%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP023_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 : Fri Sep 25 01:48:00 PM UTC 2026
% Result : Theorem 3.08s 1.08s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 9 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 27 ( 26 usr; 15 prp; 0-3 aty)
% Number of functors : 74 ( 74 usr; 26 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 30 !; 2 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
tyop_2Emin_2Ebool: d ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP0: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP1: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_4,type,
sP2: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_5,type,
sP3: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_6,type,
sP4: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_7,type,
sP5: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_8,type,
sP6: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_9,type,
sP7: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_10,type,
sP8: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_11,type,
sP9: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(pred_def_12,type,
sP10: ( mono_2Etyop_2Emin_2Ebool * ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) ) > $o ).
tff(func_def_13,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(func_def_14,type,
c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).
tff(func_def_15,type,
c_2Emin_2E_3D_2E0: u ).
tff(func_def_16,type,
c_2Emin_2E_3D_2E2: ( du * du ) > u ).
tff(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(func_def_18,type,
c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).
tff(func_def_19,type,
c_2Ebool_2E_3F_2E0: u ).
tff(func_def_20,type,
c_2Ebool_2E_3F_2E1: du > u ).
tff(func_def_21,type,
c_2Ebool_2EF_2E0: u ).
tff(func_def_22,type,
c_2Epred__set_2ESUBSET_2E0: u ).
tff(func_def_23,type,
c_2Epred__set_2ESUBSET_2E2: ( du * du ) > u ).
tff(func_def_24,type,
c_2Ebool_2ET_2E0: u ).
tff(func_def_25,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(func_def_26,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(func_def_27,type,
c_2Ereal__topology_2Eball_2E0: u ).
tff(func_def_28,type,
c_2Ereal__topology_2Eball_2E1: du > u ).
tff(func_def_29,type,
c_2Ereal__topology_2Ebounded__def_2E0: u ).
tff(func_def_30,type,
c_2Ereal__topology_2Ebounded__def_2E1: du > u ).
tff(func_def_31,type,
c_2Ereal__topology_2Ecball_2E0: u ).
tff(func_def_32,type,
c_2Ereal__topology_2Ecball_2E1: du > u ).
tff(func_def_33,type,
c_2Ebool_2E_7E_2E0: u ).
tff(func_def_34,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(func_def_35,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_36,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_37,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_38,type,
mono_2Eapp_2E2_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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 * 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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_39,type,
mono_2Eapp_2E2_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_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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_40,type,
mono_2Eapp_2E2_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_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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).
tff(func_def_41,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(func_def_42,type,
mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: 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 ).
tff(func_def_43,type,
mono_2Ec_2Epair_2E_2C_2E2_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 ).
tff(func_def_44,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_45,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_46,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_47,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_48,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_49,type,
mono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Erealax_2Ereal: 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 ).
tff(func_def_50,type,
mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_51,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(func_def_52,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_53,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_54,type,
mono_2Ec_2Ereal__topology_2Eball_2E0: 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 ).
tff(func_def_55,type,
mono_2Ec_2Ereal__topology_2Eball_2E1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_56,type,
mono_2Ec_2Ereal__topology_2Ebounded__def_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_57,type,
mono_2Ec_2Ereal__topology_2Ebounded__def_2E1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_58,type,
mono_2Ec_2Ereal__topology_2Ecball_2E0: 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 ).
tff(func_def_59,type,
mono_2Ec_2Ereal__topology_2Ecball_2E1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_60,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_61,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_62,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(func_def_63,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_64,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_65,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_66,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_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 > u ).
tff(func_def_67,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_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(func_def_68,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > u ).
tff(func_def_69,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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 > u ).
tff(func_def_70,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 > u ).
tff(func_def_71,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 ).
tff(func_def_72,type,
i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
tff(func_def_73,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(func_def_74,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_75,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_76,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_77,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_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 ).
tff(func_def_78,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_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(func_def_79,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(func_def_80,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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 ).
tff(func_def_81,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).
tff(func_def_82,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 ).
tff(func_def_83,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
tff(func_def_84,type,
sK11: mono_2Etyop_2Erealax_2Ereal ).
tff(func_def_85,type,
sK12: mono_2Etyop_2Erealax_2Ereal ).
tff(f73,axiom,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)),mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
tff(f74,axiom,
! [X0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( ( p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1))
& p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X1)) )
=> p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
tff(f75,axiom,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
tff(f86,conjecture,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
tff(f87,negated_conjecture,
~ ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)))),
inference(negated_conjecture,[status(cth)],[f86]) ).
tff(f88,plain,
? [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)))),
inference(ennf_transformation,[],[f87]) ).
tff(f94,plain,
! [X0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( ~ p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X1))
| p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X0)) ),
inference(ennf_transformation,[],[f74]) ).
tff(f95,plain,
! [X0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( ~ p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X1))
| p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X0)) ),
inference(flattening,[],[f94]) ).
tff(f112,plain,
~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(sK11,sK12)))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f88]) ).
tff(f161,plain,
~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(sK11,sK12)))),
inference(cnf_transformation,[],[f112]) ).
tff(f272,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)),mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)))),
inference(cnf_transformation,[],[f73]) ).
tff(f273,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1)))),
inference(cnf_transformation,[],[f75]) ).
tff(f274,plain,
! [X0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( ~ p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X1))
| p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X0)) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_49,negated_conjecture,
~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(sK11,sK12)))),
inference(cnf_transformation,[],[f161]) ).
tcf(c_136,plain,
! [X0_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0_mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal)),mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0_mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal)))),
inference(cnf_transformation,[],[f272]) ).
tcf(c_137,plain,
! [X0_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0_mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal)))),
inference(cnf_transformation,[],[f273]) ).
tcf(c_138,plain,
! [X0_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X1_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
( p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X0_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X1_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29))
| ~ p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,X1_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29)) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_2354,plain,
! [X0_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal] :
( p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0_mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal))))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0_mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal)))) ),
inference(superposition,[status(thm)],[c_136,c_138]) ).
tcf(c_2368,plain,
! [X0_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0_mono_2Etyop_2Erealax_2Ereal,X1_mono_2Etyop_2Erealax_2Ereal)))),
inference(forward_subsumption_resolution,[status(thm)],[c_2354,c_137]) ).
tcf(c_2409,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_2368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP023_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 17:50:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 3.08/1.08 % SZS status Started for theBenchmark.p
% 3.08/1.08 % SZS status Theorem for theBenchmark.p
% 3.08/1.08
% 3.08/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.08/1.08
% 3.08/1.08 % ------ iProver source info
% 3.08/1.08
% 3.08/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 3.08/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.08/1.08 % git: non_committed_changes: false
% 3.08/1.08
% 3.08/1.08 % ------ Parsing...
% 3.08/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 3.08/1.08 %
% 3.08/1.08
% 3.08/1.08 % ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 pe_s pe_e %
% 3.08/1.08
% 3.08/1.08 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 3.08/1.08 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 3.08/1.08 %
% 3.08/1.08
% 3.08/1.08 % ------ Preprocessing...
% 3.08/1.08 % ------ Proving...
% 3.08/1.08 % ------ Problem Properties
% 3.08/1.08
% 3.08/1.08 %
% 3.08/1.08 % clauses 6
% 3.08/1.08 % conjectures 1
% 3.08/1.08 % EPR 2
% 3.08/1.08 % Horn 5
% 3.08/1.08 % unary 3
% 3.08/1.08 % binary 0
% 3.08/1.08 % lits 12
% 3.08/1.08 % lits eq 2
% 3.08/1.08 % fd_pure 0
% 3.08/1.08 % fd_pseudo 0
% 3.08/1.08 % fd_cond 0
% 3.08/1.08 % fd_pseudo_cond 2
% 3.08/1.08 % AC symbols 0
% 3.08/1.08
% 3.08/1.08 % ------ Schedule dynamic 5 is on
% 3.08/1.08
% 3.08/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.08/1.08
% 3.08/1.08
% 3.08/1.08 % ------
% 3.08/1.08 % Current options:
% 3.08/1.08 % ------
% 3.08/1.08
% 3.08/1.08
% 3.08/1.08 %
% 3.08/1.08
% 3.08/1.08 % ------ Proving...
% 3.08/1.08 %
% 3.08/1.08
% 3.08/1.08 % SZS status Theorem for theBenchmark.p
% 3.08/1.08
% 3.08/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.08/1.08
%------------------------------------------------------------------------------