TSTP Solution File: ITP023_2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : ITP023_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.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 : Fri May  3 02:29:22 EDT 2024

% Result   : Theorem 0.47s 1.13s
% Output   : CNFRefutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   55 (  33 unt;   0 typ;   0 def)
%            Number of atoms       :  426 (   0 equ)
%            Maximal formula atoms :    5 (   7 avg)
%            Number of connectives :  104 (  52   ~;  41   |;   2   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  319 ( 319 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  17 usr;  10 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   87 (   3 sgn  49   !;   4   ?;  41   :)

% Comments : 
%------------------------------------------------------------------------------
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(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(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(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(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(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) ).

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(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(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(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(f83,plain,
    ! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
    inference(rectify,[],[f15]) ).

tff(f90,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(f124,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(f125,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(f126,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(f145,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(f146,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(f171,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,[],[f125]) ).

tff(f172,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,[],[f171]) ).

tff(f178,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,[],[f145]) ).

tff(f277,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(f278,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])],[f178,f277]) ).

tff(f279,plain,
    ! [X2: $i,X3: $i,X0: del,X1: del] :
      ( mem(ap(X2,X3),X1)
      | ~ mem(X3,X0)
      | ~ mem(X2,arr(X0,X1)) ),
    inference(cnf_transformation,[],[f146]) ).

tff(f297,plain,
    ! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
    inference(cnf_transformation,[],[f83]) ).

tff(f302,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(f305,plain,
    ! [X0: del,X1: del] : mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1)))),
    inference(cnf_transformation,[],[f90]) ).

tff(f306,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(f387,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,[],[f124]) ).

tff(f388,plain,
    ! [X0: $i,X1: $i] :
      ( 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(cnf_transformation,[],[f172]) ).

tff(f389,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,[],[f126]) ).

tff(f490,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,[],[f278]) ).

cnf(c_49,plain,
    ( ~ mem(X0,arr(X0_13,X1_13))
    | ~ mem(X1,X0_13)
    | mem(ap(X0,X1),X1_13) ),
    inference(cnf_transformation,[],[f279]) ).

cnf(c_67,plain,
    mem(inj__ty_2Erealax_2Ereal(X0_15),ty_2Erealax_2Ereal),
    inference(cnf_transformation,[],[f297]) ).

cnf(c_72,plain,
    mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
    inference(cnf_transformation,[],[f302]) ).

cnf(c_75,plain,
    mem(c_2Epair_2E_2C(X0_13,X1_13),arr(X0_13,arr(X1_13,ty_2Epair_2Eprod(X0_13,X1_13)))),
    inference(cnf_transformation,[],[f305]) ).

cnf(c_76,plain,
    mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
    inference(cnf_transformation,[],[f306]) ).

cnf(c_122,plain,
    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_15)),inj__ty_2Erealax_2Ereal(X1_15)))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))))),
    inference(cnf_transformation,[],[f387]) ).

cnf(c_123,plain,
    ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
    | ~ mem(X0,arr(ty_2Erealax_2Ereal,bool))
    | ~ mem(X1,arr(ty_2Erealax_2Ereal,bool))
    | ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
    | p(ap(c_2Ereal__topology_2Ebounded__def,X0)) ),
    inference(cnf_transformation,[],[f388]) ).

cnf(c_124,plain,
    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_15)),inj__ty_2Erealax_2Ereal(X1_15))))),
    inference(cnf_transformation,[],[f389]) ).

cnf(c_211,negated_conjecture,
    ~ 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,[],[f490]) ).

cnf(c_212,plain,
    mem(inj__ty_2Erealax_2Ereal(sK16),ty_2Erealax_2Ereal),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_3439,plain,
    ( ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))),arr(ty_2Erealax_2Ereal,bool))
    | ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))),arr(ty_2Erealax_2Ereal,bool))
    | ~ 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_15)),inj__ty_2Erealax_2Ereal(X1_15)))))
    | 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_15)),inj__ty_2Erealax_2Ereal(X1_15))))) ),
    inference(superposition,[status(thm)],[c_122,c_123]) ).

cnf(c_3453,plain,
    ( ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
    | mem(ap(c_2Ereal__topology_2Eball,X0),arr(ty_2Erealax_2Ereal,bool)) ),
    inference(superposition,[status(thm)],[c_72,c_49]) ).

cnf(c_3455,plain,
    ( ~ mem(X0,X0_13)
    | mem(ap(c_2Epair_2E_2C(X0_13,X1_13),X0),arr(X1_13,ty_2Epair_2Eprod(X0_13,X1_13))) ),
    inference(superposition,[status(thm)],[c_75,c_49]) ).

cnf(c_3456,plain,
    ( ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
    | mem(ap(c_2Ereal__topology_2Ecball,X0),arr(ty_2Erealax_2Ereal,bool)) ),
    inference(superposition,[status(thm)],[c_76,c_49]) ).

cnf(c_3473,plain,
    ( ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))),arr(ty_2Erealax_2Ereal,bool))
    | ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))),arr(ty_2Erealax_2Ereal,bool))
    | ~ 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_15)),inj__ty_2Erealax_2Ereal(X1_15)))))
    | 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_15)),inj__ty_2Erealax_2Ereal(X1_15))))) ),
    inference(superposition,[status(thm)],[c_122,c_123]) ).

cnf(c_3498,plain,
    ( ~ mem(X0,X0_13)
    | ~ mem(X1,X1_13)
    | mem(ap(ap(c_2Epair_2E_2C(X0_13,X1_13),X0),X1),ty_2Epair_2Eprod(X0_13,X1_13)) ),
    inference(superposition,[status(thm)],[c_3455,c_49]) ).

cnf(c_3506,plain,
    ( ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))),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_15)),inj__ty_2Erealax_2Ereal(X1_15))),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_15)),inj__ty_2Erealax_2Ereal(X1_15))))) ),
    inference(global_subsumption_just,[status(thm)],[c_3473,c_124,c_3439]) ).

cnf(c_3507,plain,
    ( ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))),arr(ty_2Erealax_2Ereal,bool))
    | ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))),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_15)),inj__ty_2Erealax_2Ereal(X1_15))))) ),
    inference(renaming,[status(thm)],[c_3506]) ).

cnf(c_3514,plain,
    ( ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15))),arr(ty_2Erealax_2Ereal,bool))
    | ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,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_15)),inj__ty_2Erealax_2Ereal(X1_15))))) ),
    inference(superposition,[status(thm)],[c_3453,c_3507]) ).

cnf(c_3563,plain,
    ( ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_15)),inj__ty_2Erealax_2Ereal(X1_15)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,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_15)),inj__ty_2Erealax_2Ereal(X1_15))))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3514,c_3456]) ).

cnf(c_3566,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(superposition,[status(thm)],[c_3563,c_211]) ).

cnf(c_3573,plain,
    ( ~ mem(inj__ty_2Erealax_2Ereal(sK16),ty_2Erealax_2Ereal)
    | ~ mem(inj__ty_2Erealax_2Ereal(sK17),ty_2Erealax_2Ereal) ),
    inference(superposition,[status(thm)],[c_3498,c_3566]) ).

cnf(c_3574,plain,
    ~ mem(inj__ty_2Erealax_2Ereal(sK17),ty_2Erealax_2Ereal),
    inference(global_subsumption_just,[status(thm)],[c_3573,c_212,c_3573]) ).

cnf(c_3576,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_3574,c_67]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : ITP023_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.06/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.32  % Computer : n026.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Thu May  2 22:20:36 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.19/0.45  Running first-order theorem proving
% 0.19/0.45  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.47/1.13  % SZS status Started for theBenchmark.p
% 0.47/1.13  % SZS status Theorem for theBenchmark.p
% 0.47/1.13  
% 0.47/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.47/1.13  
% 0.47/1.13  ------  iProver source info
% 0.47/1.13  
% 0.47/1.13  git: date: 2024-05-02 19:28:25 +0000
% 0.47/1.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.47/1.13  git: non_committed_changes: false
% 0.47/1.13  
% 0.47/1.13  ------ Parsing...
% 0.47/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.47/1.13  
% 0.47/1.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 0.47/1.13  
% 0.47/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.47/1.13  
% 0.47/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.47/1.13  ------ Proving...
% 0.47/1.13  ------ Problem Properties 
% 0.47/1.13  
% 0.47/1.13  
% 0.47/1.13  clauses                                 67
% 0.47/1.13  conjectures                             1
% 0.47/1.13  EPR                                     6
% 0.47/1.13  Horn                                    59
% 0.47/1.13  unary                                   33
% 0.47/1.13  binary                                  6
% 0.47/1.13  lits                                    156
% 0.47/1.13  lits eq                                 22
% 0.47/1.13  fd_pure                                 0
% 0.47/1.13  fd_pseudo                               0
% 0.47/1.13  fd_cond                                 0
% 0.47/1.13  fd_pseudo_cond                          5
% 0.47/1.13  AC symbols                              0
% 0.47/1.13  
% 0.47/1.13  ------ Input Options Time Limit: Unbounded
% 0.47/1.13  
% 0.47/1.13  
% 0.47/1.13  ------ 
% 0.47/1.13  Current options:
% 0.47/1.13  ------ 
% 0.47/1.13  
% 0.47/1.13  
% 0.47/1.13  
% 0.47/1.13  
% 0.47/1.13  ------ Proving...
% 0.47/1.13  
% 0.47/1.13  
% 0.47/1.13  ------ Proving...
% 0.47/1.13  
% 0.47/1.13  
% 0.47/1.13  % SZS status Theorem for theBenchmark.p
% 0.47/1.13  
% 0.47/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.47/1.13  
% 0.47/1.14  
%------------------------------------------------------------------------------