%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP018^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:53:59 AM UTC 2026
% Result : Theorem 2.05s 1.44s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 444 ( 9 ~; 0 |; 0 &; 434 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 58 usr; 23 con; 0-3 aty)
% Number of variables : 28 ( 0 ^; 24 !; 4 ?; 28 :)
% 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_2Erealax_2Ereal: $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_2Erealax_2Ereal: $tType ).
thf(func_def_4,type,
tyop_2Ebinary__ieee_2Efloat: d > d > d ).
thf(func_def_5,type,
tyop_2Ebool_2Eitself: d > d ).
thf(func_def_6,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_7,type,
tyop_2Emin_2Efun: d > d > 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_2Emin_2E_3D_2E0: u ).
thf(func_def_20,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_21,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_22,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_23,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_24,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_25,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_26,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_27,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_28,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_29,type,
c_2Ebinary__ieee_2Efloat__negate_2E0: u ).
thf(func_def_30,type,
c_2Ebinary__ieee_2Efloat__negate_2E1: du > u ).
thf(func_def_31,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E0: u ).
thf(func_def_32,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1: du > u ).
thf(func_def_33,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0: u ).
thf(func_def_34,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u ).
thf(func_def_35,type,
c_2Erealax_2Ereal__neg_2E0: u ).
thf(func_def_36,type,
c_2Erealax_2Ereal__neg_2E1: du > u ).
thf(func_def_37,type,
c_2Ebool_2Ethe__value_2E0: u ).
thf(func_def_38,type,
c_2Ebinary__ieee_2Eulp_2E0: u ).
thf(func_def_39,type,
c_2Ebinary__ieee_2Eulp_2E1: du > u ).
thf(func_def_40,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_41,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_42,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_43,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_44,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_45,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_46,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_49,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_50,type,
mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_51,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_52,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_53,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_54,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(func_def_55,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).
thf(func_def_56,type,
i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
thf(func_def_57,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_58,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_59,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_60,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_61,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_66,type,
sK0: d ).
thf(func_def_67,type,
sK1: d ).
thf(f79,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
!= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f77,f76]) ).
thf(f76,plain,
! [X0: d,X1: d] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
thf(f66,plain,
! [X0: d,X1: d] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X0 @ X1 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
inference(rectify,[status(thm)],[f38]) ).
thf(f38,axiom,
! [X15: d,X16: d] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X15 @ X16 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X15 @ X16 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X15 @ X16 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oIga0eidtf/DTF2THF_18832.p',thm_2Ebinary__ieee_2Eulp) ).
thf(f77,plain,
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
!= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f74,f75]) ).
thf(f75,plain,
! [X2: u,X0: d,X1: d] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ X2 ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ X2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: d,X1: d,X2: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ X2 ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: d,X0: d,X1: u] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X0 @ X2 ) @ X1 ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X0 @ X2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X0 @ X2 ) @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,axiom,
! [X0: d,X5: u,X1: d] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X0 @ X1 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X0 @ X1 ) @ X5 ) ) ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X0 @ X1 ) @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oIga0eidtf/DTF2THF_18832.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(f74,plain,
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
!= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
thf(f71,plain,
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
!= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f70]) ).
thf(f70,plain,
( ? [X0: d,X1: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
!= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
!= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1 @ sK0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f68,plain,
? [X0: d,X1: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
!= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f64]) ).
thf(f64,plain,
~ ! [X0: d,X1: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X1 @ X0 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X1 @ X0 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,negated_conjecture,
~ ! [X16: d,X15: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X15 @ X16 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X15 @ X16 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X15 @ X16 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X15 @ X16 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f41,conjecture,
! [X16: d,X15: d] :
( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X15 @ X16 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X15 @ X16 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ X15 @ X16 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ X15 @ X16 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oIga0eidtf/DTF2THF_18832.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP018^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.34 % Computer : n002.cluster.edu
% 0.19/0.34 % Model : x86_64 x86_64
% 0.19/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.34 % Memory : 8042.1875MB
% 0.19/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Tue Feb 24 08:21:48 EST 2026
% 0.19/0.34 % CPUTime :
% 0.19/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : ITP018^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.31/0.48 % Domain : Interactive Theorem Proving
% 0.31/0.48 % Problem : HOL4 syntactic export of thm_2Ebinary__ieee_2Eneg__ulp.p, bushy mode
% 0.31/0.48 % Version : [BG+19] axioms.
% 0.31/0.48 % English :
% 0.31/0.48
% 0.31/0.48 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.31/0.48 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.31/0.48 % Source : [BG+19]
% 0.31/0.48 % Names : thm_2Ebinary__ieee_2Eneg__ulp.p [Gau19]
% 0.31/0.48 % : HL408501^1.p [TPAP]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.31/0.48 % Syntax : Number of formulae : 103 ( 34 unt; 62 typ; 0 def)
% 0.31/0.48 % Number of atoms : 58 ( 35 equ; 1 cnn)
% 0.31/0.48 % Maximal formula atoms : 2 ( 1 avg)
% 0.31/0.48 % Number of connectives : 666 ( 1 ~; 1 |; 1 &; 652 @)
% 0.31/0.48 % ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 17 ( 4 avg)
% 0.31/0.48 % Number of types : 5 ( 4 usr)
% 0.31/0.48 % Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 60 ( 58 usr; 23 con; 0-3 aty)
% 0.31/0.48 % Number of variables : 89 ( 0 ^; 88 !; 1 ?; 89 :)
% 0.31/0.48 % SPC : TH0_THM_EQU_NAR
% 0.31/0.48
% 0.31/0.48 % Comments :
% 0.31/0.48 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 thf(u,type,
% 0.31/0.48 u: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(d,type,
% 0.31/0.48 d: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(du,type,
% 0.31/0.48 du: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Etyop_2Erealax_2Ereal,type,
% 0.31/0.48 mono_2Etyop_2Erealax_2Ereal: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(tyop_2Ebinary__ieee_2Efloat,type,
% 0.31/0.48 tyop_2Ebinary__ieee_2Efloat: d > d > d ).
% 0.31/0.48
% 0.31/0.48 thf(tyop_2Ebool_2Eitself,type,
% 0.31/0.48 tyop_2Ebool_2Eitself: d > d ).
% 0.31/0.48
% 0.31/0.48 thf(tyop_2Emin_2Ebool,type,
% 0.31/0.48 tyop_2Emin_2Ebool: d ).
% 0.31/0.48
% 0.31/0.48 thf(tyop_2Emin_2Efun,type,
% 0.31/0.48 tyop_2Emin_2Efun: d > d > d ).
% 0.31/0.48
% 0.31/0.48 thf(tyop_2Epair_2Eprod,type,
% 0.31/0.48 tyop_2Epair_2Eprod: d > d > d ).
% 0.31/0.48
% 0.31/0.48 thf(tyop_2Erealax_2Ereal,type,
% 0.31/0.48 tyop_2Erealax_2Ereal: d ).
% 0.31/0.48
% 0.31/0.48 thf(s,type,
% 0.31/0.48 s: d > u > du ).
% 0.31/0.48
% 0.31/0.48 thf(app_2E2,type,
% 0.31/0.48 app_2E2: du > du > u ).
% 0.31/0.48
% 0.31/0.48 thf(combin_i_2E0,type,
% 0.31/0.48 combin_i_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(combin_k_2E0,type,
% 0.31/0.48 combin_k_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(combin_s_2E0,type,
% 0.31/0.48 combin_s_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_21_2E0,type,
% 0.31/0.48 c_2Ebool_2E_21_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_21_2E1,type,
% 0.31/0.48 c_2Ebool_2E_21_2E1: du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.31/0.48 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.31/0.48 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Emin_2E_3D_2E0,type,
% 0.31/0.48 c_2Emin_2E_3D_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Emin_2E_3D_2E2,type,
% 0.31/0.48 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.31/0.48 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.31/0.48 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_3F_2E0,type,
% 0.31/0.48 c_2Ebool_2E_3F_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_3F_2E1,type,
% 0.31/0.48 c_2Ebool_2E_3F_2E1: du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2EF_2E0,type,
% 0.31/0.48 c_2Ebool_2EF_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2ET_2E0,type,
% 0.31/0.48 c_2Ebool_2ET_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.31/0.48 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.31/0.48 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebinary__ieee_2Efloat__negate_2E0,type,
% 0.31/0.48 c_2Ebinary__ieee_2Efloat__negate_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebinary__ieee_2Efloat__negate_2E1,type,
% 0.31/0.48 c_2Ebinary__ieee_2Efloat__negate_2E1: du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebinary__ieee_2Efloat__plus__min_2E0,type,
% 0.31/0.48 c_2Ebinary__ieee_2Efloat__plus__min_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebinary__ieee_2Efloat__plus__min_2E1,type,
% 0.31/0.48 c_2Ebinary__ieee_2Efloat__plus__min_2E1: du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebinary__ieee_2Efloat__to__real_2E0,type,
% 0.31/0.48 c_2Ebinary__ieee_2Efloat__to__real_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebinary__ieee_2Efloat__to__real_2E1,type,
% 0.31/0.48 c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Erealax_2Ereal__neg_2E0,type,
% 0.31/0.48 c_2Erealax_2Ereal__neg_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Erealax_2Ereal__neg_2E1,type,
% 0.31/0.48 c_2Erealax_2Ereal__neg_2E1: du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2Ethe__value_2E0,type,
% 0.31/0.48 c_2Ebool_2Ethe__value_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebinary__ieee_2Eulp_2E0,type,
% 0.31/0.48 c_2Ebinary__ieee_2Eulp_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebinary__ieee_2Eulp_2E1,type,
% 0.31/0.48 c_2Ebinary__ieee_2Eulp_2E1: du > u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_7E_2E0,type,
% 0.31/0.48 c_2Ebool_2E_7E_2E0: u ).
% 0.31/0.48
% 0.31/0.48 thf(c_2Ebool_2E_7E_2E1,type,
% 0.31/0.48 c_2Ebool_2E_7E_2E1: du > u ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.31/0.48 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.31/0.48 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
% 0.31/0.48 mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.31/0.48 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.31/0.48 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Ec_2Ebool_2EF,type,
% 0.31/0.48 mono_2Ec_2Ebool_2EF: $o ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Ec_2Ebool_2ET,type,
% 0.31/0.48 mono_2Ec_2Ebool_2ET: $o ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.31/0.48 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Ec_2Erealax_2Ereal__neg,type,
% 0.31/0.48 mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
% 0.31/0.48
% 0.31/0.48 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.31/0.48 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.31/0.48 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.31/0.48
% 0.31/0.48 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.31/0.48 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.31/0.48
% 0.31/0.48 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.31/0.48 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.31/0.48
% 0.31/0.48 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.31/0.48 i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).
% 0.31/0.48
% 0.31/0.48 thf(i_mono_2Etyop_2Erealax_2Ereal,type,
% 0.31/0.48 i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
% 0.31/0.48
% 0.31/0.48 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.31/0.48 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.31/0.48
% 0.31/0.48 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.31/0.48 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.31/0.48 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.31/0.48 j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
% 0.31/0.48
% 0.31/0.48 thf(j_mono_2Etyop_2Erealax_2Ereal,type,
% 0.31/0.48 j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.31/0.48 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.31/0.48 ( ! [V2x_2E0: u] :
% 0.31/0.48 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.31/0.48 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.31/0.48 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.31/0.48 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.31/0.48 ! [A_27a: d,V0x_2E0: u] :
% 0.31/0.48 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.31/0.48 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.31/0.48 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.31/0.48 ( ( 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 ) ) )
% 0.31/0.48 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Eho_2Es__thm,axiom,
% 0.31/0.48 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.31/0.48 ( ( 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 ) ) )
% 0.31/0.48 = ( 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 ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.31/0.48 ! [V0: $o,V1: $o] :
% 0.31/0.48 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.31/0.48 <=> ( V0
% 0.31/0.48 & V1 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.31/0.48 ! [V0: $o,V1: $o] :
% 0.31/0.48 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.31/0.48 <=> ( V0
% 0.31/0.48 | V1 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Elogic_2E_7E,axiom,
% 0.31/0.48 ! [V0: $o] :
% 0.31/0.48 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.31/0.48 <=> ( (~) @ V0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.31/0.48 ! [V0: $o,V1: $o] :
% 0.31/0.48 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.31/0.48 <=> ( V0
% 0.31/0.48 => V1 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Elogic_2E_3D,axiom,
% 0.31/0.48 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.31/0.48 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.31/0.48 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Equant_2E_21,axiom,
% 0.31/0.48 ! [A_27a: d,V0f_2E0: u] :
% 0.31/0.48 ( ( 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 ) ) ) )
% 0.31/0.48 <=> ! [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 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(reserved_2Equant_2E_3F,axiom,
% 0.31/0.48 ! [A_27a: d,V0f_2E0: u] :
% 0.31/0.48 ( ( 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 ) ) ) )
% 0.31/0.48 <=> ? [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 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.31/0.48 ! [V0_2E0: u] :
% 0.31/0.48 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.31/0.48 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.31/0.48 ! [V0_2E0: u] :
% 0.31/0.48 ( ( 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 ) ) ) )
% 0.31/0.48 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.31/0.48 ! [V0_2E0: u] :
% 0.31/0.48 ( ( 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 ) ) ) )
% 0.31/0.48 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.31/0.48 ! [V0_2E0: u] :
% 0.31/0.48 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
% 0.31/0.48 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ij_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 0.31/0.48 ! [V0_2E0: u] :
% 0.31/0.48 ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ) )
% 0.31/0.48 = ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.31/0.48 ! [V0: $o] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.31/0.48 = V0 ) ).
% 0.31/0.48
% 0.31/0.48 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.31/0.48 ! [V0: $o > $o] :
% 0.31/0.48 ( ( 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 ) ) )
% 0.31/0.48 = V0 ) ).
% 0.31/0.48
% 0.31/0.48 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.31/0.48 ! [V0: $o > $o > $o] :
% 0.31/0.48 ( ( 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 ) ) )
% 0.31/0.48 = V0 ) ).
% 0.31/0.48
% 0.31/0.48 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.31/0.48 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
% 0.31/0.48 = V0 ) ).
% 0.31/0.48
% 0.31/0.48 thf(ji_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 0.31/0.48 ! [V0: mono_2Etyop_2Erealax_2Ereal] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
% 0.31/0.48 = V0 ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.31/0.48 ! [A_27a: d,X0_2E0: u] :
% 0.31/0.48 ( ( 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 ) ) ) )
% 0.31/0.48 = ( 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 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.31/0.48 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.31/0.48 ( ( ( s @ A_27a @ X0_2E0 )
% 0.31/0.48 = ( s @ A_27a @ X1_2E0 ) )
% 0.31/0.48 <=> ( 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 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.31/0.48 ! [A_27a: d,X0_2E0: u] :
% 0.31/0.48 ( ( 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 ) ) ) )
% 0.31/0.48 = ( 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 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.31/0.48 ! [A_27a: d,A_27b: d,X0_2E0: u] :
% 0.31/0.48 ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) )
% 0.31/0.48 = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
% 0.31/0.48 ! [A_27t: d,A_27w: d,X0_2E0: u] :
% 0.31/0.48 ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) )
% 0.31/0.48 = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
% 0.31/0.48 ! [A_27t: d,A_27w: d,X0_2E0: u] :
% 0.31/0.48 ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) )
% 0.31/0.48 = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 0.31/0.48 ! [A_27a: d,A_27b: d,X0_2E0: u] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
% 0.31/0.48 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
% 0.31/0.48 ! [A_27t: d,A_27w: d,X0_2E0: u] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) )
% 0.31/0.48 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
% 0.31/0.48 ! [A_27t: d,A_27w: d,X0_2E0: u] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) )
% 0.31/0.48 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.31/0.48 ! [V0: $o > $o,V1: $o] :
% 0.31/0.48 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.31/0.48 = ( 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 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.31/0.48 ! [V0: $o > $o > $o,V1: $o] :
% 0.31/0.48 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.31/0.48 = ( 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 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
% 0.31/0.48 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
% 0.31/0.48 ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
% 0.31/0.48 = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.31/0.48 ! [V0: $o > $o,V1: $o] :
% 0.31/0.48 ( ( V0 @ V1 )
% 0.31/0.48 = ( V0 @ V1 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.31/0.48 ! [V0: $o > $o > $o,V1: $o] :
% 0.31/0.48 ( ( V0 @ V1 )
% 0.31/0.48 = ( V0 @ V1 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
% 0.31/0.48 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
% 0.31/0.48 ( ( V0 @ V1 )
% 0.31/0.48 = ( V0 @ V1 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(thm_2Ebinary__ieee_2Efloat__to__real__negate,axiom,
% 0.31/0.48 ! [A_27a: d,A_27b: d,V0x_2E0: u] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) )
% 0.31/0.48 = ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(thm_2Ebinary__ieee_2Eulp,axiom,
% 0.31/0.48 ! [A_27t: d,A_27w: d] :
% 0.31/0.48 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
% 0.31/0.48 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.31/0.48 mono_2Ec_2Ebool_2ET ).
% 0.31/0.48
% 0.31/0.48 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 0.31/0.48 ! [A_27a: d,V0x_2E0: u] :
% 0.31/0.48 ( ( ( s @ A_27a @ V0x_2E0 )
% 0.31/0.48 = ( s @ A_27a @ V0x_2E0 ) )
% 0.31/0.48 <=> mono_2Ec_2Ebool_2ET ) ).
% 0.31/0.48
% 0.31/0.48 thf(thm_2Ebinary__ieee_2Eneg__ulp,conjecture,
% 0.31/0.48 ! [A_27t: d,A_27w: d] :
% 0.31/0.48 ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
% 0.31/0.48 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 1.81/1.39 ---- Embedded in THF ---
% 1.81/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.81/1.39 %%% Generated on Tue Feb 24 08:21:49 EST 2026
% 1.81/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.81/1.39 %%% Logic specification used:
% 1.81/1.39 %%% thf(spec, logic, $$dhol).
% 1.81/1.39
% 1.81/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oIga0eidtf/DTF2DTF18832.p
% See solution above
% 1.81/1.40 ------------------------
% 2.05/1.41 ---- Cleaned THF ---
% 2.05/1.41 thf(u,type,
% 2.05/1.41 u: $tType ).
% 2.05/1.41
% 2.05/1.41 thf(d,type,
% 2.05/1.41 d: $tType ).
% 2.05/1.41
% 2.05/1.41 thf(du,type,
% 2.05/1.41 du: $tType ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Etyop_2Erealax_2Ereal,type,
% 2.05/1.41 mono_2Etyop_2Erealax_2Ereal: $tType ).
% 2.05/1.41
% 2.05/1.41 thf(tyop_2Ebinary__ieee_2Efloat,type,
% 2.05/1.41 tyop_2Ebinary__ieee_2Efloat: d > d > d ).
% 2.05/1.41
% 2.05/1.41 thf(tyop_2Ebool_2Eitself,type,
% 2.05/1.41 tyop_2Ebool_2Eitself: d > d ).
% 2.05/1.41
% 2.05/1.41 thf(tyop_2Emin_2Ebool,type,
% 2.05/1.41 tyop_2Emin_2Ebool: d ).
% 2.05/1.41
% 2.05/1.41 thf(tyop_2Emin_2Efun,type,
% 2.05/1.41 tyop_2Emin_2Efun: d > d > d ).
% 2.05/1.41
% 2.05/1.41 thf(tyop_2Epair_2Eprod,type,
% 2.05/1.41 tyop_2Epair_2Eprod: d > d > d ).
% 2.05/1.41
% 2.05/1.41 thf(tyop_2Erealax_2Ereal,type,
% 2.05/1.41 tyop_2Erealax_2Ereal: d ).
% 2.05/1.41
% 2.05/1.41 thf(s,type,
% 2.05/1.41 s: d > u > du ).
% 2.05/1.41
% 2.05/1.41 thf(app_2E2,type,
% 2.05/1.41 app_2E2: du > du > u ).
% 2.05/1.41
% 2.05/1.41 thf(combin_i_2E0,type,
% 2.05/1.41 combin_i_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(combin_k_2E0,type,
% 2.05/1.41 combin_k_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(combin_s_2E0,type,
% 2.05/1.41 combin_s_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_21_2E0,type,
% 2.05/1.41 c_2Ebool_2E_21_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_21_2E1,type,
% 2.05/1.41 c_2Ebool_2E_21_2E1: du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 2.05/1.41 c_2Ebool_2E_2F_5C_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 2.05/1.41 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Emin_2E_3D_2E0,type,
% 2.05/1.41 c_2Emin_2E_3D_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Emin_2E_3D_2E2,type,
% 2.05/1.41 c_2Emin_2E_3D_2E2: du > du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 2.05/1.41 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 2.05/1.41 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_3F_2E0,type,
% 2.05/1.41 c_2Ebool_2E_3F_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_3F_2E1,type,
% 2.05/1.41 c_2Ebool_2E_3F_2E1: du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2EF_2E0,type,
% 2.05/1.41 c_2Ebool_2EF_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2ET_2E0,type,
% 2.05/1.41 c_2Ebool_2ET_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 2.05/1.41 c_2Ebool_2E_5C_2F_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 2.05/1.41 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebinary__ieee_2Efloat__negate_2E0,type,
% 2.05/1.41 c_2Ebinary__ieee_2Efloat__negate_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebinary__ieee_2Efloat__negate_2E1,type,
% 2.05/1.41 c_2Ebinary__ieee_2Efloat__negate_2E1: du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebinary__ieee_2Efloat__plus__min_2E0,type,
% 2.05/1.41 c_2Ebinary__ieee_2Efloat__plus__min_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebinary__ieee_2Efloat__plus__min_2E1,type,
% 2.05/1.41 c_2Ebinary__ieee_2Efloat__plus__min_2E1: du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebinary__ieee_2Efloat__to__real_2E0,type,
% 2.05/1.41 c_2Ebinary__ieee_2Efloat__to__real_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebinary__ieee_2Efloat__to__real_2E1,type,
% 2.05/1.41 c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Erealax_2Ereal__neg_2E0,type,
% 2.05/1.41 c_2Erealax_2Ereal__neg_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Erealax_2Ereal__neg_2E1,type,
% 2.05/1.41 c_2Erealax_2Ereal__neg_2E1: du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2Ethe__value_2E0,type,
% 2.05/1.41 c_2Ebool_2Ethe__value_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebinary__ieee_2Eulp_2E0,type,
% 2.05/1.41 c_2Ebinary__ieee_2Eulp_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebinary__ieee_2Eulp_2E1,type,
% 2.05/1.41 c_2Ebinary__ieee_2Eulp_2E1: du > u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_7E_2E0,type,
% 2.05/1.41 c_2Ebool_2E_7E_2E0: u ).
% 2.05/1.41
% 2.05/1.41 thf(c_2Ebool_2E_7E_2E1,type,
% 2.05/1.41 c_2Ebool_2E_7E_2E1: du > u ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 2.05/1.41 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.05/1.41 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
% 2.05/1.41 mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 2.05/1.41 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 2.05/1.41 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Ec_2Ebool_2EF,type,
% 2.05/1.41 mono_2Ec_2Ebool_2EF: $o ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Ec_2Ebool_2ET,type,
% 2.05/1.41 mono_2Ec_2Ebool_2ET: $o ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 2.05/1.41 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Ec_2Erealax_2Ereal__neg,type,
% 2.05/1.41 mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
% 2.05/1.41
% 2.05/1.41 thf(mono_2Ec_2Ebool_2E_7E,type,
% 2.05/1.41 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 2.05/1.41
% 2.05/1.41 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 2.05/1.41 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 2.05/1.41
% 2.05/1.41 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.05/1.41 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 2.05/1.41
% 2.05/1.41 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.05/1.41 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 2.05/1.41
% 2.05/1.41 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 2.05/1.41 i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).
% 2.05/1.41
% 2.05/1.41 thf(i_mono_2Etyop_2Erealax_2Ereal,type,
% 2.05/1.41 i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
% 2.05/1.41
% 2.05/1.41 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 2.05/1.41 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 2.05/1.41
% 2.05/1.41 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 2.05/1.41 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 2.05/1.41
% 2.05/1.41 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 2.05/1.41 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 2.05/1.41
% 2.05/1.41 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 2.05/1.41 j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
% 2.05/1.41
% 2.05/1.41 thf(j_mono_2Etyop_2Erealax_2Ereal,type,
% 2.05/1.41 j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Eho_2Eeq__ext,axiom,
% 2.05/1.41 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 2.05/1.41 ( ! [V2x_2E0: u] :
% 2.05/1.41 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 2.05/1.41 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 2.05/1.41 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 2.05/1.41 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Eho_2Ei__thm,axiom,
% 2.05/1.41 ! [A_27a: d,V0x_2E0: u] :
% 2.05/1.41 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 2.05/1.41 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Eho_2Ek__thm,axiom,
% 2.05/1.41 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 2.05/1.41 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 2.05/1.41 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Eho_2Es__thm,axiom,
% 2.05/1.41 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 2.05/1.41 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 2.05/1.41 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 2.05/1.41 ! [V0: $o,V1: $o] :
% 2.05/1.41 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 2.05/1.41 <=> ( V0
% 2.05/1.41 & V1 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 2.05/1.41 ! [V0: $o,V1: $o] :
% 2.05/1.41 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 2.05/1.41 <=> ( V0
% 2.05/1.41 | V1 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Elogic_2E_7E,axiom,
% 2.05/1.41 ! [V0: $o] :
% 2.05/1.41 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 2.05/1.41 <=> ( (~) @ V0 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 2.05/1.41 ! [V0: $o,V1: $o] :
% 2.05/1.41 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 2.05/1.41 <=> ( V0
% 2.05/1.41 => V1 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Elogic_2E_3D,axiom,
% 2.05/1.41 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 2.05/1.41 <=> ( ( s @ A_27a @ V0_2E0 )
% 2.05/1.41 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Equant_2E_21,axiom,
% 2.05/1.41 ! [A_27a: d,V0f_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 2.05/1.41 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(reserved_2Equant_2E_3F,axiom,
% 2.05/1.41 ! [A_27a: d,V0f_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 2.05/1.41 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.05/1.41 ! [V0_2E0: u] :
% 2.05/1.41 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 2.05/1.41 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.05/1.41 ! [V0_2E0: u] :
% 2.05/1.41 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 2.05/1.41 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.05/1.41 ! [V0_2E0: u] :
% 2.05/1.41 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 2.05/1.41 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 2.05/1.41 ! [V0_2E0: u] :
% 2.05/1.41 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
% 2.05/1.41 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(ij_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 2.05/1.41 ! [V0_2E0: u] :
% 2.05/1.41 ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ) )
% 2.05/1.41 = ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 2.05/1.41 ! [V0: $o] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 2.05/1.41 = V0 ) ).
% 2.05/1.41
% 2.05/1.41 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.05/1.41 ! [V0: $o > $o] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 2.05/1.41 = V0 ) ).
% 2.05/1.41
% 2.05/1.41 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 2.05/1.41 ! [V0: $o > $o > $o] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 2.05/1.41 = V0 ) ).
% 2.05/1.41
% 2.05/1.41 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 2.05/1.41 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
% 2.05/1.41 = V0 ) ).
% 2.05/1.41
% 2.05/1.41 thf(ji_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 2.05/1.41 ! [V0: mono_2Etyop_2Erealax_2Ereal] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
% 2.05/1.41 = V0 ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 2.05/1.41 ! [A_27a: d,X0_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 2.05/1.41 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 2.05/1.41 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 2.05/1.41 ( ( ( s @ A_27a @ X0_2E0 )
% 2.05/1.41 = ( s @ A_27a @ X1_2E0 ) )
% 2.05/1.41 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 2.05/1.41 ! [A_27a: d,X0_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 2.05/1.41 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 2.05/1.41 ! [A_27a: d,A_27b: d,X0_2E0: u] :
% 2.05/1.41 ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) )
% 2.05/1.41 = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
% 2.05/1.41 ! [A_27t: d,A_27w: d,X0_2E0: u] :
% 2.05/1.41 ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) )
% 2.05/1.41 = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
% 2.05/1.41 ! [A_27t: d,A_27w: d,X0_2E0: u] :
% 2.05/1.41 ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) )
% 2.05/1.41 = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
% 2.05/1.41 ! [A_27a: d,A_27b: d,X0_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
% 2.05/1.41 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
% 2.05/1.41 ! [A_27t: d,A_27w: d,X0_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) )
% 2.05/1.41 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ X0_2E0 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
% 2.05/1.41 ! [A_27t: d,A_27w: d,X0_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) )
% 2.05/1.41 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ X0_2E0 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.05/1.41 ! [V0: $o > $o,V1: $o] :
% 2.05/1.41 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 2.05/1.41 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.05/1.41 ! [V0: $o > $o > $o,V1: $o] :
% 2.05/1.41 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 2.05/1.41 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
% 2.05/1.41 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
% 2.05/1.41 ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
% 2.05/1.41 = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 2.05/1.41 ! [V0: $o > $o,V1: $o] :
% 2.05/1.41 ( ( V0 @ V1 )
% 2.05/1.41 = ( V0 @ V1 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 2.05/1.41 ! [V0: $o > $o > $o,V1: $o] :
% 2.05/1.41 ( ( V0 @ V1 )
% 2.05/1.41 = ( V0 @ V1 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
% 2.05/1.41 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
% 2.05/1.41 ( ( V0 @ V1 )
% 2.05/1.41 = ( V0 @ V1 ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(thm_2Ebinary__ieee_2Efloat__to__real__negate,axiom,
% 2.05/1.41 ! [A_27a: d,A_27b: d,V0x_2E0: u] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) )
% 2.05/1.41 = ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(thm_2Ebinary__ieee_2Eulp,axiom,
% 2.05/1.41 ! [A_27t: d,A_27w: d] :
% 2.05/1.41 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
% 2.05/1.41 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ).
% 2.05/1.41
% 2.05/1.41 thf(thm_2Ebool_2ETRUTH,axiom,
% 2.05/1.41 mono_2Ec_2Ebool_2ET ).
% 2.05/1.41
% 2.05/1.41 thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
% 2.05/1.41 ! [A_27a: d,V0x_2E0: u] :
% 2.05/1.41 ( ( ( s @ A_27a @ V0x_2E0 )
% 2.05/1.41 = ( s @ A_27a @ V0x_2E0 ) )
% 2.05/1.41 <=> mono_2Ec_2Ebool_2ET ) ).
% 2.05/1.41
% 2.05/1.41 thf(thm_2Ebinary__ieee_2Eneg__ulp,conjecture,
% 2.05/1.41 ! [A_27t: d,A_27w: d] :
% 2.05/1.41 ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
% 2.05/1.41 = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ).
% 2.05/1.41 ------------------------
% 2.05/1.43 % (18934)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_18832 for (2999ds/4Mi)
% 2.05/1.43 % (18936)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18832 for (2999ds/2Mi)
% 2.05/1.43 % (18934)Instruction limit reached!
% 2.05/1.43 % (18934)------------------------------
% 2.05/1.43 % (18934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.43 % (18934)Termination reason: Unknown
% 2.05/1.43 % (18934)Termination phase: shuffling
% 2.05/1.43
% 2.05/1.43 % (18934)Memory used [KB]: 1151
% 2.05/1.43 % (18934)Time elapsed: 0.003 s
% 2.05/1.43 % (18934)Instructions burned: 5 (million)
% 2.05/1.43 % (18934)------------------------------
% 2.05/1.43 % (18934)------------------------------
% 2.05/1.43 % (18936)Instruction limit reached!
% 2.05/1.43 % (18936)------------------------------
% 2.05/1.43 % (18936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.43 % (18936)Termination reason: Unknown
% 2.05/1.43 % (18936)Termination phase: Property scanning
% 2.05/1.43
% 2.05/1.43 % (18936)Memory used [KB]: 1023
% 2.05/1.43 % (18936)Time elapsed: 0.002 s
% 2.05/1.43 % (18936)Instructions burned: 3 (million)
% 2.05/1.43 % (18936)------------------------------
% 2.05/1.43 % (18936)------------------------------
% 2.05/1.44 % (18933)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18832 for (2999ds/183Mi)
% 2.05/1.44 % (18935)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_18832 for (2999ds/27Mi)
% 2.05/1.44 % (18937)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_18832 for (2999ds/2Mi)
% 2.05/1.44 % (18938)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_18832 for (2999ds/275Mi)
% 2.05/1.44 % (18939)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18832 for (2999ds/18Mi)
% 2.05/1.44 % (18937)Instruction limit reached!
% 2.05/1.44 % (18937)------------------------------
% 2.05/1.44 % (18937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.44 % (18937)Termination reason: Unknown
% 2.05/1.44 % (18937)Termination phase: shuffling
% 2.05/1.44
% 2.05/1.44 % (18937)Memory used [KB]: 1023
% 2.05/1.44 % (18937)Time elapsed: 0.003 s
% 2.05/1.44 % (18937)Instructions burned: 2 (million)
% 2.05/1.44 % (18937)------------------------------
% 2.05/1.44 % (18937)------------------------------
% 2.05/1.44 % (18941)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_18832 for (2999ds/37Mi)
% 2.05/1.44 % (18940)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18832 for (2999ds/3Mi)
% 2.05/1.44 % (18940)Instruction limit reached!
% 2.05/1.44 % (18940)------------------------------
% 2.05/1.44 % (18940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.44 % (18940)Termination reason: Unknown
% 2.05/1.44 % (18940)Termination phase: shuffling
% 2.05/1.44
% 2.05/1.44 % (18940)Memory used [KB]: 1023
% 2.05/1.44 % (18940)Time elapsed: 0.003 s
% 2.05/1.44 % (18940)Instructions burned: 4 (million)
% 2.05/1.44 % (18940)------------------------------
% 2.05/1.44 % (18940)------------------------------
% 2.05/1.44 % (18938)First to succeed.
% 2.05/1.44 % (18938)Refutation found. Thanks to Tanya!
% 2.05/1.44 % SZS status Theorem for DTF2THF_18832
% 2.05/1.44 % SZS output start Proof for DTF2THF_18832
% 2.05/1.44 thf(type_def_5, type, d: $tType).
% 2.05/1.44 thf(type_def_7, type, u: $tType).
% 2.05/1.44 thf(type_def_8, type, du: $tType).
% 2.05/1.44 thf(type_def_9, type, mono_2Etyop_2Erealax_2Ereal: $tType).
% 2.05/1.44 thf(func_def_0, type, u: $tType).
% 2.05/1.44 thf(func_def_1, type, d: $tType).
% 2.05/1.44 thf(func_def_2, type, du: $tType).
% 2.05/1.44 thf(func_def_3, type, mono_2Etyop_2Erealax_2Ereal: $tType).
% 2.05/1.44 thf(func_def_4, type, tyop_2Ebinary__ieee_2Efloat: d > d > d).
% 2.05/1.44 thf(func_def_5, type, tyop_2Ebool_2Eitself: d > d).
% 2.05/1.44 thf(func_def_6, type, tyop_2Emin_2Ebool: d).
% 2.05/1.44 thf(func_def_7, type, tyop_2Emin_2Efun: d > d > d).
% 2.05/1.44 thf(func_def_8, type, tyop_2Epair_2Eprod: d > d > d).
% 2.05/1.44 thf(func_def_9, type, tyop_2Erealax_2Ereal: d).
% 2.05/1.44 thf(func_def_10, type, s: d > u > du).
% 2.05/1.44 thf(func_def_11, type, app_2E2: du > du > u).
% 2.05/1.44 thf(func_def_12, type, combin_i_2E0: u).
% 2.05/1.44 thf(func_def_13, type, combin_k_2E0: u).
% 2.05/1.44 thf(func_def_14, type, combin_s_2E0: u).
% 2.05/1.44 thf(func_def_15, type, c_2Ebool_2E_21_2E0: u).
% 2.05/1.44 thf(func_def_16, type, c_2Ebool_2E_21_2E1: du > u).
% 2.05/1.44 thf(func_def_17, type, c_2Ebool_2E_2F_5C_2E0: u).
% 2.05/1.44 thf(func_def_18, type, c_2Ebool_2E_2F_5C_2E2: du > du > u).
% 2.05/1.44 thf(func_def_19, type, c_2Emin_2E_3D_2E0: u).
% 2.05/1.44 thf(func_def_20, type, c_2Emin_2E_3D_2E2: du > du > u).
% 2.05/1.44 thf(func_def_21, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 2.05/1.44 thf(func_def_22, type, c_2Emin_2E_3D_3D_3E_2E2: du > du > u).
% 2.05/1.44 thf(func_def_23, type, c_2Ebool_2E_3F_2E0: u).
% 2.05/1.44 thf(func_def_24, type, c_2Ebool_2E_3F_2E1: du > u).
% 2.05/1.44 thf(func_def_25, type, c_2Ebool_2EF_2E0: u).
% 2.05/1.44 thf(func_def_26, type, c_2Ebool_2ET_2E0: u).
% 2.05/1.44 thf(func_def_27, type, c_2Ebool_2E_5C_2F_2E0: u).
% 2.05/1.44 thf(func_def_28, type, c_2Ebool_2E_5C_2F_2E2: du > du > u).
% 2.05/1.44 thf(func_def_29, type, c_2Ebinary__ieee_2Efloat__negate_2E0: u).
% 2.05/1.44 thf(func_def_30, type, c_2Ebinary__ieee_2Efloat__negate_2E1: du > u).
% 2.05/1.44 thf(func_def_31, type, c_2Ebinary__ieee_2Efloat__plus__min_2E0: u).
% 2.05/1.44 thf(func_def_32, type, c_2Ebinary__ieee_2Efloat__plus__min_2E1: du > u).
% 2.05/1.44 thf(func_def_33, type, c_2Ebinary__ieee_2Efloat__to__real_2E0: u).
% 2.05/1.44 thf(func_def_34, type, c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u).
% 2.05/1.44 thf(func_def_35, type, c_2Erealax_2Ereal__neg_2E0: u).
% 2.05/1.44 thf(func_def_36, type, c_2Erealax_2Ereal__neg_2E1: du > u).
% 2.05/1.44 thf(func_def_37, type, c_2Ebool_2Ethe__value_2E0: u).
% 2.05/1.44 thf(func_def_38, type, c_2Ebinary__ieee_2Eulp_2E0: u).
% 2.05/1.44 thf(func_def_39, type, c_2Ebinary__ieee_2Eulp_2E1: du > u).
% 2.05/1.44 thf(func_def_40, type, c_2Ebool_2E_7E_2E0: u).
% 2.05/1.44 thf(func_def_41, type, c_2Ebool_2E_7E_2E1: du > u).
% 2.05/1.44 thf(func_def_42, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ($o > $o) > $o > $o).
% 2.05/1.44 thf(func_def_43, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o > $o) > $o > $o > $o).
% 2.05/1.44 thf(func_def_44, type, mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: (mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal).
% 2.05/1.44 thf(func_def_45, type, mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o).
% 2.05/1.44 thf(func_def_46, type, mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 2.05/1.44 thf(func_def_49, type, mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o).
% 2.05/1.44 thf(func_def_50, type, mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal).
% 2.05/1.44 thf(func_def_51, type, mono_2Ec_2Ebool_2E_7E: $o > $o).
% 2.05/1.44 thf(func_def_52, type, i_mono_2Etyop_2Emin_2Ebool: $o > u).
% 2.05/1.44 thf(func_def_53, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o) > u).
% 2.05/1.44 thf(func_def_54, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ($o > $o > $o) > u).
% 2.05/1.44 thf(func_def_55, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: (mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal) > u).
% 2.05/1.44 thf(func_def_56, type, i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u).
% 2.05/1.44 thf(func_def_57, type, j_mono_2Etyop_2Emin_2Ebool: du > $o).
% 2.05/1.44 thf(func_def_58, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o).
% 2.05/1.44 thf(func_def_59, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o).
% 2.05/1.44 thf(func_def_60, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal).
% 2.05/1.44 thf(func_def_61, type, j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal).
% 2.05/1.44 thf(func_def_66, type, sK0: d).
% 2.05/1.44 thf(func_def_67, type, sK1: d).
% 2.05/1.44 thf(f79,plain,(
% 2.05/1.44 $false),
% 2.05/1.44 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 2.05/1.44 thf(f78,plain,(
% 2.05/1.44 ((mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0))))) != (mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0))))))),
% 2.05/1.44 inference(forward_demodulation,[status(thm)],[f77,f76])).
% 2.05/1.44 thf(f76,plain,(
% 2.05/1.44 ( ! [X0 : d,X1 : d] : (((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X0 @ X1) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X0 @ X1)) @ c_2Ebool_2Ethe__value_2E0)))))) = (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X0 @ X1)) @ c_2Ebool_2Ethe__value_2E0)))))) )),
% 2.05/1.44 inference(cnf_transformation,[status(thm)],[f66])).
% 2.05/1.44 thf(f66,plain,(
% 2.05/1.44 ! [X0 : d,X1 : d] : ((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X0 @ X1) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X0 @ X1)) @ c_2Ebool_2Ethe__value_2E0)))))) = (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X0 @ X1)) @ c_2Ebool_2Ethe__value_2E0)))))),
% 2.05/1.44 inference(rectify,[status(thm)],[f38])).
% 2.05/1.44 thf(f38,axiom,(
% 2.05/1.44 ! [X15 : d,X16 : d] : ((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X15 @ X16)) @ c_2Ebool_2Ethe__value_2E0)))) = (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X15 @ X16) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X15 @ X16)) @ c_2Ebool_2Ethe__value_2E0)))))))),
% 2.05/1.44 file('/export/starexec/sandbox/tmp/tmp.oIga0eidtf/DTF2THF_18832.p',thm_2Ebinary__ieee_2Eulp)).
% 2.05/1.44 thf(f77,plain,(
% 2.05/1.44 ((mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0))))))) != (mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0))))))),
% 2.05/1.44 inference(superposition,[status(thm)],[f74,f75])).
% 2.05/1.44 thf(f75,plain,(
% 2.05/1.44 ( ! [X2 : u,X0 : d,X1 : d] : (((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ X2)))))) = (mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ X2))))))) )),
% 2.05/1.44 inference(cnf_transformation,[status(thm)],[f72])).
% 2.05/1.44 thf(f72,plain,(
% 2.05/1.44 ! [X0 : d,X1 : d,X2 : u] : ((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ X2)))))) = (mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ X2))))))),
% 2.05/1.44 inference(rectify,[status(thm)],[f67])).
% 2.05/1.44 thf(f67,plain,(
% 2.05/1.44 ! [X2 : d,X0 : d,X1 : u] : ((mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X0 @ X2) @ X1))))) = (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X0 @ X2) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X0 @ X2) @ X1)))))))),
% 2.05/1.44 inference(rectify,[status(thm)],[f37])).
% 2.05/1.44 thf(f37,axiom,(
% 2.05/1.44 ! [X0 : d,X5 : u,X1 : d] : ((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X0 @ X1) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X0 @ X1) @ X5)))))) = (mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X0 @ X1) @ X5))))))),
% 2.05/1.44 file('/export/starexec/sandbox/tmp/tmp.oIga0eidtf/DTF2THF_18832.p',thm_2Ebinary__ieee_2Efloat__to__real__negate)).
% 2.05/1.44 thf(f74,plain,(
% 2.05/1.44 ((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0)))))))) != (mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0))))))),
% 2.05/1.44 inference(cnf_transformation,[status(thm)],[f71])).
% 2.05/1.44 thf(f71,plain,(
% 2.05/1.44 ((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0)))))))) != (mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0))))))),
% 2.05/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f70])).
% 2.05/1.44 thf(f70,plain,(
% 2.05/1.44 ? [X0 : d,X1 : d] : ((mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X1 @ X0)) @ c_2Ebool_2Ethe__value_2E0))))) != (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X1 @ X0)) @ c_2Ebool_2Ethe__value_2E0))))))))) => ((j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ sK1 @ sK0) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0)))))))) != (mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ sK1 @ sK0)) @ c_2Ebool_2Ethe__value_2E0))))))),
% 2.05/1.44 introduced(definition,[],[choice_axiom])).
% 2.05/1.44 thf(f68,plain,(
% 2.05/1.44 ? [X0 : d,X1 : d] : ((mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X1 @ X0)) @ c_2Ebool_2Ethe__value_2E0))))) != (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X1 @ X0)) @ c_2Ebool_2Ethe__value_2E0)))))))))),
% 2.05/1.44 inference(ennf_transformation,[status(thm)],[f64])).
% 2.05/1.44 thf(f64,plain,(
% 2.05/1.44 ~! [X0 : d,X1 : d] : ((mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X1 @ X0)) @ c_2Ebool_2Ethe__value_2E0))))) = (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X1 @ X0) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X1 @ X0)) @ c_2Ebool_2Ethe__value_2E0)))))))))),
% 2.05/1.44 inference(rectify,[status(thm)],[f42])).
% 2.05/1.44 thf(f42,negated_conjecture,(
% 2.05/1.44 ~! [X16 : d,X15 : d] : ((mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X15 @ X16)) @ c_2Ebool_2Ethe__value_2E0))))) = (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X15 @ X16) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X15 @ X16) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X15 @ X16)) @ c_2Ebool_2Ethe__value_2E0)))))))))),
% 2.05/1.44 inference(negated_conjecture,[status(cth)],[f41])).
% 2.05/1.44 thf(f41,conjecture,(
% 2.05/1.44 ! [X16 : d,X15 : d] : ((mono_2Ec_2Erealax_2Ereal__neg @ (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Eulp_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X15 @ X16)) @ c_2Ebool_2Ethe__value_2E0))))) = (j_mono_2Etyop_2Erealax_2Ereal @ (s @ tyop_2Erealax_2Ereal @ (c_2Ebinary__ieee_2Efloat__to__real_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X15 @ X16) @ (c_2Ebinary__ieee_2Efloat__negate_2E1 @ (s @ (tyop_2Ebinary__ieee_2Efloat @ X15 @ X16) @ (c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ (s @ (tyop_2Ebool_2Eitself @ (tyop_2Epair_2Eprod @ X15 @ X16)) @ c_2Ebool_2Ethe__value_2E0)))))))))),
% 2.05/1.44 file('/export/starexec/sandbox/tmp/tmp.oIga0eidtf/DTF2THF_18832.p',thm_2Ebinary__ieee_2Eneg__ulp)).
% 2.05/1.44 % SZS output end Proof for DTF2THF_18832
% 2.05/1.44 % (18938)------------------------------
% 2.05/1.44 % (18938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.05/1.44 % (18938)Termination reason: Refutation
% 2.05/1.44
% 2.05/1.44 % (18938)Memory used [KB]: 5628
% 2.05/1.44 % (18938)Time elapsed: 0.009 s
% 2.05/1.44 % (18938)Instructions burned: 8 (million)
% 2.05/1.44 % (18938)------------------------------
% 2.05/1.44 % (18938)------------------------------
% 2.05/1.44 % (18932)Success in time 0.02 s
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