TSTP Solution File: ITP023_2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP023_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n007.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 : Sun May  5 07:01:54 EDT 2024

% Result   : Theorem 156.13s 22.69s
% Output   : Refutation 156.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   64
% Syntax   : Number of formulae    :   97 (  25 unt;  54 typ;   0 def)
%            Number of atoms       :  280 (   0 equ)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives :   81 (  40   ~;  30   |;   2   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :  196 ( 196 fml;   0 var)
%            Number of types       :    6 (   4 usr)
%            Number of type conns  :   89 (  43   >;  46   *;   0   +;   0  <<)
%            Number of predicates  :   23 (  22 usr;   4 prp; 0-3 aty)
%            Number of functors    :   33 (  33 usr;   7 con; 0-3 aty)
%            Number of variables   :   70 (  66   !;   4   ?;  58   :)

% 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,
    sK16: tp__ty_2Erealax_2Ereal ).

tff(func_def_37,type,
    sK17: tp__ty_2Erealax_2Ereal ).

tff(func_def_38,type,
    sK18: ( del * $i ) > $i ).

tff(func_def_39,type,
    sK19: ( del * $i ) > $i ).

tff(func_def_40,type,
    sK20: ( del * $i ) > $i ).

tff(func_def_41,type,
    sK21: ( del * $i ) > $i ).

tff(func_def_42,type,
    sK22: ( del * $i * $i ) > $i ).

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

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

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

tff(pred_def_5,type,
    sP2: ( tp__o * 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_14,type,
    sP11: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_15,type,
    sP12: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_16,type,
    sP13: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_17,type,
    sP14: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_18,type,
    sP15: ( tp__o * tp__o * tp__o ) > $o ).

tff(f290854,plain,
    $false,
    inference(subsumption_resolution,[],[f290853,f310]) ).

tff(f310,plain,
    ! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
    inference(cnf_transformation,[],[f76]) ).

tff(f76,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(f290853,plain,
    ~ mem(inj__ty_2Erealax_2Ereal(sK16),ty_2Erealax_2Ereal),
    inference(subsumption_resolution,[],[f290852,f310]) ).

tff(f290852,plain,
    ( ~ mem(inj__ty_2Erealax_2Ereal(sK17),ty_2Erealax_2Ereal)
    | ~ mem(inj__ty_2Erealax_2Ereal(sK16),ty_2Erealax_2Ereal) ),
    inference(resolution,[],[f278267,f22866]) ).

tff(f22866,plain,
    ! [X2: $i,X3: del,X0: $i,X1: del] :
      ( mem(ap(ap(c_2Epair_2E_2C(X1,X3),X0),X2),ty_2Epair_2Eprod(X1,X3))
      | ~ mem(X2,X3)
      | ~ mem(X0,X1) ),
    inference(resolution,[],[f1213,f417]) ).

tff(f417,plain,
    ! [X2: $i,X3: $i,X0: del,X1: del] :
      ( ~ mem(X2,arr(X0,X1))
      | ~ mem(X3,X0)
      | mem(ap(X2,X3),X1) ),
    inference(cnf_transformation,[],[f175]) ).

tff(f175,plain,
    ! [X0: del,X1: del,X2] :
      ( ! [X3] :
          ( mem(ap(X2,X3),X1)
          | ~ mem(X3,X0) )
      | ~ mem(X2,arr(X0,X1)) ),
    inference(ennf_transformation,[],[f1]) ).

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

tff(f1213,plain,
    ! [X2: del,X0: $i,X1: del] :
      ( mem(ap(c_2Epair_2E_2C(X1,X2),X0),arr(X2,ty_2Epair_2Eprod(X1,X2)))
      | ~ mem(X0,X1) ),
    inference(resolution,[],[f417,f357]) ).

tff(f357,plain,
    ! [X0: del,X1: del] : mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1)))),
    inference(cnf_transformation,[],[f115]) ).

tff(f115,plain,
    ! [X0: del,X1: del] : mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1)))),
    inference(rectify,[],[f23]) ).

tff(f23,axiom,
    ! [X8: del,X11: 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(f278267,plain,
    ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(sK16)),inj__ty_2Erealax_2Ereal(sK17)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
    inference(resolution,[],[f218616,f294]) ).

tff(f294,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(sK16)),inj__ty_2Erealax_2Ereal(sK17))))),
    inference(cnf_transformation,[],[f202]) ).

tff(f202,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(sK16)),inj__ty_2Erealax_2Ereal(sK17))))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f146,f201]) ).

tff(f201,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)))))
   => ~ 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(sK16)),inj__ty_2Erealax_2Ereal(sK17))))) ),
    introduced(choice_axiom,[]) ).

tff(f146,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))))),
    inference(ennf_transformation,[],[f73]) ).

tff(f73,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))))),
    inference(rectify,[],[f72]) ).

tff(f72,negated_conjecture,
    ~ ! [X15: tp__ty_2Erealax_2Ereal,X23: 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,
    ! [X15: tp__ty_2Erealax_2Ereal,X23: 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(f218616,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,[],[f218615,f1222]) ).

tff(f1222,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,[],[f417,f306]) ).

tff(f306,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(f218615,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(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))
      | ~ 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(resolution,[],[f21111,f1223]) ).

tff(f1223,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,[],[f417,f307]) ).

tff(f307,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(f21111,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))
      | 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_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(subsumption_resolution,[],[f21110,f363]) ).

tff(f363,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,[],[f121]) ).

tff(f121,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,[],[f60]) ).

tff(f60,axiom,
    ! [X15: tp__ty_2Erealax_2Ereal,X23: 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(f21110,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)))))
      | ~ 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)))))
      | ~ 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,[],[f364,f352]) ).

tff(f352,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,[],[f160]) ).

tff(f160,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(flattening,[],[f159]) ).

tff(f159,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,[],[f107]) ).

tff(f107,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(f364,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(X0)),inj__ty_2Erealax_2Ereal(X1)))),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,[],[f122]) ).

tff(f122,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(X0)),inj__ty_2Erealax_2Ereal(X1)))),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,[],[f58]) ).

tff(f58,axiom,
    ! [X15: tp__ty_2Erealax_2Ereal,X23: 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
% 0.07/0.10  % Problem    : ITP023_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n007.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 19:15:23 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  % (9500)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34  % (9503)WARNING: value z3 for option sas not known
% 0.10/0.34  % (9505)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.10/0.34  % (9506)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.34  % (9504)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.34  % (9502)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.34  % (9507)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.10/0.34  % (9503)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.34  % (9501)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.36  TRYING [1,1,1,1,1]
% 0.10/0.36  TRYING [1,2,1,1,1]
% 0.10/0.37  TRYING [1,3,1,1,1]
% 0.10/0.39  TRYING [1,2,2,1,1]
% 0.15/0.40  TRYING [2,2,2,1,1]
% 0.15/0.41  TRYING [1,3,2,1,1]
% 0.15/0.43  TRYING [2,3,2,1,1]
% 0.15/0.45  TRYING [1,4,1,1,1]
% 0.15/0.49  TRYING [1,4,2,1,1]
% 1.43/0.53  TRYING [3,3,2,1,1]
% 1.59/0.56  TRYING [2,4,2,1,1]
% 1.59/0.60  TRYING [2,3,3,1,1]
% 1.59/0.62  TRYING [3,4,2,1,1]
% 2.25/0.67  TRYING [3,3,3,1,1]
% 2.66/0.69  TRYING [1]
% 2.66/0.71  TRYING [1,5,1,1,1]
% 2.66/0.74  TRYING [2]
% 3.16/0.78  TRYING [3,4,3,1,1]
% 3.44/0.84  TRYING [1,5,2,1,1]
% 3.70/0.91  TRYING [2,5,2,1,1]
% 4.34/0.96  TRYING [2,4,2,2,1]
% 4.75/0.99  TRYING [3,4,2,2,1]
% 4.75/1.04  TRYING [2,5,2,2,1]
% 5.20/1.06  TRYING [3]
% 5.34/1.11  TRYING [3,5,2,1,1]
% 5.89/1.21  TRYING [3,5,2,2,1]
% 6.74/1.28  TRYING [2,6,2,1,1]
% 7.35/1.41  TRYING [2,6,2,2,1]
% 8.54/1.54  TRYING [3,6,2,1,1]
% 8.54/1.55  TRYING [4]
% 8.83/1.57  TRYING [1,1,1,1,1]
% 8.83/1.59  TRYING [1,2,1,1,1]
% 8.83/1.62  TRYING [1,3,1,1,1]
% 9.37/1.68  TRYING [1,4,1,1,1]
% 9.58/1.73  TRYING [3,6,2,2,1]
% 10.07/1.77  TRYING [1,4,2,1,1]
% 10.73/1.89  TRYING [2,7,2,1,1]
% 10.73/1.90  TRYING [1,4,2,1,2]
% 11.67/2.04  TRYING [1,4,2,2,2]
% 12.17/2.10  TRYING [2,7,2,2,1]
% 12.55/2.17  TRYING [2,4,2,2,2]
% 13.59/2.29  TRYING [3,4,2,2,2]
% 13.59/2.31  TRYING [3,7,2,1,1]
% 14.17/2.42  TRYING [3,4,3,2,2]
% 15.70/2.59  TRYING [3,5,3,2,2]
% 16.88/2.80  TRYING [3,7,2,2,1]
% 17.33/2.83  TRYING [3,5,4,2,2]
% 18.25/2.93  TRYING [5]
% 19.95/3.18  TRYING [3,6,4,2,2]
% 20.35/3.24  TRYING [3,6,3,2,1]
% 21.05/3.38  TRYING [3,7,3,2,1]
% 22.91/3.61  TRYING [2,8,2,1,1]
% 23.06/3.66  TRYING [3,7,4,2,2]
% 25.28/3.94  TRYING [2,8,2,2,1]
% 27.41/4.25  TRYING [2,7,2,2,2]
% 27.41/4.31  TRYING [3,8,4,2,2]
% 30.09/4.66  TRYING [3,7,2,2,2]
% 34.50/5.30  TRYING [2,8,2,2,2]
% 41.67/6.28  TRYING [4,7,2,1,1]
% 45.35/6.80  TRYING [3,8,2,1,1]
% 65.80/9.77  TRYING [3,8,2,2,1]
% 76.30/11.25  TRYING [4,8,4,2,2]
% 83.35/12.33  TRYING [3,8,2,2,2]
% 106.07/15.50  TRYING [4,8,2,1,1]
% 124.86/18.23  TRYING [6]
% 145.23/21.12  TRYING [4,9,4,2,2]
% 149.86/21.75  TRYING [2,9,2,1,1]
% 153.37/22.27  TRYING [2,9,2,2,1]
% 156.08/22.65  % (9503)First to succeed.
% 156.13/22.65  % (9503)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9500"
% 156.13/22.69  % (9503)Refutation found. Thanks to Tanya!
% 156.13/22.69  % SZS status Theorem for theBenchmark
% 156.13/22.69  % SZS output start Proof for theBenchmark
% See solution above
% 156.13/22.69  % (9503)------------------------------
% 156.13/22.69  % (9503)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 156.13/22.69  % (9503)Termination reason: Refutation
% 156.13/22.69  
% 156.13/22.69  % (9503)Memory used [KB]: 263299
% 156.13/22.69  % (9503)Time elapsed: 22.310 s
% 156.13/22.69  % (9503)Instructions burned: 46896 (million)
% 156.13/22.69  % (9500)Success in time 22.345 s
%------------------------------------------------------------------------------