%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP004^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 08:53:04 AM UTC 2026
% Result : Theorem 3.95s 2.06s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 318 ( 102 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 1890 ( 18 ~; 14 |; 14 &;1770 @)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 49 usr; 23 con; 0-4 aty)
% ( 56 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 179 ( 68 ^; 111 !; 0 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_4,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_5,type,
s: d > u > du ).
thf(func_def_6,type,
app_2E2: du > du > u ).
thf(func_def_7,type,
combin_i_2E0: u ).
thf(func_def_8,type,
combin_k_2E0: u ).
thf(func_def_9,type,
combin_s_2E0: u ).
thf(func_def_10,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_11,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_12,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_13,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_14,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_15,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_16,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_18,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_19,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_20,type,
c_2Epred__set_2ECHOICE_2E0: u ).
thf(func_def_21,type,
c_2Epred__set_2ECHOICE_2E1: du > u ).
thf(func_def_22,type,
c_2Epred__set_2EDELETE_2E0: u ).
thf(func_def_23,type,
c_2Epred__set_2EDELETE_2E2: du > du > u ).
thf(func_def_24,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_25,type,
c_2Ebool_2EIN_2E0: u ).
thf(func_def_26,type,
c_2Ebool_2EIN_2E2: du > du > u ).
thf(func_def_27,type,
c_2Epred__set_2EREST_2E0: u ).
thf(func_def_28,type,
c_2Epred__set_2EREST_2E1: du > u ).
thf(func_def_29,type,
c_2Epred__set_2ESUBSET_2E0: u ).
thf(func_def_30,type,
c_2Epred__set_2ESUBSET_2E2: du > du > u ).
thf(func_def_31,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_32,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_33,type,
c_2Ebool_2E_5C_2F_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_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_39,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_42,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_43,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_44,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_45,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_46,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_47,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_48,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_49,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_69,type,
sK1: u ).
thf(func_def_70,type,
sK2: d ).
thf(func_def_71,type,
sK3: d > u > u > u ).
thf(func_def_72,type,
sK4: d > d > u > u > u ).
thf(f505,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f501]) ).
thf(f501,plain,
$false = $true,
inference(superposition,[status(thm)],[f478,f135]) ).
thf(f135,plain,
( $false
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ tyop_2Emin_2Ebool ) @ sK1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ sK2 @ tyop_2Emin_2Ebool ) @ sK1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
( ( ^ [Y0: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ sK1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ sK1 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
( $false
= ( !! @ d
@ ^ [Y0: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ sK1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ sK1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f132]) ).
thf(f132,plain,
( $false
= ( ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
( ( !! @ u
@ ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
( $true
= ( ~ ( !! @ u
@ ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
thf(f51,plain,
( $true
= ( ~ ( !! @ u
@ ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f50]) ).
thf(f50,plain,
~ ! [X0: d,X1: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,negated_conjecture,
~ ! [X0: d,X15: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
thf(f33,conjecture,
! [X0: d,X15: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2THF_823.p',thm_2Epred__set_2EREST__SUBSET) ).
thf(f478,plain,
! [X0: d,X1: u] :
( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f477]) ).
thf(f477,plain,
! [X0: d,X1: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ( $false = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f469]) ).
thf(f469,plain,
! [X0: d,X1: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ( $false = $true )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f440,f155]) ).
thf(f155,plain,
! [X2: u,X3: d,X1: u] :
( ( $false
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ ( sK3 @ X3 @ X1 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
! [X2: u,X3: d,X1: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= $true )
| ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ ( sK3 @ X3 @ X1 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ ( sK3 @ X3 @ X1 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f153]) ).
thf(f153,plain,
! [X2: u,X3: d,X1: u] :
( ( $false
= ( ^ [Y0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) )
@ ( sK3 @ X3 @ X1 @ X2 ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
! [X2: u,X3: d,X1: u] :
( ( $false
= ( !! @ u
@ ^ [Y0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
! [X2: u,X3: d,X1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= ( !! @ u
@ ^ [Y0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
! [X2: u,X3: d,X1: u] :
( $true
= ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= ( !! @ u
@ ^ [Y0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
! [X2: u,X3: d,X1: u] :
( $true
= ( ^ [Y0: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= ( !! @ u
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y0 @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y0 @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: u,X1: u] :
( $true
= ( !! @ d
@ ^ [Y0: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= ( !! @ u
@ ^ [Y1: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y0 @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y0 @ Y1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: u,X1: u] :
( ( ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
= ( !! @ u
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
! [X1: u] :
( ( !! @ u
@ ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
= ( !! @ u
@ ^ [Y2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y2 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f141]) ).
thf(f141,plain,
! [X1: u] :
( ( ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( !! @ d
@ ^ [Y2: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
= ( !! @ u
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y2 @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y2 @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
( ( !! @ u
@ ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( !! @ d
@ ^ [Y2: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
= ( !! @ u
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y2 @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y2 @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f81]) ).
thf(f81,plain,
( ( !! @ u
@ ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( !! @ d
@ ^ [Y2: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
= ( !! @ u
@ ^ [Y3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y2 @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y2 @ Y3 ) @ ( s @ ( tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f80]) ).
thf(f80,plain,
! [X0: d,X1: u,X2: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
<=> ! [X3: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,axiom,
! [X0: d,X16: u,X15: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) )
<=> ! [X4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ X4 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X16 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2THF_823.p',thm_2Epred__set_2ESUBSET__DEF) ).
thf(f440,plain,
! [X2: u,X0: d,X1: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ ( sK3 @ X0 @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f438]) ).
thf(f438,plain,
! [X2: u,X0: d,X1: u] :
( ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ ( sK3 @ X0 @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f415,f156]) ).
thf(f156,plain,
! [X2: u,X3: d,X1: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X3 @ ( sK3 @ X3 @ X1 @ X2 ) ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) )
= $true )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool ) @ X2 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f415,plain,
! [X2: u,X0: d,X1: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
= $false )
| ( $true
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ X2 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f196,f140]) ).
thf(f140,plain,
! [X2: d,X1: u] :
( ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X2 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
! [X2: d,X1: u] :
( ( ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X2 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f138]) ).
thf(f138,plain,
! [X2: d,X1: u] :
( ( ^ [Y0: d] :
( ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ Y0 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
! [X1: u] :
( $true
= ( !! @ d
@ ^ [Y0: d] :
( ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ Y0 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f136]) ).
thf(f136,plain,
! [X1: u] :
( $true
= ( ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] :
( ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ Y1 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
( $true
= ( !! @ u
@ ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] :
( ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ Y1 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
thf(f71,plain,
( $true
= ( !! @ u
@ ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] :
( ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ Y1 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f70]) ).
thf(f70,plain,
! [X0: d,X1: u] :
( ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) @ ( s @ X0 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,axiom,
! [X0: d,X15: u] :
( ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ X0 @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2THF_823.p',thm_2Epred__set_2EREST__DEF) ).
thf(f196,plain,
! [X2: d,X3: u,X1: u,X4: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X2 @ X3 ) ) ) ) ) )
= $false )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
! [X2: d,X3: u,X1: u,X4: u] :
( ( $true
= ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) )
& ( ( s @ X2 @ X3 )
!= ( s @ X2 @ X1 ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X2 @ X3 ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
! [X2: d,X3: u,X1: u,X4: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X2 @ X3 ) ) ) ) ) )
= ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) )
& ( ( s @ X2 @ X3 )
!= ( s @ X2 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f188]) ).
thf(f188,plain,
! [X2: d,X3: u,X1: u,X4: u] :
( $true
= ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) ) ) )
& ( ( s @ X2 @ X3 )
!= ( s @ X2 @ X1 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X4 ) @ ( s @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f187]) ).
thf(f187,plain,
! [X2: d,X3: u,X1: u,X4: u] :
( ( ^ [Y0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
& ( ( s @ X2 @ X3 )
!= ( s @ X2 @ X1 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ X2 @ X3 ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
! [X2: d,X3: u,X1: u] :
( ( !! @ u
@ ^ [Y0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y0 ) ) ) )
& ( ( s @ X2 @ X3 )
!= ( s @ X2 @ X1 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y0 ) @ ( s @ X2 @ X3 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f185]) ).
thf(f185,plain,
! [X2: d,X3: u,X1: u] :
( ( ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
& ( ( s @ X2 @ Y0 )
!= ( s @ X2 @ X1 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X2 @ Y0 ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
! [X2: d,X1: u] :
( ( !! @ u
@ ^ [Y0: u] :
( !! @ u
@ ^ [Y1: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y1 ) ) ) )
& ( ( s @ X2 @ Y0 )
!= ( s @ X2 @ X1 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ Y1 ) @ ( s @ X2 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: d,X1: u] :
( $true
= ( ^ [Y0: d] :
( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y0 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
& ( ( s @ Y0 @ Y1 )
!= ( s @ Y0 @ X1 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y0 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f182]) ).
thf(f182,plain,
! [X1: u] :
( ( !! @ d
@ ^ [Y0: d] :
( !! @ u
@ ^ [Y1: u] :
( !! @ u
@ ^ [Y2: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y0 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) ) ) )
& ( ( s @ Y0 @ Y1 )
!= ( s @ Y0 @ X1 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y0 @ X1 ) @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool ) @ Y2 ) @ ( s @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f181]) ).
thf(f181,plain,
! [X1: u] :
( ( ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] :
( !! @ u
@ ^ [Y2: u] :
( !! @ u
@ ^ [Y3: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
& ( ( s @ Y1 @ Y2 )
!= ( s @ Y1 @ Y0 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( !! @ u
@ ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] :
( !! @ u
@ ^ [Y2: u] :
( !! @ u
@ ^ [Y3: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
& ( ( s @ Y1 @ Y2 )
!= ( s @ Y1 @ Y0 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( ( !! @ u
@ ^ [Y0: u] :
( !! @ d
@ ^ [Y1: d] :
( !! @ u
@ ^ [Y2: u] :
( !! @ u
@ ^ [Y3: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) ) ) )
& ( ( s @ Y1 @ Y2 )
!= ( s @ Y1 @ Y0 ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ Y1 @ Y0 ) @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool ) @ Y3 ) @ ( s @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: u,X1: u,X2: d,X3: u] :
( ( ( ( s @ X2 @ X1 )
!= ( s @ X2 @ X3 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X2 @ X3 ) @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool ) @ X0 ) @ ( s @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,axiom,
! [X15: u,X17: u,X0: d,X12: u] :
( ( ( ( s @ X0 @ X12 )
!= ( s @ X0 @ X17 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ X0 @ X12 ) @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool ) @ X15 ) @ ( s @ X0 @ X17 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2THF_823.p',thm_2Epred__set_2EIN__DELETE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.17 % Problem : ITP004^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.06/0.18 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.39 % Computer : n025.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Tue Feb 24 08:17:13 EST 2026
% 0.18/0.39 % CPUTime :
% 0.18/0.39 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.24/0.51 ---- Original DTF file ---
% 0.24/0.52 thf(spec,logic,$$dhol).
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 % File : ITP004^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.24/0.52 % Domain : Interactive Theorem Proving
% 0.24/0.52 % Problem : HOL4 syntactic export of thm_2Epred__set_2EREST__SUBSET.p, bushy mode
% 0.24/0.52 % Version : [BG+19] axioms.
% 0.24/0.52 % English :
% 0.24/0.52
% 0.24/0.52 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.24/0.52 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.24/0.52 % Source : [BG+19]
% 0.24/0.52 % Names : thm_2Epred__set_2EREST__SUBSET.p [Gau19]
% 0.24/0.52 % : HL401501^1.p [TPAP]
% 0.24/0.52
% 0.24/0.52 % Status : Theorem
% 0.24/0.52 % Rating : 0.44 v9.1.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0
% 0.24/0.52 % Syntax : Number of formulae : 83 ( 25 unt; 50 typ; 0 def)
% 0.24/0.52 % Number of atoms : 58 ( 26 equ; 2 cnn)
% 0.24/0.52 % Maximal formula atoms : 4 ( 1 avg)
% 0.24/0.52 % Number of connectives : 672 ( 2 ~; 1 |; 2 &; 654 @)
% 0.24/0.52 % ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% 0.24/0.52 % Maximal formula depth : 17 ( 6 avg)
% 0.24/0.52 % Number of types : 4 ( 3 usr)
% 0.24/0.52 % Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% 0.24/0.52 % Number of symbols : 49 ( 47 usr; 21 con; 0-3 aty)
% 0.24/0.52 % Number of variables : 79 ( 0 ^; 78 !; 1 ?; 79 :)
% 0.24/0.52 % SPC : TH0_THM_EQU_NAR
% 0.24/0.52
% 0.24/0.52 % Comments :
% 0.24/0.52 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 thf(u,type,
% 0.24/0.52 u: $tType ).
% 0.24/0.52
% 0.24/0.52 thf(d,type,
% 0.24/0.52 d: $tType ).
% 0.24/0.52
% 0.24/0.52 thf(du,type,
% 0.24/0.52 du: $tType ).
% 0.24/0.52
% 0.24/0.52 thf(tyop_2Emin_2Ebool,type,
% 0.24/0.52 tyop_2Emin_2Ebool: d ).
% 0.24/0.52
% 0.24/0.52 thf(tyop_2Emin_2Efun,type,
% 0.24/0.52 tyop_2Emin_2Efun: d > d > d ).
% 0.24/0.52
% 0.24/0.52 thf(s,type,
% 0.24/0.52 s: d > u > du ).
% 0.24/0.52
% 0.24/0.52 thf(app_2E2,type,
% 0.24/0.52 app_2E2: du > du > u ).
% 0.24/0.52
% 0.24/0.52 thf(combin_i_2E0,type,
% 0.24/0.52 combin_i_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(combin_k_2E0,type,
% 0.24/0.52 combin_k_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(combin_s_2E0,type,
% 0.24/0.52 combin_s_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_21_2E0,type,
% 0.24/0.52 c_2Ebool_2E_21_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_21_2E1,type,
% 0.24/0.52 c_2Ebool_2E_21_2E1: du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.24/0.52 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.24/0.52 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Emin_2E_3D_2E0,type,
% 0.24/0.52 c_2Emin_2E_3D_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Emin_2E_3D_2E2,type,
% 0.24/0.52 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.24/0.52 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.24/0.52 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_3F_2E0,type,
% 0.24/0.52 c_2Ebool_2E_3F_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_3F_2E1,type,
% 0.24/0.52 c_2Ebool_2E_3F_2E1: du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Epred__set_2ECHOICE_2E0,type,
% 0.24/0.52 c_2Epred__set_2ECHOICE_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Epred__set_2ECHOICE_2E1,type,
% 0.24/0.52 c_2Epred__set_2ECHOICE_2E1: du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Epred__set_2EDELETE_2E0,type,
% 0.24/0.52 c_2Epred__set_2EDELETE_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Epred__set_2EDELETE_2E2,type,
% 0.24/0.52 c_2Epred__set_2EDELETE_2E2: du > du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2EF_2E0,type,
% 0.24/0.52 c_2Ebool_2EF_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2EIN_2E0,type,
% 0.24/0.52 c_2Ebool_2EIN_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2EIN_2E2,type,
% 0.24/0.52 c_2Ebool_2EIN_2E2: du > du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Epred__set_2EREST_2E0,type,
% 0.24/0.52 c_2Epred__set_2EREST_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Epred__set_2EREST_2E1,type,
% 0.24/0.52 c_2Epred__set_2EREST_2E1: du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Epred__set_2ESUBSET_2E0,type,
% 0.24/0.52 c_2Epred__set_2ESUBSET_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Epred__set_2ESUBSET_2E2,type,
% 0.24/0.52 c_2Epred__set_2ESUBSET_2E2: du > du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2ET_2E0,type,
% 0.24/0.52 c_2Ebool_2ET_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.24/0.52 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.24/0.52 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_7E_2E0,type,
% 0.24/0.52 c_2Ebool_2E_7E_2E0: u ).
% 0.24/0.52
% 0.24/0.52 thf(c_2Ebool_2E_7E_2E1,type,
% 0.24/0.52 c_2Ebool_2E_7E_2E1: du > u ).
% 0.24/0.52
% 0.24/0.52 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.24/0.52 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.24/0.52 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.24/0.52 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.24/0.52 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mono_2Ec_2Ebool_2EF,type,
% 0.24/0.52 mono_2Ec_2Ebool_2EF: $o ).
% 0.24/0.52
% 0.24/0.52 thf(mono_2Ec_2Ebool_2ET,type,
% 0.24/0.52 mono_2Ec_2Ebool_2ET: $o ).
% 0.24/0.52
% 0.24/0.52 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.24/0.52 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.24/0.52
% 0.24/0.52 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.24/0.52 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.24/0.52
% 0.24/0.52 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.24/0.52 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.24/0.52
% 0.24/0.52 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.24/0.52 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.24/0.52
% 0.24/0.52 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.24/0.52 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.24/0.52
% 0.24/0.52 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.24/0.52 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.24/0.52
% 0.24/0.52 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.24/0.52 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.24/0.52
% 0.24/0.52 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.24/0.52 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.24/0.52 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.24/0.52 ( ! [V2x_2E0: u] :
% 0.24/0.52 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.24/0.52 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.24/0.52 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.24/0.52 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.24/0.52 ! [A_27a: d,V0x_2E0: u] :
% 0.24/0.52 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.24/0.52 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.24/0.52 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.24/0.52 ( ( 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 ) ) )
% 0.24/0.52 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Eho_2Es__thm,axiom,
% 0.24/0.52 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.24/0.52 ( ( 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 ) ) )
% 0.24/0.52 = ( 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 ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.24/0.52 ! [V0: $o,V1: $o] :
% 0.24/0.52 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.24/0.52 <=> ( V0
% 0.24/0.52 & V1 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.24/0.52 ! [V0: $o,V1: $o] :
% 0.24/0.52 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.24/0.52 <=> ( V0
% 0.24/0.52 | V1 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Elogic_2E_7E,axiom,
% 0.24/0.52 ! [V0: $o] :
% 0.24/0.52 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.24/0.52 <=> ( (~) @ V0 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.24/0.52 ! [V0: $o,V1: $o] :
% 0.24/0.52 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.24/0.52 <=> ( V0
% 0.24/0.52 => V1 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Elogic_2E_3D,axiom,
% 0.24/0.52 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.24/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.24/0.52 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.24/0.52 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Equant_2E_21,axiom,
% 0.24/0.52 ! [A_27a: d,V0f_2E0: u] :
% 0.24/0.52 ( ( 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 ) ) ) )
% 0.24/0.52 <=> ! [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 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(reserved_2Equant_2E_3F,axiom,
% 0.24/0.52 ! [A_27a: d,V0f_2E0: u] :
% 0.24/0.52 ( ( 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 ) ) ) )
% 0.24/0.52 <=> ? [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 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.24/0.52 ! [V0_2E0: u] :
% 0.24/0.52 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.24/0.52 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.24/0.52 ! [V0_2E0: u] :
% 0.24/0.52 ( ( 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 ) ) ) )
% 0.24/0.52 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.24/0.52 ! [V0_2E0: u] :
% 0.24/0.52 ( ( 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 ) ) ) )
% 0.24/0.52 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.24/0.52 ! [V0: $o] :
% 0.24/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.24/0.52 = V0 ) ).
% 0.24/0.52
% 0.24/0.52 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.24/0.52 ! [V0: $o > $o] :
% 0.24/0.52 ( ( 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 ) ) )
% 0.24/0.52 = V0 ) ).
% 0.24/0.52
% 0.24/0.52 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.24/0.52 ! [V0: $o > $o > $o] :
% 0.24/0.52 ( ( 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 ) ) )
% 0.24/0.52 = V0 ) ).
% 0.24/0.52
% 0.24/0.52 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.24/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.24/0.52 ( ( 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 ) ) ) )
% 0.24/0.52 = ( 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 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.24/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.24/0.52 ( ( ( s @ A_27a @ X0_2E0 )
% 0.24/0.52 = ( s @ A_27a @ X1_2E0 ) )
% 0.24/0.52 <=> ( 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 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.24/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.24/0.52 ( ( 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 ) ) ) )
% 0.24/0.52 = ( 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 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
% 0.24/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.24/0.52 ( ( s @ A_27a @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
% 0.24/0.52 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ c_2Epred__set_2ECHOICE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
% 0.24/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.24/0.52 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
% 0.24/0.52 = ( 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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
% 0.24/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.24/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.24/0.52 = ( 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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a,axiom,
% 0.24/0.52 ! [A_27a: d,X0_2E0: u] :
% 0.24/0.52 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
% 0.24/0.52 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EREST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
% 0.24/0.52 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.24/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 0.24/0.52 = ( 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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.24/0.52 ! [V0: $o > $o,V1: $o] :
% 0.24/0.52 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.24/0.52 = ( 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 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.24/0.52 ! [V0: $o > $o > $o,V1: $o] :
% 0.24/0.52 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.24/0.52 = ( 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 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.24/0.52 ! [V0: $o > $o,V1: $o] :
% 0.24/0.52 ( ( V0 @ V1 )
% 0.24/0.52 = ( V0 @ V1 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.24/0.52 ! [V0: $o > $o > $o,V1: $o] :
% 0.24/0.52 ( ( V0 @ V1 )
% 0.24/0.52 = ( V0 @ V1 ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(thm_2Epred__set_2ESUBSET__DEF,axiom,
% 0.24/0.52 ! [A_27a: d,V0s_2E0: u,V1t_2E0: u] :
% 0.24/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) )
% 0.24/0.52 <=> ! [V2x_2E0: u] :
% 0.24/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
% 0.24/0.52 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(thm_2Epred__set_2EIN__DELETE,axiom,
% 0.24/0.52 ! [A_27a: d,V0s_2E0: u,V1x_2E0: u,V2y_2E0: u] :
% 0.24/0.52 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) )
% 0.24/0.52 <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
% 0.24/0.52 & ( (~)
% 0.24/0.52 @ ( ( s @ A_27a @ V1x_2E0 )
% 0.24/0.52 = ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(thm_2Epred__set_2EREST__DEF,axiom,
% 0.24/0.52 ! [A_27a: d,V0s_2E0: u] :
% 0.24/0.52 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
% 0.24/0.52 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ A_27a @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 thf(thm_2Epred__set_2EREST__SUBSET,conjecture,
% 0.24/0.52 ! [A_27a: d,V0s_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ).
% 0.24/0.52
% 0.24/0.52 %------------------------------------------------------------------------------
% 0.24/0.52 ------------------------
% 2.33/1.78 ---- Embedded in THF ---
% 2.33/1.78 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.33/1.78 %%% Generated on Tue Feb 24 08:17:14 EST 2026
% 2.33/1.78 %%% using '$$dhol' embedding, version 1.3.0.
% 2.33/1.78 %%% Logic specification used:
% 2.33/1.78 %%% thf(spec, logic, $$dhol).
% 2.33/1.78
% 2.33/1.78 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2DTF823.p
% See solution above
% 2.33/1.78 ------------------------
% 2.33/1.80 ---- Cleaned THF ---
% 2.53/1.80 thf(u,type,
% 2.53/1.80 u: $tType ).
% 2.53/1.80
% 2.53/1.80 thf(d,type,
% 2.53/1.80 d: $tType ).
% 2.53/1.80
% 2.53/1.80 thf(du,type,
% 2.53/1.80 du: $tType ).
% 2.53/1.80
% 2.53/1.80 thf(tyop_2Emin_2Ebool,type,
% 2.53/1.80 tyop_2Emin_2Ebool: d ).
% 2.53/1.80
% 2.53/1.80 thf(tyop_2Emin_2Efun,type,
% 2.53/1.80 tyop_2Emin_2Efun: d > d > d ).
% 2.53/1.80
% 2.53/1.80 thf(s,type,
% 2.53/1.80 s: d > u > du ).
% 2.53/1.80
% 2.53/1.80 thf(app_2E2,type,
% 2.53/1.80 app_2E2: du > du > u ).
% 2.53/1.80
% 2.53/1.80 thf(combin_i_2E0,type,
% 2.53/1.80 combin_i_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(combin_k_2E0,type,
% 2.53/1.80 combin_k_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(combin_s_2E0,type,
% 2.53/1.80 combin_s_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_21_2E0,type,
% 2.53/1.80 c_2Ebool_2E_21_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_21_2E1,type,
% 2.53/1.80 c_2Ebool_2E_21_2E1: du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 2.53/1.80 c_2Ebool_2E_2F_5C_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 2.53/1.80 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Emin_2E_3D_2E0,type,
% 2.53/1.80 c_2Emin_2E_3D_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Emin_2E_3D_2E2,type,
% 2.53/1.80 c_2Emin_2E_3D_2E2: du > du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 2.53/1.80 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 2.53/1.80 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_3F_2E0,type,
% 2.53/1.80 c_2Ebool_2E_3F_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_3F_2E1,type,
% 2.53/1.80 c_2Ebool_2E_3F_2E1: du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Epred__set_2ECHOICE_2E0,type,
% 2.53/1.80 c_2Epred__set_2ECHOICE_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Epred__set_2ECHOICE_2E1,type,
% 2.53/1.80 c_2Epred__set_2ECHOICE_2E1: du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Epred__set_2EDELETE_2E0,type,
% 2.53/1.80 c_2Epred__set_2EDELETE_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Epred__set_2EDELETE_2E2,type,
% 2.53/1.80 c_2Epred__set_2EDELETE_2E2: du > du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2EF_2E0,type,
% 2.53/1.80 c_2Ebool_2EF_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2EIN_2E0,type,
% 2.53/1.80 c_2Ebool_2EIN_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2EIN_2E2,type,
% 2.53/1.80 c_2Ebool_2EIN_2E2: du > du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Epred__set_2EREST_2E0,type,
% 2.53/1.80 c_2Epred__set_2EREST_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Epred__set_2EREST_2E1,type,
% 2.53/1.80 c_2Epred__set_2EREST_2E1: du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Epred__set_2ESUBSET_2E0,type,
% 2.53/1.80 c_2Epred__set_2ESUBSET_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Epred__set_2ESUBSET_2E2,type,
% 2.53/1.80 c_2Epred__set_2ESUBSET_2E2: du > du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2ET_2E0,type,
% 2.53/1.80 c_2Ebool_2ET_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 2.53/1.80 c_2Ebool_2E_5C_2F_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 2.53/1.80 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_7E_2E0,type,
% 2.53/1.80 c_2Ebool_2E_7E_2E0: u ).
% 2.53/1.80
% 2.53/1.80 thf(c_2Ebool_2E_7E_2E1,type,
% 2.53/1.80 c_2Ebool_2E_7E_2E1: du > u ).
% 2.53/1.80
% 2.53/1.80 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 2.53/1.80 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 2.53/1.80
% 2.53/1.80 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.80 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 2.53/1.80
% 2.53/1.80 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 2.53/1.80 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 2.53/1.80
% 2.53/1.80 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 2.53/1.80 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 2.53/1.80
% 2.53/1.80 thf(mono_2Ec_2Ebool_2EF,type,
% 2.53/1.80 mono_2Ec_2Ebool_2EF: $o ).
% 2.53/1.80
% 2.53/1.80 thf(mono_2Ec_2Ebool_2ET,type,
% 2.53/1.80 mono_2Ec_2Ebool_2ET: $o ).
% 2.53/1.80
% 2.53/1.80 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 2.53/1.80 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 2.53/1.80
% 2.53/1.80 thf(mono_2Ec_2Ebool_2E_7E,type,
% 2.53/1.80 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 2.53/1.80
% 2.53/1.80 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 2.53/1.80 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 2.53/1.80
% 2.53/1.80 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.80 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 2.53/1.80
% 2.53/1.80 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.53/1.80 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 2.53/1.80
% 2.53/1.80 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 2.53/1.80 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 2.53/1.80
% 2.53/1.80 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.53/1.80 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 2.53/1.80
% 2.53/1.80 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.53/1.80 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Eho_2Eeq__ext,axiom,
% 2.53/1.80 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 2.53/1.80 ( ! [V2x_2E0: u] :
% 2.53/1.80 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 2.53/1.80 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 2.53/1.80 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 2.53/1.80 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Eho_2Ei__thm,axiom,
% 2.53/1.80 ! [A_27a: d,V0x_2E0: u] :
% 2.53/1.80 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 2.53/1.80 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Eho_2Ek__thm,axiom,
% 2.53/1.80 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 2.53/1.80 ( ( 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 ) ) )
% 2.53/1.80 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Eho_2Es__thm,axiom,
% 2.53/1.80 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 2.53/1.80 ( ( 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 ) ) )
% 2.53/1.80 = ( 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 ) ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 2.53/1.80 ! [V0: $o,V1: $o] :
% 2.53/1.80 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 2.53/1.80 <=> ( V0
% 2.53/1.80 & V1 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 2.53/1.80 ! [V0: $o,V1: $o] :
% 2.53/1.80 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 2.53/1.80 <=> ( V0
% 2.53/1.80 | V1 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Elogic_2E_7E,axiom,
% 2.53/1.80 ! [V0: $o] :
% 2.53/1.80 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 2.53/1.80 <=> ( (~) @ V0 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 2.53/1.80 ! [V0: $o,V1: $o] :
% 2.53/1.80 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 2.53/1.80 <=> ( V0
% 2.53/1.80 => V1 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Elogic_2E_3D,axiom,
% 2.53/1.80 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 2.53/1.80 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 2.53/1.80 <=> ( ( s @ A_27a @ V0_2E0 )
% 2.53/1.80 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Equant_2E_21,axiom,
% 2.53/1.80 ! [A_27a: d,V0f_2E0: u] :
% 2.53/1.80 ( ( 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 ) ) ) )
% 2.53/1.80 <=> ! [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 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(reserved_2Equant_2E_3F,axiom,
% 2.53/1.80 ! [A_27a: d,V0f_2E0: u] :
% 2.53/1.80 ( ( 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 ) ) ) )
% 2.53/1.80 <=> ? [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 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.80 ! [V0_2E0: u] :
% 2.53/1.80 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 2.53/1.80 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.80 ! [V0_2E0: u] :
% 2.53/1.80 ( ( 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 ) ) ) )
% 2.53/1.80 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.53/1.80 ! [V0_2E0: u] :
% 2.53/1.80 ( ( 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 ) ) ) )
% 2.53/1.80 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.80 ! [V0: $o] :
% 2.53/1.80 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 2.53/1.80 = V0 ) ).
% 2.53/1.80
% 2.53/1.80 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.80 ! [V0: $o > $o] :
% 2.53/1.80 ( ( 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 ) ) )
% 2.53/1.80 = V0 ) ).
% 2.53/1.80
% 2.53/1.80 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.53/1.80 ! [V0: $o > $o > $o] :
% 2.53/1.80 ( ( 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 ) ) )
% 2.53/1.80 = V0 ) ).
% 2.53/1.80
% 2.53/1.80 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.80 ! [A_27a: d,X0_2E0: u] :
% 2.53/1.80 ( ( 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 ) ) ) )
% 2.53/1.80 = ( 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 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 2.53/1.80 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 2.53/1.80 ( ( ( s @ A_27a @ X0_2E0 )
% 2.53/1.80 = ( s @ A_27a @ X1_2E0 ) )
% 2.53/1.80 <=> ( 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 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.80 ! [A_27a: d,X0_2E0: u] :
% 2.53/1.80 ( ( 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 ) ) ) )
% 2.53/1.80 = ( 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 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.80 ! [A_27a: d,X0_2E0: u] :
% 2.53/1.80 ( ( s @ A_27a @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
% 2.53/1.80 = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ c_2Epred__set_2ECHOICE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
% 2.53/1.80 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 2.53/1.80 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
% 2.53/1.80 = ( 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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
% 2.53/1.80 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 2.53/1.80 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.53/1.80 = ( 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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a,axiom,
% 2.53/1.80 ! [A_27a: d,X0_2E0: u] :
% 2.53/1.80 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
% 2.53/1.80 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EREST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
% 2.53/1.80 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 2.53/1.80 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
% 2.53/1.80 = ( 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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.80 ! [V0: $o > $o,V1: $o] :
% 2.53/1.80 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 2.53/1.80 = ( 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 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.80 ! [V0: $o > $o > $o,V1: $o] :
% 2.53/1.80 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 2.53/1.80 = ( 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 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.53/1.80 ! [V0: $o > $o,V1: $o] :
% 2.53/1.80 ( ( V0 @ V1 )
% 2.53/1.80 = ( V0 @ V1 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.53/1.80 ! [V0: $o > $o > $o,V1: $o] :
% 2.53/1.80 ( ( V0 @ V1 )
% 2.53/1.80 = ( V0 @ V1 ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(thm_2Epred__set_2ESUBSET__DEF,axiom,
% 2.53/1.80 ! [A_27a: d,V0s_2E0: u,V1t_2E0: u] :
% 2.53/1.80 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) )
% 2.53/1.80 <=> ! [V2x_2E0: u] :
% 2.53/1.80 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
% 2.53/1.80 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1t_2E0 ) ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(thm_2Epred__set_2EIN__DELETE,axiom,
% 2.53/1.80 ! [A_27a: d,V0s_2E0: u,V1x_2E0: u,V2y_2E0: u] :
% 2.53/1.80 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) )
% 2.53/1.80 <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
% 2.53/1.80 & ( (~)
% 2.53/1.80 @ ( ( s @ A_27a @ V1x_2E0 )
% 2.53/1.80 = ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(thm_2Epred__set_2EREST__DEF,axiom,
% 2.53/1.80 ! [A_27a: d,V0s_2E0: u] :
% 2.53/1.80 ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
% 2.53/1.80 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ A_27a @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ).
% 2.53/1.80
% 2.53/1.80 thf(thm_2Epred__set_2EREST__SUBSET,conjecture,
% 2.53/1.80 ! [A_27a: d,V0s_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EREST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ).
% 2.53/1.80 ------------------------
% 2.53/1.83 % (935)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/2Mi)
% 2.53/1.83 % (932)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_823 for (2999ds/4Mi)
% 2.53/1.83 % (931)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/183Mi)
% 2.53/1.83 % (936)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_823 for (2999ds/2Mi)
% 2.53/1.83 % (938)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/18Mi)
% 2.53/1.83 % (933)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_823 for (2999ds/27Mi)
% 2.53/1.83 % (937)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_823 for (2999ds/275Mi)
% 2.53/1.83 % (935)Instruction limit reached!
% 2.53/1.83 % (935)------------------------------
% 2.53/1.83 % (935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.83 % (935)Termination reason: Unknown
% 2.53/1.83 % (935)Termination phase: shuffling
% 2.53/1.83
% 2.53/1.83 % (936)Instruction limit reached!
% 2.53/1.83 % (936)------------------------------
% 2.53/1.83 % (936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.83 % (936)Termination reason: Unknown
% 2.53/1.83 % (936)Termination phase: shuffling
% 2.53/1.83
% 2.53/1.83 % (936)Memory used [KB]: 1023
% 2.53/1.83 % (936)Time elapsed: 0.003 s
% 2.53/1.83 % (936)Instructions burned: 3 (million)
% 2.53/1.83 % (936)------------------------------
% 2.53/1.83 % (936)------------------------------
% 2.53/1.83 % (935)Memory used [KB]: 1023
% 2.53/1.83 % (935)Time elapsed: 0.003 s
% 2.53/1.83 % (935)Instructions burned: 2 (million)
% 2.53/1.83 % (935)------------------------------
% 2.53/1.83 % (935)------------------------------
% 2.53/1.83 % (932)Instruction limit reached!
% 2.53/1.83 % (932)------------------------------
% 2.53/1.83 % (932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.83 % (932)Termination reason: Unknown
% 2.53/1.83 % (932)Termination phase: shuffling
% 2.53/1.83
% 2.53/1.83 % (932)Memory used [KB]: 1023
% 2.53/1.83 % (932)Time elapsed: 0.004 s
% 2.53/1.83 % (932)Instructions burned: 4 (million)
% 2.53/1.83 % (932)------------------------------
% 2.53/1.83 % (932)------------------------------
% 2.53/1.83 % (937)Refutation not found, incomplete strategy
% 2.53/1.83 % (937)------------------------------
% 2.53/1.83 % (937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.83 % (937)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.83
% 2.53/1.83
% 2.53/1.83 % (937)Memory used [KB]: 5628
% 2.53/1.83 % (937)Time elapsed: 0.007 s
% 2.53/1.83 % (937)Instructions burned: 9 (million)
% 2.53/1.83 % (937)------------------------------
% 2.53/1.83 % (937)------------------------------
% 2.53/1.84 % (938)Instruction limit reached!
% 2.53/1.84 % (938)------------------------------
% 2.53/1.84 % (938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.84 % (938)Termination reason: Unknown
% 2.53/1.84 % (938)Termination phase: Saturation
% 2.53/1.84
% 2.53/1.84 % (938)Memory used [KB]: 5628
% 2.53/1.84 % (938)Time elapsed: 0.012 s
% 2.53/1.84 % (938)Instructions burned: 19 (million)
% 2.53/1.84 % (938)------------------------------
% 2.53/1.84 % (938)------------------------------
% 2.53/1.84 % (933)Instruction limit reached!
% 2.53/1.84 % (933)------------------------------
% 2.53/1.84 % (933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.84 % (933)Termination reason: Unknown
% 2.53/1.84 % (933)Termination phase: Saturation
% 2.53/1.84
% 2.53/1.84 % (933)Memory used [KB]: 5756
% 2.53/1.84 % (933)Time elapsed: 0.017 s
% 2.53/1.84 % (933)Instructions burned: 27 (million)
% 2.53/1.84 % (933)------------------------------
% 2.53/1.84 % (933)------------------------------
% 2.53/1.85 % (941)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_823 for (2999ds/37Mi)
% 2.53/1.85 % (940)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/3Mi)
% 2.53/1.85 % (942)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_823 for (2999ds/15Mi)
% 2.53/1.85 % (940)Instruction limit reached!
% 2.53/1.85 % (940)------------------------------
% 2.53/1.85 % (940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.85 % (940)Termination reason: Unknown
% 2.53/1.85 % (940)Termination phase: shuffling
% 2.53/1.85
% 2.53/1.85 % (940)Memory used [KB]: 1023
% 2.53/1.85 % (940)Time elapsed: 0.004 s
% 2.53/1.85 % (940)Instructions burned: 4 (million)
% 2.53/1.85 % (940)------------------------------
% 2.53/1.85 % (940)------------------------------
% 2.53/1.85 % (943)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_823 for (2999ds/3Mi)
% 2.53/1.85 % (943)Instruction limit reached!
% 2.53/1.85 % (943)------------------------------
% 2.53/1.85 % (943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.85 % (943)Termination reason: Unknown
% 2.53/1.85 % (943)Termination phase: shuffling
% 2.53/1.85
% 2.53/1.85 % (943)Memory used [KB]: 1023
% 2.53/1.85 % (943)Time elapsed: 0.003 s
% 2.53/1.85 % (943)Instructions burned: 4 (million)
% 2.53/1.85 % (943)------------------------------
% 2.53/1.85 % (943)------------------------------
% 2.53/1.86 % (944)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_823 for (2999ds/1041Mi)
% 2.53/1.86 % (942)Instruction limit reached!
% 2.53/1.86 % (942)------------------------------
% 2.53/1.86 % (942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.86 % (942)Termination reason: Unknown
% 2.53/1.86 % (942)Termination phase: Property scanning
% 2.53/1.86
% 2.53/1.86 % (942)Memory used [KB]: 1151
% 2.53/1.86 % (942)Time elapsed: 0.010 s
% 2.53/1.86 % (942)Instructions burned: 16 (million)
% 2.53/1.86 % (942)------------------------------
% 2.53/1.86 % (942)------------------------------
% 2.53/1.86 % (945)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/7Mi)
% 2.53/1.86 % (945)Instruction limit reached!
% 2.53/1.86 % (945)------------------------------
% 2.53/1.86 % (945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.86 % (945)Termination reason: Unknown
% 2.53/1.86 % (945)Termination phase: SInE selection
% 2.53/1.86
% 2.53/1.86 % (945)Memory used [KB]: 1023
% 2.53/1.86 % (945)Time elapsed: 0.005 s
% 2.53/1.86 % (945)Instructions burned: 7 (million)
% 2.53/1.86 % (945)------------------------------
% 2.53/1.86 % (945)------------------------------
% 2.53/1.87 % (941)Instruction limit reached!
% 2.53/1.87 % (941)------------------------------
% 2.53/1.87 % (941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.87 % (941)Termination reason: Unknown
% 2.53/1.87 % (941)Termination phase: Saturation
% 2.53/1.87
% 2.53/1.87 % (941)Memory used [KB]: 5884
% 2.53/1.87 % (941)Time elapsed: 0.022 s
% 2.53/1.87 % (941)Instructions burned: 38 (million)
% 2.53/1.87 % (941)------------------------------
% 2.53/1.87 % (941)------------------------------
% 2.53/1.87 % (946)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/16Mi)
% 2.53/1.87 % (947)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_823 for (2999ds/3Mi)
% 2.53/1.87 % (948)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_823 for (2999ds/3Mi)
% 2.53/1.87 % (947)Instruction limit reached!
% 2.53/1.87 % (947)------------------------------
% 2.53/1.87 % (947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.87 % (947)Termination reason: Unknown
% 2.53/1.87 % (947)Termination phase: shuffling
% 2.53/1.87
% 2.53/1.87 % (947)Memory used [KB]: 1023
% 2.53/1.87 % (947)Time elapsed: 0.004 s
% 2.53/1.87 % (947)Instructions burned: 4 (million)
% 2.53/1.87 % (947)------------------------------
% 2.53/1.87 % (947)------------------------------
% 2.53/1.87 % (948)Instruction limit reached!
% 2.53/1.87 % (948)------------------------------
% 2.53/1.87 % (948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.87 % (948)Termination reason: Unknown
% 2.53/1.87 % (948)Termination phase: shuffling
% 2.53/1.87
% 2.53/1.87 % (948)Memory used [KB]: 1023
% 2.53/1.87 % (948)Time elapsed: 0.003 s
% 2.53/1.87 % (948)Instructions burned: 3 (million)
% 2.53/1.87 % (948)------------------------------
% 2.53/1.87 % (948)------------------------------
% 2.53/1.88 % (946)Instruction limit reached!
% 2.53/1.88 % (946)------------------------------
% 2.53/1.88 % (946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.88 % (946)Termination reason: Unknown
% 2.53/1.88 % (946)Termination phase: Property scanning
% 2.53/1.88
% 2.53/1.88 % (946)Memory used [KB]: 1151
% 2.53/1.88 % (946)Time elapsed: 0.010 s
% 2.53/1.88 % (946)Instructions burned: 16 (million)
% 2.53/1.88 % (946)------------------------------
% 2.53/1.88 % (946)------------------------------
% 2.53/1.88 % (949)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/7Mi)
% 2.53/1.89 % (950)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/3Mi)
% 2.53/1.89 % (950)Instruction limit reached!
% 2.53/1.89 % (950)------------------------------
% 2.53/1.89 % (950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (950)Termination reason: Unknown
% 2.53/1.89 % (950)Termination phase: shuffling
% 2.53/1.89
% 2.53/1.89 % (950)Memory used [KB]: 1023
% 2.53/1.89 % (950)Time elapsed: 0.004 s
% 2.53/1.89 % (950)Instructions burned: 4 (million)
% 2.53/1.89 % (950)------------------------------
% 2.53/1.89 % (950)------------------------------
% 2.53/1.89 % (949)Instruction limit reached!
% 2.53/1.89 % (949)------------------------------
% 2.53/1.89 % (949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (949)Termination reason: Unknown
% 2.53/1.89 % (949)Termination phase: Property scanning
% 2.53/1.89
% 2.53/1.89 % (949)Memory used [KB]: 1151
% 2.53/1.89 % (949)Time elapsed: 0.006 s
% 2.53/1.89 % (949)Instructions burned: 8 (million)
% 2.53/1.89 % (949)------------------------------
% 2.53/1.89 % (949)------------------------------
% 2.53/1.89 % (952)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/18Mi)
% 2.53/1.89 % (951)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/4Mi)
% 2.53/1.89 % (954)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/710Mi)
% 2.53/1.89 % (951)Instruction limit reached!
% 2.53/1.89 % (951)------------------------------
% 2.53/1.89 % (951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (951)Termination reason: Unknown
% 2.53/1.89 % (951)Termination phase: Property scanning
% 2.53/1.89
% 2.53/1.89 % (951)Memory used [KB]: 1023
% 2.53/1.89 % (951)Time elapsed: 0.004 s
% 2.53/1.89 % (951)Instructions burned: 4 (million)
% 2.53/1.89 % (951)------------------------------
% 2.53/1.89 % (951)------------------------------
% 2.53/1.90 % (952)Instruction limit reached!
% 2.53/1.90 % (952)------------------------------
% 2.53/1.90 % (952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.90 % (952)Termination reason: Unknown
% 2.53/1.90 % (952)Termination phase: Saturation
% 2.53/1.90
% 2.53/1.90 % (952)Memory used [KB]: 5628
% 2.53/1.90 % (952)Time elapsed: 0.011 s
% 2.53/1.90 % (952)Instructions burned: 18 (million)
% 2.53/1.90 % (952)------------------------------
% 2.53/1.90 % (952)------------------------------
% 2.53/1.91 % (956)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/902Mi)
% 2.53/1.91 % (955)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/6Mi)
% 2.53/1.91 % (955)Instruction limit reached!
% 2.53/1.91 % (955)------------------------------
% 2.53/1.91 % (955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.91 % (955)Termination reason: Unknown
% 2.53/1.91 % (955)Termination phase: Property scanning
% 2.53/1.91
% 2.53/1.91 % (955)Memory used [KB]: 1023
% 2.53/1.91 % (955)Time elapsed: 0.005 s
% 2.53/1.91 % (955)Instructions burned: 6 (million)
% 2.53/1.91 % (955)------------------------------
% 2.53/1.91 % (955)------------------------------
% 2.53/1.91 % (957)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/21Mi)
% 2.53/1.92 % (958)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/5Mi)
% 2.53/1.92 % (956)Refutation not found, incomplete strategy
% 2.53/1.92 % (956)------------------------------
% 2.53/1.92 % (956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.92 % (956)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.92
% 2.53/1.92
% 2.53/1.92 % (956)Memory used [KB]: 5756
% 2.53/1.92 % (956)Time elapsed: 0.018 s
% 2.53/1.92 % (956)Instructions burned: 28 (million)
% 2.53/1.92 % (956)------------------------------
% 2.53/1.92 % (956)------------------------------
% 2.53/1.92 % (958)Instruction limit reached!
% 2.53/1.92 % (958)------------------------------
% 2.53/1.92 % (958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.92 % (958)Termination reason: Unknown
% 2.53/1.92 % (958)Termination phase: shuffling
% 2.53/1.92
% 2.53/1.92 % (958)Memory used [KB]: 1151
% 2.53/1.92 % (958)Time elapsed: 0.005 s
% 2.53/1.92 % (958)Instructions burned: 5 (million)
% 2.53/1.92 % (958)------------------------------
% 2.53/1.92 % (958)------------------------------
% 2.53/1.93 % (957)Instruction limit reached!
% 2.53/1.93 % (957)------------------------------
% 2.53/1.93 % (957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.93 % (957)Termination reason: Unknown
% 2.53/1.93 % (957)Termination phase: Saturation
% 2.53/1.93
% 2.53/1.93 % (957)Memory used [KB]: 5628
% 2.53/1.93 % (957)Time elapsed: 0.013 s
% 2.53/1.93 % (957)Instructions burned: 21 (million)
% 2.53/1.93 % (957)------------------------------
% 2.53/1.93 % (957)------------------------------
% 2.53/1.93 % (959)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_823 for (2999ds/6Mi)
% 2.53/1.93 % (931)Instruction limit reached!
% 2.53/1.93 % (931)------------------------------
% 2.53/1.93 % (931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.93 % (931)Termination reason: Unknown
% 2.53/1.93 % (931)Termination phase: Saturation
% 2.53/1.93
% 2.53/1.93 % (931)Memory used [KB]: 6268
% 2.53/1.93 % (931)Time elapsed: 0.107 s
% 2.53/1.93 % (931)Instructions burned: 184 (million)
% 2.53/1.93 % (931)------------------------------
% 2.53/1.93 % (931)------------------------------
% 2.53/1.93 % (959)Instruction limit reached!
% 2.53/1.93 % (959)------------------------------
% 2.53/1.93 % (959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.93 % (959)Termination reason: Unknown
% 2.53/1.93 % (959)Termination phase: shuffling
% 2.53/1.93
% 2.53/1.93 % (959)Memory used [KB]: 1151
% 2.53/1.93 % (959)Time elapsed: 0.006 s
% 2.53/1.93 % (959)Instructions burned: 7 (million)
% 2.53/1.93 % (959)------------------------------
% 2.53/1.93 % (959)------------------------------
% 2.53/1.94 % (969)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_823 for (2998ds/377Mi)
% 2.53/1.94 % (970)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_823 for (2998ds/779Mi)
% 2.53/1.94 % (971)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_823 for (2998ds/19Mi)
% 2.53/1.95 % (972)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_823 for (2998ds/879Mi)
% 2.53/1.95 % (973)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_823 for (2998ds/17Mi)
% 2.53/1.95 % (971)Instruction limit reached!
% 2.53/1.95 % (971)------------------------------
% 2.53/1.95 % (971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.95 % (971)Termination reason: Unknown
% 2.53/1.95 % (971)Termination phase: Saturation
% 2.53/1.95
% 2.53/1.95 % (971)Memory used [KB]: 5756
% 2.53/1.95 % (971)Time elapsed: 0.012 s
% 2.53/1.95 % (971)Instructions burned: 19 (million)
% 2.53/1.95 % (971)------------------------------
% 2.53/1.95 % (971)------------------------------
% 2.53/1.96 % (973)Instruction limit reached!
% 2.53/1.96 % (973)------------------------------
% 2.53/1.96 % (973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.96 % (973)Termination reason: Unknown
% 2.53/1.96 % (973)Termination phase: Property scanning
% 2.53/1.96
% 2.53/1.96 % (973)Memory used [KB]: 1151
% 2.53/1.96 % (973)Time elapsed: 0.010 s
% 2.53/1.96 % (973)Instructions burned: 17 (million)
% 2.53/1.96 % (973)------------------------------
% 2.53/1.96 % (973)------------------------------
% 2.53/1.97 % (974)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_823 for (2998ds/3Mi)
% 2.53/1.98 % (974)Instruction limit reached!
% 2.53/1.98 % (974)------------------------------
% 2.53/1.98 % (974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.98 % (974)Termination reason: Unknown
% 2.53/1.98 % (974)Termination phase: shuffling
% 2.53/1.98
% 2.53/1.98 % (974)Memory used [KB]: 1023
% 2.53/1.98 % (974)Time elapsed: 0.004 s
% 2.53/1.98 % (974)Instructions burned: 3 (million)
% 2.53/1.98 % (974)------------------------------
% 2.53/1.98 % (974)------------------------------
% 2.53/1.98 % (975)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_823 for (2998ds/30Mi)
% 2.53/2.00 % (976)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_823 for (2998ds/127Mi)
% 2.53/2.00 % (975)Instruction limit reached!
% 2.53/2.00 % (975)------------------------------
% 2.53/2.00 % (975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/2.00 % (975)Termination reason: Unknown
% 2.53/2.00 % (975)Termination phase: Saturation
% 2.53/2.00
% 2.53/2.00 % (975)Memory used [KB]: 5756
% 2.53/2.00 % (975)Time elapsed: 0.019 s
% 2.53/2.00 % (975)Instructions burned: 31 (million)
% 2.53/2.00 % (975)------------------------------
% 2.53/2.00 % (975)------------------------------
% 2.53/2.02 % (977)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_823 for (2997ds/100Mi)
% 3.95/2.05 % (970)First to succeed.
% 3.95/2.06 % (970)Refutation found. Thanks to Tanya!
% 3.95/2.06 % SZS status Theorem for DTF2THF_823
% 3.95/2.06 % SZS output start Proof for DTF2THF_823
% 3.95/2.06 thf(type_def_5, type, d: $tType).
% 3.95/2.06 thf(type_def_7, type, u: $tType).
% 3.95/2.06 thf(type_def_8, type, du: $tType).
% 3.95/2.06 thf(func_def_0, type, u: $tType).
% 3.95/2.06 thf(func_def_1, type, d: $tType).
% 3.95/2.06 thf(func_def_2, type, du: $tType).
% 3.95/2.06 thf(func_def_3, type, tyop_2Emin_2Ebool: d).
% 3.95/2.06 thf(func_def_4, type, tyop_2Emin_2Efun: d > d > d).
% 3.95/2.06 thf(func_def_5, type, s: d > u > du).
% 3.95/2.06 thf(func_def_6, type, app_2E2: du > du > u).
% 3.95/2.06 thf(func_def_7, type, combin_i_2E0: u).
% 3.95/2.06 thf(func_def_8, type, combin_k_2E0: u).
% 3.95/2.06 thf(func_def_9, type, combin_s_2E0: u).
% 3.95/2.06 thf(func_def_10, type, c_2Ebool_2E_21_2E0: u).
% 3.95/2.06 thf(func_def_11, type, c_2Ebool_2E_21_2E1: du > u).
% 3.95/2.06 thf(func_def_12, type, c_2Ebool_2E_2F_5C_2E0: u).
% 3.95/2.06 thf(func_def_13, type, c_2Ebool_2E_2F_5C_2E2: du > du > u).
% 3.95/2.06 thf(func_def_14, type, c_2Emin_2E_3D_2E0: u).
% 3.95/2.06 thf(func_def_15, type, c_2Emin_2E_3D_2E2: du > du > u).
% 3.95/2.06 thf(func_def_16, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 3.95/2.06 thf(func_def_17, type, c_2Emin_2E_3D_3D_3E_2E2: du > du > u).
% 3.95/2.06 thf(func_def_18, type, c_2Ebool_2E_3F_2E0: u).
% 3.95/2.06 thf(func_def_19, type, c_2Ebool_2E_3F_2E1: du > u).
% 3.95/2.06 thf(func_def_20, type, c_2Epred__set_2ECHOICE_2E0: u).
% 3.95/2.06 thf(func_def_21, type, c_2Epred__set_2ECHOICE_2E1: du > u).
% 3.95/2.06 thf(func_def_22, type, c_2Epred__set_2EDELETE_2E0: u).
% 3.95/2.06 thf(func_def_23, type, c_2Epred__set_2EDELETE_2E2: du > du > u).
% 3.95/2.06 thf(func_def_24, type, c_2Ebool_2EF_2E0: u).
% 3.95/2.06 thf(func_def_25, type, c_2Ebool_2EIN_2E0: u).
% 3.95/2.06 thf(func_def_26, type, c_2Ebool_2EIN_2E2: du > du > u).
% 3.95/2.06 thf(func_def_27, type, c_2Epred__set_2EREST_2E0: u).
% 3.95/2.06 thf(func_def_28, type, c_2Epred__set_2EREST_2E1: du > u).
% 3.95/2.06 thf(func_def_29, type, c_2Epred__set_2ESUBSET_2E0: u).
% 3.95/2.06 thf(func_def_30, type, c_2Epred__set_2ESUBSET_2E2: du > du > u).
% 3.95/2.06 thf(func_def_31, type, c_2Ebool_2ET_2E0: u).
% 3.95/2.06 thf(func_def_32, type, c_2Ebool_2E_5C_2F_2E0: u).
% 3.95/2.06 thf(func_def_33, type, c_2Ebool_2E_5C_2F_2E2: du > du > u).
% 3.95/2.06 thf(func_def_34, type, c_2Ebool_2E_7E_2E0: u).
% 3.95/2.06 thf(func_def_35, type, c_2Ebool_2E_7E_2E1: du > u).
% 3.95/2.06 thf(func_def_36, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ($o > $o) > $o > $o).
% 3.95/2.06 thf(func_def_37, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o > $o) > $o > $o > $o).
% 3.95/2.06 thf(func_def_38, type, mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o).
% 3.95/2.06 thf(func_def_39, type, mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 3.95/2.06 thf(func_def_42, type, mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o).
% 3.95/2.06 thf(func_def_43, type, mono_2Ec_2Ebool_2E_7E: $o > $o).
% 3.95/2.06 thf(func_def_44, type, i_mono_2Etyop_2Emin_2Ebool: $o > u).
% 3.95/2.06 thf(func_def_45, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o) > u).
% 3.95/2.06 thf(func_def_46, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ($o > $o > $o) > u).
% 3.95/2.06 thf(func_def_47, type, j_mono_2Etyop_2Emin_2Ebool: du > $o).
% 3.95/2.06 thf(func_def_48, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o).
% 3.95/2.06 thf(func_def_49, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o).
% 3.95/2.06 thf(func_def_69, type, sK1: u).
% 3.95/2.06 thf(func_def_70, type, sK2: d).
% 3.95/2.06 thf(func_def_71, type, sK3: d > u > u > u).
% 3.95/2.06 thf(func_def_72, type, sK4: d > d > u > u > u).
% 3.95/2.06 thf(f505,plain,(
% 3.95/2.06 $false),
% 3.95/2.06 inference(trivial_inequality_removal,[status(thm)],[f501])).
% 3.95/2.06 thf(f501,plain,(
% 3.95/2.06 ($false = $true)),
% 3.95/2.06 inference(superposition,[status(thm)],[f478,f135])).
% 3.95/2.06 thf(f135,plain,(
% 3.95/2.06 ($false = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ sK2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ sK2 @ tyop_2Emin_2Ebool) @ sK1))) @ (s @ (tyop_2Emin_2Efun @ sK2 @ tyop_2Emin_2Ebool) @ sK1)))))),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f134])).
% 3.95/2.06 thf(f134,plain,(
% 3.95/2.06 (((^[Y0 : d]: (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ sK1))) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ sK1))))) @ sK2) = $false)),
% 3.95/2.06 inference(sigma_clausification,[status(thm)],[f133])).
% 3.95/2.06 thf(f133,plain,(
% 3.95/2.06 ($false = (!! @ d @ (^[Y0 : d]: (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ sK1))) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ sK1)))))))),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f132])).
% 3.95/2.06 thf(f132,plain,(
% 3.95/2.06 ($false = ((^[Y0 : u]: (!! @ d @ (^[Y1 : d]: (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))))))) @ sK1))),
% 3.95/2.06 inference(sigma_clausification,[status(thm)],[f131])).
% 3.95/2.06 thf(f131,plain,(
% 3.95/2.06 ((!! @ u @ (^[Y0 : u]: (!! @ d @ (^[Y1 : d]: (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0)))))))) = $false)),
% 3.95/2.06 inference(not_proxy_clausification,[status(thm)],[f107])).
% 3.95/2.06 thf(f107,plain,(
% 3.95/2.06 ($true = (~ (!! @ u @ (^[Y0 : u]: (!! @ d @ (^[Y1 : d]: (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))))))))))),
% 3.95/2.06 inference(cnf_transformation,[status(thm)],[f51])).
% 3.95/2.06 thf(f51,plain,(
% 3.95/2.06 ($true = (~ (!! @ u @ (^[Y0 : u]: (!! @ d @ (^[Y1 : d]: (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))))))))))),
% 3.95/2.06 inference(fool_elimination,[status(thm)],[f50])).
% 3.95/2.06 thf(f50,plain,(
% 3.95/2.06 ~! [X0 : d,X1 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))),
% 3.95/2.06 inference(rectify,[status(thm)],[f34])).
% 3.95/2.06 thf(f34,negated_conjecture,(
% 3.95/2.06 ~! [X0 : d,X15 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))))),
% 3.95/2.06 inference(negated_conjecture,[status(cth)],[f33])).
% 3.95/2.06 thf(f33,conjecture,(
% 3.95/2.06 ! [X0 : d,X15 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))))),
% 3.95/2.06 file('/export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2THF_823.p',thm_2Epred__set_2EREST__SUBSET)).
% 3.95/2.06 thf(f478,plain,(
% 3.95/2.06 ( ! [X0 : d,X1 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))) )),
% 3.95/2.06 inference(trivial_inequality_removal,[status(thm)],[f477])).
% 3.95/2.06 thf(f477,plain,(
% 3.95/2.06 ( ! [X0 : d,X1 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) | ($false = $true)) )),
% 3.95/2.06 inference(duplicate_literal_removal,[status(thm)],[f469])).
% 3.95/2.06 thf(f469,plain,(
% 3.95/2.06 ( ! [X0 : d,X1 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) | ($false = $true) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))) )),
% 3.95/2.06 inference(superposition,[status(thm)],[f440,f155])).
% 3.95/2.06 thf(f155,plain,(
% 3.95/2.06 ( ! [X2 : u,X3 : d,X1 : u] : (($false = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ (sK3 @ X3 @ X1 @ X2)) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))) = $true)) )),
% 3.95/2.06 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 3.95/2.06 thf(f154,plain,(
% 3.95/2.06 ( ! [X2 : u,X3 : d,X1 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))) = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ (sK3 @ X3 @ X1 @ X2)) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ (sK3 @ X3 @ X1 @ X2)) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2))))) = $false)) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f153])).
% 3.95/2.06 thf(f153,plain,(
% 3.95/2.06 ( ! [X2 : u,X3 : d,X1 : u] : (($false = ((^[Y0 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ Y0) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ Y0) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))))) @ (sK3 @ X3 @ X1 @ X2))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))) = $true)) )),
% 3.95/2.06 inference(sigma_clausification,[status(thm)],[f148])).
% 3.95/2.06 thf(f148,plain,(
% 3.95/2.06 ( ! [X2 : u,X3 : d,X1 : u] : (($false = (!! @ u @ (^[Y0 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ Y0) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ Y0) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))) = $true)) )),
% 3.95/2.06 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 3.95/2.06 thf(f147,plain,(
% 3.95/2.06 ( ! [X2 : u,X3 : d,X1 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))) = (!! @ u @ (^[Y0 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ Y0) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ Y0) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2))))))))) )),
% 3.95/2.06 inference(binary_proxy_clausification,[status(thm)],[f146])).
% 3.95/2.06 thf(f146,plain,(
% 3.95/2.06 ( ! [X2 : u,X3 : d,X1 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))) = (!! @ u @ (^[Y0 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ Y0) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ Y0) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))))))))) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f145])).
% 3.95/2.06 thf(f145,plain,(
% 3.95/2.06 ( ! [X2 : u,X3 : d,X1 : u] : (($true = ((^[Y0 : d]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X2)))) = (!! @ u @ (^[Y1 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y0 @ Y1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y0 @ Y1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X2))))))))) @ X3))) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f144])).
% 3.95/2.06 thf(f144,plain,(
% 3.95/2.06 ( ! [X2 : u,X1 : u] : (($true = (!! @ d @ (^[Y0 : d]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X2)))) = (!! @ u @ (^[Y1 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y0 @ Y1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y0 @ Y1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X2)))))))))))) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f143])).
% 3.95/2.06 thf(f143,plain,(
% 3.95/2.06 ( ! [X2 : u,X1 : u] : ((((^[Y0 : u]: (!! @ d @ (^[Y1 : d]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0)))) = (!! @ u @ (^[Y2 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y2) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y2) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))))))))))) @ X2) = $true)) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f142])).
% 3.95/2.06 thf(f142,plain,(
% 3.95/2.06 ( ! [X1 : u] : (((!! @ u @ (^[Y0 : u]: (!! @ d @ (^[Y1 : d]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0)))) = (!! @ u @ (^[Y2 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y2) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ X1)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y2) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0)))))))))))) = $true)) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f141])).
% 3.95/2.06 thf(f141,plain,(
% 3.95/2.06 ( ! [X1 : u] : ((((^[Y0 : u]: (!! @ u @ (^[Y1 : u]: (!! @ d @ (^[Y2 : d]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y1)))) = (!! @ u @ (^[Y3 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y2 @ Y3) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y0)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y2 @ Y3) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y1))))))))))))) @ X1) = $true)) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f105])).
% 3.95/2.06 thf(f105,plain,(
% 3.95/2.06 ((!! @ u @ (^[Y0 : u]: (!! @ u @ (^[Y1 : u]: (!! @ d @ (^[Y2 : d]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y1)))) = (!! @ u @ (^[Y3 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y2 @ Y3) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y0)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y2 @ Y3) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y1)))))))))))))) = $true)),
% 3.95/2.06 inference(cnf_transformation,[status(thm)],[f81])).
% 3.95/2.06 thf(f81,plain,(
% 3.95/2.06 ((!! @ u @ (^[Y0 : u]: (!! @ u @ (^[Y1 : u]: (!! @ d @ (^[Y2 : d]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y1)))) = (!! @ u @ (^[Y3 : u]: ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y2 @ Y3) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y0)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y2 @ Y3) @ (s @ (tyop_2Emin_2Efun @ Y2 @ tyop_2Emin_2Ebool) @ Y1)))))))))))))) = $true)),
% 3.95/2.06 inference(fool_elimination,[status(thm)],[f80])).
% 3.95/2.06 thf(f80,plain,(
% 3.95/2.06 ! [X0 : d,X1 : u,X2 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))) <=> ! [X3 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))))),
% 3.95/2.06 inference(rectify,[status(thm)],[f30])).
% 3.95/2.06 thf(f30,axiom,(
% 3.95/2.06 ! [X0 : d,X16 : u,X15 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X16)))) <=> ! [X4 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15)))) => (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X16))))))),
% 3.95/2.06 file('/export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2THF_823.p',thm_2Epred__set_2ESUBSET__DEF)).
% 3.95/2.06 thf(f440,plain,(
% 3.95/2.06 ( ! [X2 : u,X0 : d,X1 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ (sK3 @ X0 @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)) @ X2)) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))) = $true)) )),
% 3.95/2.06 inference(trivial_inequality_removal,[status(thm)],[f438])).
% 3.95/2.06 thf(f438,plain,(
% 3.95/2.06 ( ! [X2 : u,X0 : d,X1 : u] : (($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ (sK3 @ X0 @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)) @ X2)) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2)))) = $true) | ($false = $true)) )),
% 3.95/2.06 inference(superposition,[status(thm)],[f415,f156])).
% 3.95/2.06 thf(f156,plain,(
% 3.95/2.06 ( ! [X2 : u,X3 : d,X1 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X3 @ (sK3 @ X3 @ X1 @ X2)) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1)))) = $true) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Epred__set_2ESUBSET_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X3 @ tyop_2Emin_2Ebool) @ X2)))) = $true)) )),
% 3.95/2.06 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 3.95/2.06 thf(f415,plain,(
% 3.95/2.06 ( ! [X2 : u,X0 : d,X1 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))) = $false) | ($true = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X2) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1)))))) )),
% 3.95/2.06 inference(superposition,[status(thm)],[f196,f140])).
% 3.95/2.06 thf(f140,plain,(
% 3.95/2.06 ( ! [X2 : d,X1 : u] : (((s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X2 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X1))))) = (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X1))))) )),
% 3.95/2.06 inference(equality_proxy_clausification,[status(thm)],[f139])).
% 3.95/2.06 thf(f139,plain,(
% 3.95/2.06 ( ! [X2 : d,X1 : u] : ((((s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X1))) = (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X2 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X1)))))) = $true)) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f138])).
% 3.95/2.06 thf(f138,plain,(
% 3.95/2.06 ( ! [X2 : d,X1 : u] : ((((^[Y0 : d]: ((s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1))) = (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ Y0 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1))))))) @ X2) = $true)) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f137])).
% 3.95/2.06 thf(f137,plain,(
% 3.95/2.06 ( ! [X1 : u] : (($true = (!! @ d @ (^[Y0 : d]: ((s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1))) = (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ Y0 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ X1)))))))))) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f136])).
% 3.95/2.06 thf(f136,plain,(
% 3.95/2.06 ( ! [X1 : u] : (($true = ((^[Y0 : u]: (!! @ d @ (^[Y1 : d]: ((s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))) = (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0) @ (s @ Y1 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))))))))) @ X1))) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f102])).
% 3.95/2.06 thf(f102,plain,(
% 3.95/2.06 ($true = (!! @ u @ (^[Y0 : u]: (!! @ d @ (^[Y1 : d]: ((s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))) = (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0) @ (s @ Y1 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0)))))))))))),
% 3.95/2.06 inference(cnf_transformation,[status(thm)],[f71])).
% 3.95/2.06 thf(f71,plain,(
% 3.95/2.06 ($true = (!! @ u @ (^[Y0 : u]: (!! @ d @ (^[Y1 : d]: ((s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0))) = (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0) @ (s @ Y1 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y0)))))))))))),
% 3.95/2.06 inference(fool_elimination,[status(thm)],[f70])).
% 3.95/2.06 thf(f70,plain,(
% 3.95/2.06 ! [X0 : d,X1 : u] : ((s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))) = (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ X0 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1))))))),
% 3.95/2.06 inference(rectify,[status(thm)],[f32])).
% 3.95/2.06 thf(f32,axiom,(
% 3.95/2.06 ! [X0 : d,X15 : u] : ((s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EREST_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))) = (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ X0 @ (c_2Epred__set_2ECHOICE_2E1 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))))))),
% 3.95/2.06 file('/export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2THF_823.p',thm_2Epred__set_2EREST__DEF)).
% 3.95/2.06 thf(f196,plain,(
% 3.95/2.06 ( ! [X2 : d,X3 : u,X1 : u,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X2 @ X3)))))) = $false) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X4)))) = $true)) )),
% 3.95/2.06 inference(binary_proxy_clausification,[status(thm)],[f191])).
% 3.95/2.06 thf(f191,plain,(
% 3.95/2.06 ( ! [X2 : d,X3 : u,X1 : u,X4 : u] : (($true = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X4)))) & (~ ((s @ X2 @ X3) = (s @ X2 @ X1))))) | ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X2 @ X3)))))) = $false)) )),
% 3.95/2.06 inference(binary_proxy_clausification,[status(thm)],[f189])).
% 3.95/2.06 thf(f189,plain,(
% 3.95/2.06 ( ! [X2 : d,X3 : u,X1 : u,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X2 @ X3)))))) = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X4)))) & (~ ((s @ X2 @ X3) = (s @ X2 @ X1)))))) )),
% 3.95/2.06 inference(binary_proxy_clausification,[status(thm)],[f188])).
% 3.95/2.06 thf(f188,plain,(
% 3.95/2.06 ( ! [X2 : d,X3 : u,X1 : u,X4 : u] : (($true = (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X4)))) & (~ ((s @ X2 @ X3) = (s @ X2 @ X1)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X4) @ (s @ X2 @ X3))))))))) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f187])).
% 3.95/2.06 thf(f187,plain,(
% 3.95/2.06 ( ! [X2 : d,X3 : u,X1 : u,X4 : u] : ((((^[Y0 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ Y0)))) & (~ ((s @ X2 @ X3) = (s @ X2 @ X1)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ Y0) @ (s @ X2 @ X3)))))))) @ X4) = $true)) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f186])).
% 3.95/2.06 thf(f186,plain,(
% 3.95/2.06 ( ! [X2 : d,X3 : u,X1 : u] : (((!! @ u @ (^[Y0 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ Y0)))) & (~ ((s @ X2 @ X3) = (s @ X2 @ X1)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ Y0) @ (s @ X2 @ X3))))))))) = $true)) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f185])).
% 3.95/2.06 thf(f185,plain,(
% 3.95/2.06 ( ! [X2 : d,X3 : u,X1 : u] : ((((^[Y0 : u]: (!! @ u @ (^[Y1 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ Y1)))) & (~ ((s @ X2 @ Y0) = (s @ X2 @ X1)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ Y1) @ (s @ X2 @ Y0)))))))))) @ X3) = $true)) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f184])).
% 3.95/2.06 thf(f184,plain,(
% 3.95/2.06 ( ! [X2 : d,X1 : u] : (((!! @ u @ (^[Y0 : u]: (!! @ u @ (^[Y1 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ Y1)))) & (~ ((s @ X2 @ Y0) = (s @ X2 @ X1)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ Y1) @ (s @ X2 @ Y0))))))))))) = $true)) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f183])).
% 3.95/2.06 thf(f183,plain,(
% 3.95/2.06 ( ! [X2 : d,X1 : u] : (($true = ((^[Y0 : d]: (!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y0 @ X1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ Y2)))) & (~ ((s @ Y0 @ Y1) = (s @ Y0 @ X1)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y0 @ X1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ Y2) @ (s @ Y0 @ Y1)))))))))))) @ X2))) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f182])).
% 3.95/2.06 thf(f182,plain,(
% 3.95/2.06 ( ! [X1 : u] : (((!! @ d @ (^[Y0 : d]: (!! @ u @ (^[Y1 : u]: (!! @ u @ (^[Y2 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y0 @ X1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ Y2)))) & (~ ((s @ Y0 @ Y1) = (s @ Y0 @ X1)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y0 @ X1) @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y0 @ tyop_2Emin_2Ebool) @ Y2) @ (s @ Y0 @ Y1))))))))))))) = $true)) )),
% 3.95/2.06 inference(beta_eta_normalization,[status(thm)],[f181])).
% 3.95/2.06 thf(f181,plain,(
% 3.95/2.06 ( ! [X1 : u] : ((((^[Y0 : u]: (!! @ d @ (^[Y1 : d]: (!! @ u @ (^[Y2 : u]: (!! @ u @ (^[Y3 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y3)))) & (~ ((s @ Y1 @ Y2) = (s @ Y1 @ Y0)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y3) @ (s @ Y1 @ Y2)))))))))))))) @ X1) = $true)) )),
% 3.95/2.06 inference(pi_clausification,[status(thm)],[f106])).
% 3.95/2.06 thf(f106,plain,(
% 3.95/2.06 ((!! @ u @ (^[Y0 : u]: (!! @ d @ (^[Y1 : d]: (!! @ u @ (^[Y2 : u]: (!! @ u @ (^[Y3 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y3)))) & (~ ((s @ Y1 @ Y2) = (s @ Y1 @ Y0)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y3) @ (s @ Y1 @ Y2))))))))))))))) = $true)),
% 3.95/2.06 inference(cnf_transformation,[status(thm)],[f55])).
% 3.95/2.06 thf(f55,plain,(
% 3.95/2.06 ((!! @ u @ (^[Y0 : u]: (!! @ d @ (^[Y1 : d]: (!! @ u @ (^[Y2 : u]: (!! @ u @ (^[Y3 : u]: (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y3)))) & (~ ((s @ Y1 @ Y2) = (s @ Y1 @ Y0)))) = (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ Y1 @ Y0) @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ Y1 @ tyop_2Emin_2Ebool) @ Y3) @ (s @ Y1 @ Y2))))))))))))))) = $true)),
% 3.95/2.06 inference(fool_elimination,[status(thm)],[f54])).
% 3.95/2.06 thf(f54,plain,(
% 3.95/2.06 ! [X0 : u,X1 : u,X2 : d,X3 : u] : (((~ ((s @ X2 @ X1) = (s @ X2 @ X3))) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X2 @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0) @ (s @ X2 @ X1)))))))),
% 3.95/2.06 inference(rectify,[status(thm)],[f31])).
% 3.95/2.06 thf(f31,axiom,(
% 3.95/2.06 ! [X15 : u,X17 : u,X0 : d,X12 : u] : (((~ ((s @ X0 @ X12) = (s @ X0 @ X17))) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X12) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15))))) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ebool_2EIN_2E2 @ (s @ X0 @ X12) @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (c_2Epred__set_2EDELETE_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X15) @ (s @ X0 @ X17)))))))),
% 3.95/2.06 file('/export/starexec/sandbox/tmp/tmp.JW7agi5u0W/DTF2THF_823.p',thm_2Epred__set_2EIN__DELETE)).
% 3.95/2.06 % SZS output end Proof for DTF2THF_823
% 3.95/2.06 % (970)------------------------------
% 3.95/2.06 % (970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.95/2.06 % (970)Termination reason: Refutation
% 3.95/2.06
% 3.95/2.06 % (970)Memory used [KB]: 6396
% 3.95/2.06 % (970)Time elapsed: 0.135 s
% 3.95/2.06 % (970)Instructions burned: 200 (million)
% 3.95/2.06 % (970)------------------------------
% 3.95/2.06 % (970)------------------------------
% 3.95/2.06 % (930)Success in time 0.26 s
%------------------------------------------------------------------------------