%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW571_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 : n012.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 01:30:49 PM UTC 2026
% Result : Theorem 2.91s 0.96s
% Output : Refutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 55 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 16 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 3 prp; 0-5 aty)
% Number of functors : 103 ( 103 usr; 19 con; 0-7 aty)
% Number of variables : 46 ( 0 sgn 44 !; 2 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bop: $tType ).
tff(type_def_6,type,
exp: $tType > $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
list: $tType > $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
option: $tType > $tType ).
tff(type_def_11,type,
char: $tType ).
tff(type_def_12,type,
ty: $tType ).
tff(type_def_13,type,
val: $tType ).
tff(type_def_14,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_15,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
binOp:
!>[X0: $tType] : ( ( exp(X0) * bop * exp(X0) ) > exp(X0) ) ).
tff(func_def_1,type,
fAss:
!>[X0: $tType] : ( ( exp(X0) * list(char) * list(char) * exp(X0) ) > exp(X0) ) ).
tff(func_def_2,type,
val1:
!>[X0: $tType] : ( val > exp(X0) ) ).
tff(func_def_3,type,
while:
!>[X0: $tType] : ( ( exp(X0) * exp(X0) ) > exp(X0) ) ).
tff(func_def_4,type,
throw:
!>[X0: $tType] : ( exp(X0) > exp(X0) ) ).
tff(func_def_5,type,
wf_J_mdecl: fun(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(list(char),fun(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char)))))),bool))) ).
tff(func_def_6,type,
map_add:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,option(X1)) * fun(X0,option(X1)) ) > fun(X0,option(X1)) ) ).
tff(func_def_7,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_8,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_9,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_10,type,
red: 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(product_prod(product_prod(exp(list(char)),product_prod(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val)))),product_prod(exp(list(char)),product_prod(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val))))),bool) ).
tff(func_def_11,type,
hp: product_prod(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val))) > fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).
tff(func_def_12,type,
transitive_rtrancl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_13,type,
nt: ty ).
tff(func_def_14,type,
void: ty ).
tff(func_def_15,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fTrue: bool ).
tff(func_def_18,type,
d: list(char) ).
tff(func_def_19,type,
e: fun(list(char),option(ty)) ).
tff(func_def_20,type,
f: list(char) ).
tff(func_def_21,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_22,type,
t_2: ty ).
tff(func_def_23,type,
t: ty ).
tff(func_def_24,type,
e_2: exp(list(char)) ).
tff(func_def_25,type,
e_a: exp(list(char)) ).
tff(func_def_26,type,
ea: exp(list(char)) ).
tff(func_def_27,type,
h_a: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).
tff(func_def_28,type,
ha: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))) ).
tff(func_def_29,type,
l_a: fun(list(char),option(val)) ).
tff(func_def_30,type,
la: fun(list(char),option(val)) ).
tff(func_def_31,type,
sK0: ty ).
tff(func_def_32,type,
sK1: ( ty * fun(list(char),option(ty)) ) > ty ).
tff(func_def_33,type,
sK2: ( ty * fun(list(char),option(ty)) ) > ty ).
tff(func_def_34,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_35,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_36,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_37,type,
sK6:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X1 ) ).
tff(func_def_38,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X0 ) ).
tff(func_def_39,type,
sK8:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_40,type,
sK9:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_41,type,
sK10:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_42,type,
sK11:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_43,type,
sK12:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_44,type,
sK13:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_45,type,
sK14:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_46,type,
sK15:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_47,type,
sK16:
!>[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_48,type,
sK17:
!>[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_49,type,
sK18:
!>[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_50,type,
sK19:
!>[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_51,type,
sK20:
!>[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_52,type,
sK21:
!>[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_53,type,
sK22:
!>[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_54,type,
sK23:
!>[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_55,type,
sK24:
!>[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_56,type,
sK25:
!>[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_57,type,
sK26:
!>[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_58,type,
sK27:
!>[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_59,type,
sK28:
!>[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_60,type,
sK29:
!>[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_61,type,
sK30:
!>[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_62,type,
sK31:
!>[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_63,type,
sK32:
!>[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_64,type,
sK33:
!>[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_65,type,
sK34:
!>[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_66,type,
sK35:
!>[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_67,type,
sK36:
!>[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_68,type,
sK37:
!>[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_69,type,
sK38:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_70,type,
sK39:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_71,type,
sK40:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_72,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_73,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_74,type,
sK43:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_75,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_76,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_77,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_78,type,
sK47:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_79,type,
sK48:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_80,type,
sK49:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_81,type,
sK50:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_82,type,
sK51:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(product_prod(X1,X0),product_prod(X1,X0)),bool) * X0 * X1 * X0 * X1 ) > X1 ) ).
tff(func_def_83,type,
sK52:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(product_prod(X1,X0),product_prod(X1,X0)),bool) * X0 * X1 * X0 * X1 ) > X0 ) ).
tff(func_def_84,type,
sK53:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X0 ) ).
tff(func_def_85,type,
sK54:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X1 ) ).
tff(func_def_86,type,
sK55:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X0 ) ).
tff(func_def_87,type,
sK56:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X1 ) ).
tff(func_def_88,type,
sK57:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X0 ) ).
tff(func_def_89,type,
sK58:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X1 ) ).
tff(func_def_90,type,
sK59:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X0 ) ).
tff(func_def_91,type,
sK60:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,bool)) * fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) * X1 * X0 ) > X1 ) ).
tff(func_def_92,type,
sK61:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) * X0 ) > X0 ) ).
tff(func_def_93,type,
sK62:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) * X0 ) > X0 ) ).
tff(func_def_94,type,
sK63:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * X0 * X0 ) > X0 ) ).
tff(func_def_95,type,
sK64:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * X0 * X0 ) > X0 ) ).
tff(func_def_96,type,
sK65:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) * X0 ) > X0 ) ).
tff(func_def_97,type,
sK66:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) * X0 ) > X0 ) ).
tff(pred_def_1,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_2,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_3,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_4,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_5,type,
typeSa976492716_sconf: ( 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(list(char),option(ty)) * product_prod(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(list(char),option(val))) ) > $o ).
tff(pred_def_6,type,
is_refT: ty > $o ).
tff(pred_def_7,type,
wf_prog:
!>[X0: $tType] : ( ( fun(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(list(char),fun(product_prod(list(char),product_prod(list(ty),product_prod(ty,X0))),bool))) * 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)))))))) ) > $o ) ).
tff(pred_def_8,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_9,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_10,type,
pp: bool > $o ).
tff(pred_def_11,type,
sQ67_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f1,axiom,
t = void,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_void) ).
tff(f2,axiom,
wTrt(p,h_a,e,e_2,t_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096P_ME_Mh_H_A_092_060turnstile_062_Ae_092_060_094isub_0622_A_058_AT_092_060_094isub_0622_096) ).
tff(f3,axiom,
wTrt(p,h_a,e,e_a,nt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096P_ME_Mh_H_A_092_060turnstile_062_Ae_H_A_058_ANT_096) ).
tff(f9,axiom,
! [X0: $tType,X1: ty,X2: 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,X2,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_widen__refl) ).
tff(f13,axiom,
! [X0: list(char),X1: list(char),X2: ty,X3: exp(list(char)),X4: exp(list(char)),X5: fun(list(char),option(ty)),X6: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X7: 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)))))))))))] :
( wTrt(X7,X6,X5,X4,nt)
=> ( wTrt(X7,X6,X5,X3,X2)
=> wTrt(X7,X6,X5,fAss(list(char),X4,X1,X0,X3),void) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_WTrtFAssNT) ).
tff(f103,conjecture,
? [X0: ty] :
( wTrt(p,h_a,e,fAss(list(char),e_a,f,d,e_2),X0)
& widen(product_prod(list(list(char)),exp(list(char))),p,X0,t) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f104,negated_conjecture,
~ ? [X0: ty] :
( wTrt(p,h_a,e,fAss(list(char),e_a,f,d,e_2),X0)
& widen(product_prod(list(list(char)),exp(list(char))),p,X0,t) ),
inference(negated_conjecture,[status(cth)],[f103]) ).
tff(f110,plain,
! [X0: list(char),X1: list(char),X2: ty,X3: exp(list(char)),X4: exp(list(char)),X5: fun(list(char),option(ty)),X6: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X7: 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)))))))))))] :
( wTrt(X7,X6,X5,fAss(list(char),X4,X1,X0,X3),void)
| ~ wTrt(X7,X6,X5,X3,X2)
| ~ wTrt(X7,X6,X5,X4,nt) ),
inference(ennf_transformation,[],[f13]) ).
tff(f111,plain,
! [X0: list(char),X1: list(char),X2: ty,X3: exp(list(char)),X4: exp(list(char)),X5: fun(list(char),option(ty)),X6: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X7: 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)))))))))))] :
( wTrt(X7,X6,X5,fAss(list(char),X4,X1,X0,X3),void)
| ~ wTrt(X7,X6,X5,X3,X2)
| ~ wTrt(X7,X6,X5,X4,nt) ),
inference(flattening,[],[f110]) ).
tff(f176,plain,
! [X0: ty] :
( ~ wTrt(p,h_a,e,fAss(list(char),e_a,f,d,e_2),X0)
| ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t) ),
inference(ennf_transformation,[],[f104]) ).
tff(f217,plain,
t = void,
inference(cnf_transformation,[],[f1]) ).
tff(f218,plain,
wTrt(p,h_a,e,e_2,t_2),
inference(cnf_transformation,[],[f2]) ).
tff(f219,plain,
wTrt(p,h_a,e,e_a,nt),
inference(cnf_transformation,[],[f3]) ).
tff(f229,plain,
! [X0: $tType,X2: 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)))))))),X1: ty] : widen(X0,X2,X1,X1),
inference(cnf_transformation,[],[f9]) ).
tff(f232,plain,
! [X2: ty,X3: exp(list(char)),X0: list(char),X1: list(char),X6: fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),X7: 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))))))))))),X4: exp(list(char)),X5: fun(list(char),option(ty))] :
( wTrt(X7,X6,X5,fAss(list(char),X4,X1,X0,X3),void)
| ~ wTrt(X7,X6,X5,X3,X2)
| ~ wTrt(X7,X6,X5,X4,nt) ),
inference(cnf_transformation,[],[f111]) ).
tff(f354,plain,
! [X0: ty] :
( ~ wTrt(p,h_a,e,fAss(list(char),e_a,f,d,e_2),X0)
| ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,t) ),
inference(cnf_transformation,[],[f176]) ).
tff(f357,plain,
! [X0: ty] :
( ~ widen(product_prod(list(list(char)),exp(list(char))),p,X0,void)
| ~ wTrt(p,h_a,e,fAss(list(char),e_a,f,d,e_2),X0) ),
inference(definition_unfolding,[],[f354,f217]) ).
tff(f435,plain,
~ wTrt(p,h_a,e,fAss(list(char),e_a,f,d,e_2),void),
inference(resolution,[],[f229,f357]) ).
tff(f652,plain,
! [X0: ty] :
( ~ wTrt(p,h_a,e,e_2,X0)
| ~ wTrt(p,h_a,e,e_a,nt) ),
inference(resolution,[],[f232,f435]) ).
tff(f654,definition,
( spl68_1
<=> wTrt(p,h_a,e,e_a,nt) ),
introduced(definition,[new_symbols(definition,[spl68_1])],[avatar_definition]) ).
tff(f655,plain,
( ~ wTrt(p,h_a,e,e_a,nt)
| spl68_1 ),
inference(avatar_component_clause,[],[f654]) ).
tff(f657,definition,
( spl68_2
<=> ! [X0: ty] : ~ wTrt(p,h_a,e,e_2,X0) ),
introduced(definition,[new_symbols(definition,[spl68_2])],[avatar_definition]) ).
tff(f658,plain,
( ! [X0: ty] : ~ wTrt(p,h_a,e,e_2,X0)
| ~ spl68_2 ),
inference(avatar_component_clause,[],[f657]) ).
tff(f659,plain,
( ~ spl68_1
| spl68_2 ),
inference(avatar_split_clause,[],[f652,f657,f654]) ).
tff(f660,plain,
( $false
| spl68_1 ),
inference(resolution,[],[f655,f219]) ).
tff(f661,plain,
spl68_1,
inference(avatar_contradiction_clause,[],[f660]) ).
tff(f662,plain,
( $false
| ~ spl68_2 ),
inference(resolution,[],[f658,f218]) ).
tff(f663,plain,
~ spl68_2,
inference(avatar_contradiction_clause,[],[f662]) ).
cnf(s1,plain,
( ~ spl68_1
| spl68_2 ),
inference(sat_conversion,[],[f659]) ).
cnf(s2,plain,
spl68_1,
inference(sat_conversion,[],[f661]) ).
cnf(s3,plain,
~ spl68_2,
inference(sat_conversion,[],[f663]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
tff(f664,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW571_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.16 % Computer : n012.cluster.edu
% 0.05/0.16 % Model : x86_64 x86_64
% 0.05/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.16 % Memory : 8046.5625MB
% 0.05/0.16 % OS : Linux 6.8.0-71-generic
% 0.05/0.16 % CPULimit : 300
% 0.05/0.16 % WCLimit : 300
% 0.05/0.16 % DateTime : Mon Sep 28 14:19:19 UTC 2026
% 0.05/0.16 % CPUTime :
% 0.05/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.18 Running first-order theorem proving
% 0.05/0.18 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
% 2.91/0.96 % (3403126)Detected formulas, will run a generic FOF schedule.
% 2.91/0.96 % (3403142)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=799858199:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.91/0.96 % (3403141)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3640228596:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.91/0.96 % (3403139)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=944017279:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.91/0.96 % (3403140)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=891682932:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.91/0.96 % (3403144)dis-21_1_sil=8000:lcm=predicate:random_seed=1528502627: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)
% 2.91/0.96 % (3403137)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=1625037764:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.91/0.96 % (3403138)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=1690198364:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.91/0.96 % (3403140)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.91/0.96 % (3403140)Refutation not found, incomplete strategy
% 2.91/0.96 % (3403140)------------------------------
% 2.91/0.96 % (3403140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/0.96 % (3403140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/0.96 % (3403140)CaDiCaL version: 2.1.3
% 2.91/0.96 % (3403140)Termination reason: Refutation not found, incomplete strategy
% 2.91/0.96 % (3403140)Time elapsed: 0.003 s
% 2.91/0.96 % (3403140)Peak memory usage: 88 MB
% 2.91/0.96 % (3403140)Instructions burned: 4 (million)
% 2.91/0.96 % (3403139)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.91/0.96 % (3403144)First to succeed.
% 2.91/0.96 % (3403144)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3403126"
% 2.91/0.96 % (3403142)Instruction limit reached!
% 2.91/0.96 % (3403142)------------------------------
% 2.91/0.96 % (3403142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/0.96 % (3403142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/0.96 % (3403142)CaDiCaL version: 2.1.3
% 2.91/0.96 % (3403142)Termination reason: Instruction limit
% 2.91/0.96 % (3403142)Termination phase: Saturation
% 2.91/0.96 % (3403142)Time elapsed: 0.031 s
% 2.91/0.96 % (3403142)Peak memory usage: 88 MB
% 2.91/0.96 % (3403142)Instructions burned: 143 (million)
% 2.91/0.96 % (3403141)Instruction limit reached!
% 2.91/0.96 % (3403141)------------------------------
% 2.91/0.96 % (3403141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/0.96 % (3403141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/0.96 % (3403141)CaDiCaL version: 2.1.3
% 2.91/0.96 % (3403141)Termination reason: Instruction limit
% 2.91/0.96 % (3403141)Termination phase: Saturation
% 2.91/0.96 % (3403141)Time elapsed: 0.058 s
% 2.91/0.96 % (3403141)Peak memory usage: 88 MB
% 2.91/0.96 % (3403141)Instructions burned: 120 (million)
% 2.91/0.96 % (3403155)lrs+10_1_sil=8000:sp=occurrence:random_seed=1967655057:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.91/0.96 % (3403155)Also succeeded, but the first one will report.
% 2.91/0.96 % (3403140)------------------------------
% 2.91/0.96 % (3403140)------------------------------
% 2.91/0.96 % (3403144)Refutation found. Thanks to Tanya!
% 2.91/0.96 % SZS status Theorem for theBenchmark
% 2.91/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 3.74/1.11 % (3403144)------------------------------
% 3.74/1.11 % (3403144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.11 % (3403144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.11 % (3403144)CaDiCaL version: 2.1.3
% 3.74/1.11 % (3403144)Termination reason: Refutation
% 3.74/1.11 % (3403144)Time elapsed: 0.019 s
% 3.74/1.11 % (3403144)Peak memory usage: 89 MB
% 3.74/1.11 % (3403144)Instructions burned: 42 (million)
% 3.74/1.11 % (3403144)------------------------------
% 3.74/1.11 % (3403144)------------------------------
% 3.74/1.11 % (3403126)Success in time 0.484 s
% 3.74/1.11 % Vampire exiting
%------------------------------------------------------------------------------