22.66/4.27 thf(func_def_15, type, c_2Emin_2E_3D_2E0: u).
% 22.66/4.27 thf(func_def_16, type, c_2Emin_2E_3D_2E2: du > du > u).
% 22.66/4.27 thf(func_def_17, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 22.66/4.27 thf(func_def_18, type, c_2Emin_2E_3D_3D_3E_2E2: du > du > u).
% 22.66/4.27 thf(func_def_19, type, c_2Ebool_2E_3F_2E0: u).
% 22.66/4.27 thf(func_def_20, type, c_2Ebool_2E_3F_2E1: du > u).
% 22.66/4.27 thf(func_def_21, type, c_2Ebool_2EF_2E0: u).
% 22.66/4.27 thf(func_def_22, type, c_2Eoption_2EIS__NONE_2E0: u).
% 22.66/4.27 thf(func_def_23, type, c_2Eoption_2EIS__NONE_2E1: du > u).
% 22.66/4.27 thf(func_def_24, type, c_2Eoption_2EIS__SOME_2E0: u).
% 22.66/4.27 thf(func_def_25, type, c_2Eoption_2EIS__SOME_2E1: du > u).
% 22.66/4.27 thf(func_def_26, type, c_2Eoption_2ENONE_2E0: u).
% 22.66/4.27 thf(func_def_27, type, c_2Eoption_2EOPTION__JOIN_2E0: u).
% 22.66/4.27 thf(func_def_28, type, c_2Eoption_2EOPTION__JOIN_2E1: du > u).
% 22.66/4.27 thf(func_def_29, type, c_2Eoption_2EOPTION__MAP_2E0: u).
% 22.66/4.27 thf(func_def_30, type, c_2Eoption_2EOPTION__MAP_2E2: du > du > u).
% 22.66/4.27 thf(func_def_31, type, c_2Eoption_2EOPTREL_2E0: u).
% 22.66/4.27 thf(func_def_32, type, c_2Eoption_2EOPTREL_2E3: du > du > du > u).
% 22.66/4.27 thf(func_def_33, type, c_2Eoption_2ESOME_2E0: u).
% 22.66/4.27 thf(func_def_34, type, c_2Eoption_2ESOME_2E1: du > u).
% 22.66/4.27 thf(func_def_35, type, c_2Ebool_2ET_2E0: u).
% 22.66/4.27 thf(func_def_36, type, c_2Eoption_2ETHE_2E0: u).
% 22.66/4.27 thf(func_def_37, type, c_2Eoption_2ETHE_2E1: du > u).
% 22.66/4.27 thf(func_def_38, type, c_2Ebool_2E_5C_2F_2E0: u).
% 22.66/4.27 thf(func_def_39, type, c_2Ebool_2E_5C_2F_2E2: du > du > u).
% 22.66/4.27 thf(func_def_40, type, c_2Eoption_2Eoption__CASE_2E0: u).
% 22.66/4.27 thf(func_def_41, type, c_2Eoption_2Eoption__CASE_2E3: du > du > du > u).
% 22.66/4.27 thf(func_def_42, type, c_2Ebool_2E_7E_2E0: u).
% 22.66/4.27 thf(func_def_43, type, c_2Ebool_2E_7E_2E1: du > u).
% 22.66/4.27 thf(func_def_44, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ($o > $o) > $o > $o).
% 22.66/4.27 thf(func_def_45, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o > $o) > $o > $o > $o).
% 22.66/4.27 thf(func_def_46, type, mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o).
% 22.66/4.27 thf(func_def_47, type, mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 22.66/4.27 thf(func_def_50, type, mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o).
% 22.66/4.27 thf(func_def_51, type, mono_2Ec_2Ebool_2E_7E: $o > $o).
% 22.66/4.27 thf(func_def_52, type, i_mono_2Etyop_2Emin_2Ebool: $o > u).
% 22.66/4.27 thf(func_def_53, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o) > u).
% 22.66/4.27 thf(func_def_54, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ($o > $o > $o) > u).
% 22.66/4.27 thf(func_def_55, type, j_mono_2Etyop_2Emin_2Ebool: du > $o).
% 22.66/4.27 thf(func_def_56, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o).
% 22.66/4.27 thf(func_def_57, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o).
% 22.66/4.27 thf(func_def_63, type, sK0: u > u > d > u > d > u).
% 22.66/4.27 thf(func_def_64, type, sK1: u > u > d > u > d > u).
% 22.66/4.27 thf(func_def_65, type, sK2: d > u > d > u > u).
% 22.66/4.27 thf(func_def_66, type, sK3: u).
% 22.66/4.27 thf(func_def_67, type, sK4: u).
% 22.66/4.27 thf(func_def_68, type, sK5: d).
% 22.66/4.27 thf(func_def_69, type, sK6: u).
% 22.66/4.27 thf(f1022,plain,(
% 22.66/4.27 $false),
% 22.66/4.27 inference(avatar_sat_refutation,[status(thm)],[f383,f581,f613,f759,f774,f832,f1021])).
% 22.66/4.27 thf(f1021,plain,(
% 22.66/4.27 ~spl7_3 | spl7_7),
% 22.66/4.27 inference(avatar_contradiction_clause,[status(thm)],[f1020])).
% 22.66/4.27 thf(f1020,plain,(
% 22.66/4.27 $false | (~spl7_3 | spl7_7)),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f1011])).
% 22.66/4.27 thf(f1011,plain,(
% 22.66/4.27 ($true = $false) | (~spl7_3 | spl7_7)),
% 22.66/4.27 inference(backward_demodulation,[status(thm)],[f366,f1006])).
% 22.66/4.27 thf(f1006,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | (~spl7_3 | spl7_7)),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f1005])).
% 22.66/4.27 thf(f1005,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | ($true = $false) | (~spl7_3 | spl7_7)),
% 22.66/4.27 inference(forward_demodulation,[status(thm)],[f1004,f834])).
% 22.66/4.27 thf(f834,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $false) | spl7_7),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f833])).
% 22.66/4.27 thf(f833,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $false) | ($true != $true) | spl7_7),
% 22.66/4.27 inference(superposition,[status(thm)],[f381,f305])).
% 22.66/4.27 thf(f305,plain,(
% 22.66/4.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 22.66/4.27 inference(not_proxy_clausification,[status(thm)],[f304])).
% 22.66/4.27 thf(f304,plain,(
% 22.66/4.27 ( ! [X0 : $o] : (((~ X0) != $true) | ($false = X0)) )),
% 22.66/4.27 inference(boolean_simplification,[status(thm)],[f238])).
% 22.66/4.27 thf(f238,plain,(
% 22.66/4.27 ( ! [X0 : $o] : (((~ X0) != $true) | ((~ $true) = X0)) )),
% 22.66/4.27 inference(definition_unfolding,[status(thm)],[f161,f227])).
% 22.66/4.27 thf(f227,plain,(
% 22.66/4.27 (mono_2Ec_2Ebool_2EF = (~ $true))),
% 22.66/4.27 inference(definition_unfolding,[status(thm)],[f172,f170])).
% 22.66/4.27 thf(f170,plain,(
% 22.66/4.27 (mono_2Ec_2Ebool_2ET = $true)),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f62])).
% 22.66/4.27 thf(f62,plain,(
% 22.66/4.27 (mono_2Ec_2Ebool_2ET = $true)),
% 22.66/4.27 inference(fool_elimination,[status(thm)],[f61])).
% 22.66/4.27 thf(f61,plain,(
% 22.66/4.27 mono_2Ec_2Ebool_2ET),
% 22.66/4.27 inference(rectify,[status(thm)],[f37])).
% 22.66/4.27 thf(f37,axiom,(
% 22.66/4.27 mono_2Ec_2Ebool_2ET),
% 22.66/4.27 file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Ebool_2ETRUTH)).
% 22.66/4.27 thf(f172,plain,(
% 22.66/4.27 (mono_2Ec_2Ebool_2EF = (~ mono_2Ec_2Ebool_2ET))),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f52])).
% 22.66/4.27 thf(f52,plain,(
% 22.66/4.27 ! [X0 : $o] : ((~ (~ X0)) = X0) & (mono_2Ec_2Ebool_2EF = (~ mono_2Ec_2Ebool_2ET)) & (mono_2Ec_2Ebool_2ET = (~ mono_2Ec_2Ebool_2EF))),
% 22.66/4.27 inference(fool_elimination,[status(thm)],[f51])).
% 22.66/4.27 thf(f51,plain,(
% 22.66/4.27 ! [X0 : $o] : (X0 <=> (~ (~ X0))) & (mono_2Ec_2Ebool_2EF <=> (~ mono_2Ec_2Ebool_2ET)) & ((~ mono_2Ec_2Ebool_2EF) <=> mono_2Ec_2Ebool_2ET)),
% 22.66/4.27 inference(rectify,[status(thm)],[f43])).
% 22.66/4.27 thf(f43,axiom,(
% 22.66/4.27 ! [X18 : $o] : (X18 <=> (~ (~ X18))) & (mono_2Ec_2Ebool_2EF <=> (~ mono_2Ec_2Ebool_2ET)) & ((~ mono_2Ec_2Ebool_2EF) <=> mono_2Ec_2Ebool_2ET)),
% 22.66/4.27 file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Ebool_2ENOT__CLAUSES)).
% 22.66/4.27 thf(f161,plain,(
% 22.66/4.27 ( ! [X0 : $o] : ((mono_2Ec_2Ebool_2EF = X0) | ((~ X0) != $true)) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f115])).
% 22.66/4.27 thf(f115,plain,(
% 22.66/4.27 ! [X0 : $o] : (((mono_2Ec_2Ebool_2EF = X0) | ((~ X0) != $true)) & (((~ X0) = $true) | (mono_2Ec_2Ebool_2EF != X0)) & ((mono_2Ec_2Ebool_2EF = X0) | ((~ X0) != $true)) & (((~ X0) = $true) | (mono_2Ec_2Ebool_2EF != X0)) & ((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0)) & ((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)))),
% 22.66/4.27 inference(flattening,[status(thm)],[f114])).
% 22.66/4.27 thf(f114,plain,(
% 22.66/4.27 ! [X0 : $o] : ((((mono_2Ec_2Ebool_2EF = X0) | ((~ X0) != $true)) & (((~ X0) = $true) | (mono_2Ec_2Ebool_2EF != X0))) & (((mono_2Ec_2Ebool_2EF = X0) | ((~ X0) != $true)) & (((~ X0) = $true) | (mono_2Ec_2Ebool_2EF != X0))) & (((mono_2Ec_2Ebool_2ET = X0) | ($true != X0)) & (($true = X0) | (mono_2Ec_2Ebool_2ET != X0))) & ((($true = X0) | (mono_2Ec_2Ebool_2ET != X0)) & ((mono_2Ec_2Ebool_2ET = X0) | ($true != X0))))),
% 22.66/4.27 inference(nnf_transformation,[status(thm)],[f82])).
% 22.66/4.27 thf(f82,plain,(
% 22.66/4.27 ! [X0 : $o] : (((mono_2Ec_2Ebool_2EF = X0) <=> ((~ X0) = $true)) & ((mono_2Ec_2Ebool_2EF = X0) <=> ((~ X0) = $true)) & ((mono_2Ec_2Ebool_2ET = X0) <=> ($true = X0)) & (($true = X0) <=> (mono_2Ec_2Ebool_2ET = X0)))),
% 22.66/4.27 inference(fool_elimination,[status(thm)],[f81])).
% 22.66/4.27 thf(f81,plain,(
% 22.66/4.27 ! [X0 : $o] : (((mono_2Ec_2Ebool_2ET = X0) <=> X0) & ((mono_2Ec_2Ebool_2EF = X0) <=> (~ X0)) & (X0 <=> (mono_2Ec_2Ebool_2ET = X0)) & ((~ X0) <=> (mono_2Ec_2Ebool_2EF = X0)))),
% 22.66/4.27 inference(rectify,[status(thm)],[f45])).
% 22.66/4.27 thf(f45,axiom,(
% 22.66/4.27 ! [X18 : $o] : (((mono_2Ec_2Ebool_2ET = X18) <=> X18) & ((mono_2Ec_2Ebool_2EF = X18) <=> (~ X18)) & (X18 <=> (mono_2Ec_2Ebool_2ET = X18)) & ((~ X18) <=> (mono_2Ec_2Ebool_2EF = X18)))),
% 22.66/4.27 file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Ebool_2EEQ__CLAUSES)).
% 22.66/4.27 thf(f381,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) != $true) | spl7_7),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f380])).
% 22.66/4.27 thf(f380,definition,(
% 22.66/4.27 spl7_7 <=> ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $true)),
% 22.66/4.27 introduced(definition,[new_symbols(naming,[spl7_7])],[avatar_definition])).
% 22.66/4.27 thf(f1004,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | ~spl7_3),
% 22.66/4.27 inference(forward_demodulation,[status(thm)],[f1003,f924])).
% 22.66/4.27 thf(f924,plain,(
% 22.66/4.27 ((s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5)) = (s @ sK5 @ sK3)) | ~spl7_3),
% 22.66/4.27 inference(forward_demodulation,[status(thm)],[f882,f192])).
% 22.66/4.27 thf(f192,plain,(
% 22.66/4.27 ( ! [X2 : d,X18 : u] : (((s @ X2 @ X18) = (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X18))))))) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f123])).
% 22.66/4.27 thf(f123,plain,(
% 22.66/4.27 ! [X0 : u,X1 : u,X2 : d,X3 : u,X4 : d] : (! [X5 : u,X6 : u,X7 : u] : ((s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ X2 @ X6))) = (s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6))) @ (s @ X4 @ X7) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5)))) & ! [X8 : u] : ((~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X8))))) = $true) & ! [X9 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X9)))) != $true) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X9))) & (mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))) & ! [X10 : u] : ($true = (~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X10))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & ! [X11 : u] : (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X11))))))) & ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ENONE_2E0)))) & ! [X12 : u,X13 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X13))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X12)))) | ((s @ X2 @ X12) != (s @ X2 @ X13))) & (((s @ X2 @ X12) = (s @ X2 @ X13)) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X13))) != (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X12)))))) & ! [X14 : u,X15 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X14) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X15))))) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X14) @ (s @ X2 @ X15)))))) & ! [X16 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X16) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & ! [X17 : u] : ((($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X17)))))) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X17) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ X17) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X17)))))))) & ! [X18 : u] : ((s @ X2 @ X18) = (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X18)))))) & ! [X19 : u] : (((s @ X4 @ X3) = (s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X19) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1)))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X19)))))) & ! [X20 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ X20) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X20) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0)))) & ! [X21 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X21)) & ! [X22 : u,X23 : u] : ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ X4 @ X22) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X23))) = (s @ X4 @ X22)) & ! [X24 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X24) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X24)))))) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X24)))))) & ! [X25 : u] : ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X25))))) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X25) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ X25) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X25))))))) & ! [X26 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ X26) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26)))))) & ! [X27 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X27))))) | ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X27) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1) @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X27))))))))),
% 22.66/4.27 inference(rectify,[status(thm)],[f122])).
% 22.66/4.27 thf(f122,plain,(
% 22.66/4.27 ! [X0 : u,X1 : u,X2 : d,X3 : u,X4 : d] : (! [X7 : u,X8 : u,X9 : u] : ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X8))) @ (s @ X4 @ X9) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X7))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X7) @ (s @ X2 @ X8)))) & ! [X15 : u] : ((~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X15))))) = $true) & ! [X21 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21))))) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X21))) & (mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))) & ! [X23 : u] : ((~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X23))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) = $true) & ! [X19 : u] : (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X19))))))) & ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ENONE_2E0)))) & ! [X12 : u,X13 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X13))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X12)))) | ((s @ X2 @ X12) != (s @ X2 @ X13))) & (((s @ X2 @ X12) = (s @ X2 @ X13)) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X13))) != (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X12)))))) & ! [X5 : u,X6 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ X2 @ X6))))) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))))) & ! [X20 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & ! [X25 : u] : ((($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X25)))))) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X25) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ X25) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ($true != (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X25)))))))) & ! [X24 : u] : ((s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X24))))) = (s @ X2 @ X24)) & ! [X26 : u] : (((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ X3)) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26)))) != $true)) & ! [X14 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ X14) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X14) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X14) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0)))) & ! [X27 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X27) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X27)) & ! [X17 : u,X18 : u] : ((s @ X4 @ X17) = (s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ X4 @ X17) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X18)))) & ! [X16 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X16))))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X16)) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X16)))))) & ! [X22 : u] : ((($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))))) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) != (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))) & (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X22)) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))))))) & ! [X10 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X10))))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X10)) & ! [X11 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11))))) | ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1) @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11))))))))),
% 22.66/4.27 inference(nnf_transformation,[status(thm)],[f109])).
% 22.66/4.27 thf(f109,plain,(
% 22.66/4.27 ! [X0 : u,X1 : u,X2 : d,X3 : u,X4 : d] : (! [X7 : u,X8 : u,X9 : u] : ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X8))) @ (s @ X4 @ X9) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X7))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X7) @ (s @ X2 @ X8)))) & ! [X15 : u] : ((~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X15))))) = $true) & ! [X21 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21))))) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X21))) & (mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))) & ! [X23 : u] : ((~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X23))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) = $true) & ! [X19 : u] : (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X19))))))) & ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ENONE_2E0)))) & ! [X12 : u,X13 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X13))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X12)))) <=> ((s @ X2 @ X12) = (s @ X2 @ X13))) & ! [X5 : u,X6 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ X2 @ X6))))) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))))) & ! [X20 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & ! [X25 : u] : (($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X25)))))) <=> ((s @ (tyop_2Eoption_2Eoption @ X2) @ X25) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & ! [X24 : u] : ((s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X24))))) = (s @ X2 @ X24)) & ! [X26 : u] : (((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ X3)) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26)))) != $true)) & ! [X14 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ X14) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X14) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X14) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0)))) & ! [X27 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X27) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X27)) & ! [X17 : u,X18 : u] : ((s @ X4 @ X17) = (s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ X4 @ X17) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X18)))) & ! [X16 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X16))))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X16)) | ($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X16)))))) & ! [X22 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))))) <=> ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))) & ! [X10 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X10))))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X10)) & ! [X11 : u] : (($true != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11))))) | ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1) @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11))))))))),
% 22.66/4.27 inference(ennf_transformation,[status(thm)],[f66])).
% 22.66/4.27 thf(f66,plain,(
% 22.66/4.27 ! [X0 : u,X1 : u,X2 : d,X3 : u,X4 : d] : (! [X25 : u] : (($true = (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X25)))))) <=> ((s @ (tyop_2Eoption_2Eoption @ X2) @ X25) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & ! [X19 : u] : (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X19))))))) & ! [X21 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21))))) => ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X21))) & ! [X22 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))))) <=> ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))) & ! [X16 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X16))))) => ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X16))))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X16))) & ! [X10 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X10))))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X10)) & ! [X26 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26)))) = $true) => ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ X3))) & ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ENONE_2E0)))) & ! [X12 : u,X13 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X13))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X12)))) <=> ((s @ X2 @ X12) = (s @ X2 @ X13))) & ! [X14 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ X14) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X14) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X14) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0)))) & ! [X11 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11))))) => ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1) @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11))))))) & ! [X7 : u,X8 : u,X9 : u] : ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X8))) @ (s @ X4 @ X9) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X7))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X7) @ (s @ X2 @ X8)))) & ! [X17 : u,X18 : u] : ((s @ X4 @ X17) = (s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ X4 @ X17) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X18)))) & ! [X23 : u] : ((~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X23))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) = $true) & ! [X5 : u,X6 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ X2 @ X6))))) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))))) & ! [X24 : u] : ((s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X24))))) = (s @ X2 @ X24)) & ! [X15 : u] : ((~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X15))))) = $true) & ! [X20 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & ! [X27 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X27) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X27)) & (mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))))),
% 22.66/4.27 inference(fool_elimination,[status(thm)],[f65])).
% 22.66/4.27 thf(f65,plain,(
% 22.66/4.27 ! [X0 : u,X1 : u,X2 : d,X3 : u,X4 : d] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ENONE_2E0)))) & ! [X5 : u,X6 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2ESOME_2E1 @ (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ X2 @ X6))))) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X5) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))))) & ! [X7 : u,X8 : u,X9 : u] : ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X8))) @ (s @ X4 @ X9) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X7))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X7) @ (s @ X2 @ X8)))) & ! [X10 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X10))))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X10)) & ! [X11 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11)))) => ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1) @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X11))))))) & (mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))) & ! [X12 : u,X13 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X13))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X12)))) <=> ((s @ X2 @ X12) = (s @ X2 @ X13))) & ! [X14 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ X14) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X14) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X14) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0)))) & ! [X15 : u] : (~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X15))))) & ! [X16 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X16)))) => ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X16))))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X16))) & ! [X17 : u,X18 : u] : ((s @ X4 @ X17) = (s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ X4 @ X17) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X18)))) & ! [X19 : u] : (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X19))))))) & ! [X20 : u] : ((s @ (tyop_2Eoption_2Eoption @ X4) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X4) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & ! [X21 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21)))) => ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X21))) & ! [X22 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X22)) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))))) & ! [X23 : u] : (~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X23))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) & ! [X24 : u] : ((s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X24))))) = (s @ X2 @ X24)) & ! [X25 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X25) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) <=> (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X25)))))) & ! [X26 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26)))) => ((s @ X4 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X26) @ (s @ X4 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ X4) @ X1))) = (s @ X4 @ X3))) & ! [X27 : u] : ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X27) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ X27)))),
% 22.66/4.27 inference(rectify,[status(thm)],[f46])).
% 22.66/4.27 thf(f46,axiom,(
% 22.66/4.27 ! [X19 : u,X2 : u,X0 : d,X20 : u,X1 : d] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ENONE_2E0)))) & ! [X40 : u,X41 : u] : ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X40) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X41))))) = (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X40) @ (s @ X0 @ X41)))))) & ! [X39 : u,X37 : u,X38 : u] : ((s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X37))) @ (s @ X1 @ X38) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X39))) = (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X39) @ (s @ X0 @ X37)))) & ! [X43 : u] : ((s @ (tyop_2Eoption_2Eoption @ X0) @ X43) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X43)))))) & ! [X33 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X33)))) => ((s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X33) @ (s @ X1 @ X20) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2))) = (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2) @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X33))))))) & (mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))) & ! [X21 : u,X22 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X21))) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X22)))) <=> ((s @ X0 @ X21) = (s @ X0 @ X22))) & ! [X31 : u] : ((s @ (tyop_2Eoption_2Eoption @ X0) @ X31) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X31) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X31) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)))) & ! [X24 : u] : (~ ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24))))) & ! [X29 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X29)))) => ((s @ (tyop_2Eoption_2Eoption @ X0) @ X29) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X29))))))) & ! [X35 : u,X36 : u] : ((s @ X1 @ X35) = (s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ X1 @ X35) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X36)))) & ! [X26 : u] : (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26))))))) & ! [X42 : u] : ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X42) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) = (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)) & ! [X34 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X34)))) => ((s @ (tyop_2Eoption_2Eoption @ X0) @ X34) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X34) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X19) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0))))) & ! [X27 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X27)) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X27))))) & ! [X25 : u] : (~ ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X25))))) & ! [X23 : u] : ((s @ X0 @ X23) = (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X23)))))) & ! [X28 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X28)) <=> (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X28)))))) & ! [X32 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X32)))) => ((s @ X1 @ X20) = (s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X32) @ (s @ X1 @ X20) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2))))) & ! [X30 : u] : ((s @ (tyop_2Eoption_2Eoption @ X0) @ X30) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X30) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)))))),
% 22.66/4.27 file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Eoption_2Eoption__CLAUSES)).
% 22.66/4.27 thf(f882,plain,(
% 22.66/4.27 ((s @ sK5 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))) = (s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5))) | ~spl7_3),
% 22.66/4.27 inference(superposition,[status(thm)],[f192,f811])).
% 22.66/4.27 thf(f811,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5)))) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ~spl7_3),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f804,f338])).
% 22.66/4.27 thf(f338,plain,(
% 22.66/4.27 ( ! [X2 : d,X10 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X10))) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) )),
% 22.66/4.27 inference(equality_proxy_clausification,[status(thm)],[f337])).
% 22.66/4.27 thf(f337,plain,(
% 22.66/4.27 ( ! [X2 : d,X10 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X10))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = $false)) )),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f336])).
% 22.66/4.27 thf(f336,plain,(
% 22.66/4.27 ( ! [X2 : d,X10 : u] : (($true = $false) | (((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X10))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = $false)) )),
% 22.66/4.27 inference(boolean_simplification,[status(thm)],[f333])).
% 22.66/4.27 thf(f333,plain,(
% 22.66/4.27 ( ! [X2 : d,X10 : u] : ((((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X10))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) = $false) | ($true = (~ $true))) )),
% 22.66/4.27 inference(cases_simplifying,[status(thm)],[f201])).
% 22.66/4.27 thf(f201,plain,(
% 22.66/4.27 ( ! [X2 : d,X10 : u] : (($true = (~ ((s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X10))) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f123])).
% 22.66/4.27 thf(f804,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5)))) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ~spl7_3),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f789])).
% 22.66/4.27 thf(f789,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5)))) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ($true != $true) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ~spl7_3),
% 22.66/4.27 inference(superposition,[status(thm)],[f179,f366])).
% 22.66/4.27 thf(f179,plain,(
% 22.66/4.27 ( ! [X2 : d,X3 : u,X0 : d,X1 : u,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) != $true) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f121])).
% 22.66/4.27 thf(f121,plain,(
% 22.66/4.27 ! [X0 : d,X1 : u,X2 : d,X3 : u,X4 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) = $true) | ((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) != (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) & ! [X5 : u,X6 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) | ($true != (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6))))) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) != (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))))) & ((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) | (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ((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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ (sK0 @ X4 @ X3 @ X2 @ X1 @ X0)))) @ (s @ X2 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))) = $true) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (sK0 @ X4 @ X3 @ X2 @ X1 @ X0)))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) != $true)))),
% 22.66/4.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f119,f120])).
% 22.66/4.27 thf(f120,plain,(
% 22.66/4.27 ! [X0 : d,X1 : u,X2 : d,X3 : u,X4 : u] : (? [X7 : u,X8 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X8)))) & ((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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X7))) @ (s @ X2 @ X8)))) = $true) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X7))) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) => (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ((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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ (sK0 @ X4 @ X3 @ X2 @ X1 @ X0)))) @ (s @ X2 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))) = $true) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (sK0 @ X4 @ X3 @ X2 @ X1 @ X0)))))))),
% 22.66/4.27 introduced(definition,[],[choice_axiom])).
% 22.66/4.27 thf(f119,plain,(
% 22.66/4.27 ! [X0 : d,X1 : u,X2 : d,X3 : u,X4 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) = $true) | ((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) != (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) & ! [X5 : u,X6 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) | ($true != (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6))))) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) != (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))))) & ((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) | ? [X7 : u,X8 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X8)))) & ((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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X7))) @ (s @ X2 @ X8)))) = $true) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X7))) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) != $true)))),
% 22.66/4.27 inference(rectify,[status(thm)],[f118])).
% 22.66/4.27 thf(f118,plain,(
% 22.66/4.27 ! [X0 : d,X1 : u,X2 : d,X3 : u,X4 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) = $true) | ((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) != (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) & ! [X5 : u,X6 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) | ($true != (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6))))) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) != (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))))) & ((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) | ? [X5 : u,X6 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) & ($true = (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6))))) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) != $true)))),
% 22.66/4.27 inference(flattening,[status(thm)],[f117])).
% 22.66/4.27 thf(f117,plain,(
% 22.66/4.27 ! [X0 : d,X1 : u,X2 : d,X3 : u,X4 : u] : ((((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) = $true) | ((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) != (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) & ! [X5 : u,X6 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) | ($true != (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6))))) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) != (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))))) & (((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) | ? [X5 : u,X6 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) & ($true = (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6))))) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) != $true)))),
% 22.66/4.27 inference(nnf_transformation,[status(thm)],[f56])).
% 22.66/4.27 thf(f56,plain,(
% 22.66/4.27 ! [X0 : d,X1 : u,X2 : d,X3 : u,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) = $true) <=> ((((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) | ? [X5 : u,X6 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) & ($true = (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6))))) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))))))),
% 22.66/4.27 inference(fool_elimination,[status(thm)],[f55])).
% 22.66/4.27 thf(f55,plain,(
% 22.66/4.27 ! [X0 : d,X1 : u,X2 : d,X3 : u,X4 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) <=> (? [X5 : u,X6 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6)))) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))) | (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) & ((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))))),
% 22.66/4.27 inference(rectify,[status(thm)],[f47])).
% 22.66/4.27 thf(f47,axiom,(
% 22.66/4.27 ! [X0 : d,X45 : u,X1 : d,X12 : u,X44 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X44) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X12) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X45)))) <=> (? [X46 : u,X47 : u] : (((s @ (tyop_2Eoption_2Eoption @ X1) @ X45) = (s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X47)))) & (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 @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X44) @ (s @ X0 @ X46))) @ (s @ X1 @ X47)))) & ((s @ (tyop_2Eoption_2Eoption @ X0) @ X12) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X46))))) | (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X12)) & ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X1) @ X45)))))),
% 22.66/4.27 file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Eoption_2EOPTREL__def)).
% 22.66/4.27 thf(f1003,plain,(
% 22.66/4.27 ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5)))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | ~spl7_3),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f996,f338])).
% 22.66/4.27 thf(f996,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)))) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5)))))) | ~spl7_3),
% 22.66/4.27 inference(superposition,[status(thm)],[f477,f984])).
% 22.66/4.27 thf(f984,plain,(
% 22.66/4.27 ((s @ sK5 @ sK4) = (s @ sK5 @ (sK0 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5))) | ~spl7_3),
% 22.66/4.27 inference(forward_demodulation,[status(thm)],[f946,f192])).
% 22.66/4.27 thf(f946,plain,(
% 22.66/4.27 ((s @ sK5 @ (sK0 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5)) = (s @ sK5 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)))))) | ~spl7_3),
% 22.66/4.27 inference(superposition,[status(thm)],[f192,f813])).
% 22.66/4.27 thf(f813,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK0 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5))))) | ~spl7_3),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f802,f338])).
% 22.66/4.27 thf(f802,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK0 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5))))) | ~spl7_3),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f787])).
% 22.66/4.27 thf(f787,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK0 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5))))) | ($true != $true) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ~spl7_3),
% 22.66/4.27 inference(superposition,[status(thm)],[f177,f366])).
% 22.66/4.27 thf(f177,plain,(
% 22.66/4.27 ( ! [X2 : d,X3 : u,X0 : d,X1 : u,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) != $true) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (sK0 @ X4 @ X3 @ X2 @ X1 @ X0)))))) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f121])).
% 22.66/4.27 thf(f477,plain,(
% 22.66/4.27 ( ! [X2 : u,X3 : u,X0 : d,X1 : d,X4 : 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 @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ (sK0 @ X2 @ X3 @ X1 @ X4 @ X0)))) @ (s @ X1 @ (sK1 @ X2 @ X3 @ X1 @ X4 @ X0))))) = $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) = $false) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) )),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f476])).
% 22.66/4.27 thf(f476,plain,(
% 22.66/4.27 ( ! [X2 : u,X3 : u,X0 : d,X1 : d,X4 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) | ($true != $true) | ((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 @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ (sK0 @ X2 @ X3 @ X1 @ X4 @ X0)))) @ (s @ X1 @ (sK1 @ X2 @ X3 @ X1 @ X4 @ X0))))) = $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) = $false)) )),
% 22.66/4.27 inference(superposition,[status(thm)],[f175,f305])).
% 22.66/4.27 thf(f175,plain,(
% 22.66/4.27 ( ! [X2 : d,X3 : u,X0 : d,X1 : u,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) != $true) | ((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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ (sK0 @ X4 @ X3 @ X2 @ X1 @ X0)))) @ (s @ X2 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))) = $true) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f121])).
% 22.66/4.27 thf(f366,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $true) | ~spl7_3),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f364])).
% 22.66/4.27 thf(f364,definition,(
% 22.66/4.27 spl7_3 <=> ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $true)),
% 22.66/4.27 introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition])).
% 22.66/4.27 thf(f832,plain,(
% 22.66/4.27 ~spl7_3 | ~spl7_4 | ~spl7_6 | ~spl7_7),
% 22.66/4.27 inference(avatar_contradiction_clause,[status(thm)],[f831])).
% 22.66/4.27 thf(f831,plain,(
% 22.66/4.27 $false | (~spl7_3 | ~spl7_4 | ~spl7_6 | ~spl7_7)),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f822])).
% 22.66/4.27 thf(f822,plain,(
% 22.66/4.27 ($true = $false) | (~spl7_3 | ~spl7_4 | ~spl7_6 | ~spl7_7)),
% 22.66/4.27 inference(backward_demodulation,[status(thm)],[f366,f779])).
% 22.66/4.27 thf(f779,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | (~spl7_4 | ~spl7_6 | ~spl7_7)),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f778])).
% 22.66/4.27 thf(f778,plain,(
% 22.66/4.27 ($true = $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | (~spl7_4 | ~spl7_6 | ~spl7_7)),
% 22.66/4.27 inference(forward_demodulation,[status(thm)],[f777,f382])).
% 22.66/4.27 thf(f382,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $true) | ~spl7_7),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f380])).
% 22.66/4.27 thf(f777,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | (~spl7_4 | ~spl7_6)),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f776,f493])).
% 22.66/4.27 thf(f493,plain,(
% 22.66/4.27 ( ! [X2 : u,X0 : d,X1 : d] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0)))) = $true)) )),
% 22.66/4.27 inference(equality_resolution,[status(thm)],[f401])).
% 22.66/4.27 thf(f401,plain,(
% 22.66/4.27 ( ! [X2 : d,X3 : u,X0 : d,X1 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) != (s @ (tyop_2Eoption_2Eoption @ X0) @ X1)) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))))) )),
% 22.66/4.27 inference(equality_resolution,[status(thm)],[f181])).
% 22.66/4.27 thf(f181,plain,(
% 22.66/4.27 ( ! [X2 : d,X3 : u,X0 : d,X1 : u,X4 : u] : (((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) != (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) = $true)) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f121])).
% 22.66/4.27 thf(f776,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | (~spl7_4 | ~spl7_6)),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f775,f369])).
% 22.66/4.27 thf(f369,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | ~spl7_4),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f368])).
% 22.66/4.27 thf(f368,definition,(
% 22.66/4.27 spl7_4 <=> ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false)),
% 22.66/4.27 introduced(definition,[new_symbols(naming,[spl7_4])],[avatar_definition])).
% 22.66/4.27 thf(f775,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) != $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $true) | ~spl7_6),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f320,f377])).
% 22.66/4.27 thf(f377,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) = $false) | ~spl7_6),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f376])).
% 22.66/4.27 thf(f376,definition,(
% 22.66/4.27 spl7_6 <=> ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) = $false)),
% 22.66/4.27 introduced(definition,[new_symbols(naming,[spl7_6])],[avatar_definition])).
% 22.66/4.27 thf(f320,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) != $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $true)),
% 22.66/4.27 inference(binary_proxy_clausification,[status(thm)],[f318])).
% 22.66/4.27 thf(f318,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) != $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))),
% 22.66/4.27 inference(boolean_simplification,[status(thm)],[f317])).
% 22.66/4.27 thf(f317,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) != (~ $true)) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $false)),
% 22.66/4.27 inference(boolean_simplification,[status(thm)],[f262])).
% 22.66/4.27 thf(f262,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != (~ $true)) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) != (~ $true)) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))),
% 22.66/4.27 inference(definition_unfolding,[status(thm)],[f226,f227,f170,f227])).
% 22.66/4.27 thf(f226,plain,(
% 22.66/4.27 (mono_2Ec_2Ebool_2EF != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))) | (mono_2Ec_2Ebool_2ET != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ 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 @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f129])).
% 22.66/4.27 thf(f129,plain,(
% 22.66/4.27 (mono_2Ec_2Ebool_2EF != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))) | (mono_2Ec_2Ebool_2ET != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ 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 @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))))),
% 22.66/4.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f111,f128])).
% 22.66/4.27 thf(f128,plain,(
% 22.66/4.27 ? [X0 : u,X1 : u,X2 : d,X3 : u] : ((mono_2Ec_2Ebool_2EF != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X1))) @ (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 @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X1))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X0)))))) != (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 @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X1))) @ (s @ X2 @ X0))))) | (mono_2Ec_2Ebool_2ET != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ 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 @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X0)))))))) => ((mono_2Ec_2Ebool_2EF != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))) | (mono_2Ec_2Ebool_2ET != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ 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 @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))))))),
% 22.66/4.27 introduced(definition,[],[choice_axiom])).
% 22.66/4.27 thf(f111,plain,(
% 22.66/4.27 ? [X0 : u,X1 : u,X2 : d,X3 : u] : ((mono_2Ec_2Ebool_2EF != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X1))) @ (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 @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X1))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X0)))))) != (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 @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X1))) @ (s @ X2 @ X0))))) | (mono_2Ec_2Ebool_2ET != (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ 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 @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X0))))))))),
% 22.66/4.27 inference(ennf_transformation,[status(thm)],[f89])).
% 22.66/4.27 thf(f89,plain,(
% 22.66/4.27 ~! [X0 : u,X1 : u,X2 : d,X3 : u] : ((mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X1))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ 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 @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X0))))))) & ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X1))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X0)))))) = (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 @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X2 @ X1))) @ (s @ X2 @ X0))))) & (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0))))))),
% 22.66/4.27 inference(rectify,[status(thm)],[f49])).
% 22.66/4.27 thf(f49,negated_conjecture,(
% 22.66/4.27 ~! [X48 : u,X12 : u,X0 : d,X49 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X12))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X48)))))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ X0 @ X12))) @ (s @ X0 @ X48))))) & (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ 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 @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X48))))))) & (mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X12))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))))),
% 22.66/4.27 inference(negated_conjecture,[status(cth)],[f48])).
% 22.66/4.27 thf(f48,conjecture,(
% 22.66/4.27 ! [X48 : u,X12 : u,X0 : d,X49 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X12))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X48)))))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ X0 @ X12))) @ (s @ X0 @ X48))))) & (mono_2Ec_2Ebool_2ET = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ 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 @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X48))))))) & (mono_2Ec_2Ebool_2EF = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X49) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X12))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))))),
% 22.66/4.27 file('/export/starexec/sandbox/tmp/tmp.gvLFi6zevo/DTF2THF_17206.p',thm_2Equotient__option_2EOPTION__REL__def)).
% 22.66/4.27 thf(f774,plain,(
% 22.66/4.27 spl7_3 | ~spl7_7),
% 22.66/4.27 inference(avatar_contradiction_clause,[status(thm)],[f773])).
% 22.66/4.27 thf(f773,plain,(
% 22.66/4.27 $false | (spl7_3 | ~spl7_7)),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f772])).
% 22.66/4.27 thf(f772,plain,(
% 22.66/4.27 ($true = $false) | (spl7_3 | ~spl7_7)),
% 22.66/4.27 inference(forward_demodulation,[status(thm)],[f771,f394])).
% 22.66/4.27 thf(f394,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | spl7_3),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f393])).
% 22.66/4.27 thf(f393,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $false) | ($true != $true) | spl7_3),
% 22.66/4.27 inference(superposition,[status(thm)],[f365,f305])).
% 22.66/4.27 thf(f365,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) != $true) | spl7_3),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f364])).
% 22.66/4.27 thf(f771,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $true) | ~spl7_7),
% 22.66/4.27 inference(equality_resolution,[status(thm)],[f766])).
% 22.66/4.27 thf(f766,plain,(
% 22.66/4.27 ( ! [X0 : u] : (((s @ (tyop_2Eoption_2Eoption @ sK5) @ X0) != (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ X0)))))) ) | ~spl7_7),
% 22.66/4.27 inference(equality_resolution,[status(thm)],[f761])).
% 22.66/4.27 thf(f761,plain,(
% 22.66/4.27 ( ! [X0 : u,X1 : u] : (((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) != (s @ (tyop_2Eoption_2Eoption @ sK5) @ X1)) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ X0)))) = $true) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ X0) != (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))) ) | ~spl7_7),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f760])).
% 22.66/4.27 thf(f760,plain,(
% 22.66/4.27 ( ! [X0 : u,X1 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ X1) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ X0)))) = $true) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) != (s @ (tyop_2Eoption_2Eoption @ sK5) @ X1)) | ($true != $true) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ X0) != (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3))))) ) | ~spl7_7),
% 22.66/4.27 inference(superposition,[status(thm)],[f180,f382])).
% 22.66/4.27 thf(f180,plain,(
% 22.66/4.27 ( ! [X2 : d,X3 : u,X0 : d,X1 : u,X6 : u,X4 : u,X5 : u] : (($true != (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 @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X0 @ X5))) @ (s @ X2 @ X6))))) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) != (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X6)))) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) != (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) = $true)) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f121])).
% 22.66/4.27 thf(f759,plain,(
% 22.66/4.27 spl7_5),
% 22.66/4.27 inference(avatar_contradiction_clause,[status(thm)],[f758])).
% 22.66/4.27 thf(f758,plain,(
% 22.66/4.27 $false | spl7_5),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f740])).
% 22.66/4.27 thf(f740,plain,(
% 22.66/4.27 ($true = $false) | spl7_5),
% 22.66/4.27 inference(superposition,[status(thm)],[f493,f385])).
% 22.66/4.27 thf(f385,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) = $false) | spl7_5),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f384])).
% 22.66/4.27 thf(f384,plain,(
% 22.66/4.27 ($true != $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) = $false) | spl7_5),
% 22.66/4.27 inference(superposition,[status(thm)],[f374,f305])).
% 22.66/4.27 thf(f374,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $true) | spl7_5),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f372])).
% 22.66/4.27 thf(f372,definition,(
% 22.66/4.27 spl7_5 <=> ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) = $true)),
% 22.66/4.27 introduced(definition,[new_symbols(naming,[spl7_5])],[avatar_definition])).
% 22.66/4.27 thf(f613,plain,(
% 22.66/4.27 spl7_4),
% 22.66/4.27 inference(avatar_contradiction_clause,[status(thm)],[f612])).
% 22.66/4.27 thf(f612,plain,(
% 22.66/4.27 $false | spl7_4),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f611,f338])).
% 22.66/4.27 thf(f611,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | spl7_4),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f607,f338])).
% 22.66/4.27 thf(f607,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK0 @ sK6 @ c_2Eoption_2ENONE_2E0 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5))))) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | spl7_4),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f597])).
% 22.66/4.27 thf(f597,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))) | ($false != $false) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK0 @ sK6 @ c_2Eoption_2ENONE_2E0 @ sK5 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)) @ sK5))))) | spl7_4),
% 22.66/4.27 inference(superposition,[status(thm)],[f370,f441])).
% 22.66/4.27 thf(f441,plain,(
% 22.66/4.27 ( ! [X2 : u,X3 : u,X0 : d,X1 : d,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) = $false) | ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (sK0 @ X2 @ X3 @ X1 @ X4 @ X0)))))) )),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f440])).
% 22.66/4.27 thf(f440,plain,(
% 22.66/4.27 ( ! [X2 : u,X3 : u,X0 : d,X1 : d,X4 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ X3) = (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (sK0 @ X2 @ X3 @ X1 @ X4 @ X0))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) = $false) | ($true != $true) | ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) )),
% 22.66/4.27 inference(superposition,[status(thm)],[f177,f305])).
% 22.66/4.27 thf(f370,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) != $false) | spl7_4),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f368])).
% 22.66/4.27 thf(f581,plain,(
% 22.66/4.27 spl7_6),
% 22.66/4.27 inference(avatar_contradiction_clause,[status(thm)],[f580])).
% 22.66/4.27 thf(f580,plain,(
% 22.66/4.27 $false | spl7_6),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f579,f338])).
% 22.66/4.27 thf(f579,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)))) | spl7_6),
% 22.66/4.27 inference(subsumption_resolution,[status(thm)],[f574,f338])).
% 22.66/4.27 thf(f574,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ c_2Eoption_2ENONE_2E0 @ sK5)))) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)))) | spl7_6),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f565])).
% 22.66/4.27 thf(f565,plain,(
% 22.66/4.27 ((s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ (sK1 @ sK6 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)) @ sK5 @ c_2Eoption_2ENONE_2E0 @ sK5)))) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)) | ((s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4)))) | ($false != $false) | spl7_6),
% 22.66/4.27 inference(superposition,[status(thm)],[f378,f418])).
% 22.66/4.27 thf(f418,plain,(
% 22.66/4.27 ( ! [X2 : u,X3 : u,X0 : d,X1 : d,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) = $false) | ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (sK1 @ X2 @ X3 @ X1 @ X4 @ X0)))) = (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) )),
% 22.66/4.27 inference(trivial_inequality_removal,[status(thm)],[f417])).
% 22.66/4.27 thf(f417,plain,(
% 22.66/4.27 ( ! [X2 : u,X3 : u,X0 : d,X1 : d,X4 : u] : (((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3)) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4)))) = $false) | ($true != $true) | ((s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (sK1 @ X2 @ X3 @ X1 @ X4 @ X0)))) = (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) )),
% 22.66/4.27 inference(superposition,[status(thm)],[f176,f305])).
% 22.66/4.27 thf(f176,plain,(
% 22.66/4.27 ( ! [X2 : d,X3 : u,X0 : d,X1 : u,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X1)))) != $true) | ((s @ (tyop_2Eoption_2Eoption @ X2) @ X1) = (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (sK1 @ X4 @ X3 @ X2 @ X1 @ X0))))) | ((s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) = (s @ (tyop_2Eoption_2Eoption @ X0) @ X3))) )),
% 22.66/4.27 inference(cnf_transformation,[status(thm)],[f121])).
% 22.66/4.27 thf(f378,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $false) | spl7_6),
% 22.66/4.27 inference(avatar_component_clause,[status(thm)],[f376])).
% 22.66/4.27 thf(f383,plain,(
% 22.66/4.27 spl7_3 | ~spl7_4 | ~spl7_5 | ~spl7_6 | spl7_7),
% 22.66/4.27 inference(avatar_split_clause,[status(thm)],[f319,f380,f376,f372,f368,f364])).
% 22.66/4.27 thf(f319,plain,(
% 22.66/4.27 ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) = $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK3)))))) != $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK5 @ sK4))) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK5) @ c_2Eoption_2ENONE_2E0)))) != $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK5 @ (tyop_2Emin_2Efun @ sK5 @ tyop_2Emin_2Ebool)) @ sK6) @ (s @ sK5 @ sK4))) @ (s @ sK5 @ sK3)))) = $true)),
% 22.66/4.27 inference(binary_proxy_clausification,[status(thm)],[f318])).
% 22.66/4.27 % SZS output end Proof for DTF2THF_17206
% 22.66/4.27 % (18020)------------------------------
% 22.66/4.27 % (18020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.66/4.27 % (18020)Termination reason: Refutation
% 22.66/4.27
% 22.66/4.27 % (18020)Memory used [KB]: 6908
% 22.66/4.27 % (18020)Time elapsed: 0.161 s
% 22.66/4.27 % (18020)Instructions burned: 518 (million)
% 22.66/4.27 % (18020)------------------------------
% 22.66/4.27 % (18020)------------------------------
% 22.66/4.27 % (17514)Success in time 3.152 s
%------------------------------------------------------------------------------