%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP023_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 : Tue Sep 29 11:28:54 AM UTC 2026
% Result : Theorem 2.93s 1.31s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 228 ( 0 equ)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 73 ( 37 ~; 30 |; 1 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 156 ( 156 fml; 0 var)
% Number of types : 6 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 4 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 7 con; 0-3 aty)
% Number of variables : 57 ( 55 !; 2 ?; 57 :)
% 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: tp__ty_2Erealax_2Ereal ).
tff(func_def_37,type,
sK12: tp__ty_2Erealax_2Ereal ).
tff(func_def_38,type,
sK13: ( del * $i ) > $i ).
tff(func_def_39,type,
sK14: ( del * $i ) > $i ).
tff(func_def_40,type,
sK15: ( 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 * 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(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/sandbox/benchmark/theBenchmark.p',ap_tp) ).
tff(f15,axiom,
! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(c_2Ereal__topology_2Ebounded__def,X1))
& p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1)) )
=> p(ap(c_2Ereal__topology_2Ebounded__def,X0)) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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: 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(f92,plain,
! [X0: $i] :
( ! [X1: $i] :
( p(ap(c_2Ereal__topology_2Ebounded__def,X0))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
| ~ mem(X1,arr(ty_2Erealax_2Ereal,bool)) )
| ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
inference(ennf_transformation,[],[f59]) ).
tff(f93,plain,
! [X0: $i] :
( ! [X1: $i] :
( p(ap(c_2Ereal__topology_2Ebounded__def,X0))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
| ~ mem(X1,arr(ty_2Erealax_2Ereal,bool)) )
| ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
inference(flattening,[],[f92]) ).
tff(f112,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f129,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(sK11)),inj__ty_2Erealax_2Ereal(sK12))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f90]) ).
tff(f190,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(sK11)),inj__ty_2Erealax_2Ereal(sK12))))),
inference(cnf_transformation,[],[f129]) ).
tff(f191,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(f192,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(f196,plain,
! [X0: tp__ty_2Erealax_2Ereal] : mem(inj__ty_2Erealax_2Ereal(X0),ty_2Erealax_2Ereal),
inference(cnf_transformation,[],[f15]) ).
tff(f198,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(f199,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(f200,plain,
! [X0: $i,X1: $i] :
( ~ 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))
| ~ mem(X1,arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
inference(cnf_transformation,[],[f93]) ).
tff(f202,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(f361,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,[],[f112]) ).
tff(f521,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,[],[f361,f198]) ).
tff(f523,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,[],[f361,f199]) ).
tff(f524,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,[],[f361,f202]) ).
tff(f567,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,[],[f523,f361]) ).
tff(f607,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,[],[f192,f200]) ).
tff(f651,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(forward_subsumption_resolution,[],[f607,f191]) ).
tff(f708,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,[],[f651,f524]) ).
tff(f709,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(forward_subsumption_resolution,[],[f708,f521]) ).
tff(f984,plain,
~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),inj__ty_2Erealax_2Ereal(sK11)),inj__ty_2Erealax_2Ereal(sK12)),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(resolution,[],[f709,f190]) ).
tff(f985,plain,
( ~ mem(inj__ty_2Erealax_2Ereal(sK12),ty_2Erealax_2Ereal)
| ~ mem(inj__ty_2Erealax_2Ereal(sK11),ty_2Erealax_2Ereal) ),
inference(resolution,[],[f984,f567]) ).
tff(f986,plain,
~ mem(inj__ty_2Erealax_2Ereal(sK11),ty_2Erealax_2Ereal),
inference(forward_subsumption_resolution,[],[f985,f196]) ).
tff(f987,plain,
$false,
inference(forward_subsumption_resolution,[],[f986,f196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP023_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 12:09:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.93/1.31 % (1924525)Detected formulas, will run a generic FOF schedule.
% 2.93/1.31 % (1924534)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2924102429:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.93/1.31 % (1924534)Instruction limit reached!
% 2.93/1.31 % (1924534)------------------------------
% 2.93/1.31 % (1924534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.31 % (1924534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.31 % (1924534)CaDiCaL version: 2.1.3
% 2.93/1.31 % (1924534)Termination reason: Instruction limit
% 2.93/1.31 % (1924534)Termination phase: Saturation
% 2.93/1.31 % (1924534)Time elapsed: 0.037 s
% 2.93/1.31 % (1924534)Peak memory usage: 88 MB
% 2.93/1.31 % (1924534)Instructions burned: 123 (million)
% 2.93/1.31 % (1924533)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2393227056:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.93/1.31 % (1924530)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=465222404:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.93/1.31 % (1924536)dis-21_1_sil=8000:lcm=predicate:random_seed=2190904170:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.93/1.31 % (1924535)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4272031641:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.93/1.31 % (1924531)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3557768814:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.93/1.31 % (1924532)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2574809036:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.93/1.31 % (1924533)Refutation not found, incomplete strategy
% 2.93/1.31 % (1924533)------------------------------
% 2.93/1.31 % (1924533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.31 % (1924533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.31 % (1924533)CaDiCaL version: 2.1.3
% 2.93/1.31 % (1924533)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.31 % (1924533)Time elapsed: 0.001 s
% 2.93/1.31 % (1924533)Peak memory usage: 87 MB
% 2.93/1.31 % (1924536)Instruction limit reached!
% 2.93/1.31 % (1924536)------------------------------
% 2.93/1.31 % (1924536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.31 % (1924536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.31 % (1924536)CaDiCaL version: 2.1.3
% 2.93/1.31 % (1924536)Termination reason: Instruction limit
% 2.93/1.31 % (1924536)Termination phase: Saturation
% 2.93/1.31 % (1924536)Time elapsed: 0.079 s
% 2.93/1.31 % (1924536)Peak memory usage: 90 MB
% 2.93/1.31 % (1924536)Instructions burned: 130 (million)
% 2.93/1.31 % (1924535)Instruction limit reached!
% 2.93/1.31 % (1924535)------------------------------
% 2.93/1.31 % (1924535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.31 % (1924535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.31 % (1924535)CaDiCaL version: 2.1.3
% 2.93/1.31 % (1924535)Termination reason: Instruction limit
% 2.93/1.31 % (1924535)Termination phase: Saturation
% 2.93/1.31 % (1924535)Time elapsed: 0.095 s
% 2.93/1.31 % (1924535)Peak memory usage: 90 MB
% 2.93/1.31 % (1924535)Instructions burned: 139 (million)
% 2.93/1.31 % (1924538)lrs+10_1_sil=8000:sp=occurrence:random_seed=445597999:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.93/1.31 % (1924538)First to succeed.
% 2.93/1.31 % (1924538)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1924525"
% 2.93/1.31 % (1924545)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2929529800:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.93/1.31 % (1924545)Refutation not found, incomplete strategy
% 2.93/1.31 % (1924545)------------------------------
% 2.93/1.31 % (1924545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.93/1.31 % (1924545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/1.31 % (1924545)CaDiCaL version: 2.1.3
% 2.93/1.31 % (1924545)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.31 % (1924545)Time elapsed: 0.003 s
% 2.93/1.31 % (1924545)Peak memory usage: 88 MB
% 2.93/1.31 % (1924545)Instructions burned: 2 (million)
% 2.93/1.31 % (1924533)------------------------------
% 2.93/1.31 % (1924533)------------------------------
% 2.93/1.31 % (1924546)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4274903625:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.93/1.31 % (1924538)Refutation found. Thanks to Tanya!
% 2.93/1.31 % SZS status Theorem for theBenchmark
% 2.93/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.40 % (1924538)------------------------------
% 0.15/1.40 % (1924538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.40 % (1924538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.40 % (1924538)CaDiCaL version: 2.1.3
% 0.15/1.40 % (1924538)Termination reason: Refutation
% 0.15/1.40 % (1924538)Time elapsed: 0.013 s
% 0.15/1.40 % (1924538)Peak memory usage: 89 MB
% 0.15/1.40 % (1924538)Instructions burned: 33 (million)
% 0.15/1.40 % (1924538)------------------------------
% 0.15/1.40 % (1924538)------------------------------
% 0.15/1.40 % (1924525)Success in time 0.467 s
% 0.15/1.40 % Vampire exiting
%------------------------------------------------------------------------------