%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n003.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 : Tue Sep 29 11:35:56 AM UTC 2026
% Result : Theorem 1.07s 0.58s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 9 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 91 ( 91 usr; 32 con; 0-4 aty)
% Number of variables : 46 ( 44 !; 2 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
u: $tType ).
tff(type_def_6,type,
d: $tType ).
tff(type_def_7,type,
du: $tType ).
tff(type_def_8,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(type_def_9,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(type_def_10,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(type_def_11,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(type_def_12,type,
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: $tType ).
tff(type_def_13,type,
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: $tType ).
tff(type_def_14,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(type_def_15,type,
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: $tType ).
tff(type_def_16,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $tType ).
tff(type_def_17,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
tff(type_def_18,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
tff(func_def_0,type,
tyop_2Emin_2Ebool: d ).
tff(func_def_1,type,
tyop_2Emin_2Efun: ( d * d ) > d ).
tff(func_def_2,type,
tyop_2Epair_2Eprod: ( d * d ) > d ).
tff(func_def_3,type,
tyop_2Erealax_2Ereal: d ).
tff(func_def_4,type,
s: ( d * u ) > du ).
tff(func_def_5,type,
app_2E2: ( du * du ) > u ).
tff(func_def_6,type,
combin_i_2E0: u ).
tff(func_def_7,type,
combin_k_2E0: u ).
tff(func_def_8,type,
combin_s_2E0: u ).
tff(func_def_9,type,
c_2Ebool_2E_21_2E0: u ).
tff(func_def_10,type,
c_2Ebool_2E_21_2E1: du > u ).
tff(func_def_11,type,
c_2Epair_2E_2C_2E0: u ).
tff(func_def_12,type,
c_2Epair_2E_2C_2E2: ( du * du ) > u ).
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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > 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_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_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_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_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_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_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_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_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_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_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 ).
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,
sK0: ( d * d * u * u ) > u ).
tff(func_def_85,type,
sK1: ( d * u ) > u ).
tff(func_def_86,type,
sK2: ( d * u ) > u ).
tff(func_def_87,type,
sK3: ( d * u ) > u ).
tff(func_def_88,type,
sK4: ( d * u ) > u ).
tff(func_def_89,type,
sK11: mono_2Etyop_2Erealax_2Ereal ).
tff(func_def_90,type,
sK12: mono_2Etyop_2Erealax_2Ereal ).
tff(pred_def_1,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP5: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP6: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP7: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP8: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP9: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP10: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > $o ).
tff(f39,axiom,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal) ).
tff(f44,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] : ( mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(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_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal) ).
tff(f46,axiom,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ( mono_2Ec_2Ereal__topology_2Eball_2E1(X0) = 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_2Ec_2Ereal__topology_2Eball_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ereal__topology_2Eball_2E1) ).
tff(f47,axiom,
! [X0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ereal__topology_2Ebounded__def_2E1) ).
tff(f48,axiom,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ( mono_2Ec_2Ereal__topology_2Ecball_2E1(X0) = 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_2Ec_2Ereal__topology_2Ecball_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ereal__topology_2Ecball_2E1) ).
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/sandbox/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_2Ereal__topology_2Ebounded__def_2E1(X1))
& p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1)) )
=> p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X0)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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(f100,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_2Ereal__topology_2Ebounded__def_2E1(X0))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X1))
| ~ p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1)) ),
inference(ennf_transformation,[],[f74]) ).
tff(f101,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_2Ereal__topology_2Ebounded__def_2E1(X0))
| ~ p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X1))
| ~ p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1)) ),
inference(flattening,[],[f100]) ).
tff(f111,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(f161,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(X0,X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1) ),
inference(cnf_transformation,[],[f39]) ).
tff(f171,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] : ( mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(X0,X1) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(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_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) ),
inference(cnf_transformation,[],[f44]) ).
tff(f175,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ( mono_2Ec_2Ereal__topology_2Eball_2E1(X0) = 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_2Ec_2Ereal__topology_2Eball_2E0,X0) ),
inference(cnf_transformation,[],[f46]) ).
tff(f176,plain,
! [X0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(X0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,X0) ),
inference(cnf_transformation,[],[f47]) ).
tff(f177,plain,
! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : ( mono_2Ec_2Ereal__topology_2Ecball_2E1(X0) = 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_2Ec_2Ereal__topology_2Ecball_2E0,X0) ),
inference(cnf_transformation,[],[f48]) ).
tff(f217,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(f218,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,[],[f101]) ).
tff(f219,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(f279,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,[],[f111]) ).
tff(f282,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(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_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Erealax_2Ereal,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_2Ec_2Ereal__topology_2Eball_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),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_2Ec_2Ereal__topology_2Ecball_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1)))),
inference(definition_unfolding,[],[f217,f171,f175,f161,f177,f161]) ).
tff(f283,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_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(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_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Erealax_2Ereal,X0),X1))
| ~ p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,X1))
| p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,X0)) ),
inference(definition_unfolding,[],[f218,f171,f176,f176]) ).
tff(f284,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,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_2Ec_2Ereal__topology_2Ecball_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1)))),
inference(definition_unfolding,[],[f219,f176,f177,f161]) ).
tff(f285,plain,
~ p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,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_2Ec_2Ereal__topology_2Eball_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK11),sK12)))),
inference(definition_unfolding,[],[f279,f176,f175,f161]) ).
tff(f1648,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ~ p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,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_2Ec_2Ereal__topology_2Ecball_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))))
| p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,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_2Ec_2Ereal__topology_2Eball_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1)))) ),
inference(resolution,[],[f282,f283]) ).
tff(f1668,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ereal__topology_2Ebounded__def_2E0,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_2Ec_2Ereal__topology_2Eball_2E0,mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(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_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1)))),
inference(forward_subsumption_resolution,[],[f1648,f284]) ).
tff(f4371,plain,
$false,
inference(backward_subsumption_resolution,[],[f285,f1668]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 12:11:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.07/0.58 % (421511)Will run a generic schedule for satisfiability detection.
% 1.07/0.58 % (421520)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=857992261:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.07/0.58 % (421517)% WARNING: option uhcvi not known.
% 1.07/0.58 % (421516)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1922245383_2999 on theBenchmark for (2999ds/0Mi)
% 1.07/0.58 % (421518)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1506346856:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.07/0.58 % (421519)dis+10_1_sil=32000:sp=arity:random_seed=2292575764:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.07/0.58 % (421521)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1422036255:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.07/0.58 % (421522)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3079628847:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.07/0.58 % (421517)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=982925982:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.07/0.58 % (421520)Instruction limit reached!
% 1.07/0.58 % (421520)------------------------------
% 1.07/0.58 % (421520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (421520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (421520)CaDiCaL version: 2.1.3
% 1.07/0.58 % (421520)Termination reason: Instruction limit
% 1.07/0.58 % (421520)Termination phase: Saturation
% 1.07/0.58 % (421520)Time elapsed: 0.037 s
% 1.07/0.58 % (421520)Peak memory usage: 13 MB
% 1.07/0.58 % (421520)Instructions burned: 118 (million)
% 1.07/0.58 % (421530)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2249946295:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.07/0.58 % (421519)Instruction limit reached!
% 1.07/0.58 % (421519)------------------------------
% 1.07/0.58 % (421519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (421519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (421519)CaDiCaL version: 2.1.3
% 1.07/0.58 % (421519)Termination reason: Instruction limit
% 1.07/0.58 % (421519)Termination phase: Saturation
% 1.07/0.58 % (421519)Time elapsed: 0.056 s
% 1.07/0.58 % (421519)Peak memory usage: 12 MB
% 1.07/0.58 % (421519)Instructions burned: 105 (million)
% 1.07/0.58 % TRYING [1]
% 1.07/0.58 % TRYING [2]
% 1.07/0.58 % Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1,1,1]
% 1.07/0.58 % Detected maximum model sizes of [max,max,2,max,max,max,max,max,max,max,max,max,max]
% 1.07/0.58 % TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,1,1,1,1,1,1,1,1,1,1]
% 1.07/0.58 % TRYING [3]
% 1.07/0.58 % TRYING [1,1,2,2,1,1,1,1,1,1,1,1,1]
% 1.07/0.58 % (421521)Instruction limit reached!
% 1.07/0.58 % (421521)------------------------------
% 1.07/0.58 % (421521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (421521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (421521)CaDiCaL version: 2.1.3
% 1.07/0.58 % (421521)Termination reason: Instruction limit
% 1.07/0.58 % (421521)Termination phase: Saturation
% 1.07/0.58 % (421521)Time elapsed: 0.075 s
% 1.07/0.58 % (421521)Peak memory usage: 13 MB
% 1.07/0.58 % (421521)Instructions burned: 132 (million)
% 1.07/0.58 % TRYING [1,1,2,2,1,1,2,1,1,1,1,1,1]
% 1.07/0.58 % (421532)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2654495362:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.07/0.58 % TRYING [1,1,2,2,1,1,1,1,2,1,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,2,1,1,1,1,1,2,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,2,1,1,1,1,1,1,2,1,1]
% 1.07/0.58 % TRYING [1,1,2,2,1,1,2,1,2,1,1,1,1]
% 1.07/0.58 % (421522)Instruction limit reached!
% 1.07/0.58 % (421522)------------------------------
% 1.07/0.58 % (421522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (421522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (421522)CaDiCaL version: 2.1.3
% 1.07/0.58 % (421522)Termination reason: Instruction limit
% 1.07/0.58 % (421522)Termination phase: Saturation
% 1.07/0.58 % (421522)Time elapsed: 0.091 s
% 1.07/0.58 % (421522)Peak memory usage: 13 MB
% 1.07/0.58 % (421522)Instructions burned: 163 (million)
% 1.07/0.58 % TRYING [1,1,2,3,1,1,2,1,2,1,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,2,2,1,2,1,2,1,1,1,1]
% 1.07/0.58 % (421534)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1439514344:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.07/0.58 % TRYING [1,1,2,3,2,1,2,1,2,1,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,3,2,2,2,1,2,1,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,4,2,2,2,1,2,1,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,3,3,2,2,1,2,1,1,1,1]
% 1.07/0.58 % (421535)ott-21_1_sil=16000:fs=off:random_seed=2033062613:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.07/0.58 % TRYING [1,1,2,4,3,2,2,1,2,1,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,4,3,3,2,1,2,1,1,1,1]
% 1.07/0.58 % TRYING [1,1,2,4,3,2,3,1,2,1,1,1,1]
% 1.07/0.58 % TRYING [2,1,2,4,3,2,3,1,2,1,1,1,1]
% 1.07/0.58 % (421517) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-421511-421517"...
% 1.07/0.58 % (421517)...printing done.
% 1.07/0.58 % (421517)Refutation found. Thanks to Tanya!
% 1.07/0.58 % SZS status Theorem for theBenchmark
% 1.07/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.07/0.58 % (421517)------------------------------
% 1.07/0.58 % (421517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.58 % (421517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.58 % (421517)CaDiCaL version: 2.1.3
% 1.07/0.58 % (421517)Termination reason: Refutation
% 1.07/0.58 % (421517)Time elapsed: 0.124 s
% 1.07/0.58 % (421517)Peak memory usage: 14 MB
% 1.07/0.58 % (421517)Instructions burned: 217 (million)
% 1.07/0.58 % (421511)Success in time 0.169 s
% 1.07/0.58 % Vampire exiting
%------------------------------------------------------------------------------