%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP019^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 08:54:06 AM UTC 2026
% Result : Theorem 1.97s 1.35s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 49 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 99 ( 31 ~; 4 |; 5 &; 52 @)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 22 con; 0-3 aty)
% Number of variables : 10 ( 0 ^; 8 !; 2 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(type_def_9,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(type_def_10,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(func_def_4,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(func_def_5,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_6,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_7,type,
tyop_2Enum_2Enum: d ).
thf(func_def_8,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(func_def_9,type,
tyop_2Erealax_2Ereal: d ).
thf(func_def_10,type,
s: d > u > du ).
thf(func_def_11,type,
app_2E2: du > du > u ).
thf(func_def_12,type,
combin_i_2E0: u ).
thf(func_def_13,type,
combin_k_2E0: u ).
thf(func_def_14,type,
combin_s_2E0: u ).
thf(func_def_15,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_16,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_17,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_18,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_19,type,
c_2Enum_2E0_2E0: u ).
thf(func_def_20,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_21,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_22,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_23,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_24,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_25,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_26,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_27,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_28,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_29,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_30,type,
c_2Ecomplex_2Ecomplex__inv_2E0: u ).
thf(func_def_31,type,
c_2Ecomplex_2Ecomplex__inv_2E1: du > u ).
thf(func_def_32,type,
c_2Ecomplex_2Ecomplex__of__num_2E0: u ).
thf(func_def_33,type,
c_2Ecomplex_2Ecomplex__of__num_2E1: du > u ).
thf(func_def_34,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_35,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_36,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_37,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_38,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_39,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_40,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_41,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(func_def_42,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_45,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_46,type,
mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_47,type,
mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_48,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_49,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_50,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_51,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_52,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
thf(func_def_53,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
thf(func_def_54,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(func_def_55,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
thf(func_def_56,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_57,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_58,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_59,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_60,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_61,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(func_def_62,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_68,type,
sK0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(f93,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f92,f90]) ).
thf(f90,plain,
( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= sK0 ),
inference(equality_proxy_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= sK0 ) ),
inference(not_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true
!= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0 ) ) )
& ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f73,f74]) ).
thf(f74,plain,
( ? [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( $true
!= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 ) ) )
& ( $true
= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= X0 ) ) )
=> ( ( $true
!= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0 ) ) )
& ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f73,plain,
? [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( $true
!= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 ) ) )
& ( $true
= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f61]) ).
thf(f61,plain,
~ ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( $true
= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= X0 ) )
=> ( $true
= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f60]) ).
thf(f60,plain,
~ ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= X0 )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,negated_conjecture,
~ ! [X16: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= X16 )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X16 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f41,conjecture,
! [X16: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= X16 )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X16 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OB2tIq8qel/DTF2THF_9785.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(f92,plain,
( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= sK0 ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= sK0 )
| ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(superposition,[status(thm)],[f84,f88]) ).
thf(f88,plain,
( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( $true
= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( $true
!= ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
thf(f84,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 ) )
| ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= X0 ) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= X0 )
| ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 ) ) )
& ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 ) )
| ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
!= X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= X0 )
<=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,axiom,
! [X16: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
= X16 )
<=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X16 )
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OB2tIq8qel/DTF2THF_9785.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP019^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n008.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 08:22:09 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : ITP019^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.30/0.45 % Domain : Interactive Theorem Proving
% 0.30/0.45 % Problem : HOL4 syntactic export of thm_2Ecomplex_2ECOMPLEX__INV__NZ.p, bushy mode
% 0.30/0.45 % Version : [BG+19] axioms.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.30/0.45 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [BG+19]
% 0.30/0.45 % Names : thm_2Ecomplex_2ECOMPLEX__INV__NZ.p [Gau19]
% 0.30/0.45 % : HL409001^1.p [TPAP]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0
% 0.30/0.45 % Syntax : Number of formulae : 104 ( 31 unt; 63 typ; 0 def)
% 0.30/0.45 % Number of atoms : 67 ( 35 equ; 4 cnn)
% 0.30/0.45 % Maximal formula atoms : 8 ( 1 avg)
% 0.30/0.45 % Number of connectives : 558 ( 4 ~; 1 |; 5 &; 525 @)
% 0.30/0.45 % ( 15 <=>; 8 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 17 ( 4 avg)
% 0.30/0.45 % Number of types : 6 ( 5 usr)
% 0.30/0.45 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 60 ( 58 usr; 22 con; 0-3 aty)
% 0.30/0.45 % Number of variables : 76 ( 0 ^; 75 !; 1 ?; 76 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments :
% 0.30/0.45 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(u,type,
% 0.30/0.45 u: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(d,type,
% 0.30/0.45 d: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(du,type,
% 0.30/0.45 du: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Etyop_2Enum_2Enum,type,
% 0.30/0.45 mono_2Etyop_2Enum_2Enum: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.30/0.45 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(tyop_2Emin_2Ebool,type,
% 0.30/0.45 tyop_2Emin_2Ebool: d ).
% 0.30/0.45
% 0.30/0.45 thf(tyop_2Emin_2Efun,type,
% 0.30/0.45 tyop_2Emin_2Efun: d > d > d ).
% 0.30/0.45
% 0.30/0.45 thf(tyop_2Enum_2Enum,type,
% 0.30/0.45 tyop_2Enum_2Enum: d ).
% 0.30/0.45
% 0.30/0.45 thf(tyop_2Epair_2Eprod,type,
% 0.30/0.45 tyop_2Epair_2Eprod: d > d > d ).
% 0.30/0.45
% 0.30/0.45 thf(tyop_2Erealax_2Ereal,type,
% 0.30/0.45 tyop_2Erealax_2Ereal: d ).
% 0.30/0.45
% 0.30/0.45 thf(s,type,
% 0.30/0.45 s: d > u > du ).
% 0.30/0.45
% 0.30/0.45 thf(app_2E2,type,
% 0.30/0.45 app_2E2: du > du > u ).
% 0.30/0.45
% 0.30/0.45 thf(combin_i_2E0,type,
% 0.30/0.45 combin_i_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(combin_k_2E0,type,
% 0.30/0.45 combin_k_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(combin_s_2E0,type,
% 0.30/0.45 combin_s_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_21_2E0,type,
% 0.30/0.45 c_2Ebool_2E_21_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_21_2E1,type,
% 0.30/0.45 c_2Ebool_2E_21_2E1: du > u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.30/0.45 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.30/0.45 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Enum_2E0_2E0,type,
% 0.30/0.45 c_2Enum_2E0_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Emin_2E_3D_2E0,type,
% 0.30/0.45 c_2Emin_2E_3D_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Emin_2E_3D_2E2,type,
% 0.30/0.45 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.30/0.45 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.30/0.45 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_3F_2E0,type,
% 0.30/0.45 c_2Ebool_2E_3F_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_3F_2E1,type,
% 0.30/0.45 c_2Ebool_2E_3F_2E1: du > u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2EF_2E0,type,
% 0.30/0.45 c_2Ebool_2EF_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2ET_2E0,type,
% 0.30/0.45 c_2Ebool_2ET_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.30/0.45 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.30/0.45 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ecomplex_2Ecomplex__inv_2E0,type,
% 0.30/0.45 c_2Ecomplex_2Ecomplex__inv_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ecomplex_2Ecomplex__inv_2E1,type,
% 0.30/0.45 c_2Ecomplex_2Ecomplex__inv_2E1: du > u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ecomplex_2Ecomplex__of__num_2E0,type,
% 0.30/0.45 c_2Ecomplex_2Ecomplex__of__num_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ecomplex_2Ecomplex__of__num_2E1,type,
% 0.30/0.45 c_2Ecomplex_2Ecomplex__of__num_2E1: du > u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_7E_2E0,type,
% 0.30/0.45 c_2Ebool_2E_7E_2E0: u ).
% 0.30/0.45
% 0.30/0.45 thf(c_2Ebool_2E_7E_2E1,type,
% 0.30/0.45 c_2Ebool_2E_7E_2E1: du > u ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.30/0.45 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.30/0.45 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.30/0.45 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.30/0.45 mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.30/0.45 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Enum_2E0,type,
% 0.30/0.45 mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.30/0.45 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Ebool_2EF,type,
% 0.30/0.45 mono_2Ec_2Ebool_2EF: $o ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Ebool_2ET,type,
% 0.30/0.45 mono_2Ec_2Ebool_2ET: $o ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.30/0.45 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Ecomplex_2Ecomplex__inv,type,
% 0.30/0.45 mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num,type,
% 0.30/0.45 mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.30/0.45
% 0.30/0.45 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.30/0.45 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.30/0.45 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.30/0.45
% 0.30/0.45 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.30/0.45 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.30/0.45
% 0.30/0.45 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.30/0.45 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.30/0.45
% 0.30/0.45 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.30/0.45 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
% 0.30/0.45
% 0.30/0.45 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.30/0.45 i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
% 0.30/0.45
% 0.30/0.45 thf(i_mono_2Etyop_2Enum_2Enum,type,
% 0.30/0.45 i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
% 0.30/0.45
% 0.30/0.45 thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.30/0.45 i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
% 0.30/0.45
% 0.30/0.45 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.30/0.45 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.30/0.45
% 0.30/0.45 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.30/0.45 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.30/0.45 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.30/0.45 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.30/0.45
% 0.30/0.45 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.30/0.45 j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.30/0.45
% 0.30/0.45 thf(j_mono_2Etyop_2Enum_2Enum,type,
% 0.30/0.45 j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
% 0.30/0.45
% 0.30/0.45 thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.30/0.45 j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.30/0.45 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.30/0.45 ( ! [V2x_2E0: u] :
% 0.30/0.45 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.30/0.45 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.30/0.45 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.30/0.45 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.30/0.45 ! [A_27a: d,V0x_2E0: u] :
% 0.30/0.45 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.30/0.45 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.30/0.45 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.30/0.45 ( ( 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 ) ) )
% 0.30/0.45 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Eho_2Es__thm,axiom,
% 0.30/0.45 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.30/0.45 ( ( 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 ) ) )
% 0.30/0.45 = ( 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 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.30/0.45 ! [V0: $o,V1: $o] :
% 0.30/0.45 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.30/0.45 <=> ( V0
% 0.30/0.45 & V1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.30/0.45 ! [V0: $o,V1: $o] :
% 0.30/0.45 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.30/0.45 <=> ( V0
% 0.30/0.45 | V1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Elogic_2E_7E,axiom,
% 0.30/0.45 ! [V0: $o] :
% 0.30/0.45 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.30/0.45 <=> ( (~) @ V0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.30/0.45 ! [V0: $o,V1: $o] :
% 0.30/0.45 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.30/0.45 <=> ( V0
% 0.30/0.45 => V1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Elogic_2E_3D,axiom,
% 0.30/0.45 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.30/0.45 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.30/0.45 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.30/0.45 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Equant_2E_21,axiom,
% 0.30/0.45 ! [A_27a: d,V0f_2E0: u] :
% 0.30/0.45 ( ( 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 ) ) ) )
% 0.30/0.45 <=> ! [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 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(reserved_2Equant_2E_3F,axiom,
% 0.30/0.45 ! [A_27a: d,V0f_2E0: u] :
% 0.30/0.45 ( ( 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 ) ) ) )
% 0.30/0.45 <=> ? [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 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.30/0.45 ! [V0_2E0: u] :
% 0.30/0.45 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.30/0.45 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.30/0.45 ! [V0_2E0: u] :
% 0.30/0.45 ( ( 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 ) ) ) )
% 0.30/0.45 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.30/0.45 ! [V0_2E0: u] :
% 0.30/0.45 ( ( 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 ) ) ) )
% 0.30/0.45 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.30/0.45 ! [V0_2E0: u] :
% 0.30/0.45 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
% 0.30/0.45 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.30/0.45 ! [V0_2E0: u] :
% 0.30/0.45 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
% 0.30/0.45 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
% 0.30/0.45 ! [V0_2E0: u] :
% 0.30/0.45 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
% 0.30/0.45 = ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.30/0.45 ! [V0_2E0: u] :
% 0.30/0.45 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
% 0.30/0.45 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.30/0.45 ! [V0: $o] :
% 0.30/0.45 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.30/0.45 = V0 ) ).
% 0.30/0.45
% 0.30/0.45 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.30/0.45 ! [V0: $o > $o] :
% 0.30/0.45 ( ( 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 ) ) )
% 0.30/0.45 = V0 ) ).
% 0.30/0.45
% 0.30/0.45 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.30/0.45 ! [V0: $o > $o > $o] :
% 0.30/0.45 ( ( 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 ) ) )
% 0.30/0.45 = V0 ) ).
% 0.30/0.45
% 0.30/0.45 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.30/0.45 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.30/0.45 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
% 0.30/0.45 = V0 ) ).
% 0.30/0.45
% 0.30/0.45 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.30/0.45 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.30/0.45 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
% 0.30/0.45 = V0 ) ).
% 0.30/0.45
% 0.30/0.45 thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
% 0.30/0.45 ! [V0: mono_2Etyop_2Enum_2Enum] :
% 0.30/0.45 ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
% 0.30/0.45 = V0 ) ).
% 0.30/0.45
% 0.30/0.45 thf(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.30/0.45 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.30/0.45 ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
% 0.30/0.45 = V0 ) ).
% 0.30/0.45
% 0.30/0.45 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.30/0.45 ! [A_27a: d,X0_2E0: u] :
% 0.30/0.45 ( ( 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 ) ) ) )
% 0.30/0.45 = ( 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 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.30/0.45 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.30/0.45 ( ( ( s @ A_27a @ X0_2E0 )
% 0.30/0.45 = ( s @ A_27a @ X1_2E0 ) )
% 0.30/0.45 <=> ( 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 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.30/0.45 ! [A_27a: d,X0_2E0: u] :
% 0.30/0.45 ( ( 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 ) ) ) )
% 0.30/0.45 = ( 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 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.30/0.45 ! [V0: $o > $o,V1: $o] :
% 0.30/0.45 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.30/0.45 = ( 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 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.30/0.45 ! [V0: $o > $o > $o,V1: $o] :
% 0.30/0.45 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.30/0.45 = ( 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 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.30/0.45 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Enum_2Enum] :
% 0.30/0.45 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
% 0.30/0.45 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.30/0.45 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.30/0.45 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
% 0.30/0.45 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.30/0.45 ! [V0: $o > $o,V1: $o] :
% 0.30/0.45 ( ( V0 @ V1 )
% 0.30/0.45 = ( V0 @ V1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.30/0.45 ! [V0: $o > $o > $o,V1: $o] :
% 0.30/0.45 ( ( V0 @ V1 )
% 0.30/0.45 = ( V0 @ V1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.30/0.45 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Enum_2Enum] :
% 0.30/0.45 ( ( V0 @ V1 )
% 0.30/0.45 = ( V0 @ V1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.30/0.45 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.30/0.45 ( ( V0 @ V1 )
% 0.30/0.45 = ( V0 @ V1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.30/0.45 mono_2Ec_2Ebool_2ET ).
% 0.30/0.45
% 0.30/0.45 thf(thm_2Ebool_2EFORALL__SIMP,axiom,
% 0.30/0.45 ! [A_27a: d,V0t: $o] :
% 0.30/0.45 ( ! [V1x_2E0: u] : V0t
% 0.30/0.45 <=> V0t ) ).
% 0.30/0.45
% 0.30/0.45 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.30/0.45 ! [V0t: $o] :
% 0.30/0.45 ( ( ( mono_2Ec_2Ebool_2ET
% 0.30/0.45 => V0t )
% 0.30/0.45 <=> V0t )
% 0.30/0.45 & ( ( V0t
% 0.30/0.45 => mono_2Ec_2Ebool_2ET )
% 0.30/0.45 <=> mono_2Ec_2Ebool_2ET )
% 0.30/0.45 & ( ( mono_2Ec_2Ebool_2EF
% 0.30/0.45 => V0t )
% 0.30/0.45 <=> mono_2Ec_2Ebool_2ET )
% 0.30/0.45 & ( ( V0t
% 0.30/0.45 => V0t )
% 0.30/0.45 <=> mono_2Ec_2Ebool_2ET )
% 0.30/0.45 & ( ( V0t
% 0.30/0.45 => mono_2Ec_2Ebool_2EF )
% 0.30/0.45 <=> ( (~) @ V0t ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
% 0.30/0.45 ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.30/0.45 ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
% 0.30/0.45 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
% 0.30/0.45 <=> ( V0z
% 0.30/0.45 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
% 0.30/0.45 ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.30/0.45 ( ( (~)
% 0.30/0.45 @ ( V0z
% 0.30/0.45 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
% 0.30/0.45 => ( (~)
% 0.30/0.45 @ ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
% 0.30/0.45 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.97/1.31 ---- Embedded in THF ---
% 1.97/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.97/1.31 %%% Generated on Tue Feb 24 08:22:10 EST 2026
% 1.97/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.97/1.31 %%% Logic specification used:
% 1.97/1.31 %%% thf(spec, logic, $$dhol).
% 1.97/1.31
% 1.97/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.OB2tIq8qel/DTF2DTF9785.p
% See solution above
% 1.97/1.31 ------------------------
% 1.97/1.33 ---- Cleaned THF ---
% 1.97/1.33 thf(u,type,
% 1.97/1.33 u: $tType ).
% 1.97/1.33
% 1.97/1.33 thf(d,type,
% 1.97/1.33 d: $tType ).
% 1.97/1.33
% 1.97/1.33 thf(du,type,
% 1.97/1.33 du: $tType ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Etyop_2Enum_2Enum,type,
% 1.97/1.33 mono_2Etyop_2Enum_2Enum: $tType ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 1.97/1.33 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
% 1.97/1.33
% 1.97/1.33 thf(tyop_2Emin_2Ebool,type,
% 1.97/1.33 tyop_2Emin_2Ebool: d ).
% 1.97/1.33
% 1.97/1.33 thf(tyop_2Emin_2Efun,type,
% 1.97/1.33 tyop_2Emin_2Efun: d > d > d ).
% 1.97/1.33
% 1.97/1.33 thf(tyop_2Enum_2Enum,type,
% 1.97/1.33 tyop_2Enum_2Enum: d ).
% 1.97/1.33
% 1.97/1.33 thf(tyop_2Epair_2Eprod,type,
% 1.97/1.33 tyop_2Epair_2Eprod: d > d > d ).
% 1.97/1.33
% 1.97/1.33 thf(tyop_2Erealax_2Ereal,type,
% 1.97/1.33 tyop_2Erealax_2Ereal: d ).
% 1.97/1.33
% 1.97/1.33 thf(s,type,
% 1.97/1.33 s: d > u > du ).
% 1.97/1.33
% 1.97/1.33 thf(app_2E2,type,
% 1.97/1.33 app_2E2: du > du > u ).
% 1.97/1.33
% 1.97/1.33 thf(combin_i_2E0,type,
% 1.97/1.33 combin_i_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(combin_k_2E0,type,
% 1.97/1.33 combin_k_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(combin_s_2E0,type,
% 1.97/1.33 combin_s_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_21_2E0,type,
% 1.97/1.33 c_2Ebool_2E_21_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_21_2E1,type,
% 1.97/1.33 c_2Ebool_2E_21_2E1: du > u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 1.97/1.33 c_2Ebool_2E_2F_5C_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 1.97/1.33 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Enum_2E0_2E0,type,
% 1.97/1.33 c_2Enum_2E0_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Emin_2E_3D_2E0,type,
% 1.97/1.33 c_2Emin_2E_3D_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Emin_2E_3D_2E2,type,
% 1.97/1.33 c_2Emin_2E_3D_2E2: du > du > u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 1.97/1.33 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 1.97/1.33 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_3F_2E0,type,
% 1.97/1.33 c_2Ebool_2E_3F_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_3F_2E1,type,
% 1.97/1.33 c_2Ebool_2E_3F_2E1: du > u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2EF_2E0,type,
% 1.97/1.33 c_2Ebool_2EF_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2ET_2E0,type,
% 1.97/1.33 c_2Ebool_2ET_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 1.97/1.33 c_2Ebool_2E_5C_2F_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 1.97/1.33 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ecomplex_2Ecomplex__inv_2E0,type,
% 1.97/1.33 c_2Ecomplex_2Ecomplex__inv_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ecomplex_2Ecomplex__inv_2E1,type,
% 1.97/1.33 c_2Ecomplex_2Ecomplex__inv_2E1: du > u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ecomplex_2Ecomplex__of__num_2E0,type,
% 1.97/1.33 c_2Ecomplex_2Ecomplex__of__num_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ecomplex_2Ecomplex__of__num_2E1,type,
% 1.97/1.33 c_2Ecomplex_2Ecomplex__of__num_2E1: du > u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_7E_2E0,type,
% 1.97/1.33 c_2Ebool_2E_7E_2E0: u ).
% 1.97/1.33
% 1.97/1.33 thf(c_2Ebool_2E_7E_2E1,type,
% 1.97/1.33 c_2Ebool_2E_7E_2E1: du > u ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 1.97/1.33 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 1.97/1.33 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 1.97/1.33 mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 1.97/1.33 mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 1.97/1.33 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Enum_2E0,type,
% 1.97/1.33 mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 1.97/1.33 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Ebool_2EF,type,
% 1.97/1.33 mono_2Ec_2Ebool_2EF: $o ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Ebool_2ET,type,
% 1.97/1.33 mono_2Ec_2Ebool_2ET: $o ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 1.97/1.33 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Ecomplex_2Ecomplex__inv,type,
% 1.97/1.33 mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num,type,
% 1.97/1.33 mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 1.97/1.33
% 1.97/1.33 thf(mono_2Ec_2Ebool_2E_7E,type,
% 1.97/1.33 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 1.97/1.33
% 1.97/1.33 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 1.97/1.33 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 1.97/1.33
% 1.97/1.33 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 1.97/1.33 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 1.97/1.33
% 1.97/1.33 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 1.97/1.33 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 1.97/1.33
% 1.97/1.33 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 1.97/1.33 i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
% 1.97/1.33
% 1.97/1.33 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 1.97/1.33 i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
% 1.97/1.33
% 1.97/1.33 thf(i_mono_2Etyop_2Enum_2Enum,type,
% 1.97/1.33 i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
% 1.97/1.33
% 1.97/1.33 thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 1.97/1.33 i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
% 1.97/1.33
% 1.97/1.33 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 1.97/1.33 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 1.97/1.33
% 1.97/1.33 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 1.97/1.33 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 1.97/1.33
% 1.97/1.33 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 1.97/1.33 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 1.97/1.33
% 1.97/1.33 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 1.97/1.33 j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 1.97/1.33
% 1.97/1.33 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 1.97/1.33 j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 1.97/1.33
% 1.97/1.33 thf(j_mono_2Etyop_2Enum_2Enum,type,
% 1.97/1.33 j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
% 1.97/1.33
% 1.97/1.33 thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 1.97/1.33 j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Eho_2Eeq__ext,axiom,
% 1.97/1.33 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 1.97/1.33 ( ! [V2x_2E0: u] :
% 1.97/1.33 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 1.97/1.33 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 1.97/1.33 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 1.97/1.33 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Eho_2Ei__thm,axiom,
% 1.97/1.33 ! [A_27a: d,V0x_2E0: u] :
% 1.97/1.33 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 1.97/1.33 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Eho_2Ek__thm,axiom,
% 1.97/1.33 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 1.97/1.33 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 1.97/1.33 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Eho_2Es__thm,axiom,
% 1.97/1.33 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 1.97/1.33 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 1.97/1.33 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 1.97/1.33 ! [V0: $o,V1: $o] :
% 1.97/1.33 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 1.97/1.33 <=> ( V0
% 1.97/1.33 & V1 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 1.97/1.33 ! [V0: $o,V1: $o] :
% 1.97/1.33 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 1.97/1.33 <=> ( V0
% 1.97/1.33 | V1 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Elogic_2E_7E,axiom,
% 1.97/1.33 ! [V0: $o] :
% 1.97/1.33 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 1.97/1.33 <=> ( (~) @ V0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 1.97/1.33 ! [V0: $o,V1: $o] :
% 1.97/1.33 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 1.97/1.33 <=> ( V0
% 1.97/1.33 => V1 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Elogic_2E_3D,axiom,
% 1.97/1.33 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 1.97/1.33 <=> ( ( s @ A_27a @ V0_2E0 )
% 1.97/1.33 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Equant_2E_21,axiom,
% 1.97/1.33 ! [A_27a: d,V0f_2E0: u] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 1.97/1.33 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(reserved_2Equant_2E_3F,axiom,
% 1.97/1.33 ! [A_27a: d,V0f_2E0: u] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 1.97/1.33 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 1.97/1.33 ! [V0_2E0: u] :
% 1.97/1.33 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 1.97/1.33 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 1.97/1.33 ! [V0_2E0: u] :
% 1.97/1.33 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 1.97/1.33 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 1.97/1.33 ! [V0_2E0: u] :
% 1.97/1.33 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 1.97/1.33 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 1.97/1.33 ! [V0_2E0: u] :
% 1.97/1.33 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
% 1.97/1.33 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 1.97/1.33 ! [V0_2E0: u] :
% 1.97/1.33 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
% 1.97/1.33 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
% 1.97/1.33 ! [V0_2E0: u] :
% 1.97/1.33 ( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
% 1.97/1.33 = ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 1.97/1.33 ! [V0_2E0: u] :
% 1.97/1.33 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
% 1.97/1.33 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 1.97/1.33 ! [V0: $o] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 1.97/1.33 = V0 ) ).
% 1.97/1.33
% 1.97/1.33 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 1.97/1.33 ! [V0: $o > $o] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 1.97/1.33 = V0 ) ).
% 1.97/1.33
% 1.97/1.33 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 1.97/1.33 ! [V0: $o > $o > $o] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 1.97/1.33 = V0 ) ).
% 1.97/1.33
% 1.97/1.33 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 1.97/1.33 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
% 1.97/1.33 = V0 ) ).
% 1.97/1.33
% 1.97/1.33 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 1.97/1.33 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
% 1.97/1.33 = V0 ) ).
% 1.97/1.33
% 1.97/1.33 thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
% 1.97/1.33 ! [V0: mono_2Etyop_2Enum_2Enum] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
% 1.97/1.33 = V0 ) ).
% 1.97/1.33
% 1.97/1.33 thf(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 1.97/1.33 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
% 1.97/1.33 = V0 ) ).
% 1.97/1.33
% 1.97/1.33 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 1.97/1.33 ! [A_27a: d,X0_2E0: u] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 1.97/1.33 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 1.97/1.33 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 1.97/1.33 ( ( ( s @ A_27a @ X0_2E0 )
% 1.97/1.33 = ( s @ A_27a @ X1_2E0 ) )
% 1.97/1.33 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 1.97/1.33 ! [A_27a: d,X0_2E0: u] :
% 1.97/1.33 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 1.97/1.33 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 1.97/1.33 ! [V0: $o > $o,V1: $o] :
% 1.97/1.33 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 1.97/1.33 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 1.97/1.33 ! [V0: $o > $o > $o,V1: $o] :
% 1.97/1.33 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 1.97/1.33 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 1.97/1.33 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Enum_2Enum] :
% 1.97/1.33 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
% 1.97/1.33 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 1.97/1.33 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 1.97/1.33 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
% 1.97/1.33 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V1 ) ) ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 1.97/1.33 ! [V0: $o > $o,V1: $o] :
% 1.97/1.33 ( ( V0 @ V1 )
% 1.97/1.33 = ( V0 @ V1 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 1.97/1.33 ! [V0: $o > $o > $o,V1: $o] :
% 1.97/1.33 ( ( V0 @ V1 )
% 1.97/1.33 = ( V0 @ V1 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 1.97/1.33 ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Enum_2Enum] :
% 1.97/1.33 ( ( V0 @ V1 )
% 1.97/1.33 = ( V0 @ V1 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 1.97/1.33 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 1.97/1.33 ( ( V0 @ V1 )
% 1.97/1.33 = ( V0 @ V1 ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(thm_2Ebool_2ETRUTH,axiom,
% 1.97/1.33 mono_2Ec_2Ebool_2ET ).
% 1.97/1.33
% 1.97/1.33 thf(thm_2Ebool_2EFORALL__SIMP,axiom,
% 1.97/1.33 ! [A_27a: d,V0t: $o] :
% 1.97/1.33 ( ! [V1x_2E0: u] : V0t
% 1.97/1.33 <=> V0t ) ).
% 1.97/1.33
% 1.97/1.33 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 1.97/1.33 ! [V0t: $o] :
% 1.97/1.33 ( ( ( mono_2Ec_2Ebool_2ET
% 1.97/1.33 => V0t )
% 1.97/1.33 <=> V0t )
% 1.97/1.33 & ( ( V0t
% 1.97/1.33 => mono_2Ec_2Ebool_2ET )
% 1.97/1.33 <=> mono_2Ec_2Ebool_2ET )
% 1.97/1.33 & ( ( mono_2Ec_2Ebool_2EF
% 1.97/1.33 => V0t )
% 1.97/1.33 <=> mono_2Ec_2Ebool_2ET )
% 1.97/1.33 & ( ( V0t
% 1.97/1.33 => V0t )
% 1.97/1.33 <=> mono_2Ec_2Ebool_2ET )
% 1.97/1.33 & ( ( V0t
% 1.97/1.33 => mono_2Ec_2Ebool_2EF )
% 1.97/1.33 <=> ( (~) @ V0t ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
% 1.97/1.33 ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 1.97/1.33 ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
% 1.97/1.33 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
% 1.97/1.33 <=> ( V0z
% 1.97/1.33 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
% 1.97/1.33
% 1.97/1.33 thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
% 1.97/1.33 ! [V0z: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 1.97/1.33 ( ( (~)
% 1.97/1.33 @ ( V0z
% 1.97/1.33 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
% 1.97/1.33 => ( (~)
% 1.97/1.33 @ ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ V0z )
% 1.97/1.33 = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
% 1.97/1.33 ------------------------
% 1.97/1.35 % (9929)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_9785 for (2999ds/275Mi)
% 1.97/1.35 % (9927)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9785 for (2999ds/2Mi)
% 1.97/1.35 % (9927)Instruction limit reached!
% 1.97/1.35 % (9927)------------------------------
% 1.97/1.35 % (9927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.35 % (9927)Termination reason: Unknown
% 1.97/1.35 % (9927)Termination phase: shuffling
% 1.97/1.35
% 1.97/1.35 % (9927)Memory used [KB]: 1023
% 1.97/1.35 % (9927)Time elapsed: 0.002 s
% 1.97/1.35 % (9927)Instructions burned: 2 (million)
% 1.97/1.35 % (9927)------------------------------
% 1.97/1.35 % (9927)------------------------------
% 1.97/1.35 % (9929)First to succeed.
% 1.97/1.35 % (9929)Refutation found. Thanks to Tanya!
% 1.97/1.35 % SZS status Theorem for DTF2THF_9785
% 1.97/1.35 % SZS output start Proof for DTF2THF_9785
% 1.97/1.35 thf(type_def_5, type, d: $tType).
% 1.97/1.35 thf(type_def_7, type, u: $tType).
% 1.97/1.35 thf(type_def_8, type, du: $tType).
% 1.97/1.35 thf(type_def_9, type, mono_2Etyop_2Enum_2Enum: $tType).
% 1.97/1.35 thf(type_def_10, type, mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType).
% 1.97/1.35 thf(func_def_0, type, u: $tType).
% 1.97/1.35 thf(func_def_1, type, d: $tType).
% 1.97/1.35 thf(func_def_2, type, du: $tType).
% 1.97/1.35 thf(func_def_3, type, mono_2Etyop_2Enum_2Enum: $tType).
% 1.97/1.35 thf(func_def_4, type, mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType).
% 1.97/1.35 thf(func_def_5, type, tyop_2Emin_2Ebool: d).
% 1.97/1.35 thf(func_def_6, type, tyop_2Emin_2Efun: d > d > d).
% 1.97/1.35 thf(func_def_7, type, tyop_2Enum_2Enum: d).
% 1.97/1.35 thf(func_def_8, type, tyop_2Epair_2Eprod: d > d > d).
% 1.97/1.35 thf(func_def_9, type, tyop_2Erealax_2Ereal: d).
% 1.97/1.35 thf(func_def_10, type, s: d > u > du).
% 1.97/1.35 thf(func_def_11, type, app_2E2: du > du > u).
% 1.97/1.35 thf(func_def_12, type, combin_i_2E0: u).
% 1.97/1.35 thf(func_def_13, type, combin_k_2E0: u).
% 1.97/1.35 thf(func_def_14, type, combin_s_2E0: u).
% 1.97/1.35 thf(func_def_15, type, c_2Ebool_2E_21_2E0: u).
% 1.97/1.35 thf(func_def_16, type, c_2Ebool_2E_21_2E1: du > u).
% 1.97/1.35 thf(func_def_17, type, c_2Ebool_2E_2F_5C_2E0: u).
% 1.97/1.35 thf(func_def_18, type, c_2Ebool_2E_2F_5C_2E2: du > du > u).
% 1.97/1.35 thf(func_def_19, type, c_2Enum_2E0_2E0: u).
% 1.97/1.35 thf(func_def_20, type, c_2Emin_2E_3D_2E0: u).
% 1.97/1.35 thf(func_def_21, type, c_2Emin_2E_3D_2E2: du > du > u).
% 1.97/1.35 thf(func_def_22, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 1.97/1.35 thf(func_def_23, type, c_2Emin_2E_3D_3D_3E_2E2: du > du > u).
% 1.97/1.35 thf(func_def_24, type, c_2Ebool_2E_3F_2E0: u).
% 1.97/1.35 thf(func_def_25, type, c_2Ebool_2E_3F_2E1: du > u).
% 1.97/1.35 thf(func_def_26, type, c_2Ebool_2EF_2E0: u).
% 1.97/1.35 thf(func_def_27, type, c_2Ebool_2ET_2E0: u).
% 1.97/1.35 thf(func_def_28, type, c_2Ebool_2E_5C_2F_2E0: u).
% 1.97/1.35 thf(func_def_29, type, c_2Ebool_2E_5C_2F_2E2: du > du > u).
% 1.97/1.35 thf(func_def_30, type, c_2Ecomplex_2Ecomplex__inv_2E0: u).
% 1.97/1.35 thf(func_def_31, type, c_2Ecomplex_2Ecomplex__inv_2E1: du > u).
% 1.97/1.35 thf(func_def_32, type, c_2Ecomplex_2Ecomplex__of__num_2E0: u).
% 1.97/1.35 thf(func_def_33, type, c_2Ecomplex_2Ecomplex__of__num_2E1: du > u).
% 1.97/1.35 thf(func_def_34, type, c_2Ebool_2E_7E_2E0: u).
% 1.97/1.35 thf(func_def_35, type, c_2Ebool_2E_7E_2E1: du > u).
% 1.97/1.35 thf(func_def_36, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ($o > $o) > $o > $o).
% 1.97/1.35 thf(func_def_37, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o > $o) > $o > $o > $o).
% 1.97/1.35 thf(func_def_38, type, mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29).
% 1.97/1.35 thf(func_def_39, type, mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: (mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29).
% 1.97/1.35 thf(func_def_40, type, mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o).
% 1.97/1.35 thf(func_def_41, type, mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum).
% 1.97/1.35 thf(func_def_42, type, mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 1.97/1.35 thf(func_def_45, type, mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o).
% 1.97/1.35 thf(func_def_46, type, mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29).
% 1.97/1.35 thf(func_def_47, type, mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29).
% 1.97/1.35 thf(func_def_48, type, mono_2Ec_2Ebool_2E_7E: $o > $o).
% 1.97/1.35 thf(func_def_49, type, i_mono_2Etyop_2Emin_2Ebool: $o > u).
% 1.97/1.35 thf(func_def_50, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o) > u).
% 1.97/1.35 thf(func_def_51, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ($o > $o > $o) > u).
% 1.97/1.35 thf(func_def_52, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: (mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) > u).
% 1.97/1.35 thf(func_def_53, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: (mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) > u).
% 1.97/1.35 thf(func_def_54, type, i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u).
% 1.97/1.35 thf(func_def_55, type, i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u).
% 1.97/1.35 thf(func_def_56, type, j_mono_2Etyop_2Emin_2Ebool: du > $o).
% 1.97/1.35 thf(func_def_57, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o).
% 1.97/1.35 thf(func_def_58, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o).
% 1.97/1.35 thf(func_def_59, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29).
% 1.97/1.35 thf(func_def_60, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29).
% 1.97/1.35 thf(func_def_61, type, j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum).
% 1.97/1.35 thf(func_def_62, type, j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29).
% 1.97/1.35 thf(func_def_68, type, sK0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29).
% 1.97/1.35 thf(f93,plain,(
% 1.97/1.35 $false),
% 1.97/1.35 inference(subsumption_resolution,[status(thm)],[f92,f90])).
% 1.97/1.35 thf(f90,plain,(
% 1.97/1.35 ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) != sK0)),
% 1.97/1.35 inference(equality_proxy_clausification,[status(thm)],[f89])).
% 1.97/1.35 thf(f89,plain,(
% 1.97/1.35 ($false = ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = sK0))),
% 1.97/1.35 inference(not_proxy_clausification,[status(thm)],[f80])).
% 1.97/1.35 thf(f80,plain,(
% 1.97/1.35 ((~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = sK0)) = $true)),
% 1.97/1.35 inference(cnf_transformation,[status(thm)],[f75])).
% 1.97/1.35 thf(f75,plain,(
% 1.97/1.35 ($true != (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0)))) & ((~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = sK0)) = $true)),
% 1.97/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f73,f74])).
% 1.97/1.35 thf(f74,plain,(
% 1.97/1.35 ? [X0 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (($true != (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0)))) & ($true = (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X0)))) => (($true != (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0)))) & ((~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = sK0)) = $true))),
% 1.97/1.35 introduced(definition,[],[choice_axiom])).
% 1.97/1.35 thf(f73,plain,(
% 1.97/1.35 ? [X0 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (($true != (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0)))) & ($true = (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X0))))),
% 1.97/1.35 inference(ennf_transformation,[status(thm)],[f61])).
% 1.97/1.35 thf(f61,plain,(
% 1.97/1.35 ~! [X0 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (($true = (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X0))) => ($true = (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0)))))),
% 1.97/1.35 inference(fool_elimination,[status(thm)],[f60])).
% 1.97/1.35 thf(f60,plain,(
% 1.97/1.35 ~! [X0 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ((~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X0)) => (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0))))),
% 1.97/1.35 inference(rectify,[status(thm)],[f42])).
% 1.97/1.35 thf(f42,negated_conjecture,(
% 1.97/1.35 ~! [X16 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ((~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X16)) => (~ ((mono_2Ec_2Ecomplex_2Ecomplex__inv @ X16) = (mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0))))),
% 1.97/1.35 inference(negated_conjecture,[status(cth)],[f41])).
% 1.97/1.35 thf(f41,conjecture,(
% 1.97/1.35 ! [X16 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ((~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X16)) => (~ ((mono_2Ec_2Ecomplex_2Ecomplex__inv @ X16) = (mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0))))),
% 1.97/1.35 file('/export/starexec/sandbox2/tmp/tmp.OB2tIq8qel/DTF2THF_9785.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ)).
% 1.97/1.35 thf(f92,plain,(
% 1.97/1.35 ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = sK0)),
% 1.97/1.35 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.97/1.35 thf(f91,plain,(
% 1.97/1.35 ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = sK0) | ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) != (mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0))),
% 1.97/1.35 inference(superposition,[status(thm)],[f84,f88])).
% 1.97/1.35 thf(f88,plain,(
% 1.97/1.35 ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0))),
% 1.97/1.35 inference(equality_proxy_clausification,[status(thm)],[f87])).
% 1.97/1.35 thf(f87,plain,(
% 1.97/1.35 ($true = ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0)))),
% 1.97/1.35 inference(not_proxy_clausification,[status(thm)],[f81])).
% 1.97/1.35 thf(f81,plain,(
% 1.97/1.35 ($true != (~ ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK0))))),
% 1.97/1.35 inference(cnf_transformation,[status(thm)],[f75])).
% 1.97/1.35 thf(f84,plain,(
% 1.97/1.35 ( ! [X0 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) != (mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0)) | ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X0)) )),
% 1.97/1.35 inference(cnf_transformation,[status(thm)],[f76])).
% 1.97/1.35 thf(f76,plain,(
% 1.97/1.35 ! [X0 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ((((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X0) | ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) != (mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0))) & (((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0)) | ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) != X0)))),
% 1.97/1.35 inference(nnf_transformation,[status(thm)],[f72])).
% 1.97/1.35 thf(f72,plain,(
% 1.97/1.35 ! [X0 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X0) <=> ((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = (mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0)))),
% 1.97/1.35 inference(rectify,[status(thm)],[f40])).
% 1.97/1.35 thf(f40,axiom,(
% 1.97/1.35 ! [X16 : mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (((mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0) = X16) <=> ((mono_2Ec_2Ecomplex_2Ecomplex__inv @ X16) = (mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0)))),
% 1.97/1.35 file('/export/starexec/sandbox2/tmp/tmp.OB2tIq8qel/DTF2THF_9785.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0)).
% 1.97/1.35 % SZS output end Proof for DTF2THF_9785
% 1.97/1.35 % (9929)------------------------------
% 1.97/1.35 % (9929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.97/1.35 % (9929)Termination reason: Refutation
% 1.97/1.35
% 1.97/1.35 % (9929)Memory used [KB]: 5628
% 1.97/1.35 % (9929)Time elapsed: 0.004 s
% 1.97/1.35 % (9929)Instructions burned: 6 (million)
% 1.97/1.35 % (9929)------------------------------
% 1.97/1.35 % (9929)------------------------------
% 1.97/1.35 % (9920)Success in time 0.016 s
%------------------------------------------------------------------------------