TSTP Solution File: ITP023_2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : ITP023_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 17:17:01 EDT 2022

% Result   : Theorem 0.18s 0.58s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   62
% Syntax   : Number of formulae    :   97 (  26 unt;  52 typ;   0 def)
%            Number of atoms       :  291 (   0 equ)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives :   83 (  40   ~;  30   |;   2   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :  203 ( 203 fml;   0 var)
%            Number of types       :    6 (   4 usr)
%            Number of type conns  :   81 (  41   >;  40   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  20 usr;   4 prp; 0-3 aty)
%            Number of functors    :   33 (  33 usr;   7 con; 0-3 aty)
%            Number of variables   :   76 (  72   !;   4   ?;  62   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    del: $tType ).

tff(type_def_6,type,
    tp__o: $tType ).

tff(type_def_7,type,
    tp__ty_2Erealax_2Ereal: $tType ).

tff(type_def_8,type,
    tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType ).

tff(func_def_0,type,
    bool: del ).

tff(func_def_1,type,
    ind: del ).

tff(func_def_2,type,
    arr: ( del * del ) > del ).

tff(func_def_4,type,
    k: ( del * $i ) > $i ).

tff(func_def_5,type,
    i: del > $i ).

tff(func_def_6,type,
    inj__o: tp__o > $i ).

tff(func_def_7,type,
    surj__o: $i > tp__o ).

tff(func_def_9,type,
    fo__c_2Ebool_2ET: tp__o ).

tff(func_def_10,type,
    c_2Ebool_2E_3F: del > $i ).

tff(func_def_11,type,
    ty_2Erealax_2Ereal: del ).

tff(func_def_12,type,
    inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).

tff(func_def_13,type,
    surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).

tff(func_def_14,type,
    ty_2Epair_2Eprod: ( del * del ) > del ).

tff(func_def_15,type,
    inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > $i ).

tff(func_def_16,type,
    surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $i > tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).

tff(func_def_18,type,
    fo__c_2Ereal__topology_2Eball: ( tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__o ).

tff(func_def_19,type,
    c_2Epred__set_2ESUBSET: del > $i ).

tff(func_def_20,type,
    c_2Epair_2E_2C: ( del * del ) > $i ).

tff(func_def_22,type,
    fo__c_2Ereal__topology_2Ecball: ( tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > tp__o ).

tff(func_def_25,type,
    fo__c_2Ebool_2EF: tp__o ).

tff(func_def_27,type,
    fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).

tff(func_def_29,type,
    fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).

tff(func_def_31,type,
    fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).

tff(func_def_33,type,
    fo__c_2Ebool_2E_7E: tp__o > tp__o ).

tff(func_def_34,type,
    c_2Emin_2E_3D: del > $i ).

tff(func_def_35,type,
    c_2Ebool_2E_21: del > $i ).

tff(func_def_36,type,
    sK11: ( $i * del ) > $i ).

tff(func_def_37,type,
    sK12: ( $i * del ) > $i ).

tff(func_def_38,type,
    sK13: tp__ty_2Erealax_2Ereal ).

tff(func_def_39,type,
    sK14: tp__ty_2Erealax_2Ereal ).

tff(func_def_40,type,
    sK15: ( del * $i * $i ) > $i ).

tff(func_def_41,type,
    sK16: ( $i * del ) > $i ).

tff(func_def_42,type,
    sK17: ( del * $i ) > $i ).

tff(pred_def_1,type,
    mem: ( $i * del ) > $o ).

tff(pred_def_3,type,
    sP0: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_4,type,
    sP1: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_5,type,
    sP2: ( tp__o * tp__o ) > $o ).

tff(pred_def_6,type,
    sP3: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_7,type,
    sP4: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_8,type,
    sP5: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_9,type,
    sP6: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_10,type,
    sP7: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_11,type,
    sP8: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_12,type,
    sP9: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_13,type,
    sP10: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_15,type,
    sQ19_eqProxy: ( tp__ty_2Erealax_2Ereal * tp__ty_2Erealax_2Ereal ) > $o ).

tff(pred_def_16,type,
    sQ20_eqProxy: ( tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal * tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) > $o ).

tff(pred_def_17,type,
    sQ21_eqProxy: ( tp__o * tp__o ) > $o ).

tff(f813,plain,
    $false,
    inference(subsumption_resolution,[],[f812,f327]) ).

tff(f327,plain,
    ! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
    inference(cnf_transformation,[],[f119]) ).

tff(f119,plain,
    ! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
    inference(rectify,[],[f15]) ).

tff(f15,axiom,
    ! [X3: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X3),ty_2Erealax_2Ereal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_inj_mem_ty_2Erealax_2Ereal) ).

tff(f812,plain,
    ~ mem(inj__ty_2Erealax_2Ereal(sK14),ty_2Erealax_2Ereal),
    inference(subsumption_resolution,[],[f811,f327]) ).

tff(f811,plain,
    ( ~ mem(inj__ty_2Erealax_2Ereal(sK13),ty_2Erealax_2Ereal)
    | ~ mem(inj__ty_2Erealax_2Ereal(sK14),ty_2Erealax_2Ereal) ),
    inference(resolution,[],[f810,f713]) ).

tff(f713,plain,
    ! [X2: del,X3: $i,X0: $i,X1: del] :
      ( mem(ap(ap(c_2Epair_2E_2C(X1,X2),X0),X3),ty_2Epair_2Eprod(X1,X2))
      | ~ mem(X3,X2)
      | ~ mem(X0,X1) ),
    inference(resolution,[],[f625,f414]) ).

tff(f414,plain,
    ! [X2: del,X3: $i,X0: $i,X1: del] :
      ( ~ mem(X0,arr(X1,X2))
      | mem(ap(X0,X3),X2)
      | ~ mem(X3,X1) ),
    inference(cnf_transformation,[],[f178]) ).

tff(f178,plain,
    ! [X0,X1: del,X2: del] :
      ( ! [X3] :
          ( ~ mem(X3,X1)
          | mem(ap(X0,X3),X2) )
      | ~ mem(X0,arr(X1,X2)) ),
    inference(ennf_transformation,[],[f115]) ).

tff(f115,plain,
    ! [X0,X1: del,X2: del] :
      ( mem(X0,arr(X1,X2))
     => ! [X3] :
          ( mem(X3,X1)
         => mem(ap(X0,X3),X2) ) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X2,X0: del,X1: del] :
      ( mem(X2,arr(X0,X1))
     => ! [X3] :
          ( mem(X3,X0)
         => mem(ap(X2,X3),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_tp) ).

tff(f625,plain,
    ! [X2: del,X3: $i,X1: del] :
      ( mem(ap(c_2Epair_2E_2C(X1,X2),X3),arr(X2,ty_2Epair_2Eprod(X1,X2)))
      | ~ mem(X3,X1) ),
    inference(resolution,[],[f414,f360]) ).

tff(f360,plain,
    ! [X0: del,X1: del] : mem(c_2Epair_2E_2C(X1,X0),arr(X1,arr(X0,ty_2Epair_2Eprod(X1,X0)))),
    inference(cnf_transformation,[],[f128]) ).

tff(f128,plain,
    ! [X0: del,X1: del] : mem(c_2Epair_2E_2C(X1,X0),arr(X1,arr(X0,ty_2Epair_2Eprod(X1,X0)))),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X11: del,X8: del] : mem(c_2Epair_2E_2C(X8,X11),arr(X8,arr(X11,ty_2Epair_2Eprod(X8,X11)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epair_2E_2C) ).

tff(f810,plain,
    ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(sK14)),inj__ty_2Erealax_2Ereal(sK13)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
    inference(resolution,[],[f764,f347]) ).

tff(f347,plain,
    ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(sK14)),inj__ty_2Erealax_2Ereal(sK13))))),
    inference(cnf_transformation,[],[f222]) ).

tff(f222,plain,
    ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(sK14)),inj__ty_2Erealax_2Ereal(sK13))))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f152,f221]) ).

tff(f221,plain,
    ( ? [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X1)),inj__ty_2Erealax_2Ereal(X0)))))
   => ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(sK14)),inj__ty_2Erealax_2Ereal(sK13))))) ),
    introduced(choice_axiom,[]) ).

tff(f152,plain,
    ? [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X1)),inj__ty_2Erealax_2Ereal(X0))))),
    inference(ennf_transformation,[],[f77]) ).

tff(f77,plain,
    ~ ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X1)),inj__ty_2Erealax_2Ereal(X0))))),
    inference(rectify,[],[f72]) ).

tff(f72,negated_conjecture,
    ~ ! [X23: tp__ty_2Erealax_2Ereal,X15: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X15)),inj__ty_2Erealax_2Ereal(X23))))),
    inference(negated_conjecture,[],[f71]) ).

tff(f71,conjecture,
    ! [X23: tp__ty_2Erealax_2Ereal,X15: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X15)),inj__ty_2Erealax_2Ereal(X23))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__BALL) ).

tff(f764,plain,
    ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] :
      ( p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))
      | ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
    inference(subsumption_resolution,[],[f763,f624]) ).

tff(f624,plain,
    ! [X0: $i] :
      ( mem(ap(c_2Ereal__topology_2Eball,X0),arr(ty_2Erealax_2Ereal,bool))
      | ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
    inference(resolution,[],[f414,f418]) ).

tff(f418,plain,
    mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
    inference(cnf_transformation,[],[f20]) ).

tff(f20,axiom,
    mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ereal__topology_2Eball) ).

tff(f763,plain,
    ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] :
      ( p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))
      | ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
      | ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1))),arr(ty_2Erealax_2Ereal,bool)) ),
    inference(resolution,[],[f693,f694]) ).

tff(f694,plain,
    ! [X0: $i] :
      ( mem(ap(c_2Ereal__topology_2Ecball,X0),arr(ty_2Erealax_2Ereal,bool))
      | ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
    inference(resolution,[],[f409,f414]) ).

tff(f409,plain,
    mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
    inference(cnf_transformation,[],[f24]) ).

tff(f24,axiom,
    mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ereal__topology_2Ecball) ).

tff(f693,plain,
    ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] :
      ( ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1))),arr(ty_2Erealax_2Ereal,bool))
      | ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1))),arr(ty_2Erealax_2Ereal,bool))
      | p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1))))) ),
    inference(subsumption_resolution,[],[f692,f499]) ).

tff(f499,plain,
    ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1))))),
    inference(cnf_transformation,[],[f289]) ).

tff(f289,plain,
    ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1))))),
    inference(rectify,[],[f78]) ).

tff(f78,plain,
    ! [X1: tp__ty_2Erealax_2Ereal,X0: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X1)),inj__ty_2Erealax_2Ereal(X0))))),
    inference(rectify,[],[f60]) ).

tff(f60,axiom,
    ! [X23: tp__ty_2Erealax_2Ereal,X15: tp__ty_2Erealax_2Ereal] : p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X15)),inj__ty_2Erealax_2Ereal(X23))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__CBALL) ).

tff(f692,plain,
    ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] :
      ( ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))
      | p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1)))))
      | ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1))),arr(ty_2Erealax_2Ereal,bool))
      | ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0)),inj__ty_2Erealax_2Ereal(X1))),arr(ty_2Erealax_2Ereal,bool)) ),
    inference(resolution,[],[f307,f496]) ).

tff(f496,plain,
    ! [X0: $i,X1: $i] :
      ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
      | p(ap(c_2Ereal__topology_2Ebounded__def,X0))
      | ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
      | ~ mem(X1,arr(ty_2Erealax_2Ereal,bool))
      | ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
    inference(cnf_transformation,[],[f162]) ).

tff(f162,plain,
    ! [X0] :
      ( ~ mem(X0,arr(ty_2Erealax_2Ereal,bool))
      | ! [X1] :
          ( p(ap(c_2Ereal__topology_2Ebounded__def,X0))
          | ~ mem(X1,arr(ty_2Erealax_2Ereal,bool))
          | ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
          | ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1)) ) ),
    inference(flattening,[],[f161]) ).

tff(f161,plain,
    ! [X0] :
      ( ! [X1] :
          ( p(ap(c_2Ereal__topology_2Ebounded__def,X0))
          | ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
          | ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
          | ~ mem(X1,arr(ty_2Erealax_2Ereal,bool)) )
      | ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
    inference(ennf_transformation,[],[f127]) ).

tff(f127,plain,
    ! [X0] :
      ( mem(X0,arr(ty_2Erealax_2Ereal,bool))
     => ! [X1] :
          ( mem(X1,arr(ty_2Erealax_2Ereal,bool))
         => ( ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
              & p(ap(c_2Ereal__topology_2Ebounded__def,X1)) )
           => p(ap(c_2Ereal__topology_2Ebounded__def,X0)) ) ) ),
    inference(rectify,[],[f59]) ).

tff(f59,axiom,
    ! [X24] :
      ( mem(X24,arr(ty_2Erealax_2Ereal,bool))
     => ! [X25] :
          ( mem(X25,arr(ty_2Erealax_2Ereal,bool))
         => ( ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X24),X25))
              & p(ap(c_2Ereal__topology_2Ebounded__def,X25)) )
           => p(ap(c_2Ereal__topology_2Ebounded__def,X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__SUBSET) ).

tff(f307,plain,
    ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X1)),inj__ty_2Erealax_2Ereal(X0)))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X1)),inj__ty_2Erealax_2Ereal(X0))))),
    inference(cnf_transformation,[],[f133]) ).

tff(f133,plain,
    ! [X0: tp__ty_2Erealax_2Ereal,X1: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X1)),inj__ty_2Erealax_2Ereal(X0)))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X1)),inj__ty_2Erealax_2Ereal(X0))))),
    inference(rectify,[],[f58]) ).

tff(f58,axiom,
    ! [X23: tp__ty_2Erealax_2Ereal,X15: tp__ty_2Erealax_2Ereal] : p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X15)),inj__ty_2Erealax_2Ereal(X23)))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X15)),inj__ty_2Erealax_2Ereal(X23))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : ITP023_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.33  % Computer : n021.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Tue Aug 30 00:16:10 EDT 2022
% 0.11/0.33  % CPUTime    : 
% 0.18/0.47  % (8924)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.18/0.49  % (8942)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.18/0.49  % (8943)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.18/0.49  % (8935)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.49  % (8934)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.50  % (8938)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.50  % (8924)Refutation not found, incomplete strategy% (8924)------------------------------
% 0.18/0.50  % (8924)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (8934)Instruction limit reached!
% 0.18/0.50  % (8934)------------------------------
% 0.18/0.50  % (8934)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (8924)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (8924)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.50  
% 0.18/0.50  % (8924)Memory used [KB]: 1791
% 0.18/0.50  % (8924)Time elapsed: 0.101 s
% 0.18/0.50  % (8924)Instructions burned: 10 (million)
% 0.18/0.50  % (8924)------------------------------
% 0.18/0.50  % (8924)------------------------------
% 0.18/0.50  % (8934)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (8934)Termination reason: Unknown
% 0.18/0.50  % (8934)Termination phase: Preprocessing 3
% 0.18/0.50  
% 0.18/0.50  % (8923)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.50  % (8934)Memory used [KB]: 1535
% 0.18/0.50  % (8934)Time elapsed: 0.003 s
% 0.18/0.50  % (8934)Instructions burned: 3 (million)
% 0.18/0.50  % (8934)------------------------------
% 0.18/0.50  % (8934)------------------------------
% 0.18/0.50  % (8926)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.50  % (8922)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.50  % (8922)Refutation not found, incomplete strategy% (8922)------------------------------
% 0.18/0.50  % (8922)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (8922)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (8922)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.50  
% 0.18/0.50  % (8922)Memory used [KB]: 6012
% 0.18/0.50  % (8922)Time elapsed: 0.116 s
% 0.18/0.50  % (8922)Instructions burned: 2 (million)
% 0.18/0.50  % (8922)------------------------------
% 0.18/0.50  % (8922)------------------------------
% 0.18/0.50  % (8930)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.18/0.50  % (8920)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.51  % (8920)Refutation not found, incomplete strategy% (8920)------------------------------
% 0.18/0.51  % (8920)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (8920)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (8920)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.51  
% 0.18/0.51  % (8920)Memory used [KB]: 6140
% 0.18/0.51  % (8920)Time elapsed: 0.109 s
% 0.18/0.51  % (8920)Instructions burned: 5 (million)
% 0.18/0.51  % (8920)------------------------------
% 0.18/0.51  % (8920)------------------------------
% 0.18/0.51  % (8938)Instruction limit reached!
% 0.18/0.51  % (8938)------------------------------
% 0.18/0.51  % (8938)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (8943)Refutation not found, incomplete strategy% (8943)------------------------------
% 0.18/0.51  % (8943)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (8943)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (8943)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.51  
% 0.18/0.51  % (8943)Memory used [KB]: 1918
% 0.18/0.51  % (8943)Time elapsed: 0.085 s
% 0.18/0.51  % (8943)Instructions burned: 12 (million)
% 0.18/0.51  % (8943)------------------------------
% 0.18/0.51  % (8943)------------------------------
% 0.18/0.51  % (8932)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.51  % (8941)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.51  % (8948)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.18/0.51  % (8948)Instruction limit reached!
% 0.18/0.51  % (8948)------------------------------
% 0.18/0.51  % (8948)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (8948)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (8948)Termination reason: Unknown
% 0.18/0.51  % (8948)Termination phase: Saturation
% 0.18/0.51  
% 0.18/0.51  % (8948)Memory used [KB]: 1663
% 0.18/0.51  % (8948)Time elapsed: 0.004 s
% 0.18/0.51  % (8948)Instructions burned: 8 (million)
% 0.18/0.51  % (8948)------------------------------
% 0.18/0.51  % (8948)------------------------------
% 0.18/0.51  % (8937)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.51  % (8940)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.18/0.51  % (8938)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (8938)Termination reason: Unknown
% 0.18/0.51  % (8938)Termination phase: Preprocessing 1
% 0.18/0.51  
% 0.18/0.51  % (8938)Memory used [KB]: 1407
% 0.18/0.51  % (8938)Time elapsed: 0.003 s
% 0.18/0.51  % (8938)Instructions burned: 2 (million)
% 0.18/0.51  % (8938)------------------------------
% 0.18/0.51  % (8938)------------------------------
% 0.18/0.52  % (8935)Instruction limit reached!
% 0.18/0.52  % (8935)------------------------------
% 0.18/0.52  % (8935)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (8935)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (8935)Termination reason: Unknown
% 0.18/0.52  % (8935)Termination phase: Saturation
% 0.18/0.52  
% 0.18/0.52  % (8935)Memory used [KB]: 6140
% 0.18/0.52  % (8935)Time elapsed: 0.007 s
% 0.18/0.52  % (8935)Instructions burned: 9 (million)
% 0.18/0.52  % (8935)------------------------------
% 0.18/0.52  % (8935)------------------------------
% 0.18/0.52  % (8945)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.18/0.52  % (8923)Instruction limit reached!
% 0.18/0.52  % (8923)------------------------------
% 0.18/0.52  % (8923)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (8930)Instruction limit reached!
% 0.18/0.52  % (8930)------------------------------
% 0.18/0.52  % (8930)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (8930)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (8930)Termination reason: Unknown
% 0.18/0.52  % (8930)Termination phase: Saturation
% 0.18/0.52  
% 0.18/0.52  % (8930)Memory used [KB]: 6268
% 0.18/0.52  % (8930)Time elapsed: 0.137 s
% 0.18/0.52  % (8930)Instructions burned: 13 (million)
% 0.18/0.52  % (8930)------------------------------
% 0.18/0.52  % (8930)------------------------------
% 0.18/0.52  % (8919)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.18/0.52  % (8925)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.52  % (8923)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (8923)Termination reason: Unknown
% 0.18/0.52  % (8923)Termination phase: Property scanning
% 0.18/0.52  
% 0.18/0.52  % (8923)Memory used [KB]: 1663
% 0.18/0.52  % (8923)Time elapsed: 0.007 s
% 0.18/0.52  % (8923)Instructions burned: 14 (million)
% 0.18/0.52  % (8923)------------------------------
% 0.18/0.52  % (8923)------------------------------
% 0.18/0.52  % (8933)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.52  % (8921)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.52  % (8921)Instruction limit reached!
% 0.18/0.52  % (8921)------------------------------
% 0.18/0.52  % (8921)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (8921)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (8921)Termination reason: Unknown
% 0.18/0.52  % (8921)Termination phase: Preprocessing 3
% 0.18/0.52  
% 0.18/0.52  % (8921)Memory used [KB]: 1535
% 0.18/0.52  % (8921)Time elapsed: 0.003 s
% 0.18/0.52  % (8921)Instructions burned: 3 (million)
% 0.18/0.52  % (8921)------------------------------
% 0.18/0.52  % (8921)------------------------------
% 0.18/0.52  % (8927)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.18/0.52  % (8932)Refutation not found, incomplete strategy% (8932)------------------------------
% 0.18/0.52  % (8932)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (8932)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (8932)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.52  
% 0.18/0.52  % (8932)Memory used [KB]: 1791
% 0.18/0.52  % (8932)Time elapsed: 0.140 s
% 0.18/0.52  % (8932)Instructions burned: 10 (million)
% 0.18/0.52  % (8932)------------------------------
% 0.18/0.52  % (8932)------------------------------
% 0.18/0.52  % (8927)Refutation not found, incomplete strategy% (8927)------------------------------
% 0.18/0.52  % (8927)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (8927)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.53  % (8927)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.53  
% 0.18/0.53  % (8927)Memory used [KB]: 6140
% 0.18/0.53  % (8927)Time elapsed: 0.131 s
% 0.18/0.53  % (8927)Instructions burned: 6 (million)
% 0.18/0.53  % (8927)------------------------------
% 0.18/0.53  % (8927)------------------------------
% 0.18/0.53  % (8939)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.18/0.53  % (8941)Refutation not found, incomplete strategy% (8941)------------------------------
% 0.18/0.53  % (8941)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.53  % (8949)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.18/0.53  % (8941)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.53  % (8941)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.53  
% 0.18/0.53  % (8941)Memory used [KB]: 6396
% 0.18/0.53  % (8941)Time elapsed: 0.150 s
% 0.18/0.53  % (8941)Instructions burned: 10 (million)
% 0.18/0.53  % (8941)------------------------------
% 0.18/0.53  % (8941)------------------------------
% 0.18/0.53  % (8929)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.18/0.53  % (8937)Instruction limit reached!
% 0.18/0.53  % (8937)------------------------------
% 0.18/0.53  % (8937)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.53  % (8937)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.53  % (8937)Termination reason: Unknown
% 0.18/0.53  % (8937)Termination phase: Preprocessing 3
% 0.18/0.53  
% 0.18/0.53  % (8937)Memory used [KB]: 1535
% 0.18/0.53  % (8937)Time elapsed: 0.003 s
% 0.18/0.53  % (8937)Instructions burned: 3 (million)
% 0.18/0.53  % (8937)------------------------------
% 0.18/0.53  % (8937)------------------------------
% 0.18/0.53  % (8944)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.53  % (8931)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.53  % (8947)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.18/0.53  % (8936)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.54  % (8946)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.54  % (8931)Instruction limit reached!
% 0.18/0.54  % (8931)------------------------------
% 0.18/0.54  % (8931)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.54  % (8946)Refutation not found, incomplete strategy% (8946)------------------------------
% 0.18/0.54  % (8946)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.54  % (8939)Instruction limit reached!
% 0.18/0.54  % (8939)------------------------------
% 0.18/0.54  % (8939)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.55  % (8949)Instruction limit reached!
% 0.18/0.55  % (8949)------------------------------
% 0.18/0.55  % (8949)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.55  % (8949)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.55  % (8949)Termination reason: Unknown
% 0.18/0.55  % (8949)Termination phase: Saturation
% 0.18/0.55  
% 0.18/0.55  % (8949)Memory used [KB]: 6268
% 0.18/0.55  % (8949)Time elapsed: 0.169 s
% 0.18/0.55  % (8949)Instructions burned: 24 (million)
% 0.18/0.55  % (8949)------------------------------
% 0.18/0.55  % (8949)------------------------------
% 0.18/0.55  % (8931)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.55  % (8931)Termination reason: Unknown
% 0.18/0.55  % (8931)Termination phase: Saturation
% 0.18/0.55  
% 0.18/0.55  % (8931)Memory used [KB]: 6140
% 0.18/0.55  % (8931)Time elapsed: 0.006 s
% 0.18/0.55  % (8931)Instructions burned: 9 (million)
% 0.18/0.55  % (8931)------------------------------
% 0.18/0.55  % (8931)------------------------------
% 0.18/0.55  % (8939)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.55  % (8939)Termination reason: Unknown
% 0.18/0.55  % (8939)Termination phase: Saturation
% 0.18/0.55  
% 0.18/0.55  % (8939)Memory used [KB]: 6268
% 0.18/0.55  % (8939)Time elapsed: 0.157 s
% 0.18/0.55  % (8939)Instructions burned: 12 (million)
% 0.18/0.55  % (8939)------------------------------
% 0.18/0.55  % (8939)------------------------------
% 0.18/0.55  % (8940)Instruction limit reached!
% 0.18/0.55  % (8940)------------------------------
% 0.18/0.55  % (8940)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.55  % (8940)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.55  % (8940)Termination reason: Unknown
% 0.18/0.55  % (8940)Termination phase: Saturation
% 0.18/0.55  
% 0.18/0.55  % (8940)Memory used [KB]: 6524
% 0.18/0.55  % (8940)Time elapsed: 0.169 s
% 0.18/0.55  % (8940)Instructions burned: 31 (million)
% 0.18/0.55  % (8940)------------------------------
% 0.18/0.55  % (8940)------------------------------
% 0.18/0.56  % (8929)Refutation not found, incomplete strategy% (8929)------------------------------
% 0.18/0.56  % (8929)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.56  % (8929)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56  % (8929)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.56  
% 0.18/0.56  % (8929)Memory used [KB]: 6268
% 0.18/0.56  % (8929)Time elapsed: 0.164 s
% 0.18/0.56  % (8929)Instructions burned: 9 (million)
% 0.18/0.56  % (8929)------------------------------
% 0.18/0.56  % (8929)------------------------------
% 0.18/0.56  % (8946)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56  % (8946)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.56  
% 0.18/0.56  % (8946)Memory used [KB]: 6524
% 0.18/0.56  % (8946)Time elapsed: 0.155 s
% 0.18/0.56  % (8946)Instructions burned: 12 (million)
% 0.18/0.56  % (8946)------------------------------
% 0.18/0.56  % (8946)------------------------------
% 0.18/0.56  % (8926)Instruction limit reached!
% 0.18/0.56  % (8926)------------------------------
% 0.18/0.56  % (8926)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.56  % (8926)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56  % (8926)Termination reason: Unknown
% 0.18/0.56  % (8926)Termination phase: Saturation
% 0.18/0.56  
% 0.18/0.56  % (8926)Memory used [KB]: 6780
% 0.18/0.56  % (8926)Time elapsed: 0.145 s
% 0.18/0.56  % (8926)Instructions burned: 41 (million)
% 0.18/0.56  % (8926)------------------------------
% 0.18/0.56  % (8926)------------------------------
% 0.18/0.56  % (8936)Refutation not found, incomplete strategy% (8936)------------------------------
% 0.18/0.56  % (8936)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.56  % (8936)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56  % (8936)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.56  
% 0.18/0.56  % (8936)Memory used [KB]: 6524
% 0.18/0.56  % (8936)Time elapsed: 0.177 s
% 0.18/0.56  % (8936)Instructions burned: 13 (million)
% 0.18/0.56  % (8936)------------------------------
% 0.18/0.56  % (8936)------------------------------
% 0.18/0.57  % (8947)Instruction limit reached!
% 0.18/0.57  % (8947)------------------------------
% 0.18/0.57  % (8947)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.57  % (8947)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.57  % (8947)Termination reason: Unknown
% 0.18/0.57  % (8947)Termination phase: Saturation
% 0.18/0.57  
% 0.18/0.57  % (8947)Memory used [KB]: 6524
% 0.18/0.57  % (8947)Time elapsed: 0.178 s
% 0.18/0.57  % (8947)Instructions burned: 25 (million)
% 0.18/0.57  % (8947)------------------------------
% 0.18/0.57  % (8947)------------------------------
% 0.18/0.57  % (8944)First to succeed.
% 0.18/0.58  % (8933)Instruction limit reached!
% 0.18/0.58  % (8933)------------------------------
% 0.18/0.58  % (8933)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.58  % (8944)Refutation found. Thanks to Tanya!
% 0.18/0.58  % SZS status Theorem for theBenchmark
% 0.18/0.58  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.58  % (8944)------------------------------
% 0.18/0.58  % (8944)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.58  % (8944)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.58  % (8944)Termination reason: Refutation
% 0.18/0.58  
% 0.18/0.58  % (8944)Memory used [KB]: 6396
% 0.18/0.58  % (8944)Time elapsed: 0.189 s
% 0.18/0.58  % (8944)Instructions burned: 22 (million)
% 0.18/0.58  % (8944)------------------------------
% 0.18/0.58  % (8944)------------------------------
% 0.18/0.58  % (8915)Success in time 0.253 s
%------------------------------------------------------------------------------