%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP023^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:56 AM UTC 2026
% Result : Theorem 0.21s 0.33s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 29 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 160 ( 17 ~; 9 |; 3 &; 128 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 99 usr; 25 con; 0-4 aty)
% Number of variables : 48 ( 0 ^; 44 !; 4 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
u: $tType ).
thf(type_def_6,type,
d: $tType ).
thf(type_def_7,type,
du: $tType ).
thf(type_def_8,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(type_def_9,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(type_def_10,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_1,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_2,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(func_def_3,type,
tyop_2Erealax_2Ereal: d ).
thf(func_def_4,type,
s: d > u > du ).
thf(func_def_5,type,
app_2E2: du > du > u ).
thf(func_def_6,type,
combin_i_2E0: u ).
thf(func_def_7,type,
combin_k_2E0: u ).
thf(func_def_8,type,
combin_s_2E0: u ).
thf(func_def_9,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_10,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_11,type,
c_2Epair_2E_2C_2E0: u ).
thf(func_def_12,type,
c_2Epair_2E_2C_2E2: du > du > u ).
thf(func_def_13,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_14,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_15,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_16,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_18,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_19,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_20,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_21,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_22,type,
c_2Epred__set_2ESUBSET_2E0: u ).
thf(func_def_23,type,
c_2Epred__set_2ESUBSET_2E2: du > du > u ).
thf(func_def_24,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_25,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_26,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_27,type,
c_2Ereal__topology_2Eball_2E0: u ).
thf(func_def_28,type,
c_2Ereal__topology_2Eball_2E1: du > u ).
thf(func_def_29,type,
c_2Ereal__topology_2Ebounded__def_2E0: u ).
thf(func_def_30,type,
c_2Ereal__topology_2Ebounded__def_2E1: du > u ).
thf(func_def_31,type,
c_2Ereal__topology_2Ecball_2E0: u ).
thf(func_def_32,type,
c_2Ereal__topology_2Ecball_2E1: du > u ).
thf(func_def_33,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_34,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_35,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_44,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_45,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(func_def_46,type,
mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(func_def_47,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(func_def_48,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_49,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_50,type,
mono_2Ec_2Ereal__topology_2Ebounded__def: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(func_def_51,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_52,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_53,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_54,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_55,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_56,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_57,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_58,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_59,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
thf(func_def_60,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_61,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_62,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_63,type,
i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
thf(func_def_64,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_65,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_66,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_67,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_68,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_69,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_70,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(func_def_71,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_72,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_73,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_74,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_76,type,
vNOT: $o > $o ).
thf(func_def_79,type,
vOR: $o > $o > $o ).
thf(func_def_80,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_81,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_82,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_83,type,
vAND: $o > $o > $o ).
thf(func_def_84,type,
sP0: $o > $o > $o > $o ).
thf(func_def_85,type,
sP1: $o > $o > $o > $o ).
thf(func_def_86,type,
sP2: $o > $o > $o > $o ).
thf(func_def_87,type,
sP3: $o > $o > $o > $o ).
thf(func_def_88,type,
sP4: $o > $o > $o > $o ).
thf(func_def_89,type,
sP5: $o > $o > $o > $o ).
thf(func_def_90,type,
sP6: $o > $o > $o > $o ).
thf(func_def_91,type,
sP7: $o > $o > $o > $o ).
thf(func_def_92,type,
sP8: $o > $o > $o > $o ).
thf(func_def_93,type,
sP9: $o > $o > $o > $o ).
thf(func_def_94,type,
sK10: d > u > d > u > u ).
thf(func_def_95,type,
sK11: mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_96,type,
sK12: mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_97,type,
sK13: u > d > u ).
thf(func_def_98,type,
sK14: d > u > u ).
thf(func_def_99,type,
sK15: d > u > u ).
thf(func_def_100,type,
sK16: u > d > u ).
thf(f67,axiom,
! [X1: mono_2Etyop_2Erealax_2Ereal,X0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
thf(f68,axiom,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
thf(f69,axiom,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
thf(f80,conjecture,
! [X1: mono_2Etyop_2Erealax_2Ereal,X0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
thf(f81,negated_conjecture,
~ ! [X1: mono_2Etyop_2Erealax_2Ereal,X0: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f80]) ).
thf(f84,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 ) ),
inference(rectify,[],[f68]) ).
thf(f85,plain,
! [X1: mono_2Etyop_2Erealax_2Ereal > $o,X0: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
= $true )
& ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
= $true ) )
=> ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true ) ),
inference(fool_elimination,[],[f84]) ).
thf(f122,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) ),
inference(rectify,[],[f69]) ).
thf(f123,plain,
! [X1: mono_2Etyop_2Erealax_2Ereal,X0: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
= $true ),
inference(fool_elimination,[],[f122]) ).
thf(f134,plain,
~ ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ),
inference(rectify,[],[f81]) ).
thf(f135,plain,
~ ! [X1: mono_2Etyop_2Erealax_2Ereal,X0: mono_2Etyop_2Erealax_2Ereal] :
( $true
= ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f134]) ).
thf(f144,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ),
inference(rectify,[],[f67]) ).
thf(f145,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( $true
= ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f144]) ).
thf(f165,plain,
? [X1: mono_2Etyop_2Erealax_2Ereal,X0: mono_2Etyop_2Erealax_2Ereal] :
( $true
!= ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f135]) ).
thf(f173,plain,
! [X1: mono_2Etyop_2Erealax_2Ereal > $o,X0: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true )
| ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
!= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f85]) ).
thf(f174,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true )
| ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
!= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
!= $true ) ),
inference(flattening,[],[f173]) ).
thf(f235,plain,
? [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
!= $true ),
inference(rectify,[],[f165]) ).
thf(f236,plain,
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK11 @ sK12 ) ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f235]) ).
thf(f270,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
= $true ),
inference(rectify,[],[f123]) ).
thf(f309,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( $true
= ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f145]) ).
thf(f353,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
!= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f174]) ).
thf(f381,plain,
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK11 @ sK12 ) ) )
!= $true ),
inference(cnf_transformation,[],[f236]) ).
thf(f473,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
= $true ),
inference(cnf_transformation,[],[f270]) ).
thf(f855,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( $true != $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
!= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
= $true ) ),
inference(constrained_superposition,[],[f353,f309]) ).
thf(f856,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f855]) ).
thf(f857,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
= $true ),
inference(forward_subsumption_resolution,[],[f856,f473]) ).
thf(f860,plain,
$true != $true,
inference(constrained_superposition,[],[f381,f857]) ).
thf(f861,plain,
$false,
inference(trivial_inequality_removal,[],[f860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP023^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:31:08 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.33 % (792003)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.33 % (792025)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1185271454:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.33 % (792031)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.33 % (792031)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.33 % (792026)lrs+10_16_si=on:nwc=1.5:random_seed=3463440300:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.33 % (792029)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2594752761:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.33 % (792027)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3102785323:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.33 % (792028)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=855421057:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.33 % (792030)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=130588281:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.33 % (792031)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3932741881:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.33 % (792027)Instruction limit reached!
% 0.21/0.33 % (792027)------------------------------
% 0.21/0.33 % (792027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (792027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (792027)CaDiCaL version: 2.1.3
% 0.21/0.33 % (792027)Termination reason: Instruction limit
% 0.21/0.33 % (792027)Termination phase: shuffling
% 0.21/0.33 % (792027)Time elapsed: 0.002 s
% 0.21/0.33 % (792027)Peak memory usage: 10 MB
% 0.21/0.33 % (792027)Instructions burned: 4 (million)
% 0.21/0.33 % (792025) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-792003-792025"...
% 0.21/0.33 % (792025)...printing done.
% 0.21/0.33 % (792025)Refutation found. Thanks to Tanya!
% 0.21/0.33 % SZS status Theorem for theBenchmark
% 0.21/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.34 % (792025)------------------------------
% 0.21/0.34 % (792025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (792025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (792025)CaDiCaL version: 2.1.3
% 0.21/0.34 % (792025)Termination reason: Refutation
% 0.21/0.34 % (792025)Time elapsed: 0.016 s
% 0.21/0.34 % (792025)Peak memory usage: 13 MB
% 0.21/0.34 % (792025)Instructions burned: 55 (million)
% 0.21/0.34 % (792003)Success in time 0.06 s
% 0.21/0.34 % Vampire exiting
%------------------------------------------------------------------------------