TSTP Solution File: ITP023^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP023^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.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 : Mon May 20 22:47:18 EDT 2024
% Result : Theorem 0.15s 0.41s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 122
% Syntax : Number of formulae : 145 ( 18 unt; 117 typ; 0 def)
% Number of atoms : 273 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 9 avg)
% Number of connectives : 37 ( 20 ~; 10 |; 3 &; 0 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 221 ( 220 >; 1 *; 0 +; 0 <<)
% Number of symbols : 111 ( 108 usr; 25 con; 0-6 aty)
% Number of variables : 57 ( 0 ^ 46 !; 4 ?; 57 :)
% ( 7 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $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(type_def_10,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(func_def_4,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(func_def_5,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_6,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_7,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(func_def_8,type,
tyop_2Erealax_2Ereal: d ).
thf(func_def_9,type,
s: d > u > du ).
thf(func_def_10,type,
app_2E2: du > du > u ).
thf(func_def_11,type,
combin_i_2E0: u ).
thf(func_def_12,type,
combin_k_2E0: u ).
thf(func_def_13,type,
combin_s_2E0: u ).
thf(func_def_14,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_15,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_16,type,
c_2Epair_2E_2C_2E0: u ).
thf(func_def_17,type,
c_2Epair_2E_2C_2E2: du > du > u ).
thf(func_def_18,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_19,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_20,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_21,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_22,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_23,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_24,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_25,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_26,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_27,type,
c_2Epred__set_2ESUBSET_2E0: u ).
thf(func_def_28,type,
c_2Epred__set_2ESUBSET_2E2: du > du > u ).
thf(func_def_29,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_30,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_31,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_32,type,
c_2Ereal__topology_2Eball_2E0: u ).
thf(func_def_33,type,
c_2Ereal__topology_2Eball_2E1: du > u ).
thf(func_def_34,type,
c_2Ereal__topology_2Ebounded__def_2E0: u ).
thf(func_def_35,type,
c_2Ereal__topology_2Ebounded__def_2E1: du > u ).
thf(func_def_36,type,
c_2Ereal__topology_2Ecball_2E0: u ).
thf(func_def_37,type,
c_2Ereal__topology_2Ecball_2E1: du > u ).
thf(func_def_38,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_39,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_40,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_41,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_42,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(func_def_43,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(func_def_44,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(func_def_45,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_46,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_47,type,
mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_48,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_49,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_50,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(func_def_51,type,
mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(func_def_52,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(func_def_53,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_54,type,
mono_2Ec_2Ereal__topology_2Eball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(func_def_55,type,
mono_2Ec_2Ereal__topology_2Ebounded__def: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(func_def_56,type,
mono_2Ec_2Ereal__topology_2Ecball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(func_def_57,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_58,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_59,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_60,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_61,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ) > u ).
thf(func_def_62,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ) > u ).
thf(func_def_63,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
thf(func_def_64,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
thf(func_def_65,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
thf(func_def_66,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).
thf(func_def_67,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
thf(func_def_68,type,
i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
thf(func_def_69,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_70,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_71,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_72,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(func_def_73,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(func_def_74,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(func_def_75,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(func_def_76,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_77,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_78,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(func_def_79,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_81,type,
vNOT: $o > $o ).
thf(func_def_84,type,
vAND: $o > $o > $o ).
thf(func_def_85,type,
vOR: $o > $o > $o ).
thf(func_def_86,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_87,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_88,type,
sP0: $o > $o > $o ).
thf(func_def_89,type,
sP1: $o > $o > $o ).
thf(func_def_90,type,
sP2: $o > $o > $o ).
thf(func_def_91,type,
sP3: $o > $o > $o > $o ).
thf(func_def_92,type,
sP4: $o > $o > $o > $o ).
thf(func_def_93,type,
sP5: $o > $o > $o > $o ).
thf(func_def_94,type,
sP6: $o > $o > $o > $o ).
thf(func_def_95,type,
sP7: $o > $o > $o > $o ).
thf(func_def_96,type,
sP8: $o > $o > $o > $o ).
thf(func_def_97,type,
sP9: $o > $o > $o > $o ).
thf(func_def_98,type,
sP10: $o > $o > $o > $o ).
thf(func_def_99,type,
sP11: $o > $o > $o > $o ).
thf(func_def_100,type,
sP12: $o > $o > $o > $o ).
thf(func_def_101,type,
sP13: $o > $o > $o > $o ).
thf(func_def_102,type,
sP14: $o > $o > $o > $o ).
thf(func_def_103,type,
sP15: $o > $o > $o > $o ).
thf(func_def_104,type,
sK16: mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_105,type,
sK17: mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_106,type,
sK18: u > d > u ).
thf(func_def_107,type,
sK19: u > d > u ).
thf(func_def_108,type,
sK20: u > d > u ).
thf(func_def_109,type,
sK21: u > u > d > d > u ).
thf(func_def_111,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_112,type,
vIMP: $o > $o > $o ).
thf(func_def_113,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_114,type,
sK23: u > d > u ).
thf(f5267,plain,
$false,
inference(equality_resolution,[],[f5166]) ).
thf(f5166,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1)) != vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17)) ),
inference(trivial_inequality_removal,[],[f5165]) ).
thf(f5165,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( $true != $true )
| ( vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1)) != vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17)) ) ),
inference(constrained_superposition,[],[f321,f5162]) ).
thf(f5162,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
inference(subsumption_resolution,[],[f5157,f454]) ).
thf(f454,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
inference(cnf_transformation,[],[f131]) ).
thf(f131,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
inference(fool_elimination,[],[f130]) ).
thf(f130,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),
inference(rectify,[],[f69]) ).
thf(f69,axiom,
! [X22: mono_2Etyop_2Erealax_2Ereal,X23: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
thf(f5157,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) )
| ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ) ),
inference(trivial_inequality_removal,[],[f5156]) ).
thf(f5156,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( $true != $true )
| ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) )
| ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ) ),
inference(superposition,[],[f407,f455]) ).
thf(f455,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
inference(cnf_transformation,[],[f133]) ).
thf(f133,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
inference(fool_elimination,[],[f132]) ).
thf(f132,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X22: mono_2Etyop_2Erealax_2Ereal,X23: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
thf(f407,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) )
| ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) )
| ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) ) ),
inference(cnf_transformation,[],[f205]) ).
thf(f205,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) )
| ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) )
| ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) ) ),
inference(flattening,[],[f204]) ).
thf(f204,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) )
| ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) )
| ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) ) ),
inference(ennf_transformation,[],[f107]) ).
thf(f107,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) )
& ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) ) )
=> ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) ) ),
inference(fool_elimination,[],[f106]) ).
thf(f106,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1)
& vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) )
=> vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) ),
inference(rectify,[],[f68]) ).
thf(f68,axiom,
! [X24: mono_2Etyop_2Erealax_2Ereal > $o,X25: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X24),X25)
& vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X25) )
=> vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
thf(f321,plain,
$true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17))),
inference(cnf_transformation,[],[f238]) ).
thf(f238,plain,
$true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f195,f237]) ).
thf(f237,plain,
( ? [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) )
=> ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17))) ) ),
introduced(choice_axiom,[]) ).
thf(f195,plain,
? [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
inference(ennf_transformation,[],[f85]) ).
thf(f85,plain,
~ ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
inference(fool_elimination,[],[f84]) ).
thf(f84,plain,
~ ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),
inference(rectify,[],[f81]) ).
thf(f81,negated_conjecture,
~ ! [X22: mono_2Etyop_2Erealax_2Ereal,X23: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),
inference(negated_conjecture,[],[f80]) ).
thf(f80,conjecture,
! [X22: mono_2Etyop_2Erealax_2Ereal,X23: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ITP023^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sat May 18 17:46:22 EDT 2024
% 0.11/0.30 % CPUTime :
% 0.11/0.31 % (2615)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32 % (2618)WARNING: value z3 for option sas not known
% 0.15/0.33 % (2618)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.33 % (2619)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33 % (2616)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33 % (2621)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.33 % (2620)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.33 % (2622)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.33 % (2617)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33 % Exception at run slice level
% 0.15/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.34 % Exception at run slice level
% 0.15/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.34 % (2622)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.34 % Exception at run slice level
% 0.15/0.34 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.34 % (2623)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.35 % (2624)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.35 % (2623)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.35 % Exception at run slice level
% 0.15/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35 % (2624)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.36 % (2625)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.36 % (2626)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.15/0.40 % (2618)First to succeed.
% 0.15/0.40 % (2618)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2615"
% 0.15/0.41 % (2618)Refutation found. Thanks to Tanya!
% 0.15/0.41 % SZS status Theorem for theBenchmark
% 0.15/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.41 % (2618)------------------------------
% 0.15/0.41 % (2618)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.41 % (2618)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (2618)Memory used [KB]: 1815
% 0.15/0.41 % (2618)Time elapsed: 0.080 s
% 0.15/0.41 % (2618)Instructions burned: 300 (million)
% 0.15/0.41 % (2615)Success in time 0.103 s
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