%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP012^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 08:53:28 AM UTC 2026
% Result : Theorem 2.17s 1.54s
% Output : Refutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 77 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 425 ( 135 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 530 ( 81 ~; 107 |; 10 &; 307 @)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 70 usr; 28 con; 0-3 aty)
% Number of variables : 97 ( 0 ^; 91 !; 6 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(type_def_9,type,
mono_2Etyop_2Einteger_2Eint: $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,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(func_def_4,type,
tyop_2Einteger_2Eint: d ).
thf(func_def_5,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_6,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_7,type,
s: d > u > du ).
thf(func_def_8,type,
app_2E2: du > du > u ).
thf(func_def_9,type,
combin_i_2E0: u ).
thf(func_def_10,type,
combin_k_2E0: u ).
thf(func_def_11,type,
combin_s_2E0: u ).
thf(func_def_12,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_13,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_14,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_15,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_16,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_17,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_18,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_19,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_20,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_21,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_22,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_23,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_24,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_25,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_26,type,
c_2Einteger_2Eint__add_2E0: u ).
thf(func_def_27,type,
c_2Einteger_2Eint__add_2E2: du > du > u ).
thf(func_def_28,type,
c_2Einteger_2Eint__divides_2E0: u ).
thf(func_def_29,type,
c_2Einteger_2Eint__divides_2E2: du > du > u ).
thf(func_def_30,type,
c_2Einteger_2Eint__neg_2E0: u ).
thf(func_def_31,type,
c_2Einteger_2Eint__neg_2E1: du > u ).
thf(func_def_32,type,
c_2Einteger_2Eint__sub_2E0: u ).
thf(func_def_33,type,
c_2Einteger_2Eint__sub_2E2: du > du > u ).
thf(func_def_34,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_35,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_36,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_37,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_38,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_39,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_40,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_41,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_42,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_43,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_46,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_47,type,
mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_48,type,
mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_49,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_50,type,
mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
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,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > $o ) > u ).
thf(func_def_56,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
thf(func_def_57,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(func_def_58,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(func_def_59,type,
i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
thf(func_def_60,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_61,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_62,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,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_64,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(func_def_65,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_66,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_67,type,
j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
thf(func_def_77,type,
sK0: mono_2Etyop_2Einteger_2Eint ).
thf(func_def_78,type,
sK1: mono_2Etyop_2Einteger_2Eint ).
thf(func_def_79,type,
sK2: mono_2Etyop_2Einteger_2Eint ).
thf(f666,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f203,f212,f417,f422,f651,f658]) ).
thf(f658,plain,
( spl3_8
| ~ spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f657,f209,f427]) ).
thf(f427,definition,
( spl3_8
<=> ! [X1: $o] :
( ( $false = X1 )
| ( $true = X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f209,definition,
( spl3_4
<=> ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f657,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( $true = X0 ) )
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f656]) ).
thf(f656,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = $true )
| ( $false = X0 ) )
| ~ spl3_4 ),
inference(forward_demodulation,[status(thm)],[f491,f211]) ).
thf(f211,plain,
( ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f209]) ).
thf(f491,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) )
| ( $false = X0 ) )
| ~ spl3_4 ),
inference(binary_proxy_clausification,[status(thm)],[f490]) ).
thf(f490,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) )
= X0 ) )
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f483]) ).
thf(f483,plain,
( ! [X0: $o] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) )
= X0 )
| ( $false = $true )
| ( $true = X0 ) )
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f211,f166]) ).
thf(f166,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
thf(f145,plain,
! [X0: $o,X1: $o] :
( ( X0 = X1 )
| ( ( $true = X1 )
& ( $true != X0 ) )
| ( ( $true = X0 )
& ( $true != X1 ) ) ),
inference(flattening,[status(thm)],[f144]) ).
thf(f144,plain,
! [X0: $o,X1: $o] :
( ( X0 = X1 )
| ( ( $true = X0 )
& ( $true != X1 ) )
| ( ( $true = X1 )
& ( $true != X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: $o,X1: $o] :
( ( ( $true = X1 )
=> ( $true = X0 ) )
=> ( ( ( $true = X0 )
=> ( $true = X1 ) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f87]) ).
thf(f87,plain,
! [X0: $o,X1: $o] :
( ( X1
=> X0 )
=> ( ( X0
=> X1 )
=> ( X0 = X1 ) ) ),
inference(rectify,[status(thm)],[f44]) ).
thf(f44,axiom,
! [X16: $o,X15: $o] :
( ( X15
=> X16 )
=> ( ( X16
=> X15 )
=> ( X15 = X16 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(f651,plain,
( spl3_3
| ~ spl3_4
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f650]) ).
thf(f650,plain,
( $false
| spl3_3
| ~ spl3_4
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f649,f173]) ).
thf(f173,plain,
( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f150]) ).
thf(f150,plain,
( ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2 )
= $true )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 )
!= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f146,f149]) ).
thf(f149,plain,
( ? [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 )
= $true )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X0 )
!= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X2 ) ) ) )
=> ( ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2 )
= $true )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 )
!= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f146,plain,
? [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 )
= $true )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X0 )
!= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f122]) ).
thf(f122,plain,
~ ! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 )
= $true )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X0 )
= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f121]) ).
thf(f121,plain,
~ ! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ X0 )
= ( mono_2Ec_2Einteger_2Eint__divides @ X1 @ ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f69]) ).
thf(f69,negated_conjecture,
~ ! [X29: mono_2Etyop_2Einteger_2Eint,X27: mono_2Etyop_2Einteger_2Eint,X28: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ X29 )
= ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ ( mono_2Ec_2Einteger_2Eint__sub @ X29 @ X28 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
thf(f68,conjecture,
! [X29: mono_2Etyop_2Einteger_2Eint,X27: mono_2Etyop_2Einteger_2Eint,X28: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ X29 )
= ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ ( mono_2Ec_2Einteger_2Eint__sub @ X29 @ X28 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).
thf(f649,plain,
( ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2 )
!= $true )
| spl3_3
| ~ spl3_4
| ~ spl3_8 ),
inference(subsumption_resolution,[status(thm)],[f632,f206]) ).
thf(f206,plain,
( ( $false
!= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f205]) ).
thf(f205,definition,
( spl3_3
<=> ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f632,plain,
( ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2 )
!= $true )
| ~ spl3_4
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f629]) ).
thf(f629,plain,
( ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| ( $false = $true )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2 )
!= $true )
| ~ spl3_4
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f211,f598]) ).
thf(f598,plain,
( ! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1 ) )
= $true )
| ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ X0 ) )
| ( $true
!= ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ X1 ) ) )
| ~ spl3_8 ),
inference(forward_demodulation,[status(thm)],[f577,f167]) ).
thf(f167,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
thf(f142,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ X0 ) @ X1 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f57]) ).
thf(f57,axiom,
! [X27: mono_2Etyop_2Einteger_2Eint,X28: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28 )
= ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ X27 ) @ X28 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28 )
= ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ ( mono_2Ec_2Einteger_2Eint__neg @ X28 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).
thf(f577,plain,
( ! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ X0 ) )
| ( $true
!= ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) ) )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1 ) )
= $true ) )
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f511,f156]) ).
thf(f156,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1 )
= ( mono_2Ec_2Einteger_2Eint__add @ X0 @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
thf(f141,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1 )
= ( mono_2Ec_2Einteger_2Eint__add @ X0 @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) ) ),
inference(rectify,[status(thm)],[f55]) ).
thf(f55,axiom,
! [X25: mono_2Etyop_2Einteger_2Eint,X26: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ X25 @ X26 )
= ( mono_2Ec_2Einteger_2Eint__add @ X25 @ ( mono_2Ec_2Einteger_2Eint__neg @ X26 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Einteger_2Eint__sub) ).
thf(f511,plain,
( ! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__add @ X1 @ X2 ) )
= $true )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= $false )
| ( $true
!= ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2 ) ) )
| ~ spl3_8 ),
inference(forward_demodulation,[status(thm)],[f510,f168]) ).
thf(f168,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ X0 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
thf(f510,plain,
( ! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__add @ X1 @ X2 ) )
= $true )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= $false )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ X0 ) @ X2 )
!= $true ) )
| ~ spl3_8 ),
inference(forward_demodulation,[status(thm)],[f503,f168]) ).
thf(f503,plain,
( ! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__add @ X1 @ X2 ) )
= $true )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ X0 ) @ X1 )
= $false )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ X0 ) @ X2 )
!= $true ) )
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f154,f438]) ).
thf(f438,plain,
( ! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ X0 ) @ X1 )
= $false )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= $true ) )
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f168,f428]) ).
thf(f428,plain,
( ! [X1: $o] :
( ( $true = X1 )
| ( $false = X1 ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f427]) ).
thf(f154,plain,
! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__add @ X2 @ X1 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2 ) )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
thf(f143,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
!= $true )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__add @ X2 @ X1 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f104]) ).
thf(f104,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= $true )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__add @ X2 @ X1 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f103]) ).
thf(f103,plain,
! [X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint,X2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__add @ X2 @ X1 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f56]) ).
thf(f56,axiom,
! [X27: mono_2Etyop_2Einteger_2Eint,X28: mono_2Etyop_2Einteger_2Eint,X29: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28 )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ ( mono_2Ec_2Einteger_2Eint__add @ X29 @ X28 ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ X27 @ X29 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).
thf(f422,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f421]) ).
thf(f421,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f420]) ).
thf(f420,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f198,f207]) ).
thf(f207,plain,
( ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f205]) ).
thf(f198,plain,
( ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f196]) ).
thf(f196,definition,
( spl3_1
<=> ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f417,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f416]) ).
thf(f416,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f415]) ).
thf(f415,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f414,f207]) ).
thf(f414,plain,
( ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| ~ spl3_2
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f400,f173]) ).
thf(f400,plain,
( ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2 )
!= $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f392]) ).
thf(f392,plain,
( ( $false = $true )
| ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2 )
!= $true )
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f202,f326]) ).
thf(f326,plain,
( ! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1 ) )
= $false )
| ( $true
!= ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ X1 ) )
| ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ X0 ) ) )
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f312,f167]) ).
thf(f312,plain,
( ! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ X0 ) )
| ( $true
!= ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ ( mono_2Ec_2Einteger_2Eint__neg @ X1 ) ) )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ X2 @ ( mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1 ) )
= $false ) )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f225,f156]) ).
thf(f225,plain,
( ! [X2: mono_2Etyop_2Einteger_2Eint,X0: mono_2Etyop_2Einteger_2Eint,X1: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ ( mono_2Ec_2Einteger_2Eint__add @ X1 @ X2 ) )
= $false )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1 )
= $true )
| ( $true
!= ( mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2 ) ) )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f154,f219]) ).
thf(f219,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f218]) ).
thf(f218,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 )
| ( $false = $true ) )
| ~ spl3_3 ),
inference(forward_demodulation,[status(thm)],[f215,f207]) ).
thf(f215,plain,
( ! [X0: $o] :
( ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) )
| ( $false = X0 )
| ( $true = X0 ) )
| ~ spl3_3 ),
inference(binary_proxy_clausification,[status(thm)],[f214]) ).
thf(f214,plain,
( ! [X0: $o] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 )
= X0 )
| ( $true = X0 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f213]) ).
thf(f213,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = $true )
| ( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 )
= X0 ) )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f207,f166]) ).
thf(f202,plain,
( ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f200]) ).
thf(f200,definition,
( spl3_2
<=> ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f212,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f194,f209,f205]) ).
thf(f194,plain,
( ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) )
| ( $false
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f172]) ).
thf(f172,plain,
( ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 )
!= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
thf(f203,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f193,f200,f196]) ).
thf(f193,plain,
( ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ ( mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2 ) ) )
| ( $true
= ( mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP012^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:21:20 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.50 ---- Original DTF file ---
% 0.27/0.50 thf(spec,logic,$$dhol).
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 % File : ITP012^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.27/0.50 % Domain : Interactive Theorem Proving
% 0.27/0.50 % Problem : HOL4 syntactic export of thm_2Einteger_2EINT__DIVIDES__RSUB.p, bushy mode
% 0.27/0.50 % Version : [BG+19] axioms.
% 0.27/0.50 % English :
% 0.27/0.50
% 0.27/0.50 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.27/0.50 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.27/0.50 % Source : [BG+19]
% 0.27/0.50 % Names : thm_2Einteger_2EINT__DIVIDES__RSUB.p [Gau19]
% 0.27/0.50 % : HL405501^1.p [TPAP]
% 0.27/0.50
% 0.27/0.50 % Status : Theorem
% 0.27/0.50 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0
% 0.27/0.50 % Syntax : Number of formulae : 136 ( 39 unt; 68 typ; 0 def)
% 0.27/0.50 % Number of atoms : 161 ( 48 equ; 46 cnn)
% 0.27/0.50 % Maximal formula atoms : 8 ( 2 avg)
% 0.27/0.50 % Number of connectives : 879 ( 46 ~; 34 |; 27 &; 702 @)
% 0.27/0.50 % ( 39 <=>; 31 =>; 0 <=; 0 <~>)
% 0.27/0.50 % Maximal formula depth : 17 ( 5 avg)
% 0.27/0.50 % Number of types : 5 ( 4 usr)
% 0.27/0.50 % Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% 0.27/0.50 % Number of symbols : 66 ( 64 usr; 21 con; 0-3 aty)
% 0.27/0.50 % Number of variables : 135 ( 0 ^; 133 !; 2 ?; 135 :)
% 0.27/0.50 % SPC : TH0_THM_EQU_NAR
% 0.27/0.50
% 0.27/0.50 % Comments :
% 0.27/0.50 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 thf(u,type,
% 0.27/0.50 u: $tType ).
% 0.27/0.50
% 0.27/0.50 thf(d,type,
% 0.27/0.50 d: $tType ).
% 0.27/0.50
% 0.27/0.50 thf(du,type,
% 0.27/0.50 du: $tType ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Etyop_2Einteger_2Eint,type,
% 0.27/0.50 mono_2Etyop_2Einteger_2Eint: $tType ).
% 0.27/0.50
% 0.27/0.50 thf(tyop_2Einteger_2Eint,type,
% 0.27/0.50 tyop_2Einteger_2Eint: d ).
% 0.27/0.50
% 0.27/0.50 thf(tyop_2Emin_2Ebool,type,
% 0.27/0.50 tyop_2Emin_2Ebool: d ).
% 0.27/0.50
% 0.27/0.50 thf(tyop_2Emin_2Efun,type,
% 0.27/0.50 tyop_2Emin_2Efun: d > d > d ).
% 0.27/0.50
% 0.27/0.50 thf(s,type,
% 0.27/0.50 s: d > u > du ).
% 0.27/0.50
% 0.27/0.50 thf(app_2E2,type,
% 0.27/0.50 app_2E2: du > du > u ).
% 0.27/0.50
% 0.27/0.50 thf(combin_i_2E0,type,
% 0.27/0.50 combin_i_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(combin_k_2E0,type,
% 0.27/0.50 combin_k_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(combin_s_2E0,type,
% 0.27/0.50 combin_s_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_21_2E0,type,
% 0.27/0.50 c_2Ebool_2E_21_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_21_2E1,type,
% 0.27/0.50 c_2Ebool_2E_21_2E1: du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.27/0.50 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.27/0.50 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Emin_2E_3D_2E0,type,
% 0.27/0.50 c_2Emin_2E_3D_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Emin_2E_3D_2E2,type,
% 0.27/0.50 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.27/0.50 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.27/0.50 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_3F_2E0,type,
% 0.27/0.50 c_2Ebool_2E_3F_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_3F_2E1,type,
% 0.27/0.50 c_2Ebool_2E_3F_2E1: du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2EF_2E0,type,
% 0.27/0.50 c_2Ebool_2EF_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2ET_2E0,type,
% 0.27/0.50 c_2Ebool_2ET_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.27/0.50 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.27/0.50 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Einteger_2Eint__add_2E0,type,
% 0.27/0.50 c_2Einteger_2Eint__add_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Einteger_2Eint__add_2E2,type,
% 0.27/0.50 c_2Einteger_2Eint__add_2E2: du > du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Einteger_2Eint__divides_2E0,type,
% 0.27/0.50 c_2Einteger_2Eint__divides_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Einteger_2Eint__divides_2E2,type,
% 0.27/0.50 c_2Einteger_2Eint__divides_2E2: du > du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Einteger_2Eint__neg_2E0,type,
% 0.27/0.50 c_2Einteger_2Eint__neg_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Einteger_2Eint__neg_2E1,type,
% 0.27/0.50 c_2Einteger_2Eint__neg_2E1: du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Einteger_2Eint__sub_2E0,type,
% 0.27/0.50 c_2Einteger_2Eint__sub_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Einteger_2Eint__sub_2E2,type,
% 0.27/0.50 c_2Einteger_2Eint__sub_2E2: du > du > u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_7E_2E0,type,
% 0.27/0.50 c_2Ebool_2E_7E_2E0: u ).
% 0.27/0.50
% 0.27/0.50 thf(c_2Ebool_2E_7E_2E1,type,
% 0.27/0.50 c_2Ebool_2E_7E_2E1: du > u ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.27/0.50 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.27/0.50 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,type,
% 0.27/0.50 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 0.27/0.50 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 0.27/0.50 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
% 0.27/0.50 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.27/0.50 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.27/0.50 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Ebool_2EF,type,
% 0.27/0.50 mono_2Ec_2Ebool_2EF: $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Ebool_2ET,type,
% 0.27/0.50 mono_2Ec_2Ebool_2ET: $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.27/0.50 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Einteger_2Eint__add,type,
% 0.27/0.50 mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Einteger_2Eint__divides,type,
% 0.27/0.50 mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Einteger_2Eint__neg,type,
% 0.27/0.50 mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Einteger_2Eint__sub,type,
% 0.27/0.50 mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.27/0.50
% 0.27/0.50 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.27/0.50 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.27/0.50
% 0.27/0.50 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.27/0.50 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.27/0.50
% 0.27/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.27/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.27/0.50
% 0.27/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.27/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.27/0.50
% 0.27/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 0.27/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > $o ) > u ).
% 0.27/0.50
% 0.27/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.27/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
% 0.27/0.50
% 0.27/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
% 0.27/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
% 0.27/0.50
% 0.27/0.50 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 0.27/0.50 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
% 0.27/0.50
% 0.27/0.50 thf(i_mono_2Etyop_2Einteger_2Eint,type,
% 0.27/0.50 i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
% 0.27/0.50
% 0.27/0.50 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.27/0.50 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.27/0.50
% 0.27/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.27/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.27/0.50
% 0.27/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.27/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.27/0.50
% 0.27/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 0.27/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.27/0.50
% 0.27/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.27/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 0.27/0.50
% 0.27/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
% 0.27/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.27/0.50
% 0.27/0.50 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 0.27/0.50 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 0.27/0.50
% 0.27/0.50 thf(j_mono_2Etyop_2Einteger_2Eint,type,
% 0.27/0.50 j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.27/0.50 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.27/0.50 ( ! [V2x_2E0: u] :
% 0.27/0.50 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.27/0.50 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.27/0.50 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.27/0.50 ! [A_27a: d,V0x_2E0: u] :
% 0.27/0.50 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.27/0.50 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.27/0.50 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.27/0.50 ( ( 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 ) ) )
% 0.27/0.50 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Eho_2Es__thm,axiom,
% 0.27/0.50 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.27/0.50 ( ( 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 ) ) )
% 0.27/0.50 = ( 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 ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.27/0.50 ! [V0: $o,V1: $o] :
% 0.27/0.50 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.27/0.50 <=> ( V0
% 0.27/0.50 & V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.27/0.50 ! [V0: $o,V1: $o] :
% 0.27/0.50 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.27/0.50 <=> ( V0
% 0.27/0.50 | V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Elogic_2E_7E,axiom,
% 0.27/0.50 ! [V0: $o] :
% 0.27/0.50 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.27/0.50 <=> ( (~) @ V0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.27/0.50 ! [V0: $o,V1: $o] :
% 0.27/0.50 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.27/0.50 <=> ( V0
% 0.27/0.50 => V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Elogic_2E_3D,axiom,
% 0.27/0.50 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.27/0.50 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.27/0.50 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.27/0.50 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Equant_2E_21,axiom,
% 0.27/0.50 ! [A_27a: d,V0f_2E0: u] :
% 0.27/0.50 ( ( 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 ) ) ) )
% 0.27/0.50 <=> ! [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 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(reserved_2Equant_2E_3F,axiom,
% 0.27/0.50 ! [A_27a: d,V0f_2E0: u] :
% 0.27/0.50 ( ( 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 ) ) ) )
% 0.27/0.50 <=> ? [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 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.27/0.50 ! [V0_2E0: u] :
% 0.27/0.50 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.27/0.50 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.27/0.50 ! [V0_2E0: u] :
% 0.27/0.50 ( ( 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 ) ) ) )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.27/0.50 ! [V0_2E0: u] :
% 0.27/0.50 ( ( 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 ) ) ) )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.27/0.50 ! [V0_2E0: u] :
% 0.27/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.27/0.50 ! [V0_2E0: u] :
% 0.27/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
% 0.27/0.50 ! [V0_2E0: u] :
% 0.27/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ) )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 0.27/0.50 ! [V0_2E0: u] :
% 0.27/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ij_2Emono_2Etyop_2Einteger_2Eint,axiom,
% 0.27/0.50 ! [V0_2E0: u] :
% 0.27/0.50 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ) )
% 0.27/0.50 = ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.27/0.50 ! [V0: $o] :
% 0.27/0.50 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.27/0.50 = V0 ) ).
% 0.27/0.50
% 0.27/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.27/0.50 ! [V0: $o > $o] :
% 0.27/0.50 ( ( 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 ) ) )
% 0.27/0.50 = V0 ) ).
% 0.27/0.50
% 0.27/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.27/0.50 ! [V0: $o > $o > $o] :
% 0.27/0.50 ( ( 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 ) ) )
% 0.27/0.50 = V0 ) ).
% 0.27/0.50
% 0.27/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > $o] :
% 0.27/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.27/0.50 = V0 ) ).
% 0.27/0.50
% 0.27/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
% 0.27/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.27/0.50 = V0 ) ).
% 0.27/0.50
% 0.27/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) )
% 0.27/0.50 = V0 ) ).
% 0.27/0.50
% 0.27/0.50 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
% 0.27/0.50 = V0 ) ).
% 0.27/0.50
% 0.27/0.50 thf(ji_2Emono_2Etyop_2Einteger_2Eint,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V0 ) ) )
% 0.27/0.50 = V0 ) ).
% 0.27/0.50
% 0.27/0.50 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.27/0.50 ! [A_27a: d,X0_2E0: u] :
% 0.27/0.50 ( ( 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 ) ) ) )
% 0.27/0.50 = ( 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 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.27/0.50 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.27/0.50 ( ( ( s @ A_27a @ X0_2E0 )
% 0.27/0.50 = ( s @ A_27a @ X1_2E0 ) )
% 0.27/0.50 <=> ( 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 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.27/0.50 ! [A_27a: d,X0_2E0: u] :
% 0.27/0.50 ( ( 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 ) ) ) )
% 0.27/0.50 = ( 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 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.27/0.50 ! [V0: $o > $o,V1: $o] :
% 0.27/0.50 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.27/0.50 = ( 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 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.27/0.50 ! [V0: $o > $o > $o,V1: $o] :
% 0.27/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.27/0.50 = ( 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 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.27/0.50 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( V0 @ V1 ) ) )
% 0.27/0.50 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
% 0.27/0.50 = ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.27/0.50 ! [V0: $o > $o,V1: $o] :
% 0.27/0.50 ( ( V0 @ V1 )
% 0.27/0.50 = ( V0 @ V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.27/0.50 ! [V0: $o > $o > $o,V1: $o] :
% 0.27/0.50 ( ( V0 @ V1 )
% 0.27/0.50 = ( V0 @ V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( V0 @ V1 )
% 0.27/0.50 = ( V0 @ V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( V0 @ V1 )
% 0.27/0.50 = ( V0 @ V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( V0 @ V1 )
% 0.27/0.50 = ( V0 @ V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
% 0.27/0.50 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( V0 @ V1 )
% 0.27/0.50 = ( V0 @ V1 ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.27/0.50 mono_2Ec_2Ebool_2ET ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.27/0.50 ! [V0t1: $o,V1t2: $o] :
% 0.27/0.50 ( ( V0t1
% 0.27/0.50 => V1t2 )
% 0.27/0.50 => ( ( V1t2
% 0.27/0.50 => V0t1 )
% 0.27/0.50 => ( V0t1 = V1t2 ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EIMP__F,axiom,
% 0.27/0.50 ! [V0t: $o] :
% 0.27/0.50 ( ( V0t
% 0.27/0.50 => mono_2Ec_2Ebool_2EF )
% 0.27/0.50 => ( (~) @ V0t ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EF__IMP,axiom,
% 0.27/0.50 ! [V0t: $o] :
% 0.27/0.50 ( ( (~) @ V0t )
% 0.27/0.50 => ( V0t
% 0.27/0.50 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.27/0.50 ! [V0t: $o] :
% 0.27/0.50 ( ( ( mono_2Ec_2Ebool_2ET
% 0.27/0.50 => V0t )
% 0.27/0.50 <=> V0t )
% 0.27/0.50 & ( ( V0t
% 0.27/0.50 => mono_2Ec_2Ebool_2ET )
% 0.27/0.50 <=> mono_2Ec_2Ebool_2ET )
% 0.27/0.50 & ( ( mono_2Ec_2Ebool_2EF
% 0.27/0.50 => V0t )
% 0.27/0.50 <=> mono_2Ec_2Ebool_2ET )
% 0.27/0.50 & ( ( V0t
% 0.27/0.50 => V0t )
% 0.27/0.50 <=> mono_2Ec_2Ebool_2ET )
% 0.27/0.50 & ( ( V0t
% 0.27/0.50 => mono_2Ec_2Ebool_2EF )
% 0.27/0.50 <=> ( (~) @ V0t ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.27/0.50 ( ! [V0t: $o] :
% 0.27/0.50 ( ( (~) @ ( (~) @ V0t ) )
% 0.27/0.50 <=> V0t )
% 0.27/0.50 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 0.27/0.50 <=> mono_2Ec_2Ebool_2EF )
% 0.27/0.50 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 0.27/0.50 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.27/0.50 ! [V0t: $o] :
% 0.27/0.50 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 0.27/0.50 <=> V0t )
% 0.27/0.50 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 0.27/0.50 <=> V0t )
% 0.27/0.50 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 0.27/0.50 <=> ( (~) @ V0t ) )
% 0.27/0.50 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 0.27/0.50 <=> ( (~) @ V0t ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2ENOT__FORALL__THM,axiom,
% 0.27/0.50 ! [A_27a: d,V0P_2E0: u] :
% 0.27/0.50 ( ( (~)
% 0.27/0.50 @ ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
% 0.27/0.50 <=> ? [V2x_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EFORALL__AND__THM,axiom,
% 0.27/0.50 ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
% 0.27/0.50 ( ! [V2x_2E0: u] :
% 0.27/0.50 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.27/0.50 & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
% 0.27/0.50 <=> ( ! [V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
% 0.27/0.50 & ! [V4x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EDISJ__ASSOC,axiom,
% 0.27/0.50 ! [V0A: $o,V1B: $o,V2C: $o] :
% 0.27/0.50 ( ( V0A
% 0.27/0.50 | V1B
% 0.27/0.50 | V2C )
% 0.27/0.50 <=> ( V0A
% 0.27/0.50 | V1B
% 0.27/0.50 | V2C ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EDISJ__SYM,axiom,
% 0.27/0.50 ! [V0A: $o,V1B: $o] :
% 0.27/0.50 ( ( V0A
% 0.27/0.50 | V1B )
% 0.27/0.50 <=> ( V1B
% 0.27/0.50 | V0A ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Ebool_2EDE__MORGAN__THM,axiom,
% 0.27/0.50 ! [V0A: $o,V1B: $o] :
% 0.27/0.50 ( ( ( (~)
% 0.27/0.50 @ ( V0A
% 0.27/0.50 & V1B ) )
% 0.27/0.50 <=> ( ( (~) @ V0A )
% 0.27/0.50 | ( (~) @ V1B ) ) )
% 0.27/0.50 & ( ( (~)
% 0.27/0.50 @ ( V0A
% 0.27/0.50 | V1B ) )
% 0.27/0.50 <=> ( ( (~) @ V0A )
% 0.27/0.50 & ( (~) @ V1B ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Einteger_2Eint__sub,axiom,
% 0.27/0.50 ! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y )
% 0.27/0.50 = ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
% 0.27/0.50 ! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
% 0.27/0.50 => ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__add @ V2r @ V1q ) )
% 0.27/0.50 = ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V2r ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
% 0.27/0.50 ! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
% 0.27/0.50 = ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q ) )
% 0.27/0.50 & ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) @ V1q )
% 0.27/0.50 = ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2ENOT__NOT,axiom,
% 0.27/0.50 ! [V0t: $o] :
% 0.27/0.50 ( ( (~) @ ( (~) @ V0t ) )
% 0.27/0.50 <=> V0t ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 0.27/0.50 ! [V0A: $o] :
% 0.27/0.50 ( V0A
% 0.27/0.50 => ( ( (~) @ V0A )
% 0.27/0.50 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 0.27/0.50 ! [V0B: $o,V1A: $o] :
% 0.27/0.50 ( ( ( (~)
% 0.27/0.50 @ ( V1A
% 0.27/0.50 | V0B ) )
% 0.27/0.50 => mono_2Ec_2Ebool_2EF )
% 0.27/0.50 <=> ( ( V1A
% 0.27/0.50 => mono_2Ec_2Ebool_2EF )
% 0.27/0.50 => ( ( (~) @ V0B )
% 0.27/0.50 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 0.27/0.50 ! [V0B: $o,V1A: $o] :
% 0.27/0.50 ( ( ( (~)
% 0.27/0.50 @ ( ( (~) @ V1A )
% 0.27/0.50 | V0B ) )
% 0.27/0.50 => mono_2Ec_2Ebool_2EF )
% 0.27/0.50 <=> ( V1A
% 0.27/0.50 => ( ( (~) @ V0B )
% 0.27/0.50 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2EAND__INV2,axiom,
% 0.27/0.50 ! [V0A: $o] :
% 0.27/0.50 ( ( ( (~) @ V0A )
% 0.27/0.50 => mono_2Ec_2Ebool_2EF )
% 0.27/0.50 => ( ( V0A
% 0.27/0.50 => mono_2Ec_2Ebool_2EF )
% 0.27/0.50 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2Edc__eq,axiom,
% 0.27/0.50 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.27/0.50 ( ( V2p
% 0.27/0.50 <=> ( V1q = V0r ) )
% 0.27/0.50 <=> ( ( V2p
% 0.27/0.50 | V1q
% 0.27/0.50 | V0r )
% 0.27/0.50 & ( V2p
% 0.27/0.50 | ( (~) @ V0r )
% 0.27/0.50 | ( (~) @ V1q ) )
% 0.27/0.50 & ( V1q
% 0.27/0.50 | ( (~) @ V0r )
% 0.27/0.50 | ( (~) @ V2p ) )
% 0.27/0.50 & ( V0r
% 0.27/0.50 | ( (~) @ V1q )
% 0.27/0.50 | ( (~) @ V2p ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2Edc__conj,axiom,
% 0.27/0.50 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.27/0.50 ( ( V2p
% 0.27/0.50 <=> ( V1q
% 0.27/0.50 & V0r ) )
% 0.27/0.50 <=> ( ( V2p
% 0.27/0.50 | ( (~) @ V1q )
% 0.27/0.50 | ( (~) @ V0r ) )
% 0.27/0.50 & ( V1q
% 0.27/0.50 | ( (~) @ V2p ) )
% 0.27/0.50 & ( V0r
% 0.27/0.50 | ( (~) @ V2p ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2Edc__disj,axiom,
% 0.27/0.50 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.27/0.50 ( ( V2p
% 0.27/0.50 <=> ( V1q
% 0.27/0.50 | V0r ) )
% 0.27/0.50 <=> ( ( V2p
% 0.27/0.50 | ( (~) @ V1q ) )
% 0.27/0.50 & ( V2p
% 0.27/0.50 | ( (~) @ V0r ) )
% 0.27/0.50 & ( V1q
% 0.27/0.50 | V0r
% 0.27/0.50 | ( (~) @ V2p ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2Edc__imp,axiom,
% 0.27/0.50 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.27/0.50 ( ( V2p
% 0.27/0.50 <=> ( V1q
% 0.27/0.50 => V0r ) )
% 0.27/0.50 <=> ( ( V2p
% 0.27/0.50 | V1q )
% 0.27/0.50 & ( V2p
% 0.27/0.50 | ( (~) @ V0r ) )
% 0.27/0.50 & ( ( (~) @ V1q )
% 0.27/0.50 | V0r
% 0.27/0.50 | ( (~) @ V2p ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Esat_2Edc__neg,axiom,
% 0.27/0.50 ! [V0q: $o,V1p: $o] :
% 0.27/0.50 ( ( V1p
% 0.27/0.50 <=> ( (~) @ V0q ) )
% 0.27/0.50 <=> ( ( V1p
% 0.27/0.50 | V0q )
% 0.27/0.50 & ( ( (~) @ V0q )
% 0.27/0.50 | ( (~) @ V1p ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
% 0.27/0.50 ! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
% 0.27/0.50 ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
% 0.27/0.50 => ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__sub @ V2r @ V1q ) )
% 0.27/0.50 = ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V2r ) ) ) ).
% 0.27/0.50
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 ------------------------
% 2.04/1.44 ---- Embedded in THF ---
% 2.04/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.04/1.44 %%% Generated on Tue Feb 24 08:21:21 EST 2026
% 2.04/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 2.04/1.44 %%% Logic specification used:
% 2.04/1.44 %%% thf(spec, logic, $$dhol).
% 2.04/1.44
% 2.04/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2DTF19586.p
% See solution above
% 2.04/1.44 ------------------------
% 2.04/1.46 ---- Cleaned THF ---
% 2.04/1.46 thf(u,type,
% 2.04/1.46 u: $tType ).
% 2.04/1.46
% 2.04/1.46 thf(d,type,
% 2.04/1.46 d: $tType ).
% 2.04/1.46
% 2.04/1.46 thf(du,type,
% 2.04/1.46 du: $tType ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Etyop_2Einteger_2Eint,type,
% 2.04/1.46 mono_2Etyop_2Einteger_2Eint: $tType ).
% 2.04/1.46
% 2.04/1.46 thf(tyop_2Einteger_2Eint,type,
% 2.04/1.46 tyop_2Einteger_2Eint: d ).
% 2.04/1.46
% 2.04/1.46 thf(tyop_2Emin_2Ebool,type,
% 2.04/1.46 tyop_2Emin_2Ebool: d ).
% 2.04/1.46
% 2.04/1.46 thf(tyop_2Emin_2Efun,type,
% 2.04/1.46 tyop_2Emin_2Efun: d > d > d ).
% 2.04/1.46
% 2.04/1.46 thf(s,type,
% 2.04/1.46 s: d > u > du ).
% 2.04/1.46
% 2.04/1.46 thf(app_2E2,type,
% 2.04/1.46 app_2E2: du > du > u ).
% 2.04/1.46
% 2.04/1.46 thf(combin_i_2E0,type,
% 2.04/1.46 combin_i_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(combin_k_2E0,type,
% 2.04/1.46 combin_k_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(combin_s_2E0,type,
% 2.04/1.46 combin_s_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_21_2E0,type,
% 2.04/1.46 c_2Ebool_2E_21_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_21_2E1,type,
% 2.04/1.46 c_2Ebool_2E_21_2E1: du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 2.04/1.46 c_2Ebool_2E_2F_5C_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 2.04/1.46 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Emin_2E_3D_2E0,type,
% 2.04/1.46 c_2Emin_2E_3D_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Emin_2E_3D_2E2,type,
% 2.04/1.46 c_2Emin_2E_3D_2E2: du > du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 2.04/1.46 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 2.04/1.46 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_3F_2E0,type,
% 2.04/1.46 c_2Ebool_2E_3F_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_3F_2E1,type,
% 2.04/1.46 c_2Ebool_2E_3F_2E1: du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2EF_2E0,type,
% 2.04/1.46 c_2Ebool_2EF_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2ET_2E0,type,
% 2.04/1.46 c_2Ebool_2ET_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 2.04/1.46 c_2Ebool_2E_5C_2F_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 2.04/1.46 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Einteger_2Eint__add_2E0,type,
% 2.04/1.46 c_2Einteger_2Eint__add_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Einteger_2Eint__add_2E2,type,
% 2.04/1.46 c_2Einteger_2Eint__add_2E2: du > du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Einteger_2Eint__divides_2E0,type,
% 2.04/1.46 c_2Einteger_2Eint__divides_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Einteger_2Eint__divides_2E2,type,
% 2.04/1.46 c_2Einteger_2Eint__divides_2E2: du > du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Einteger_2Eint__neg_2E0,type,
% 2.04/1.46 c_2Einteger_2Eint__neg_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Einteger_2Eint__neg_2E1,type,
% 2.04/1.46 c_2Einteger_2Eint__neg_2E1: du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Einteger_2Eint__sub_2E0,type,
% 2.04/1.46 c_2Einteger_2Eint__sub_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Einteger_2Eint__sub_2E2,type,
% 2.04/1.46 c_2Einteger_2Eint__sub_2E2: du > du > u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_7E_2E0,type,
% 2.04/1.46 c_2Ebool_2E_7E_2E0: u ).
% 2.04/1.46
% 2.04/1.46 thf(c_2Ebool_2E_7E_2E1,type,
% 2.04/1.46 c_2Ebool_2E_7E_2E1: du > u ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 2.04/1.46 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.04/1.46 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,type,
% 2.04/1.46 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 2.04/1.46 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 2.04/1.46 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
% 2.04/1.46 mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 2.04/1.46 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 2.04/1.46 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Ebool_2EF,type,
% 2.04/1.46 mono_2Ec_2Ebool_2EF: $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Ebool_2ET,type,
% 2.04/1.46 mono_2Ec_2Ebool_2ET: $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 2.04/1.46 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Einteger_2Eint__add,type,
% 2.04/1.46 mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Einteger_2Eint__divides,type,
% 2.04/1.46 mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Einteger_2Eint__neg,type,
% 2.04/1.46 mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Einteger_2Eint__sub,type,
% 2.04/1.46 mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.04/1.46
% 2.04/1.46 thf(mono_2Ec_2Ebool_2E_7E,type,
% 2.04/1.46 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 2.04/1.46
% 2.04/1.46 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 2.04/1.46 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 2.04/1.46
% 2.04/1.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.04/1.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 2.04/1.46
% 2.04/1.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.04/1.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 2.04/1.46
% 2.04/1.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 2.04/1.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > $o ) > u ).
% 2.04/1.46
% 2.04/1.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.04/1.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
% 2.04/1.46
% 2.04/1.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
% 2.04/1.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
% 2.04/1.46
% 2.04/1.46 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 2.04/1.46 i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
% 2.04/1.46
% 2.04/1.46 thf(i_mono_2Etyop_2Einteger_2Eint,type,
% 2.04/1.46 i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
% 2.04/1.46
% 2.04/1.46 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 2.04/1.46 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 2.04/1.46
% 2.04/1.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.04/1.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 2.04/1.46
% 2.04/1.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.04/1.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 2.04/1.46
% 2.04/1.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
% 2.04/1.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.04/1.46
% 2.04/1.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.04/1.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
% 2.04/1.46
% 2.04/1.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
% 2.04/1.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.04/1.46
% 2.04/1.46 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
% 2.04/1.46 j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
% 2.04/1.46
% 2.04/1.46 thf(j_mono_2Etyop_2Einteger_2Eint,type,
% 2.04/1.46 j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Eho_2Eeq__ext,axiom,
% 2.04/1.46 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 2.04/1.46 ( ! [V2x_2E0: u] :
% 2.04/1.46 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 2.04/1.46 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 2.04/1.46 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Eho_2Ei__thm,axiom,
% 2.04/1.46 ! [A_27a: d,V0x_2E0: u] :
% 2.04/1.46 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 2.04/1.46 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Eho_2Ek__thm,axiom,
% 2.04/1.46 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 2.04/1.46 ( ( 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 ) ) )
% 2.04/1.46 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Eho_2Es__thm,axiom,
% 2.04/1.46 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 2.04/1.46 ( ( 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 ) ) )
% 2.04/1.46 = ( 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 ) ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 2.04/1.46 ! [V0: $o,V1: $o] :
% 2.04/1.46 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 2.04/1.46 <=> ( V0
% 2.04/1.46 & V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 2.04/1.46 ! [V0: $o,V1: $o] :
% 2.04/1.46 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 2.04/1.46 <=> ( V0
% 2.04/1.46 | V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Elogic_2E_7E,axiom,
% 2.04/1.46 ! [V0: $o] :
% 2.04/1.46 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 2.04/1.46 <=> ( (~) @ V0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 2.04/1.46 ! [V0: $o,V1: $o] :
% 2.04/1.46 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 2.04/1.46 <=> ( V0
% 2.04/1.46 => V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Elogic_2E_3D,axiom,
% 2.04/1.46 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 2.04/1.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 2.04/1.46 <=> ( ( s @ A_27a @ V0_2E0 )
% 2.04/1.46 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Equant_2E_21,axiom,
% 2.04/1.46 ! [A_27a: d,V0f_2E0: u] :
% 2.04/1.46 ( ( 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 ) ) ) )
% 2.04/1.46 <=> ! [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 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(reserved_2Equant_2E_3F,axiom,
% 2.04/1.46 ! [A_27a: d,V0f_2E0: u] :
% 2.04/1.46 ( ( 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 ) ) ) )
% 2.04/1.46 <=> ? [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 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.04/1.46 ! [V0_2E0: u] :
% 2.04/1.46 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 2.04/1.46 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.04/1.46 ! [V0_2E0: u] :
% 2.04/1.46 ( ( 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 ) ) ) )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.04/1.46 ! [V0_2E0: u] :
% 2.04/1.46 ( ( 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 ) ) ) )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.04/1.46 ! [V0_2E0: u] :
% 2.04/1.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.04/1.46 ! [V0_2E0: u] :
% 2.04/1.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
% 2.04/1.46 ! [V0_2E0: u] :
% 2.04/1.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ) )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 2.04/1.46 ! [V0_2E0: u] :
% 2.04/1.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ij_2Emono_2Etyop_2Einteger_2Eint,axiom,
% 2.04/1.46 ! [V0_2E0: u] :
% 2.04/1.46 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ) )
% 2.04/1.46 = ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.04/1.46 ! [V0: $o] :
% 2.04/1.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 2.04/1.46 = V0 ) ).
% 2.04/1.46
% 2.04/1.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.04/1.46 ! [V0: $o > $o] :
% 2.04/1.46 ( ( 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 ) ) )
% 2.04/1.46 = V0 ) ).
% 2.04/1.46
% 2.04/1.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.04/1.46 ! [V0: $o > $o > $o] :
% 2.04/1.46 ( ( 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 ) ) )
% 2.04/1.46 = V0 ) ).
% 2.04/1.46
% 2.04/1.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > $o] :
% 2.04/1.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 2.04/1.46 = V0 ) ).
% 2.04/1.46
% 2.04/1.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
% 2.04/1.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 2.04/1.46 = V0 ) ).
% 2.04/1.46
% 2.04/1.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) )
% 2.04/1.46 = V0 ) ).
% 2.04/1.46
% 2.04/1.46 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
% 2.04/1.46 = V0 ) ).
% 2.04/1.46
% 2.04/1.46 thf(ji_2Emono_2Etyop_2Einteger_2Eint,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V0 ) ) )
% 2.04/1.46 = V0 ) ).
% 2.04/1.46
% 2.04/1.46 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 2.04/1.46 ! [A_27a: d,X0_2E0: u] :
% 2.04/1.46 ( ( 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 ) ) ) )
% 2.04/1.46 = ( 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 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 2.04/1.46 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 2.04/1.46 ( ( ( s @ A_27a @ X0_2E0 )
% 2.04/1.46 = ( s @ A_27a @ X1_2E0 ) )
% 2.04/1.46 <=> ( 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 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 2.04/1.46 ! [A_27a: d,X0_2E0: u] :
% 2.04/1.46 ( ( 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 ) ) ) )
% 2.04/1.46 = ( 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 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.04/1.46 ! [V0: $o > $o,V1: $o] :
% 2.04/1.46 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 2.04/1.46 = ( 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 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.04/1.46 ! [V0: $o > $o > $o,V1: $o] :
% 2.04/1.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 2.04/1.46 = ( 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 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 2.04/1.46 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( V0 @ V1 ) ) )
% 2.04/1.46 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
% 2.04/1.46 = ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.04/1.46 ! [V0: $o > $o,V1: $o] :
% 2.04/1.46 ( ( V0 @ V1 )
% 2.04/1.46 = ( V0 @ V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.04/1.46 ! [V0: $o > $o > $o,V1: $o] :
% 2.04/1.46 ( ( V0 @ V1 )
% 2.04/1.46 = ( V0 @ V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( V0 @ V1 )
% 2.04/1.46 = ( V0 @ V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( V0 @ V1 )
% 2.04/1.46 = ( V0 @ V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( V0 @ V1 )
% 2.04/1.46 = ( V0 @ V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
% 2.04/1.46 ! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( V0 @ V1 )
% 2.04/1.46 = ( V0 @ V1 ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2ETRUTH,axiom,
% 2.04/1.46 mono_2Ec_2Ebool_2ET ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 2.04/1.46 ! [V0t1: $o,V1t2: $o] :
% 2.04/1.46 ( ( V0t1
% 2.04/1.46 => V1t2 )
% 2.04/1.46 => ( ( V1t2
% 2.04/1.46 => V0t1 )
% 2.04/1.46 => ( V0t1 = V1t2 ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EIMP__F,axiom,
% 2.04/1.46 ! [V0t: $o] :
% 2.04/1.46 ( ( V0t
% 2.04/1.46 => mono_2Ec_2Ebool_2EF )
% 2.04/1.46 => ( (~) @ V0t ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EF__IMP,axiom,
% 2.04/1.46 ! [V0t: $o] :
% 2.04/1.46 ( ( (~) @ V0t )
% 2.04/1.46 => ( V0t
% 2.04/1.46 => mono_2Ec_2Ebool_2EF ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 2.04/1.46 ! [V0t: $o] :
% 2.04/1.46 ( ( ( mono_2Ec_2Ebool_2ET
% 2.04/1.46 => V0t )
% 2.04/1.46 <=> V0t )
% 2.04/1.46 & ( ( V0t
% 2.04/1.46 => mono_2Ec_2Ebool_2ET )
% 2.04/1.46 <=> mono_2Ec_2Ebool_2ET )
% 2.04/1.46 & ( ( mono_2Ec_2Ebool_2EF
% 2.04/1.46 => V0t )
% 2.04/1.46 <=> mono_2Ec_2Ebool_2ET )
% 2.04/1.46 & ( ( V0t
% 2.04/1.46 => V0t )
% 2.04/1.46 <=> mono_2Ec_2Ebool_2ET )
% 2.04/1.46 & ( ( V0t
% 2.04/1.46 => mono_2Ec_2Ebool_2EF )
% 2.04/1.46 <=> ( (~) @ V0t ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 2.04/1.46 ( ! [V0t: $o] :
% 2.04/1.46 ( ( (~) @ ( (~) @ V0t ) )
% 2.04/1.46 <=> V0t )
% 2.04/1.46 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 2.04/1.46 <=> mono_2Ec_2Ebool_2EF )
% 2.04/1.46 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 2.04/1.46 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 2.04/1.46 ! [V0t: $o] :
% 2.04/1.46 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 2.04/1.46 <=> V0t )
% 2.04/1.46 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 2.04/1.46 <=> V0t )
% 2.04/1.46 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 2.04/1.46 <=> ( (~) @ V0t ) )
% 2.04/1.46 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 2.04/1.46 <=> ( (~) @ V0t ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2ENOT__FORALL__THM,axiom,
% 2.04/1.46 ! [A_27a: d,V0P_2E0: u] :
% 2.04/1.46 ( ( (~)
% 2.04/1.46 @ ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
% 2.04/1.46 <=> ? [V2x_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EFORALL__AND__THM,axiom,
% 2.04/1.46 ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
% 2.04/1.46 ( ! [V2x_2E0: u] :
% 2.04/1.46 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 2.04/1.46 & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
% 2.04/1.46 <=> ( ! [V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
% 2.04/1.46 & ! [V4x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EDISJ__ASSOC,axiom,
% 2.04/1.46 ! [V0A: $o,V1B: $o,V2C: $o] :
% 2.04/1.46 ( ( V0A
% 2.04/1.46 | V1B
% 2.04/1.46 | V2C )
% 2.04/1.46 <=> ( V0A
% 2.04/1.46 | V1B
% 2.04/1.46 | V2C ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EDISJ__SYM,axiom,
% 2.04/1.46 ! [V0A: $o,V1B: $o] :
% 2.04/1.46 ( ( V0A
% 2.04/1.46 | V1B )
% 2.04/1.46 <=> ( V1B
% 2.04/1.46 | V0A ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Ebool_2EDE__MORGAN__THM,axiom,
% 2.04/1.46 ! [V0A: $o,V1B: $o] :
% 2.04/1.46 ( ( ( (~)
% 2.04/1.46 @ ( V0A
% 2.04/1.46 & V1B ) )
% 2.04/1.46 <=> ( ( (~) @ V0A )
% 2.04/1.46 | ( (~) @ V1B ) ) )
% 2.04/1.46 & ( ( (~)
% 2.04/1.46 @ ( V0A
% 2.04/1.46 | V1B ) )
% 2.04/1.46 <=> ( ( (~) @ V0A )
% 2.04/1.46 & ( (~) @ V1B ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Einteger_2Eint__sub,axiom,
% 2.04/1.46 ! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y )
% 2.04/1.46 = ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
% 2.04/1.46 ! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
% 2.04/1.46 => ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__add @ V2r @ V1q ) )
% 2.04/1.46 = ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V2r ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
% 2.04/1.46 ! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
% 2.04/1.46 = ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q ) )
% 2.04/1.46 & ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) @ V1q )
% 2.04/1.46 = ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2ENOT__NOT,axiom,
% 2.04/1.46 ! [V0t: $o] :
% 2.04/1.46 ( ( (~) @ ( (~) @ V0t ) )
% 2.04/1.46 <=> V0t ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 2.04/1.46 ! [V0A: $o] :
% 2.04/1.46 ( V0A
% 2.04/1.46 => ( ( (~) @ V0A )
% 2.04/1.46 => mono_2Ec_2Ebool_2EF ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 2.04/1.46 ! [V0B: $o,V1A: $o] :
% 2.04/1.46 ( ( ( (~)
% 2.04/1.46 @ ( V1A
% 2.04/1.46 | V0B ) )
% 2.04/1.46 => mono_2Ec_2Ebool_2EF )
% 2.04/1.46 <=> ( ( V1A
% 2.04/1.46 => mono_2Ec_2Ebool_2EF )
% 2.04/1.46 => ( ( (~) @ V0B )
% 2.04/1.46 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 2.04/1.46 ! [V0B: $o,V1A: $o] :
% 2.04/1.46 ( ( ( (~)
% 2.04/1.46 @ ( ( (~) @ V1A )
% 2.04/1.46 | V0B ) )
% 2.04/1.46 => mono_2Ec_2Ebool_2EF )
% 2.04/1.46 <=> ( V1A
% 2.04/1.46 => ( ( (~) @ V0B )
% 2.04/1.46 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2EAND__INV2,axiom,
% 2.04/1.46 ! [V0A: $o] :
% 2.04/1.46 ( ( ( (~) @ V0A )
% 2.04/1.46 => mono_2Ec_2Ebool_2EF )
% 2.04/1.46 => ( ( V0A
% 2.04/1.46 => mono_2Ec_2Ebool_2EF )
% 2.04/1.46 => mono_2Ec_2Ebool_2EF ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2Edc__eq,axiom,
% 2.04/1.46 ! [V0r: $o,V1q: $o,V2p: $o] :
% 2.04/1.46 ( ( V2p
% 2.04/1.46 <=> ( V1q = V0r ) )
% 2.04/1.46 <=> ( ( V2p
% 2.04/1.46 | V1q
% 2.04/1.46 | V0r )
% 2.04/1.46 & ( V2p
% 2.04/1.46 | ( (~) @ V0r )
% 2.04/1.46 | ( (~) @ V1q ) )
% 2.04/1.46 & ( V1q
% 2.04/1.46 | ( (~) @ V0r )
% 2.04/1.46 | ( (~) @ V2p ) )
% 2.04/1.46 & ( V0r
% 2.04/1.46 | ( (~) @ V1q )
% 2.04/1.46 | ( (~) @ V2p ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2Edc__conj,axiom,
% 2.04/1.46 ! [V0r: $o,V1q: $o,V2p: $o] :
% 2.04/1.46 ( ( V2p
% 2.04/1.46 <=> ( V1q
% 2.04/1.46 & V0r ) )
% 2.04/1.46 <=> ( ( V2p
% 2.04/1.46 | ( (~) @ V1q )
% 2.04/1.46 | ( (~) @ V0r ) )
% 2.04/1.46 & ( V1q
% 2.04/1.46 | ( (~) @ V2p ) )
% 2.04/1.46 & ( V0r
% 2.04/1.46 | ( (~) @ V2p ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2Edc__disj,axiom,
% 2.04/1.46 ! [V0r: $o,V1q: $o,V2p: $o] :
% 2.04/1.46 ( ( V2p
% 2.04/1.46 <=> ( V1q
% 2.04/1.46 | V0r ) )
% 2.04/1.46 <=> ( ( V2p
% 2.04/1.46 | ( (~) @ V1q ) )
% 2.04/1.46 & ( V2p
% 2.04/1.46 | ( (~) @ V0r ) )
% 2.04/1.46 & ( V1q
% 2.04/1.46 | V0r
% 2.04/1.46 | ( (~) @ V2p ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2Edc__imp,axiom,
% 2.04/1.46 ! [V0r: $o,V1q: $o,V2p: $o] :
% 2.04/1.46 ( ( V2p
% 2.04/1.46 <=> ( V1q
% 2.04/1.46 => V0r ) )
% 2.04/1.46 <=> ( ( V2p
% 2.04/1.46 | V1q )
% 2.04/1.46 & ( V2p
% 2.04/1.46 | ( (~) @ V0r ) )
% 2.04/1.46 & ( ( (~) @ V1q )
% 2.04/1.46 | V0r
% 2.04/1.46 | ( (~) @ V2p ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Esat_2Edc__neg,axiom,
% 2.04/1.46 ! [V0q: $o,V1p: $o] :
% 2.04/1.46 ( ( V1p
% 2.04/1.46 <=> ( (~) @ V0q ) )
% 2.04/1.46 <=> ( ( V1p
% 2.04/1.46 | V0q )
% 2.04/1.46 & ( ( (~) @ V0q )
% 2.04/1.46 | ( (~) @ V1p ) ) ) ) ).
% 2.04/1.46
% 2.04/1.46 thf(thm_2Einteger_2EINT__DIVIDES__RSUB,conjecture,
% 2.04/1.46 ! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
% 2.04/1.46 ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
% 2.04/1.46 => ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__sub @ V2r @ V1q ) )
% 2.04/1.46 = ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V2r ) ) ) ).
% 2.04/1.46 ------------------------
% 2.04/1.48 % (19690)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_19586 for (2999ds/2Mi)
% 2.04/1.48 % (19690)Instruction limit reached!
% 2.04/1.48 % (19690)------------------------------
% 2.04/1.48 % (19690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.48 % (19690)Termination reason: Unknown
% 2.04/1.48 % (19690)Termination phase: shuffling
% 2.04/1.48
% 2.04/1.48 % (19690)Memory used [KB]: 1151
% 2.04/1.48 % (19690)Time elapsed: 0.003 s
% 2.04/1.48 % (19690)Instructions burned: 5 (million)
% 2.04/1.48 % (19690)------------------------------
% 2.04/1.48 % (19690)------------------------------
% 2.04/1.48 % (19692)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19586 for (2999ds/18Mi)
% 2.04/1.48 % (19686)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19586 for (2999ds/183Mi)
% 2.04/1.48 % (19687)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_19586 for (2999ds/4Mi)
% 2.04/1.48 % (19688)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_19586 for (2999ds/27Mi)
% 2.04/1.48 % (19689)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19586 for (2999ds/2Mi)
% 2.04/1.48 % (19691)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_19586 for (2999ds/275Mi)
% 2.04/1.49 % (19689)Instruction limit reached!
% 2.04/1.49 % (19689)------------------------------
% 2.04/1.49 % (19689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.49 % (19689)Termination reason: Unknown
% 2.04/1.49 % (19689)Termination phase: shuffling
% 2.04/1.49
% 2.04/1.49 % (19689)Memory used [KB]: 1151
% 2.04/1.49 % (19689)Time elapsed: 0.003 s
% 2.04/1.49 % (19689)Instructions burned: 3 (million)
% 2.04/1.49 % (19689)------------------------------
% 2.04/1.49 % (19689)------------------------------
% 2.04/1.49 % (19687)Instruction limit reached!
% 2.04/1.49 % (19687)------------------------------
% 2.04/1.49 % (19687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.49 % (19687)Termination reason: Unknown
% 2.04/1.49 % (19687)Termination phase: shuffling
% 2.04/1.49
% 2.04/1.49 % (19687)Memory used [KB]: 1151
% 2.04/1.49 % (19687)Time elapsed: 0.004 s
% 2.04/1.49 % (19687)Instructions burned: 5 (million)
% 2.04/1.49 % (19687)------------------------------
% 2.04/1.49 % (19687)------------------------------
% 2.04/1.49 % (19692)Instruction limit reached!
% 2.04/1.49 % (19692)------------------------------
% 2.04/1.49 % (19692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.49 % (19692)Termination reason: Unknown
% 2.04/1.49 % (19692)Termination phase: Property scanning
% 2.04/1.49
% 2.04/1.49 % (19692)Memory used [KB]: 1279
% 2.04/1.49 % (19692)Time elapsed: 0.009 s
% 2.04/1.49 % (19692)Instructions burned: 18 (million)
% 2.04/1.49 % (19692)------------------------------
% 2.04/1.49 % (19692)------------------------------
% 2.04/1.49 % (19693)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19586 for (2999ds/3Mi)
% 2.04/1.49 % (19693)Instruction limit reached!
% 2.04/1.49 % (19693)------------------------------
% 2.04/1.49 % (19693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.49 % (19693)Termination reason: Unknown
% 2.04/1.49 % (19693)Termination phase: shuffling
% 2.04/1.49
% 2.04/1.49 % (19693)Memory used [KB]: 1151
% 2.04/1.49 % (19693)Time elapsed: 0.002 s
% 2.04/1.49 % (19693)Instructions burned: 3 (million)
% 2.04/1.49 % (19693)------------------------------
% 2.04/1.49 % (19693)------------------------------
% 2.17/1.50 % (19697)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_19586 for (2999ds/1041Mi)
% 2.17/1.50 % (19688)Instruction limit reached!
% 2.17/1.50 % (19688)------------------------------
% 2.17/1.50 % (19688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.50 % (19688)Termination reason: Unknown
% 2.17/1.50 % (19688)Termination phase: Property scanning
% 2.17/1.50
% 2.17/1.50 % (19688)Memory used [KB]: 1407
% 2.17/1.50 % (19688)Time elapsed: 0.016 s
% 2.17/1.50 % (19688)Instructions burned: 29 (million)
% 2.17/1.50 % (19688)------------------------------
% 2.17/1.50 % (19688)------------------------------
% 2.17/1.50 % (19696)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_19586 for (2999ds/3Mi)
% 2.17/1.50 % (19696)Instruction limit reached!
% 2.17/1.50 % (19696)------------------------------
% 2.17/1.50 % (19696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.50 % (19696)Termination reason: Unknown
% 2.17/1.50 % (19696)Termination phase: shuffling
% 2.17/1.50
% 2.17/1.50 % (19696)Memory used [KB]: 1151
% 2.17/1.50 % (19696)Time elapsed: 0.003 s
% 2.17/1.50 % (19696)Instructions burned: 3 (million)
% 2.17/1.50 % (19696)------------------------------
% 2.17/1.50 % (19696)------------------------------
% 2.17/1.50 % (19694)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_19586 for (2999ds/37Mi)
% 2.17/1.50 % (19695)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_19586 for (2999ds/15Mi)
% 2.17/1.51 % (19699)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19586 for (2999ds/16Mi)
% 2.17/1.51 % (19695)Instruction limit reached!
% 2.17/1.51 % (19695)------------------------------
% 2.17/1.51 % (19695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.51 % (19695)Termination reason: Unknown
% 2.17/1.51 % (19695)Termination phase: Clausification
% 2.17/1.51
% 2.17/1.51 % (19695)Memory used [KB]: 1407
% 2.17/1.51 % (19695)Time elapsed: 0.010 s
% 2.17/1.51 % (19695)Instructions burned: 15 (million)
% 2.17/1.51 % (19695)------------------------------
% 2.17/1.51 % (19695)------------------------------
% 2.17/1.52 % (19698)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19586 for (2999ds/7Mi)
% 2.17/1.52 % (19699)Instruction limit reached!
% 2.17/1.52 % (19699)------------------------------
% 2.17/1.52 % (19699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.52 % (19699)Termination reason: Unknown
% 2.17/1.52 % (19699)Termination phase: Property scanning
% 2.17/1.52
% 2.17/1.52 % (19699)Memory used [KB]: 1279
% 2.17/1.52 % (19699)Time elapsed: 0.007 s
% 2.17/1.52 % (19699)Instructions burned: 18 (million)
% 2.17/1.52 % (19699)------------------------------
% 2.17/1.52 % (19699)------------------------------
% 2.17/1.52 % (19698)Instruction limit reached!
% 2.17/1.52 % (19698)------------------------------
% 2.17/1.52 % (19698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.52 % (19698)Termination reason: Unknown
% 2.17/1.52 % (19698)Termination phase: SInE selection
% 2.17/1.52
% 2.17/1.52 % (19698)Memory used [KB]: 1151
% 2.17/1.52 % (19698)Time elapsed: 0.006 s
% 2.17/1.52 % (19698)Instructions burned: 8 (million)
% 2.17/1.52 % (19698)------------------------------
% 2.17/1.52 % (19698)------------------------------
% 2.17/1.52 % (19694)Instruction limit reached!
% 2.17/1.52 % (19694)------------------------------
% 2.17/1.52 % (19694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.52 % (19694)Termination reason: Unknown
% 2.17/1.52 % (19694)Termination phase: Saturation
% 2.17/1.52
% 2.17/1.52 % (19694)Memory used [KB]: 5884
% 2.17/1.52 % (19694)Time elapsed: 0.020 s
% 2.17/1.52 % (19694)Instructions burned: 38 (million)
% 2.17/1.52 % (19694)------------------------------
% 2.17/1.52 % (19694)------------------------------
% 2.17/1.53 % (19700)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_19586 for (2999ds/3Mi)
% 2.17/1.53 % (19700)Instruction limit reached!
% 2.17/1.53 % (19700)------------------------------
% 2.17/1.53 % (19700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.53 % (19700)Termination reason: Unknown
% 2.17/1.53 % (19700)Termination phase: shuffling
% 2.17/1.53
% 2.17/1.53 % (19700)Memory used [KB]: 1151
% 2.17/1.53 % (19700)Time elapsed: 0.002 s
% 2.17/1.53 % (19700)Instructions burned: 3 (million)
% 2.17/1.53 % (19700)------------------------------
% 2.17/1.53 % (19700)------------------------------
% 2.17/1.53 % (19701)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_19586 for (2999ds/3Mi)
% 2.17/1.53 % (19701)Instruction limit reached!
% 2.17/1.53 % (19701)------------------------------
% 2.17/1.53 % (19701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.53 % (19701)Termination reason: Unknown
% 2.17/1.53 % (19701)Termination phase: shuffling
% 2.17/1.53
% 2.17/1.53 % (19701)Memory used [KB]: 1151
% 2.17/1.53 % (19701)Time elapsed: 0.003 s
% 2.17/1.53 % (19701)Instructions burned: 4 (million)
% 2.17/1.53 % (19701)------------------------------
% 2.17/1.53 % (19701)------------------------------
% 2.17/1.53 % (19691)First to succeed.
% 2.17/1.54 % (19691)Refutation found. Thanks to Tanya!
% 2.17/1.54 % SZS status Theorem for DTF2THF_19586
% 2.17/1.54 % SZS output start Proof for DTF2THF_19586
% 2.17/1.54 thf(type_def_5, type, d: $tType).
% 2.17/1.54 thf(type_def_7, type, u: $tType).
% 2.17/1.54 thf(type_def_8, type, du: $tType).
% 2.17/1.54 thf(type_def_9, type, mono_2Etyop_2Einteger_2Eint: $tType).
% 2.17/1.54 thf(func_def_0, type, u: $tType).
% 2.17/1.54 thf(func_def_1, type, d: $tType).
% 2.17/1.54 thf(func_def_2, type, du: $tType).
% 2.17/1.54 thf(func_def_3, type, mono_2Etyop_2Einteger_2Eint: $tType).
% 2.17/1.54 thf(func_def_4, type, tyop_2Einteger_2Eint: d).
% 2.17/1.54 thf(func_def_5, type, tyop_2Emin_2Ebool: d).
% 2.17/1.54 thf(func_def_6, type, tyop_2Emin_2Efun: d > d > d).
% 2.17/1.54 thf(func_def_7, type, s: d > u > du).
% 2.17/1.54 thf(func_def_8, type, app_2E2: du > du > u).
% 2.17/1.54 thf(func_def_9, type, combin_i_2E0: u).
% 2.17/1.54 thf(func_def_10, type, combin_k_2E0: u).
% 2.17/1.54 thf(func_def_11, type, combin_s_2E0: u).
% 2.17/1.54 thf(func_def_12, type, c_2Ebool_2E_21_2E0: u).
% 2.17/1.54 thf(func_def_13, type, c_2Ebool_2E_21_2E1: du > u).
% 2.17/1.54 thf(func_def_14, type, c_2Ebool_2E_2F_5C_2E0: u).
% 2.17/1.54 thf(func_def_15, type, c_2Ebool_2E_2F_5C_2E2: du > du > u).
% 2.17/1.54 thf(func_def_16, type, c_2Emin_2E_3D_2E0: u).
% 2.17/1.54 thf(func_def_17, type, c_2Emin_2E_3D_2E2: du > du > u).
% 2.17/1.54 thf(func_def_18, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 2.17/1.54 thf(func_def_19, type, c_2Emin_2E_3D_3D_3E_2E2: du > du > u).
% 2.17/1.54 thf(func_def_20, type, c_2Ebool_2E_3F_2E0: u).
% 2.17/1.54 thf(func_def_21, type, c_2Ebool_2E_3F_2E1: du > u).
% 2.17/1.54 thf(func_def_22, type, c_2Ebool_2EF_2E0: u).
% 2.17/1.54 thf(func_def_23, type, c_2Ebool_2ET_2E0: u).
% 2.17/1.54 thf(func_def_24, type, c_2Ebool_2E_5C_2F_2E0: u).
% 2.17/1.54 thf(func_def_25, type, c_2Ebool_2E_5C_2F_2E2: du > du > u).
% 2.17/1.54 thf(func_def_26, type, c_2Einteger_2Eint__add_2E0: u).
% 2.17/1.54 thf(func_def_27, type, c_2Einteger_2Eint__add_2E2: du > du > u).
% 2.17/1.54 thf(func_def_28, type, c_2Einteger_2Eint__divides_2E0: u).
% 2.17/1.54 thf(func_def_29, type, c_2Einteger_2Eint__divides_2E2: du > du > u).
% 2.17/1.54 thf(func_def_30, type, c_2Einteger_2Eint__neg_2E0: u).
% 2.17/1.54 thf(func_def_31, type, c_2Einteger_2Eint__neg_2E1: du > u).
% 2.17/1.54 thf(func_def_32, type, c_2Einteger_2Eint__sub_2E0: u).
% 2.17/1.54 thf(func_def_33, type, c_2Einteger_2Eint__sub_2E2: du > du > u).
% 2.17/1.54 thf(func_def_34, type, c_2Ebool_2E_7E_2E0: u).
% 2.17/1.54 thf(func_def_35, type, c_2Ebool_2E_7E_2E1: du > u).
% 2.17/1.54 thf(func_def_36, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ($o > $o) > $o > $o).
% 2.17/1.54 thf(func_def_37, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o > $o) > $o > $o > $o).
% 2.17/1.54 thf(func_def_38, type, mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: (mono_2Etyop_2Einteger_2Eint > $o) > mono_2Etyop_2Einteger_2Eint > $o).
% 2.17/1.54 thf(func_def_39, type, mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o).
% 2.17/1.54 thf(func_def_40, type, mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_41, type, mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_42, type, mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o).
% 2.17/1.54 thf(func_def_43, type, mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 2.17/1.54 thf(func_def_46, type, mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o).
% 2.17/1.54 thf(func_def_47, type, mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_48, type, mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o).
% 2.17/1.54 thf(func_def_49, type, mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_50, type, mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_51, type, mono_2Ec_2Ebool_2E_7E: $o > $o).
% 2.17/1.54 thf(func_def_52, type, i_mono_2Etyop_2Emin_2Ebool: $o > u).
% 2.17/1.54 thf(func_def_53, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o) > u).
% 2.17/1.54 thf(func_def_54, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ($o > $o > $o) > u).
% 2.17/1.54 thf(func_def_55, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: (mono_2Etyop_2Einteger_2Eint > $o) > u).
% 2.17/1.54 thf(func_def_56, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o) > u).
% 2.17/1.54 thf(func_def_57, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint) > u).
% 2.17/1.54 thf(func_def_58, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: (mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint) > u).
% 2.17/1.54 thf(func_def_59, type, i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u).
% 2.17/1.54 thf(func_def_60, type, j_mono_2Etyop_2Emin_2Ebool: du > $o).
% 2.17/1.54 thf(func_def_61, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o).
% 2.17/1.54 thf(func_def_62, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o).
% 2.17/1.54 thf(func_def_63, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o).
% 2.17/1.54 thf(func_def_64, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o).
% 2.17/1.54 thf(func_def_65, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_66, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_67, type, j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_77, type, sK0: mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_78, type, sK1: mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(func_def_79, type, sK2: mono_2Etyop_2Einteger_2Eint).
% 2.17/1.54 thf(f666,plain,(
% 2.17/1.54 $false),
% 2.17/1.54 inference(avatar_sat_refutation,[status(thm)],[f203,f212,f417,f422,f651,f658])).
% 2.17/1.54 thf(f658,plain,(
% 2.17/1.54 spl3_8 | ~spl3_4),
% 2.17/1.54 inference(avatar_split_clause,[status(thm)],[f657,f209,f427])).
% 2.17/1.54 thf(f427,definition,(
% 2.17/1.54 spl3_8 <=> ! [X1 : $o] : (($false = X1) | ($true = X1))),
% 2.17/1.54 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 2.17/1.54 thf(f209,definition,(
% 2.17/1.54 spl3_4 <=> ($false = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2)))),
% 2.17/1.54 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 2.17/1.54 thf(f657,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (($false = X0) | ($true = X0)) ) | ~spl3_4),
% 2.17/1.54 inference(trivial_inequality_removal,[status(thm)],[f656])).
% 2.17/1.54 thf(f656,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (($true = X0) | ($false = $true) | ($false = X0)) ) | ~spl3_4),
% 2.17/1.54 inference(forward_demodulation,[status(thm)],[f491,f211])).
% 2.17/1.54 thf(f211,plain,(
% 2.17/1.54 ($false = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2))) | ~spl3_4),
% 2.17/1.54 inference(avatar_component_clause,[status(thm)],[f209])).
% 2.17/1.54 thf(f491,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (($true = X0) | ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2))) | ($false = X0)) ) | ~spl3_4),
% 2.17/1.54 inference(binary_proxy_clausification,[status(thm)],[f490])).
% 2.17/1.54 thf(f490,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (($true = X0) | ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2)) = X0)) ) | ~spl3_4),
% 2.17/1.54 inference(trivial_inequality_removal,[status(thm)],[f483])).
% 2.17/1.54 thf(f483,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2)) = X0) | ($false = $true) | ($true = X0)) ) | ~spl3_4),
% 2.17/1.54 inference(superposition,[status(thm)],[f211,f166])).
% 2.17/1.54 thf(f166,plain,(
% 2.17/1.54 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true = X0) | (X0 = X1)) )),
% 2.17/1.54 inference(cnf_transformation,[status(thm)],[f145])).
% 2.17/1.54 thf(f145,plain,(
% 2.17/1.54 ! [X0 : $o,X1 : $o] : ((X0 = X1) | (($true = X1) & ($true != X0)) | (($true = X0) & ($true != X1)))),
% 2.17/1.54 inference(flattening,[status(thm)],[f144])).
% 2.17/1.54 thf(f144,plain,(
% 2.17/1.54 ! [X0 : $o,X1 : $o] : (((X0 = X1) | (($true = X0) & ($true != X1))) | (($true = X1) & ($true != X0)))),
% 2.17/1.54 inference(ennf_transformation,[status(thm)],[f88])).
% 2.17/1.54 thf(f88,plain,(
% 2.17/1.54 ! [X0 : $o,X1 : $o] : ((($true = X1) => ($true = X0)) => ((($true = X0) => ($true = X1)) => (X0 = X1)))),
% 2.17/1.54 inference(fool_elimination,[status(thm)],[f87])).
% 2.17/1.54 thf(f87,plain,(
% 2.17/1.54 ! [X0 : $o,X1 : $o] : ((X1 => X0) => ((X0 => X1) => (X0 = X1)))),
% 2.17/1.54 inference(rectify,[status(thm)],[f44])).
% 2.17/1.54 thf(f44,axiom,(
% 2.17/1.54 ! [X16 : $o,X15 : $o] : ((X15 => X16) => ((X16 => X15) => (X15 = X16)))),
% 2.17/1.54 file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Ebool_2EIMP__ANTISYM__AX)).
% 2.17/1.54 thf(f651,plain,(
% 2.17/1.54 spl3_3 | ~spl3_4 | ~spl3_8),
% 2.17/1.54 inference(avatar_contradiction_clause,[status(thm)],[f650])).
% 2.17/1.54 thf(f650,plain,(
% 2.17/1.54 $false | (spl3_3 | ~spl3_4 | ~spl3_8)),
% 2.17/1.54 inference(subsumption_resolution,[status(thm)],[f649,f173])).
% 2.17/1.54 thf(f173,plain,(
% 2.17/1.54 ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2) = $true)),
% 2.17/1.54 inference(cnf_transformation,[status(thm)],[f150])).
% 2.17/1.54 thf(f150,plain,(
% 2.17/1.54 ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2) = $true) & ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0) != (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2)))),
% 2.17/1.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f146,f149])).
% 2.17/1.54 thf(f149,plain,(
% 2.17/1.54 ? [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint,X2 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2) = $true) & ((mono_2Ec_2Einteger_2Eint__divides @ X1 @ X0) != (mono_2Ec_2Einteger_2Eint__divides @ X1 @ (mono_2Ec_2Einteger_2Eint__sub @ X0 @ X2)))) => (((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2) = $true) & ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0) != (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2))))),
% 2.17/1.54 introduced(definition,[],[choice_axiom])).
% 2.17/1.54 thf(f146,plain,(
% 2.17/1.54 ? [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint,X2 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2) = $true) & ((mono_2Ec_2Einteger_2Eint__divides @ X1 @ X0) != (mono_2Ec_2Einteger_2Eint__divides @ X1 @ (mono_2Ec_2Einteger_2Eint__sub @ X0 @ X2))))),
% 2.17/1.54 inference(ennf_transformation,[status(thm)],[f122])).
% 2.17/1.54 thf(f122,plain,(
% 2.17/1.54 ~! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint,X2 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2) = $true) => ((mono_2Ec_2Einteger_2Eint__divides @ X1 @ X0) = (mono_2Ec_2Einteger_2Eint__divides @ X1 @ (mono_2Ec_2Einteger_2Eint__sub @ X0 @ X2))))),
% 2.17/1.54 inference(fool_elimination,[status(thm)],[f121])).
% 2.17/1.54 thf(f121,plain,(
% 2.17/1.54 ~! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint,X2 : mono_2Etyop_2Einteger_2Eint] : ((mono_2Ec_2Einteger_2Eint__divides @ X1 @ X2) => ((mono_2Ec_2Einteger_2Eint__divides @ X1 @ X0) = (mono_2Ec_2Einteger_2Eint__divides @ X1 @ (mono_2Ec_2Einteger_2Eint__sub @ X0 @ X2))))),
% 2.17/1.54 inference(rectify,[status(thm)],[f69])).
% 2.17/1.54 thf(f69,negated_conjecture,(
% 2.17/1.54 ~! [X29 : mono_2Etyop_2Einteger_2Eint,X27 : mono_2Etyop_2Einteger_2Eint,X28 : mono_2Etyop_2Einteger_2Eint] : ((mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28) => ((mono_2Ec_2Einteger_2Eint__divides @ X27 @ X29) = (mono_2Ec_2Einteger_2Eint__divides @ X27 @ (mono_2Ec_2Einteger_2Eint__sub @ X29 @ X28))))),
% 2.17/1.54 inference(negated_conjecture,[status(cth)],[f68])).
% 2.17/1.54 thf(f68,conjecture,(
% 2.17/1.54 ! [X29 : mono_2Etyop_2Einteger_2Eint,X27 : mono_2Etyop_2Einteger_2Eint,X28 : mono_2Etyop_2Einteger_2Eint] : ((mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28) => ((mono_2Ec_2Einteger_2Eint__divides @ X27 @ X29) = (mono_2Ec_2Einteger_2Eint__divides @ X27 @ (mono_2Ec_2Einteger_2Eint__sub @ X29 @ X28))))),
% 2.17/1.54 file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Einteger_2EINT__DIVIDES__RSUB)).
% 2.17/1.54 thf(f649,plain,(
% 2.17/1.54 ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2) != $true) | (spl3_3 | ~spl3_4 | ~spl3_8)),
% 2.17/1.54 inference(subsumption_resolution,[status(thm)],[f632,f206])).
% 2.17/1.54 thf(f206,plain,(
% 2.17/1.54 ($false != (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | spl3_3),
% 2.17/1.54 inference(avatar_component_clause,[status(thm)],[f205])).
% 2.17/1.54 thf(f205,definition,(
% 2.17/1.54 spl3_3 <=> ($false = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0))),
% 2.17/1.54 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 2.17/1.54 thf(f632,plain,(
% 2.17/1.54 ($false = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2) != $true) | (~spl3_4 | ~spl3_8)),
% 2.17/1.54 inference(trivial_inequality_removal,[status(thm)],[f629])).
% 2.17/1.54 thf(f629,plain,(
% 2.17/1.54 ($false = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | ($false = $true) | ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2) != $true) | (~spl3_4 | ~spl3_8)),
% 2.17/1.54 inference(superposition,[status(thm)],[f211,f598])).
% 2.17/1.54 thf(f598,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X2 @ (mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1)) = $true) | ($false = (mono_2Ec_2Einteger_2Eint__divides @ X2 @ X0)) | ($true != (mono_2Ec_2Einteger_2Eint__divides @ X2 @ X1))) ) | ~spl3_8),
% 2.17/1.54 inference(forward_demodulation,[status(thm)],[f577,f167])).
% 2.17/1.54 thf(f167,plain,(
% 2.17/1.54 ( ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = (mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__neg @ X1)))) )),
% 2.17/1.54 inference(cnf_transformation,[status(thm)],[f142])).
% 2.17/1.54 thf(f142,plain,(
% 2.17/1.54 ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = (mono_2Ec_2Einteger_2Eint__divides @ (mono_2Ec_2Einteger_2Eint__neg @ X0) @ X1)) & ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = (mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__neg @ X1))))),
% 2.17/1.54 inference(rectify,[status(thm)],[f57])).
% 2.17/1.54 thf(f57,axiom,(
% 2.17/1.54 ! [X27 : mono_2Etyop_2Einteger_2Eint,X28 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28) = (mono_2Ec_2Einteger_2Eint__divides @ (mono_2Ec_2Einteger_2Eint__neg @ X27) @ X28)) & ((mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28) = (mono_2Ec_2Einteger_2Eint__divides @ X27 @ (mono_2Ec_2Einteger_2Eint__neg @ X28))))),
% 2.17/1.54 file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Einteger_2EINT__DIVIDES__NEG)).
% 2.17/1.54 thf(f577,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (($false = (mono_2Ec_2Einteger_2Eint__divides @ X2 @ X0)) | ($true != (mono_2Ec_2Einteger_2Eint__divides @ X2 @ (mono_2Ec_2Einteger_2Eint__neg @ X1))) | ((mono_2Ec_2Einteger_2Eint__divides @ X2 @ (mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1)) = $true)) ) | ~spl3_8),
% 2.17/1.54 inference(superposition,[status(thm)],[f511,f156])).
% 2.17/1.54 thf(f156,plain,(
% 2.17/1.54 ( ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1) = (mono_2Ec_2Einteger_2Eint__add @ X0 @ (mono_2Ec_2Einteger_2Eint__neg @ X1)))) )),
% 2.17/1.54 inference(cnf_transformation,[status(thm)],[f141])).
% 2.17/1.54 thf(f141,plain,(
% 2.17/1.54 ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : ((mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1) = (mono_2Ec_2Einteger_2Eint__add @ X0 @ (mono_2Ec_2Einteger_2Eint__neg @ X1)))),
% 2.17/1.54 inference(rectify,[status(thm)],[f55])).
% 2.17/1.54 thf(f55,axiom,(
% 2.17/1.54 ! [X25 : mono_2Etyop_2Einteger_2Eint,X26 : mono_2Etyop_2Einteger_2Eint] : ((mono_2Ec_2Einteger_2Eint__sub @ X25 @ X26) = (mono_2Ec_2Einteger_2Eint__add @ X25 @ (mono_2Ec_2Einteger_2Eint__neg @ X26)))),
% 2.17/1.54 file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Einteger_2Eint__sub)).
% 2.17/1.54 thf(f511,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__add @ X1 @ X2)) = $true) | ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = $false) | ($true != (mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2))) ) | ~spl3_8),
% 2.17/1.54 inference(forward_demodulation,[status(thm)],[f510,f168])).
% 2.17/1.54 thf(f168,plain,(
% 2.17/1.54 ( ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = (mono_2Ec_2Einteger_2Eint__divides @ (mono_2Ec_2Einteger_2Eint__neg @ X0) @ X1))) )),
% 2.17/1.54 inference(cnf_transformation,[status(thm)],[f142])).
% 2.17/1.54 thf(f510,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__add @ X1 @ X2)) = $true) | ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = $false) | ((mono_2Ec_2Einteger_2Eint__divides @ (mono_2Ec_2Einteger_2Eint__neg @ X0) @ X2) != $true)) ) | ~spl3_8),
% 2.17/1.54 inference(forward_demodulation,[status(thm)],[f503,f168])).
% 2.17/1.54 thf(f503,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__add @ X1 @ X2)) = $true) | ((mono_2Ec_2Einteger_2Eint__divides @ (mono_2Ec_2Einteger_2Eint__neg @ X0) @ X1) = $false) | ((mono_2Ec_2Einteger_2Eint__divides @ (mono_2Ec_2Einteger_2Eint__neg @ X0) @ X2) != $true)) ) | ~spl3_8),
% 2.17/1.54 inference(superposition,[status(thm)],[f154,f438])).
% 2.17/1.54 thf(f438,plain,(
% 2.17/1.54 ( ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ (mono_2Ec_2Einteger_2Eint__neg @ X0) @ X1) = $false) | ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = $true)) ) | ~spl3_8),
% 2.17/1.54 inference(superposition,[status(thm)],[f168,f428])).
% 2.17/1.54 thf(f428,plain,(
% 2.17/1.54 ( ! [X1 : $o] : (($true = X1) | ($false = X1)) ) | ~spl3_8),
% 2.17/1.54 inference(avatar_component_clause,[status(thm)],[f427])).
% 2.17/1.54 thf(f154,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__add @ X2 @ X1)) = (mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2)) | ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) != $true)) )),
% 2.17/1.54 inference(cnf_transformation,[status(thm)],[f143])).
% 2.17/1.54 thf(f143,plain,(
% 2.17/1.54 ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint,X2 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) != $true) | ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__add @ X2 @ X1)) = (mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2)))),
% 2.17/1.54 inference(ennf_transformation,[status(thm)],[f104])).
% 2.17/1.54 thf(f104,plain,(
% 2.17/1.54 ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint,X2 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = $true) => ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__add @ X2 @ X1)) = (mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2)))),
% 2.17/1.54 inference(fool_elimination,[status(thm)],[f103])).
% 2.17/1.54 thf(f103,plain,(
% 2.17/1.54 ! [X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint,X2 : mono_2Etyop_2Einteger_2Eint] : ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) => ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__add @ X2 @ X1)) = (mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2)))),
% 2.17/1.54 inference(rectify,[status(thm)],[f56])).
% 2.17/1.54 thf(f56,axiom,(
% 2.17/1.54 ! [X27 : mono_2Etyop_2Einteger_2Eint,X28 : mono_2Etyop_2Einteger_2Eint,X29 : mono_2Etyop_2Einteger_2Eint] : ((mono_2Ec_2Einteger_2Eint__divides @ X27 @ X28) => ((mono_2Ec_2Einteger_2Eint__divides @ X27 @ (mono_2Ec_2Einteger_2Eint__add @ X29 @ X28)) = (mono_2Ec_2Einteger_2Eint__divides @ X27 @ X29)))),
% 2.17/1.54 file('/export/starexec/sandbox2/tmp/tmp.6MnAvUUruD/DTF2THF_19586.p',thm_2Einteger_2EINT__DIVIDES__RADD)).
% 2.17/1.54 thf(f422,plain,(
% 2.17/1.54 ~spl3_1 | ~spl3_3),
% 2.17/1.54 inference(avatar_contradiction_clause,[status(thm)],[f421])).
% 2.17/1.54 thf(f421,plain,(
% 2.17/1.54 $false | (~spl3_1 | ~spl3_3)),
% 2.17/1.54 inference(trivial_inequality_removal,[status(thm)],[f420])).
% 2.17/1.54 thf(f420,plain,(
% 2.17/1.54 ($false = $true) | (~spl3_1 | ~spl3_3)),
% 2.17/1.54 inference(forward_demodulation,[status(thm)],[f198,f207])).
% 2.17/1.54 thf(f207,plain,(
% 2.17/1.54 ($false = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | ~spl3_3),
% 2.17/1.54 inference(avatar_component_clause,[status(thm)],[f205])).
% 2.17/1.54 thf(f198,plain,(
% 2.17/1.54 ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | ~spl3_1),
% 2.17/1.54 inference(avatar_component_clause,[status(thm)],[f196])).
% 2.17/1.54 thf(f196,definition,(
% 2.17/1.54 spl3_1 <=> ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0))),
% 2.17/1.54 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 2.17/1.54 thf(f417,plain,(
% 2.17/1.54 ~spl3_2 | ~spl3_3),
% 2.17/1.54 inference(avatar_contradiction_clause,[status(thm)],[f416])).
% 2.17/1.54 thf(f416,plain,(
% 2.17/1.54 $false | (~spl3_2 | ~spl3_3)),
% 2.17/1.54 inference(trivial_inequality_removal,[status(thm)],[f415])).
% 2.17/1.54 thf(f415,plain,(
% 2.17/1.54 ($false = $true) | (~spl3_2 | ~spl3_3)),
% 2.17/1.54 inference(forward_demodulation,[status(thm)],[f414,f207])).
% 2.17/1.54 thf(f414,plain,(
% 2.17/1.54 ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | (~spl3_2 | ~spl3_3)),
% 2.17/1.54 inference(subsumption_resolution,[status(thm)],[f400,f173])).
% 2.17/1.54 thf(f400,plain,(
% 2.17/1.54 ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2) != $true) | (~spl3_2 | ~spl3_3)),
% 2.17/1.54 inference(trivial_inequality_removal,[status(thm)],[f392])).
% 2.17/1.54 thf(f392,plain,(
% 2.17/1.54 ($false = $true) | ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK2) != $true) | (~spl3_2 | ~spl3_3)),
% 2.17/1.54 inference(superposition,[status(thm)],[f202,f326])).
% 2.17/1.54 thf(f326,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X2 @ (mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1)) = $false) | ($true != (mono_2Ec_2Einteger_2Eint__divides @ X2 @ X1)) | ($true = (mono_2Ec_2Einteger_2Eint__divides @ X2 @ X0))) ) | ~spl3_3),
% 2.17/1.54 inference(forward_demodulation,[status(thm)],[f312,f167])).
% 2.17/1.54 thf(f312,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (($true = (mono_2Ec_2Einteger_2Eint__divides @ X2 @ X0)) | ($true != (mono_2Ec_2Einteger_2Eint__divides @ X2 @ (mono_2Ec_2Einteger_2Eint__neg @ X1))) | ((mono_2Ec_2Einteger_2Eint__divides @ X2 @ (mono_2Ec_2Einteger_2Eint__sub @ X0 @ X1)) = $false)) ) | ~spl3_3),
% 2.17/1.54 inference(superposition,[status(thm)],[f225,f156])).
% 2.17/1.54 thf(f225,plain,(
% 2.17/1.54 ( ! [X2 : mono_2Etyop_2Einteger_2Eint,X0 : mono_2Etyop_2Einteger_2Eint,X1 : mono_2Etyop_2Einteger_2Eint] : (((mono_2Ec_2Einteger_2Eint__divides @ X0 @ (mono_2Ec_2Einteger_2Eint__add @ X1 @ X2)) = $false) | ((mono_2Ec_2Einteger_2Eint__divides @ X0 @ X1) = $true) | ($true != (mono_2Ec_2Einteger_2Eint__divides @ X0 @ X2))) ) | ~spl3_3),
% 2.17/1.54 inference(superposition,[status(thm)],[f154,f219])).
% 2.17/1.54 thf(f219,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl3_3),
% 2.17/1.54 inference(trivial_inequality_removal,[status(thm)],[f218])).
% 2.17/1.54 thf(f218,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (($true = X0) | ($false = X0) | ($false = $true)) ) | ~spl3_3),
% 2.17/1.54 inference(forward_demodulation,[status(thm)],[f215,f207])).
% 2.17/1.54 thf(f215,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0)) | ($false = X0) | ($true = X0)) ) | ~spl3_3),
% 2.17/1.54 inference(binary_proxy_clausification,[status(thm)],[f214])).
% 2.17/1.54 thf(f214,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0) = X0) | ($true = X0)) ) | ~spl3_3),
% 2.17/1.54 inference(trivial_inequality_removal,[status(thm)],[f213])).
% 2.17/1.54 thf(f213,plain,(
% 2.17/1.54 ( ! [X0 : $o] : (($true = X0) | ($false = $true) | ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0) = X0)) ) | ~spl3_3),
% 2.17/1.54 inference(superposition,[status(thm)],[f207,f166])).
% 2.17/1.54 thf(f202,plain,(
% 2.17/1.54 ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2))) | ~spl3_2),
% 2.17/1.54 inference(avatar_component_clause,[status(thm)],[f200])).
% 2.17/1.54 thf(f200,definition,(
% 2.17/1.54 spl3_2 <=> ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2)))),
% 2.17/1.54 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 2.17/1.54 thf(f212,plain,(
% 2.17/1.54 spl3_3 | spl3_4),
% 2.17/1.54 inference(avatar_split_clause,[status(thm)],[f194,f209,f205])).
% 2.17/1.54 thf(f194,plain,(
% 2.17/1.54 ($false = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2))) | ($false = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0))),
% 2.17/1.54 inference(binary_proxy_clausification,[status(thm)],[f172])).
% 2.17/1.54 thf(f172,plain,(
% 2.17/1.54 ((mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0) != (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2)))),
% 2.17/1.54 inference(cnf_transformation,[status(thm)],[f150])).
% 2.17/1.54 thf(f203,plain,(
% 2.17/1.54 spl3_1 | spl3_2),
% 2.17/1.54 inference(avatar_split_clause,[status(thm)],[f193,f200,f196])).
% 2.17/1.54 thf(f193,plain,(
% 2.17/1.54 ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ (mono_2Ec_2Einteger_2Eint__sub @ sK0 @ sK2))) | ($true = (mono_2Ec_2Einteger_2Eint__divides @ sK1 @ sK0))),
% 2.17/1.54 inference(binary_proxy_clausification,[status(thm)],[f172])).
% 2.17/1.54 % SZS output end Proof for DTF2THF_19586
% 2.17/1.54 % (19691)------------------------------
% 2.17/1.54 % (19691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.17/1.54 % (19691)Termination reason: Refutation
% 2.17/1.54
% 2.17/1.54 % (19691)Memory used [KB]: 5756
% 2.17/1.54 % (19691)Time elapsed: 0.051 s
% 2.17/1.54 % (19691)Instructions burned: 80 (million)
% 2.17/1.54 % (19691)------------------------------
% 2.17/1.54 % (19691)------------------------------
% 2.17/1.54 % (19685)Success in time 0.067 s
%------------------------------------------------------------------------------