%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW553_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 01:30:48 PM UTC 2026
% Result : Theorem 4.59s 1.54s
% Output : Refutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 42 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 40 ( 17 ~; 14 |; 7 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-6 aty)
% Number of functors : 106 ( 106 usr; 16 con; 0-7 aty)
% Number of variables : 44 ( 41 !; 3 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
exp: $tType > $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
option: $tType > $tType ).
tff(type_def_10,type,
char: $tType ).
tff(type_def_11,type,
ty: $tType ).
tff(type_def_12,type,
val: $tType ).
tff(type_def_13,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_14,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_1,type,
start_heap:
!>[X0: $tType] : ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) > fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) ).
tff(func_def_2,type,
fAss:
!>[X0: $tType] : ( ( exp(X0) * list(char) * list(char) * exp(X0) ) > exp(X0) ) ).
tff(func_def_3,type,
val1:
!>[X0: $tType] : ( val > exp(X0) ) ).
tff(func_def_4,type,
fun_upd:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 * X1 ) > fun(X0,X1) ) ).
tff(func_def_5,type,
map_comp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,option(X1)) * fun(X2,option(X0)) * X2 ) > option(X1) ) ).
tff(func_def_6,type,
typeof_h: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * val ) > option(ty) ).
tff(func_def_7,type,
none:
!>[X0: $tType] : option(X0) ).
tff(func_def_8,type,
some:
!>[X0: $tType] : ( X0 > option(X0) ) ).
tff(func_def_9,type,
option_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,X0) * option(X1) ) > X0 ) ).
tff(func_def_10,type,
set:
!>[X0: $tType] : ( option(X0) > fun(X0,bool) ) ).
tff(func_def_11,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_12,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_13,type,
default_val: ty > val ).
tff(func_def_14,type,
the_Addr: val > nat ).
tff(func_def_15,type,
addr: nat > val ).
tff(func_def_16,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_17,type,
fFalse: bool ).
tff(func_def_18,type,
fTrue: bool ).
tff(func_def_19,type,
c: list(char) ).
tff(func_def_20,type,
d: list(char) ).
tff(func_def_21,type,
e: fun(list(char),option(ty)) ).
tff(func_def_22,type,
f: list(char) ).
tff(func_def_23,type,
p: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) ).
tff(func_def_24,type,
tf: ty ).
tff(func_def_25,type,
t: ty ).
tff(func_def_26,type,
tv: ty ).
tff(func_def_27,type,
a: nat ).
tff(func_def_28,type,
fs: fun(product_prod(list(char),list(char)),option(val)) ).
tff(func_def_29,type,
ha: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).
tff(func_def_30,type,
v: val ).
tff(func_def_31,type,
sK0: ty ).
tff(func_def_32,type,
sK1: ty ).
tff(func_def_33,type,
sK2:
!>[X0: $tType] : ( ( ty * val * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) ) > ty ) ).
tff(func_def_34,type,
sK3: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > nat ).
tff(func_def_35,type,
sK4: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > list(char) ).
tff(func_def_36,type,
sK5: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > fun(product_prod(list(char),list(char)),option(val)) ).
tff(func_def_37,type,
sK6: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * nat * list(char) ) > fun(product_prod(list(char),list(char)),option(val)) ).
tff(func_def_38,type,
sK7: ( list(char) * nat * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > fun(product_prod(list(char),list(char)),option(val)) ).
tff(func_def_39,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_40,type,
sK9:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_41,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_42,type,
sK11: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > nat ).
tff(func_def_43,type,
sK12: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > list(char) ).
tff(func_def_44,type,
sK13: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > fun(product_prod(list(char),list(char)),option(val)) ).
tff(func_def_45,type,
sK14:
!>[X0: $tType] : ( ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) ) > nat ) ).
tff(func_def_46,type,
sK15:
!>[X0: $tType] : ( ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) ) > product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))) ) ).
tff(func_def_47,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_48,type,
sK17:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_49,type,
sK18:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_50,type,
sK19:
!>[X0: $tType] : ( ( fun(X0,bool) * option(X0) ) > X0 ) ).
tff(func_def_51,type,
sK20:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X1 ) ).
tff(func_def_52,type,
sK21:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X0 ) ).
tff(func_def_53,type,
sK22:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_54,type,
sK23:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_55,type,
sK24:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_56,type,
sK25:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_57,type,
sK26:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_58,type,
sK27:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_59,type,
sK28:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_60,type,
sK29:
!>[X0: $tType] : ( ( fun(list(char),option(ty)) * fun(list(char),option(val)) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) ) > list(char) ) ).
tff(func_def_61,type,
sK30:
!>[X0: $tType] : ( ( fun(list(char),option(ty)) * fun(list(char),option(val)) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) ) > val ) ).
tff(func_def_62,type,
sK31:
!>[X0: $tType] : ( ( fun(list(char),option(ty)) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * list(char) * val ) > ty ) ).
tff(func_def_63,type,
sK32:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X5 ) ).
tff(func_def_64,type,
sK33:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X4 ) ).
tff(func_def_65,type,
sK34:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X3 ) ).
tff(func_def_66,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X2 ) ).
tff(func_def_67,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X1 ) ).
tff(func_def_68,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X0 ) ).
tff(func_def_69,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).
tff(func_def_70,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).
tff(func_def_71,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).
tff(func_def_72,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).
tff(func_def_73,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).
tff(func_def_74,type,
sK43:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).
tff(func_def_75,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).
tff(func_def_76,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).
tff(func_def_77,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).
tff(func_def_78,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).
tff(func_def_79,type,
sK48:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).
tff(func_def_80,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X4 ) ).
tff(func_def_81,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X3 ) ).
tff(func_def_82,type,
sK51:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X2 ) ).
tff(func_def_83,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X1 ) ).
tff(func_def_84,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X0 ) ).
tff(func_def_85,type,
sK54:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_86,type,
sK55:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_87,type,
sK56:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_88,type,
sK57:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_89,type,
sK58:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_90,type,
sK59:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_91,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_92,type,
sK61:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_93,type,
sK62:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_94,type,
sK63:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_95,type,
sK64:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_96,type,
sK65:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_97,type,
sK66:
!>[X0: $tType] : ( option(X0) > X0 ) ).
tff(func_def_98,type,
sK67:
!>[X0: $tType] : ( option(X0) > X0 ) ).
tff(func_def_99,type,
sK68:
!>[X0: $tType,X1: $tType] : ( ( X1 * X0 * fun(X0,option(X1)) ) > X0 ) ).
tff(func_def_100,type,
sK69:
!>[X0: $tType] : ( option(X0) > X0 ) ).
tff(pred_def_1,type,
conf:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * val * ty ) > $o ) ).
tff(pred_def_2,type,
hconf:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > $o ) ).
tff(pred_def_3,type,
lconf:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(list(char),option(val)) * fun(list(char),option(ty)) ) > $o ) ).
tff(pred_def_4,type,
oconf:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))) ) > $o ) ).
tff(pred_def_5,type,
is_type:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * ty ) > $o ) ).
tff(pred_def_6,type,
preallocated: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) > $o ).
tff(pred_def_7,type,
hext: ( fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ) > $o ).
tff(pred_def_8,type,
has_field:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * list(char) * list(char) * ty * list(char) ) > $o ) ).
tff(pred_def_9,type,
widen:
!>[X0: $tType] : ( ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))) * ty * ty ) > $o ) ).
tff(pred_def_10,type,
wTrt: ( list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))) * fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) * fun(list(char),option(ty)) * exp(list(char)) * ty ) > $o ).
tff(pred_def_11,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(pred_def_13,type,
sQ70_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f1,axiom,
widen(product_prod(list(list(char)),exp(list(char))),p,tv,tf),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_sub) ).
tff(f2,axiom,
typeof_h(ha,v) = some(ty,tv),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_typeofv) ).
tff(f11,axiom,
! [X0: $tType,X1: ty,X2: val,X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
( conf(X0,X4,X3,X2,X1)
<=> ? [X5: ty] :
( ( typeof_h(X3,X2) = some(ty,X5) )
& widen(X0,X4,X5,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_conf__def) ).
tff(f104,conjecture,
conf(product_prod(list(list(char)),exp(list(char))),p,ha,v,tf),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f105,negated_conjecture,
~ conf(product_prod(list(list(char)),exp(list(char))),p,ha,v,tf),
inference(negated_conjecture,[status(cth)],[f104]) ).
tff(f106,plain,
~ conf(product_prod(list(list(char)),exp(list(char))),p,ha,v,tf),
inference(flattening,[],[f105]) ).
tff(f187,plain,
! [X0: $tType,X1: ty,X2: val,X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
( ( conf(X0,X4,X3,X2,X1)
| ! [X5: ty] :
( ( typeof_h(X3,X2) != some(ty,X5) )
| ~ widen(X0,X4,X5,X1) ) )
& ( ? [X5: ty] :
( ( typeof_h(X3,X2) = some(ty,X5) )
& widen(X0,X4,X5,X1) )
| ~ conf(X0,X4,X3,X2,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
tff(f188,plain,
! [X0: $tType,X1: ty,X2: val,X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
( ( conf(X0,X4,X3,X2,X1)
| ! [X5: ty] :
( ( typeof_h(X3,X2) != some(ty,X5) )
| ~ widen(X0,X4,X5,X1) ) )
& ( ? [X6: ty] :
( ( typeof_h(X3,X2) = some(ty,X6) )
& widen(X0,X4,X6,X1) )
| ~ conf(X0,X4,X3,X2,X1) ) ),
inference(rectify,[],[f187]) ).
tff(f189,plain,
! [X0: $tType,X1: ty,X2: val,X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
( ( conf(X0,X4,X3,X2,X1)
| ! [X5: ty] :
( ( typeof_h(X3,X2) != some(ty,X5) )
| ~ widen(X0,X4,X5,X1) ) )
& ( ( ( typeof_h(X3,X2) = some(ty,sK2(X0,X1,X2,X3,X4)) )
& widen(X0,X4,sK2(X0,X1,X2,X3,X4),X1) )
| ~ conf(X0,X4,X3,X2,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X6,sK2(X0,X1,X2,X3,X4))],[f188]) ).
tff(f244,plain,
widen(product_prod(list(list(char)),exp(list(char))),p,tv,tf),
inference(cnf_transformation,[],[f1]) ).
tff(f245,plain,
typeof_h(ha,v) = some(ty,tv),
inference(cnf_transformation,[],[f2]) ).
tff(f258,plain,
! [X0: $tType,X2: val,X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: ty,X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X5: ty] :
( conf(X0,X4,X3,X2,X1)
| ( typeof_h(X3,X2) != some(ty,X5) )
| ~ widen(X0,X4,X5,X1) ),
inference(cnf_transformation,[],[f189]) ).
tff(f388,plain,
~ conf(product_prod(list(list(char)),exp(list(char))),p,ha,v,tf),
inference(cnf_transformation,[],[f106]) ).
tff(f413,definition,
! [X0: $tType,X2: X0,X1: X0] :
( sQ70_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(definition,[new_symbols(definition,[sQ70_eqProxy])],[equality_proxy_definition]) ).
tff(f414,plain,
sQ70_eqProxy(option(ty),typeof_h(ha,v),some(ty,tv)),
inference(equality_proxy_replacement,[],[f245,f413]) ).
tff(f417,plain,
! [X0: $tType,X2: val,X3: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X1: ty,X4: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0)))))))),X5: ty] :
( ~ sQ70_eqProxy(option(ty),typeof_h(X3,X2),some(ty,X5))
| conf(X0,X4,X3,X2,X1)
| ~ widen(X0,X4,X5,X1) ),
inference(equality_proxy_replacement,[],[f258,f413]) ).
tff(f614,plain,
! [X0: $tType,X2: ty,X1: list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))))))))] :
( ~ widen(X0,X1,tv,X2)
| conf(X0,X1,ha,v,X2) ),
inference(resolution,[],[f417,f414]) ).
tff(f621,plain,
conf(product_prod(list(list(char)),exp(list(char))),p,ha,v,tf),
inference(resolution,[],[f614,f244]) ).
tff(f632,plain,
$false,
inference(resolution,[],[f621,f388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW553_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 % Computer : n002.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8046.5625MB
% 0.09/0.27 % OS : Linux 6.8.0-71-generic
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Mon Sep 28 14:21:52 UTC 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running first-order theorem proving
% 0.25/0.32 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
% 4.59/1.54 % (380575)Detected formulas, will run a generic FOF schedule.
% 4.59/1.54 % (380583)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=2042302465:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.59/1.54 % (380588)dis-21_1_sil=8000:lcm=predicate:random_seed=3117864182: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)
% 4.59/1.54 % (380588)First to succeed.
% 4.59/1.54 % (380588)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-380575"
% 4.59/1.54 % (380586)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2000932620:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.59/1.54 % (380585)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3442134145:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.59/1.54 % (380582)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=3794384413:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.59/1.54 % (380584)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=2198685379:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.59/1.54 % (380585)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.59/1.54 % (380585)Refutation not found, incomplete strategy
% 4.59/1.54 % (380585)------------------------------
% 4.59/1.54 % (380585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.54 % (380585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.54 % (380585)CaDiCaL version: 2.1.3
% 4.59/1.54 % (380585)Termination reason: Refutation not found, incomplete strategy
% 4.59/1.54 % (380585)Time elapsed: 0.002 s
% 4.59/1.54 % (380585)Peak memory usage: 87 MB
% 4.59/1.54 % (380585)Instructions burned: 1 (million)
% 4.59/1.54 % (380584)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.59/1.54 % (380587)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3945050104:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.59/1.54 % (380587)Also succeeded, but the first one will report.
% 4.59/1.54 % (380586)Instruction limit reached!
% 4.59/1.54 % (380586)------------------------------
% 4.59/1.54 % (380586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.59/1.54 % (380586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.59/1.54 % (380586)CaDiCaL version: 2.1.3
% 4.59/1.54 % (380586)Termination reason: Instruction limit
% 4.59/1.54 % (380586)Termination phase: Saturation
% 4.59/1.54 % (380586)Time elapsed: 0.101 s
% 4.59/1.54 % (380586)Peak memory usage: 88 MB
% 4.59/1.54 % (380586)Instructions burned: 120 (million)
% 4.59/1.54 % Exception at run slice level
% 4.59/1.54 User error: GNN currently only supports monomorphic FOL.
% 4.59/1.54 % (380588)Refutation found. Thanks to Tanya!
% 4.59/1.54 % SZS status Theorem for theBenchmark
% 4.59/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.28/1.79 % (380588)------------------------------
% 5.28/1.79 % (380588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.79 % (380588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.79 % (380588)CaDiCaL version: 2.1.3
% 5.28/1.79 % (380588)Termination reason: Refutation
% 5.28/1.79 % (380588)Time elapsed: 0.024 s
% 5.28/1.79 % (380588)Peak memory usage: 89 MB
% 5.28/1.79 % (380588)Instructions burned: 23 (million)
% 5.28/1.79 % (380588)------------------------------
% 5.28/1.79 % (380588)------------------------------
% 5.28/1.79 % (380575)Success in time 0.627 s
% 5.28/1.79 % Vampire exiting
%------------------------------------------------------------------------------