%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP020_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 11:28:36 AM UTC 2026
% Result : Theorem 1.34s 1.13s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 0 equ)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 131 ( 60 ~; 48 |; 17 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 128 ( 128 fml; 0 var)
% Number of types : 6 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 2 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 5 con; 0-4 aty)
% Number of variables : 73 ( 62 !; 11 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(type_def_7,type,
tp__ty_2Enum_2Enum: $tType ).
tff(type_def_8,type,
tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $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_11,type,
fo__c_2Ebool_2EF: tp__o ).
tff(func_def_13,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_15,type,
fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).
tff(func_def_17,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_19,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_20,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_21,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_22,type,
c_2Epred__set_2EUNIV: del > $i ).
tff(func_def_23,type,
ty_2Epair_2Eprod: ( del * del ) > del ).
tff(func_def_24,type,
c_2Epred__set_2ECROSS: ( del * del ) > $i ).
tff(func_def_25,type,
c_2Epred__set_2EBIJ: ( del * del ) > $i ).
tff(func_def_26,type,
ty_2Enum_2Enum: del ).
tff(func_def_27,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
tff(func_def_28,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
tff(func_def_29,type,
inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > $i ).
tff(func_def_30,type,
surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $i > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum ).
tff(func_def_31,type,
c_2Ebool_2E_3F: del > $i ).
tff(func_def_32,type,
sK11: ( del * $i * $i ) > $i ).
tff(func_def_33,type,
sK12: ( del * $i * $i ) > $i ).
tff(func_def_34,type,
sK13: ( del * del * $i ) > $i ).
tff(func_def_35,type,
sK14: ( del * del * $i ) > $i ).
tff(func_def_36,type,
sK15: ( del * $i ) > $i ).
tff(func_def_37,type,
sK16: ( del * tp__o * $i ) > $i ).
tff(func_def_38,type,
sK17: ( del * $i ) > $i ).
tff(func_def_39,type,
sK18: ( del * tp__o * $i ) > $i ).
tff(func_def_40,type,
sK19: ( del * tp__o * $i ) > $i ).
tff(func_def_41,type,
sK20: ( del * $i ) > $i ).
tff(func_def_42,type,
sK21: ( del * $i * tp__o ) > $i ).
tff(func_def_43,type,
sK22: ( del * $i ) > $i ).
tff(func_def_44,type,
sK23: ( del * $i ) > $i ).
tff(func_def_45,type,
sK24: ( del * tp__o * $i ) > $i ).
tff(func_def_46,type,
sK25: ( del * $i ) > $i ).
tff(func_def_47,type,
sK26: ( del * $i * tp__o ) > $i ).
tff(func_def_48,type,
sK27: ( del * tp__o * $i ) > $i ).
tff(func_def_49,type,
sK28: ( del * $i ) > $i ).
tff(func_def_50,type,
sK29: ( del * $i * tp__o ) > $i ).
tff(func_def_51,type,
sK30: ( del * $i ) > $i ).
tff(func_def_52,type,
sK31: ( del * $i ) > $i ).
tff(func_def_53,type,
sK32: ( del * $i ) > $i ).
tff(func_def_55,type,
sK34: ( del * del * $i * $i ) > $i ).
tff(func_def_56,type,
sK35: ( del * 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/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
tff(f31,axiom,
! [X0: del] : mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2EUNIV) ).
tff(f32,axiom,
! [X0: del,X1: del] : mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECROSS) ).
tff(f61,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,bool))
=> ! [X3: $i] :
( mem(X3,arr(X1,bool))
=> ( ? [X4: $i] :
( mem(X4,arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) )
<=> ? [X5: $i] :
( mem(X5,arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EBIJ__SYM) ).
tff(f72,axiom,
? [X0: $i] :
( mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ) ).
tff(f73,conjecture,
? [X0: $i] :
( mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
tff(f74,negated_conjecture,
~ ? [X0: $i] :
( mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ),
inference(negated_conjecture,[status(cth)],[f73]) ).
tff(f92,plain,
! [X0: $i] :
( ~ mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ),
inference(ennf_transformation,[],[f74]) ).
tff(f105,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(f106,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( ? [X4: $i] :
( mem(X4,arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) )
<=> ? [X5: $i] :
( mem(X5,arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,bool)) ),
inference(ennf_transformation,[],[f61]) ).
tff(f171,plain,
( mem(sK33,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK33),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(X0,sK33)],[f72]) ).
tff(f172,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( ( ? [X4: $i] :
( mem(X4,arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) )
| ! [X5: $i] :
( ~ mem(X5,arr(X1,X0))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) )
& ( ? [X5: $i] :
( mem(X5,arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) )
| ! [X4: $i] :
( ~ mem(X4,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) ) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,bool)) ),
inference(nnf_transformation,[],[f106]) ).
tff(f173,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( ( ? [X4: $i] :
( mem(X4,arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)) )
| ! [X5: $i] :
( ~ mem(X5,arr(X1,X0))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) )
& ( ? [X6: $i] :
( mem(X6,arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X6),X3),X2)) )
| ! [X7: $i] :
( ~ mem(X7,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3)) ) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,bool)) ),
inference(rectify,[],[f172]) ).
tff(f174,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( ( ( mem(sK34(X0,X1,X2,X3),arr(X0,X1))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),sK34(X0,X1,X2,X3)),X2),X3)) )
| ! [X5: $i] :
( ~ mem(X5,arr(X1,X0))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2)) ) )
& ( ( mem(sK35(X0,X1,X2,X3),arr(X1,X0))
& p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),sK35(X0,X1,X2,X3)),X3),X2)) )
| ! [X7: $i] :
( ~ mem(X7,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3)) ) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,bool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35]),skolemize(X4,sK34(X0,X1,X2,X3)),skolemize(X6,sK35(X0,X1,X2,X3))],[f173]) ).
tff(f225,plain,
! [X0: $i] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
| ~ mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(cnf_transformation,[],[f92]) ).
tff(f294,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,[],[f105]) ).
tff(f295,plain,
p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK33),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),
inference(cnf_transformation,[],[f171]) ).
tff(f296,plain,
mem(sK33,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)),
inference(cnf_transformation,[],[f171]) ).
tff(f297,plain,
! [X0: del] : mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool)),
inference(cnf_transformation,[],[f31]) ).
tff(f298,plain,
! [X0: del,X1: del] : mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool)))),
inference(cnf_transformation,[],[f32]) ).
tff(f299,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X7: $i] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),sK35(X0,X1,X2,X3)),X3),X2))
| ~ mem(X7,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,bool)) ),
inference(cnf_transformation,[],[f174]) ).
tff(f300,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X7: $i] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3))
| ~ mem(X7,arr(X0,X1))
| mem(sK35(X0,X1,X2,X3),arr(X1,X0))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,bool)) ),
inference(cnf_transformation,[],[f174]) ).
tff(f696,plain,
! [X0: $i] :
( ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))
| ~ mem(sK35(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum,ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(resolution,[],[f299,f225]) ).
tff(f703,plain,
! [X0: $i] :
( ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ),
inference(forward_subsumption_resolution,[],[f696,f300]) ).
tff(f704,plain,
! [X0: $i] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
| ~ mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ),
inference(forward_subsumption_resolution,[],[f703,f297]) ).
tff(f705,plain,
( ~ mem(sK33,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum))
| ~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)) ),
inference(resolution,[],[f704,f295]) ).
tff(f708,plain,
~ mem(ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)),
inference(forward_subsumption_resolution,[],[f705,f296]) ).
tff(f709,plain,
! [X0: del] :
( ~ mem(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),arr(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool)))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),X0) ),
inference(resolution,[],[f708,f294]) ).
tff(f719,plain,
! [X0: del,X1: del] :
( ~ mem(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(X1,arr(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),bool))))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),X1)
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),X0) ),
inference(resolution,[],[f709,f294]) ).
tff(f738,plain,
( ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool))
| ~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool)) ),
inference(resolution,[],[f719,f298]) ).
tff(f739,plain,
~ mem(c_2Epred__set_2EUNIV(ty_2Enum_2Enum),arr(ty_2Enum_2Enum,bool)),
inference(duplicate_literal_removal,[],[f738]) ).
tff(f740,plain,
$false,
inference(forward_subsumption_resolution,[],[f739,f297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP020_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 12:06:30 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.34/1.13 % (2282675)Detected formulas, will run a generic FOF schedule.
% 1.34/1.13 % (2282684)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3858963775:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.34/1.13 % (2282684)First to succeed.
% 1.34/1.13 % (2282684)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2282675"
% 1.34/1.13 % (2282685)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=280851733:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.34/1.13 % (2282680)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=4114221596:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.34/1.13 % (2282683)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1332664191:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.34/1.13 % (2282686)dis-21_1_sil=8000:lcm=predicate:random_seed=823484026: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)
% 1.34/1.13 % (2282681)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=536977635:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.34/1.13 % (2282682)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=3527291984:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.34/1.13 % (2282683)Refutation not found, incomplete strategy
% 1.34/1.13 % (2282683)------------------------------
% 1.34/1.13 % (2282683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/1.13 % (2282683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/1.13 % (2282683)CaDiCaL version: 2.1.3
% 1.34/1.13 % (2282683)Termination reason: Refutation not found, incomplete strategy
% 1.34/1.13 % (2282683)Time elapsed: 0.010 s
% 1.34/1.13 % (2282683)Peak memory usage: 88 MB
% 1.34/1.13 % (2282683)Instructions burned: 16 (million)
% 1.34/1.13 % (2282686)Instruction limit reached!
% 1.34/1.13 % (2282686)------------------------------
% 1.34/1.13 % (2282686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/1.13 % (2282686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/1.13 % (2282686)CaDiCaL version: 2.1.3
% 1.34/1.13 % (2282686)Termination reason: Instruction limit
% 1.34/1.13 % (2282686)Termination phase: Saturation
% 1.34/1.13 % (2282686)Time elapsed: 0.059 s
% 1.34/1.13 % (2282686)Peak memory usage: 89 MB
% 1.34/1.13 % (2282686)Instructions burned: 130 (million)
% 1.34/1.13 % (2282685)Instruction limit reached!
% 1.34/1.13 % (2282685)------------------------------
% 1.34/1.13 % (2282685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.34/1.13 % (2282685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/1.13 % (2282685)CaDiCaL version: 2.1.3
% 1.34/1.13 % (2282685)Termination reason: Instruction limit
% 1.34/1.13 % (2282685)Termination phase: Saturation
% 1.34/1.13 % (2282685)Time elapsed: 0.094 s
% 1.34/1.13 % (2282685)Peak memory usage: 91 MB
% 1.34/1.13 % (2282685)Instructions burned: 140 (million)
% 1.34/1.13 % (2282684)Refutation found. Thanks to Tanya!
% 1.34/1.13 % SZS status Theorem for theBenchmark
% 1.34/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.33 % (2282684)------------------------------
% 2.65/1.33 % (2282684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.33 % (2282684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.33 % (2282684)CaDiCaL version: 2.1.3
% 2.65/1.33 % (2282684)Termination reason: Refutation
% 2.65/1.33 % (2282684)Time elapsed: 0.007 s
% 2.65/1.33 % (2282684)Peak memory usage: 88 MB
% 2.65/1.33 % (2282684)Instructions burned: 22 (million)
% 2.65/1.33 % (2282684)------------------------------
% 2.65/1.33 % (2282684)------------------------------
% 2.65/1.33 % (2282675)Success in time 0.292 s
% 2.65/1.33 % Vampire exiting
%------------------------------------------------------------------------------