%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP023_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 : Fri Sep 25 01:48:00 PM UTC 2026
% Result : Theorem 3.99s 1.42s
% Output : CNFRefutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 527 ( 0 equ)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 96 ( 49 ~; 41 |; 1 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 432 ( 432 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 23 usr; 9 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 4 con; 0-3 aty)
% Number of variables : 74 ( 0 sgn 72 !; 2 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
bool: del ).
tff(pred_def_1,type,
mem: ( del * $i ) > $o ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
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 * 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 ) > $o ).
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__ty_2Erealax_2Ereal * tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_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__ty_2Erealax_2Ereal * tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_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 * ( $i * del ) ) > $i ).
tff(func_def_37,type,
sK12: ( $i * del ) > $i ).
tff(func_def_38,type,
sK13: ( $i * del ) > $i ).
tff(func_def_39,type,
sK14: ( $i * del ) > $i ).
tff(func_def_40,type,
sK15: ( $i * del ) > $i ).
tff(func_def_41,type,
sK16: tp__ty_2Erealax_2Ereal ).
tff(func_def_42,type,
sK17: tp__ty_2Erealax_2Ereal ).
tff(f1,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,X1))
=> ! [X3: $i] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001_2.ax',ap_tp) ).
tff(f15,axiom,
! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),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,
! [X0: del,X1: del] : mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1)))),
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,
! [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))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
tff(f59,axiom,
! [X0: $i] :
( mem(X0,arr(ty_2Erealax_2Ereal,bool))
=> ! [X1: $i] :
( 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)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
tff(f60,axiom,
! [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))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__CBALL) ).
tff(f71,conjecture,
! [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))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ereal__topology_2EBOUNDED__BALL) ).
tff(f72,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f71]) ).
tff(f90,plain,
! [X0: del,X1: del,X2: $i] :
( ~ mem(X2,arr(X0,X1))
| ! [X3: $i] :
( ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ) ),
inference(ennf_transformation,[],[f1]) ).
tff(f115,plain,
! [X0: $i] :
( ~ mem(X0,arr(ty_2Erealax_2Ereal,bool))
| ! [X1: $i] :
( ~ 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(ennf_transformation,[],[f59]) ).
tff(f116,plain,
! [X0: $i] :
( ~ mem(X0,arr(ty_2Erealax_2Ereal,bool))
| ! [X1: $i] :
( ~ 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(flattening,[],[f115]) ).
tff(f122,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,[],[f72]) ).
tff(f213,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(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f122]) ).
tff(f214,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,[],[f90]) ).
tff(f232,plain,
! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
inference(cnf_transformation,[],[f15]) ).
tff(f237,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(f240,plain,
! [X0: del,X1: del] : mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1)))),
inference(cnf_transformation,[],[f23]) ).
tff(f241,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(f322,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,[],[f58]) ).
tff(f323,plain,
! [X0: $i,X1: $i] :
( ~ mem(X0,arr(ty_2Erealax_2Ereal,bool))
| ~ 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(cnf_transformation,[],[f116]) ).
tff(f324,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,[],[f60]) ).
tff(f425,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,[],[f213]) ).
tcf(c_49,plain,
! [X0: $i,X0_del: del,X1: $i,X1_del: del] :
( mem(ap(X0,X1),X1_del)
| ~ mem(X1,X0_del)
| ~ mem(X0,arr(X0_del,X1_del)) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_67,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0_tp__ty_2Erealax_2Ereal),ty_2Erealax_2Ereal),
inference(cnf_transformation,[],[f232]) ).
tcf(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,[],[f237]) ).
tcf(c_75,plain,
! [X0_del: del,X1_del: del] : mem(c_2Epair_2E_2C(X0_del,X1_del),arr(X0_del,arr(X1_del,ty_2Epair_2Eprod(X0_del,X1_del)))),
inference(cnf_transformation,[],[f240]) ).
tcf(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,[],[f241]) ).
tcf(c_122,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal,X1_tp__ty_2Erealax_2Ereal: 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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal)))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))))),
inference(cnf_transformation,[],[f322]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( 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))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1)) ),
inference(cnf_transformation,[],[f323]) ).
tcf(c_124,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal,X1_tp__ty_2Erealax_2Ereal: 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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))))),
inference(cnf_transformation,[],[f324]) ).
tcf(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,[],[f425]) ).
tcf(c_230,plain,
mem(inj__ty_2Erealax_2Ereal(sK16),ty_2Erealax_2Ereal),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_240,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal,X1_tp__ty_2Erealax_2Ereal: 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_tp__ty_2Erealax_2Ereal)),inj__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_tp__ty_2Erealax_2Ereal)),inj__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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),arr(ty_2Erealax_2Ereal,bool)) ),
inference(superposition,[status(thm)],[c_122,c_123]) ).
tcf(c_259,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(superposition,[status(thm)],[c_72,c_49]) ).
tcf(c_261,plain,
! [X0: $i,X0_del: del,X1_del: del] :
( mem(ap(c_2Epair_2E_2C(X0_del,X1_del),X0),arr(X1_del,ty_2Epair_2Eprod(X0_del,X1_del)))
| ~ mem(X0,X0_del) ),
inference(superposition,[status(thm)],[c_75,c_49]) ).
tcf(c_262,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(superposition,[status(thm)],[c_76,c_49]) ).
tcf(c_279,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal,X1_tp__ty_2Erealax_2Ereal: 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_tp__ty_2Erealax_2Ereal)),inj__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_tp__ty_2Erealax_2Ereal)),inj__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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),arr(ty_2Erealax_2Ereal,bool)) ),
inference(superposition,[status(thm)],[c_122,c_123]) ).
tcf(c_304,plain,
! [X0: $i,X0_del: del,X1: $i,X1_del: del] :
( mem(ap(ap(c_2Epair_2E_2C(X0_del,X1_del),X0),X1),ty_2Epair_2Eprod(X0_del,X1_del))
| ~ mem(X1,X1_del)
| ~ mem(X0,X0_del) ),
inference(superposition,[status(thm)],[c_261,c_49]) ).
tcf(c_312,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal,X1_tp__ty_2Erealax_2Ereal: 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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),arr(ty_2Erealax_2Ereal,bool)) ),
inference(global_subsumption_just,[status(thm)],[c_279,c_124,c_240]) ).
tcf(c_313,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal,X1_tp__ty_2Erealax_2Ereal: 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_tp__ty_2Erealax_2Ereal)),inj__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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),arr(ty_2Erealax_2Ereal,bool)) ),
inference(renaming,[status(thm)],[c_312]) ).
tcf(c_320,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal,X1_tp__ty_2Erealax_2Ereal: 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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal)))))
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal))),arr(ty_2Erealax_2Ereal,bool)) ),
inference(superposition,[status(thm)],[c_259,c_313]) ).
tcf(c_369,plain,
! [X0_tp__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal,X1_tp__ty_2Erealax_2Ereal: 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_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal)))))
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(X0_tp__ty_2Erealax_2Ereal)),inj__ty_2Erealax_2Ereal(X1_tp__ty_2Erealax_2Ereal)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_320,c_262]) ).
tcf(c_376,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_369,c_211]) ).
tcf(c_383,plain,
( ~ mem(inj__ty_2Erealax_2Ereal(sK17),ty_2Erealax_2Ereal)
| ~ mem(inj__ty_2Erealax_2Ereal(sK16),ty_2Erealax_2Ereal) ),
inference(superposition,[status(thm)],[c_304,c_376]) ).
tcf(c_384,plain,
~ mem(inj__ty_2Erealax_2Ereal(sK17),ty_2Erealax_2Ereal),
inference(global_subsumption_just,[status(thm)],[c_383,c_230,c_383]) ).
tcf(c_386,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_384,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP023_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 17:54:26 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.51
% 0.26/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.51
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.53 % Proving...
% 3.99/1.42 % SZS status Started for theBenchmark.p
% 3.99/1.42 % SZS status Theorem for theBenchmark.p
% 3.99/1.42
% 3.99/1.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.99/1.42
% 3.99/1.42 % ------ iProver source info
% 3.99/1.42
% 3.99/1.42 % git: date: 2026-07-19 20:42:38 +0200
% 3.99/1.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.99/1.42 % git: non_committed_changes: false
% 3.99/1.42
% 3.99/1.42 % ------ Parsing...
% 3.99/1.42 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.99/1.42 % ------ Proving...
% 3.99/1.42 % ------ Problem Properties
% 3.99/1.42
% 3.99/1.42 %
% 3.99/1.42 % clauses 163
% 3.99/1.42 % conjectures 1
% 3.99/1.42 % EPR 14
% 3.99/1.42 % Horn 112
% 3.99/1.42 % unary 33
% 3.99/1.42 % binary 32
% 3.99/1.42 % lits 454
% 3.99/1.42 % lits eq 24
% 3.99/1.42 % fd_pure 0
% 3.99/1.42 % fd_pseudo 0
% 3.99/1.42 % fd_cond 0
% 3.99/1.42 % fd_pseudo_cond 5
% 3.99/1.42 % AC symbols 0
% 3.99/1.42
% 3.99/1.42 % ------ Input Options Time Limit: Unbounded
% 3.99/1.42
% 3.99/1.42
% 3.99/1.42 % ------
% 3.99/1.42 % Current options:
% 3.99/1.42 % ------
% 3.99/1.42
% 3.99/1.42
% 3.99/1.42 %
% 3.99/1.42
% 3.99/1.42 % ------ Proving...
% 3.99/1.42 %
% 3.99/1.42
% 3.99/1.42 % ------ Proving...
% 3.99/1.42 %
% 3.99/1.42
% 3.99/1.42 % SZS status Theorem for theBenchmark.p
% 3.99/1.42
% 3.99/1.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.99/1.43
%------------------------------------------------------------------------------