↑ Up

Vampire---5.0.1.THM-Ref.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : ITP019^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n012.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 08:07:51 AM UTC 2026

% Result   : Theorem 0.08s 0.18s
% Output   : Refutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   18 (   8 unt;   0 typ;   0 def)
%            Number of atoms       :   50 (  39 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   80 (  25   ~;   4   |;   3   &;  43   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   68 (  65 usr;  24 con; 0-4 aty)
%            Number of variables   :    8 (   0   ^;   7   !;   1   ?;   8   :)

% 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_2Enum_2Enum: $tType ).

thf(type_def_9,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $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_2Enum_2Enum: d ).

thf(func_def_3,type,
    tyop_2Epair_2Eprod: d > d > d ).

thf(func_def_4,type,
    tyop_2Erealax_2Ereal: d ).

thf(func_def_5,type,
    s: d > u > du ).

thf(func_def_6,type,
    app_2E2: du > du > u ).

thf(func_def_7,type,
    combin_i_2E0: u ).

thf(func_def_8,type,
    combin_k_2E0: u ).

thf(func_def_9,type,
    combin_s_2E0: u ).

thf(func_def_10,type,
    c_2Ebool_2E_21_2E0: u ).

thf(func_def_11,type,
    c_2Ebool_2E_21_2E1: du > u ).

thf(func_def_12,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

thf(func_def_13,type,
    c_2Ebool_2E_2F_5C_2E2: du > du > u ).

thf(func_def_14,type,
    c_2Enum_2E0_2E0: 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_2Ebool_2ET_2E0: u ).

thf(func_def_23,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

thf(func_def_24,type,
    c_2Ebool_2E_5C_2F_2E2: du > du > u ).

thf(func_def_25,type,
    c_2Ecomplex_2Ecomplex__inv_2E0: u ).

thf(func_def_26,type,
    c_2Ecomplex_2Ecomplex__inv_2E1: du > u ).

thf(func_def_27,type,
    c_2Ecomplex_2Ecomplex__of__num_2E0: u ).

thf(func_def_28,type,
    c_2Ecomplex_2Ecomplex__of__num_2E1: du > u ).

thf(func_def_29,type,
    c_2Ebool_2E_7E_2E0: u ).

thf(func_def_30,type,
    c_2Ebool_2E_7E_2E1: du > u ).

thf(func_def_31,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).

thf(func_def_32,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_33,type,
    mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_34,type,
    mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_35,type,
    mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(func_def_36,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(func_def_37,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(func_def_38,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(func_def_39,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(func_def_40,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(func_def_41,type,
    mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_42,type,
    mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_43,type,
    mono_2Ec_2Ebool_2E_7E: $o > $o ).

thf(func_def_44,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(func_def_45,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).

thf(func_def_46,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_47,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(func_def_48,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( 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_49,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

thf(func_def_50,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_51,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(func_def_52,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).

thf(func_def_53,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_54,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_55,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_56,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

thf(func_def_57,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_59,type,
    vNOT: $o > $o ).

thf(func_def_60,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_63,type,
    sK0: d > u > d > u > u ).

thf(func_def_64,type,
    sK1: u > d > u ).

thf(func_def_65,type,
    sK2: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_66,type,
    sK3: u > d > u ).

thf(f40,axiom,
    ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( X0
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    <=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).

thf(f41,conjecture,
    ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( X0
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).

thf(f42,negated_conjecture,
    ~ ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( X0
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
       => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(negated_conjecture,[status(cth)],[f41]) ).

thf(f43,plain,
    ~ ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( X0
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
       => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(rectify,[],[f42]) ).

thf(f44,plain,
    ~ ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
           != X0 )
          = $true )
       => ( $true
          = ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
           != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ),
    inference(fool_elimination,[],[f43]) ).

thf(f78,plain,
    ? [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
         != X0 )
        = $true )
      & ( $true
       != ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ),
    inference(ennf_transformation,[],[f44]) ).

thf(f104,plain,
    ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( X0
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
      & ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
         != X0 ) ) ),
    inference(nnf_transformation,[],[f40]) ).

thf(f106,plain,
    ( ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
       != sK2 )
      = $true )
    & ( $true
     != ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK2 )
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f78]) ).

thf(f167,plain,
    ! [X0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X0 )
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      | ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
        = X0 ) ),
    inference(cnf_transformation,[],[f104]) ).

thf(f169,plain,
    ( $true
   != ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK2 )
     != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(cnf_transformation,[],[f106]) ).

thf(f170,plain,
    ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
     != sK2 )
    = $true ),
    inference(cnf_transformation,[],[f106]) ).

thf(f211,plain,
    ( $true
    = ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK2 )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(not_proxy_clausification,[],[f169]) ).

thf(f212,plain,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ sK2 ) ),
    inference(equality_proxy_clausification,[],[f211]) ).

thf(f213,plain,
    ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
      = sK2 )
    = $false ),
    inference(not_proxy_clausification,[],[f170]) ).

thf(f214,plain,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
   != sK2 ),
    inference(equality_proxy_clausification,[],[f213]) ).

thf(f329,plain,
    ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
     != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    | ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
      = sK2 ) ),
    inference(superposition,[],[f167,f212]) ).

thf(f330,plain,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
    = sK2 ),
    inference(trivial_inequality_removal,[],[f329]) ).

thf(f331,plain,
    $false,
    inference(forward_subsumption_resolution,[],[f330,f214]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : ITP019^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10  % Computer : n012.cluster.edu
% 0.00/0.10  % Model    : x86_64 x86_64
% 0.00/0.10  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10  % Memory   : 8046.5625MB
% 0.00/0.10  % OS       : Linux 6.8.0-71-generic
% 0.00/0.10  % CPULimit : 300
% 0.00/0.10  % WCLimit  : 300
% 0.00/0.10  % DateTime : Tue Sep 29 19:32:48 UTC 2026
% 0.00/0.10  % CPUTime  : 
% 0.00/0.10  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12  Running higher-order theorem proving
% 0.08/0.13  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18  % (574787)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.18  % (574798)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.18  % (574798)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
% 0.08/0.18  % (574794)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1744380347:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.18  % (574796)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3763059942:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.18  % (574793)lrs+10_16_si=on:nwc=1.5:random_seed=1259597822:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.18  % (574792)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3970355137:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.18  % (574797)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1385432768:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.18  % (574795)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=3101658081: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)
% 0.08/0.18  % (574798)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=3451878953:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.18  % (574794)Instruction limit reached! 
% 0.08/0.18  % (574794)------------------------------
% 0.08/0.18  % (574794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18  % (574794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18  % (574794)CaDiCaL version: 2.1.3
% 0.08/0.18  % (574794)Termination reason: Instruction limit
% 0.08/0.18  % (574794)Termination phase: Property scanning
% 0.08/0.18  % (574794)Time elapsed: 0.003 s
% 0.08/0.18  % (574794)Peak memory usage: 10 MB
% 0.08/0.18  % (574794)Instructions burned: 16 (million)
% 0.08/0.18  % (574793)Instruction limit reached! 
% 0.08/0.18  % (574793)------------------------------
% 0.08/0.18  % (574793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18  % (574793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18  % (574793)CaDiCaL version: 2.1.3
% 0.08/0.18  % (574793)Termination reason: Instruction limit
% 0.08/0.18  % (574793)Termination phase: Saturation
% 0.08/0.18  % (574793)Time elapsed: 0.005 s
% 0.08/0.18  % (574793)Peak memory usage: 11 MB
% 0.08/0.18  % (574793)Instructions burned: 19 (million)
% 0.08/0.18  % (574796) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-574787-574796"...
% 0.08/0.18  % (574792) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-574787-574792"...
% 0.08/0.18  % (574798) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-574787-574798"...
% 0.08/0.18  % (574795) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-574787-574795"...
% 0.08/0.18  % (574796)...printing done.
% 0.08/0.18  % (574797) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-574787-574797"...
% 0.08/0.18  % (574792)...printing done.
% 0.08/0.18  % (574795)...printing done.
% 0.08/0.18  % (574796)Refutation found. Thanks to Tanya!
% 0.08/0.18  % SZS status Theorem for theBenchmark
% 0.08/0.18  % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.18  % (574796)------------------------------
% 0.08/0.18  % (574796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18  % (574796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18  % (574796)CaDiCaL version: 2.1.3
% 0.08/0.18  % (574796)Termination reason: Refutation
% 0.08/0.18  % (574796)Time elapsed: 0.006 s
% 0.08/0.18  % (574796)Peak memory usage: 12 MB
% 0.08/0.18  % (574796)Instructions burned: 22 (million)
% 0.08/0.18  % (574787)Success in time 0.039 s
% 0.08/0.18  % Vampire exiting
%------------------------------------------------------------------------------