%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SCT187_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:37:44 PM UTC 2026
% Result : Theorem 1.44s 0.80s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 29
% Syntax : Number of formulae : 257 ( 13 unt; 0 typ; 27 def)
% Number of atoms : 948 ( 188 equ)
% Maximal formula atoms : 47 ( 3 avg)
% Number of connectives : 1103 ( 412 ~; 566 |; 92 &)
% ( 27 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 40 ( 38 usr; 28 prp; 0-5 aty)
% Number of functors : 113 ( 113 usr; 11 con; 0-7 aty)
% Number of variables : 121 ( 0 sgn 114 !; 7 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_8,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).
tff(func_def_1,type,
arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_2,type,
arrow_319942042_below: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_3,type,
arrow_276188178_mkbot: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_4,type,
arrow_424895264_mktop: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_5,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_6,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).
tff(func_def_7,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).
tff(func_def_8,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_9,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_10,type,
product_prod_case:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_11,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_12,type,
product_scomp:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( fun(X0,product_prod(X1,X2)) * fun(X1,fun(X2,X3)) ) > fun(X0,X3) ) ).
tff(func_def_13,type,
id_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_14,type,
converse:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > fun(product_prod(X1,X0),bool) ) ).
tff(func_def_15,type,
inv_image:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X1,X0) ) > fun(product_prod(X1,X1),bool) ) ).
tff(func_def_16,type,
lex_prod:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(product_prod(X1,X1),bool) ) > fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) ) ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
l: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_21,type,
x: arrow_411405190le_alt ).
tff(func_def_22,type,
y: arrow_411405190le_alt ).
tff(func_def_23,type,
sK0:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_24,type,
sK1:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_25,type,
sK2:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_26,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_27,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_28,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_29,type,
sK6:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_30,type,
sK7:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_31,type,
sK8:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_32,type,
sK9:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_33,type,
sK10:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_34,type,
sK11:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_35,type,
sK12:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_36,type,
sK13:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_37,type,
sK14:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_38,type,
sK15:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_39,type,
sK16:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_40,type,
sK17:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_41,type,
sK18:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_42,type,
sK19:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_43,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)))) > X0 ) ).
tff(func_def_44,type,
sK21:
!>[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_45,type,
sK22:
!>[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_46,type,
sK23:
!>[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_47,type,
sK24:
!>[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_48,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) > X4 ) ).
tff(func_def_49,type,
sK26:
!>[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_50,type,
sK27:
!>[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_51,type,
sK28:
!>[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_52,type,
sK29:
!>[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_53,type,
sK30:
!>[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_54,type,
sK31:
!>[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_55,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))))) > X2 ) ).
tff(func_def_56,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))))) > X3 ) ).
tff(func_def_57,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))))) > X4 ) ).
tff(func_def_58,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))))) > X5 ) ).
tff(func_def_59,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) > X5 ) ).
tff(func_def_60,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) > X4 ) ).
tff(func_def_61,type,
sK38:
!>[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_62,type,
sK39:
!>[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_63,type,
sK40:
!>[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_64,type,
sK41:
!>[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_65,type,
sK42: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_66,type,
sK43:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_67,type,
sK44:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_68,type,
sK45:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_69,type,
sK46:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_70,type,
sK47:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_71,type,
sK48:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_72,type,
sK49:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X0 ) ).
tff(func_def_73,type,
sK50:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X1 ) ).
tff(func_def_74,type,
sK51:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X1 ) ).
tff(func_def_75,type,
sK52:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X0 ) ).
tff(func_def_76,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_77,type,
sK54:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_78,type,
sK55:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X0 ) ).
tff(func_def_79,type,
sK56:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_80,type,
sK57:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X1 ) ).
tff(func_def_81,type,
sK58:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X0 ) ).
tff(func_def_82,type,
sK59:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).
tff(func_def_83,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).
tff(func_def_84,type,
sK61:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_85,type,
sK62:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * product_prod(X0,X1) ) > X0 ) ).
tff(func_def_86,type,
sK63:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_87,type,
sK64:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_88,type,
sK65:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X0 ) ).
tff(func_def_89,type,
sK66:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X2 ) ).
tff(func_def_90,type,
sK67:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X0 ) ).
tff(func_def_91,type,
sK68:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X2 ) ).
tff(func_def_92,type,
sK69:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_93,type,
sK70:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_94,type,
sK71:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_95,type,
sK72:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_96,type,
sK73:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_97,type,
sK74:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_98,type,
sK75:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_99,type,
sK76:
!>[X0: $tType] : ( ( fun(X0,bool) * product_prod(X0,X0) ) > X0 ) ).
tff(func_def_100,type,
sK77:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_101,type,
sK78:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_102,type,
sK79:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_103,type,
sK80:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_104,type,
sK81: arrow_411405190le_alt ).
tff(func_def_105,type,
sK82: arrow_411405190le_alt ).
tff(func_def_106,type,
sK83: arrow_411405190le_alt ).
tff(func_def_107,type,
sK84: arrow_411405190le_alt ).
tff(func_def_108,type,
sK87: arrow_411405190le_alt > arrow_411405190le_alt ).
tff(func_def_109,type,
sK88: arrow_411405190le_alt > arrow_411405190le_alt ).
tff(func_def_110,type,
sK89: ( arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_411405190le_alt ).
tff(pred_def_1,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_2,type,
refl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_3,type,
antisym:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_4,type,
irrefl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_5,type,
sym:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_6,type,
total_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_7,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_8,type,
pp: bool > $o ).
tff(pred_def_9,type,
sP85: ( arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_10,type,
sP86: ( arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_11,type,
sP90: ( arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(f93,axiom,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
=> ! [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ) )
& ! [X0: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X0),l)
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 != X1 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),l) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f94,conjecture,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| ( X0 = x )
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) ) )
& ( ( X1 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ( X0 = x )
| ! [X2: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ) )
& ( ( X0 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| ( X2 = y )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) ) ) )
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 = X1 )
| ( ( X0 = x )
& ( X1 = y ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( X0 != x )
& ( X1 != x ) )
| ( ( X1 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
& ( X0 != x ) )
| ( ( X0 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
& ( X1 != x ) )
| ( ( X1 = x )
& ( X0 = y ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),l)
& ( X1 != x )
& ( X0 != x ) )
| ( ( X0 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ( X1 != x ) )
| ( ( X1 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
& ( X0 != x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f95,negated_conjecture,
~ ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| ( X0 = x )
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) ) )
& ( ( X1 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ( X0 = x )
| ! [X2: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ) )
& ( ( X0 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| ( X2 = y )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) ) ) )
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 = X1 )
| ( ( X0 = x )
& ( X1 = y ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( X0 != x )
& ( X1 != x ) )
| ( ( X1 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
& ( X0 != x ) )
| ( ( X0 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
& ( X1 != x ) )
| ( ( X1 = x )
& ( X0 = y ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),l)
& ( X1 != x )
& ( X0 != x ) )
| ( ( X0 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ( X1 != x ) )
| ( ( X1 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
& ( X0 != x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
tff(f97,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
=> ! [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ) )
& ! [X3: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( ( X4 != X5 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X5),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X4),l) ) ) ),
inference(rectify,[],[f93]) ).
tff(f98,plain,
~ ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| ( X0 = x )
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) ) )
& ( ( X1 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ( X0 = x )
| ! [X3: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X3),l)
| ( x = X3 )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),l) ) )
& ( ( X0 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ( X1 = x )
| ! [X4: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),l)
| ( x = X4 )
| ( y = X4 )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X4),l) )
& ( ( x != X4 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) ) ) )
& ! [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 = X6 )
| ( ( x = X5 )
& ( y = X6 ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X6),l)
& ( x != X5 )
& ( x != X6 ) )
| ( ( x = X6 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),y),l)
& ( x != X5 ) )
| ( ( x = X5 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X6),l)
& ( x != X6 ) )
| ( ( x = X6 )
& ( y = X5 ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),l)
& ( x != X6 )
& ( x != X5 ) )
| ( ( x = X5 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),y),l)
& ( x != X6 ) )
| ( ( x = X6 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X5),l)
& ( x != X5 ) ) ) ),
inference(rectify,[],[f95]) ).
tff(f161,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ! [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l) )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l) )
& ! [X3: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X5),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X4),l)
| ( X4 = X5 ) ) ),
inference(ennf_transformation,[],[f97]) ).
tff(f162,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ! [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l) )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l) )
& ! [X3: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X5),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X4),l)
| ( X4 = X5 ) ) ),
inference(flattening,[],[f161]) ).
tff(f163,plain,
( ? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( x != X0 )
& ( x != X1 )
& ? [X2: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
& ( x != X2 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
| ( ( x = X2 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) ) )
| ( ( x = X1 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
& ( x != X0 )
& ? [X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X3),l)
& ( x != X3 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),l) ) )
| ( ( x = X0 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
& ( x != X1 )
& ? [X4: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),l)
& ( x != X4 )
& ( y != X4 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X4),l) )
| ( ( x = X4 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) ) ) )
| ? [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
& ( ( x != X5 )
| ( y != X6 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X6),l)
| ( x = X5 )
| ( x = X6 ) )
& ( ( x != X6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),y),l)
| ( x = X5 ) )
& ( ( x != X5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X6),l)
| ( x = X6 ) )
& ( ( x != X6 )
| ( y != X5 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),l)
| ( x = X6 )
| ( x = X5 ) )
& ( ( x != X5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),y),l)
| ( x = X6 ) )
& ( ( x != X6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X5),l)
| ( x = X5 ) ) ) ),
inference(ennf_transformation,[],[f98]) ).
tff(f334,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ),
inference(cnf_transformation,[],[f162]) ).
tff(f335,plain,
! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X4),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X5),l)
| ( X4 = X5 ) ),
inference(cnf_transformation,[],[f162]) ).
tff(f336,plain,
! [X3: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X3),l),
inference(cnf_transformation,[],[f162]) ).
tff(f339,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP86(X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK89(X0,X1)),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f341,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP86(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),sK89(X0,X1)),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f342,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP86(X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK89(X0,X1)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f344,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP86(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),sK89(X0,X1)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f345,plain,
! [X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X4),l)
| ~ sP90(X4,X1) ),
inference(cnf_transformation,[],[f163]) ).
tff(f348,plain,
! [X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),l)
| ~ sP90(X4,X1) ),
inference(cnf_transformation,[],[f163]) ).
tff(f351,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| sP90(sK87(X1),X1)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| sP86(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f353,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| sP90(sK87(X1),X1)
| ( x = X1 )
| sP86(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f355,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| sP90(sK87(X1),X1)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK88(X0)),l)
| sP86(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f361,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( x != X1 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK88(X0)),l)
| sP86(X1,X0)
| ~ sP85(X1,X0) ),
inference(cnf_transformation,[],[f163]) ).
tff(f366,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK88(X0)),l)
| sP86(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f369,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK88(X0)),l)
| sP86(X1,X0)
| ( x = X0 ) ),
inference(cnf_transformation,[],[f163]) ).
tff(f370,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( x != X1 )
| ~ sP86(X1,X0) ),
inference(cnf_transformation,[],[f163]) ).
tff(f371,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( x != X0 )
| ~ sP86(X1,X0) ),
inference(cnf_transformation,[],[f163]) ).
tff(f372,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| ~ sP86(X1,X0) ),
inference(cnf_transformation,[],[f163]) ).
tff(f373,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| sP86(X1,X0)
| ( x = X0 ) ),
inference(cnf_transformation,[],[f163]) ).
tff(f374,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| ( x = X1 )
| sP86(X1,X0)
| ( x = X0 ) ),
inference(cnf_transformation,[],[f163]) ).
tff(f375,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ( x != X0 )
| sP86(X1,X0)
| ~ sP85(X1,X0) ),
inference(cnf_transformation,[],[f163]) ).
tff(f376,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| sP86(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f377,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP85(X1,X0)
| ( x = X1 )
| sP86(X1,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l) ),
inference(cnf_transformation,[],[f163]) ).
tff(f380,plain,
( ( y != sK82 )
| ( x != sK81 )
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f381,plain,
( ( x = sK82 )
| ( x = sK81 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK81),sK82),l)
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f382,plain,
( ( x = sK81 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK81),y),l)
| ( x != sK82 )
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f383,plain,
( ( x = sK82 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK82),l)
| ( x != sK81 )
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f384,plain,
( ( y != sK81 )
| ( x != sK82 )
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f385,plain,
( ( x = sK81 )
| ( x = sK82 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK82),sK81),l)
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f386,plain,
( ( x = sK82 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK82),y),l)
| ( x != sK81 )
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f387,plain,
( ( x = sK81 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK81),l)
| ( x != sK82 )
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f388,plain,
( ( sK81 != sK82 )
| sP85(sK84,sK83) ),
inference(cnf_transformation,[],[f163]) ).
tff(f435,plain,
! [X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| sP86(X1,x)
| ~ sP85(X1,x) ),
inference(equality_resolution,[],[f375]) ).
tff(f436,plain,
! [X1: arrow_411405190le_alt] : ~ sP86(X1,x),
inference(equality_resolution,[],[f371]) ).
tff(f437,plain,
! [X0: arrow_411405190le_alt] : ~ sP86(x,X0),
inference(equality_resolution,[],[f370]) ).
tff(f440,plain,
! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK88(X0)),l)
| sP86(x,X0)
| ~ sP85(x,X0) ),
inference(equality_resolution,[],[f361]) ).
tff(f467,definition,
( spl91_3
<=> sP85(sK84,sK83) ),
introduced(definition,[new_symbols(definition,[spl91_3])],[avatar_definition]) ).
tff(f469,plain,
( sP85(sK84,sK83)
| ~ spl91_3 ),
inference(avatar_component_clause,[],[f467]) ).
tff(f471,definition,
( spl91_4
<=> ( x = sK81 ) ),
introduced(definition,[new_symbols(definition,[spl91_4])],[avatar_definition]) ).
tff(f472,plain,
( ( x = sK81 )
| ~ spl91_4 ),
inference(avatar_component_clause,[],[f471]) ).
tff(f475,definition,
( spl91_5
<=> ( y = sK82 ) ),
introduced(definition,[new_symbols(definition,[spl91_5])],[avatar_definition]) ).
tff(f477,plain,
( ( y != sK82 )
| spl91_5 ),
inference(avatar_component_clause,[],[f475]) ).
tff(f478,plain,
( spl91_3
| ~ spl91_4
| ~ spl91_5 ),
inference(avatar_split_clause,[],[f380,f475,f471,f467]) ).
tff(f480,definition,
( spl91_6
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK81),sK82),l) ),
introduced(definition,[new_symbols(definition,[spl91_6])],[avatar_definition]) ).
tff(f482,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK81),sK82),l)
| spl91_6 ),
inference(avatar_component_clause,[],[f480]) ).
tff(f484,definition,
( spl91_7
<=> ( x = sK82 ) ),
introduced(definition,[new_symbols(definition,[spl91_7])],[avatar_definition]) ).
tff(f486,plain,
( ( x = sK82 )
| ~ spl91_7 ),
inference(avatar_component_clause,[],[f484]) ).
tff(f487,plain,
( spl91_3
| ~ spl91_6
| spl91_4
| spl91_7 ),
inference(avatar_split_clause,[],[f381,f484,f471,f480,f467]) ).
tff(f489,definition,
( spl91_8
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK81),y),l) ),
introduced(definition,[new_symbols(definition,[spl91_8])],[avatar_definition]) ).
tff(f491,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK81),y),l)
| spl91_8 ),
inference(avatar_component_clause,[],[f489]) ).
tff(f492,plain,
( spl91_3
| ~ spl91_7
| ~ spl91_8
| spl91_4 ),
inference(avatar_split_clause,[],[f382,f471,f489,f484,f467]) ).
tff(f494,definition,
( spl91_9
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK82),l) ),
introduced(definition,[new_symbols(definition,[spl91_9])],[avatar_definition]) ).
tff(f496,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK82),l)
| spl91_9 ),
inference(avatar_component_clause,[],[f494]) ).
tff(f497,plain,
( spl91_3
| ~ spl91_4
| ~ spl91_9
| spl91_7 ),
inference(avatar_split_clause,[],[f383,f484,f494,f471,f467]) ).
tff(f499,definition,
( spl91_10
<=> ( y = sK81 ) ),
introduced(definition,[new_symbols(definition,[spl91_10])],[avatar_definition]) ).
tff(f502,plain,
( spl91_3
| ~ spl91_7
| ~ spl91_10 ),
inference(avatar_split_clause,[],[f384,f499,f484,f467]) ).
tff(f504,definition,
( spl91_11
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK82),sK81),l) ),
introduced(definition,[new_symbols(definition,[spl91_11])],[avatar_definition]) ).
tff(f507,plain,
( spl91_3
| ~ spl91_11
| spl91_7
| spl91_4 ),
inference(avatar_split_clause,[],[f385,f471,f484,f504,f467]) ).
tff(f509,definition,
( spl91_12
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK82),y),l) ),
introduced(definition,[new_symbols(definition,[spl91_12])],[avatar_definition]) ).
tff(f511,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK82),y),l)
| spl91_12 ),
inference(avatar_component_clause,[],[f509]) ).
tff(f512,plain,
( spl91_3
| ~ spl91_4
| ~ spl91_12
| spl91_7 ),
inference(avatar_split_clause,[],[f386,f484,f509,f471,f467]) ).
tff(f514,definition,
( spl91_13
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK81),l) ),
introduced(definition,[new_symbols(definition,[spl91_13])],[avatar_definition]) ).
tff(f517,plain,
( spl91_3
| ~ spl91_7
| ~ spl91_13
| spl91_4 ),
inference(avatar_split_clause,[],[f387,f471,f514,f484,f467]) ).
tff(f519,definition,
( spl91_14
<=> ( sK81 = sK82 ) ),
introduced(definition,[new_symbols(definition,[spl91_14])],[avatar_definition]) ).
tff(f521,plain,
( ( sK81 != sK82 )
| spl91_14 ),
inference(avatar_component_clause,[],[f519]) ).
tff(f522,plain,
( spl91_3
| ~ spl91_14 ),
inference(avatar_split_clause,[],[f388,f519,f467]) ).
tff(f550,plain,
! [X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ~ sP85(X1,x) ),
inference(forward_subsumption_resolution,[],[f435,f436]) ).
tff(f556,plain,
! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK88(X0)),l)
| ~ sP85(x,X0) ),
inference(forward_subsumption_resolution,[],[f440,f437]) ).
tff(f607,plain,
! [X0: arrow_411405190le_alt] : ~ sP86(X0,X0),
inference(resolution,[],[f336,f372]) ).
tff(f842,plain,
! [X0: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK88(X0)),X0),l)
| ( sK88(X0) = X0 )
| ~ sP85(x,X0) ),
inference(resolution,[],[f335,f556]) ).
tff(f929,definition,
( spl91_21
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK84),l) ),
introduced(definition,[new_symbols(definition,[spl91_21])],[avatar_definition]) ).
tff(f930,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK84),l)
| spl91_21 ),
inference(avatar_component_clause,[],[f929]) ).
tff(f931,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK84),l)
| ~ spl91_21 ),
inference(avatar_component_clause,[],[f929]) ).
tff(f933,definition,
( spl91_22
<=> sP86(sK84,sK83) ),
introduced(definition,[new_symbols(definition,[spl91_22])],[avatar_definition]) ).
tff(f935,plain,
( sP86(sK84,sK83)
| ~ spl91_22 ),
inference(avatar_component_clause,[],[f933]) ).
tff(f937,definition,
( spl91_23
<=> ( x = sK84 ) ),
introduced(definition,[new_symbols(definition,[spl91_23])],[avatar_definition]) ).
tff(f939,plain,
( ( x = sK84 )
| ~ spl91_23 ),
inference(avatar_component_clause,[],[f937]) ).
tff(f942,definition,
( spl91_24
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l) ),
introduced(definition,[new_symbols(definition,[spl91_24])],[avatar_definition]) ).
tff(f943,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| spl91_24 ),
inference(avatar_component_clause,[],[f942]) ).
tff(f944,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| ~ spl91_24 ),
inference(avatar_component_clause,[],[f942]) ).
tff(f947,definition,
( spl91_25
<=> ( x = sK83 ) ),
introduced(definition,[new_symbols(definition,[spl91_25])],[avatar_definition]) ).
tff(f948,plain,
( ( x != sK83 )
| spl91_25 ),
inference(avatar_component_clause,[],[f947]) ).
tff(f949,plain,
( ( x = sK83 )
| ~ spl91_25 ),
inference(avatar_component_clause,[],[f947]) ).
tff(f953,definition,
( spl91_26
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK88(sK83)),l) ),
introduced(definition,[new_symbols(definition,[spl91_26])],[avatar_definition]) ).
tff(f955,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK88(sK83)),l)
| ~ spl91_26 ),
inference(avatar_component_clause,[],[f953]) ).
tff(f968,definition,
( spl91_29
<=> sP90(sK87(sK84),sK84) ),
introduced(definition,[new_symbols(definition,[spl91_29])],[avatar_definition]) ).
tff(f970,plain,
( sP90(sK87(sK84),sK84)
| ~ spl91_29 ),
inference(avatar_component_clause,[],[f968]) ).
tff(f973,definition,
( spl91_30
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),y),l) ),
introduced(definition,[new_symbols(definition,[spl91_30])],[avatar_definition]) ).
tff(f975,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),y),l)
| ~ spl91_30 ),
inference(avatar_component_clause,[],[f973]) ).
tff(f990,definition,
( spl91_31
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),sK89(sK83,sK84)),l) ),
introduced(definition,[new_symbols(definition,[spl91_31])],[avatar_definition]) ).
tff(f992,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),sK89(sK83,sK84)),l)
| spl91_31 ),
inference(avatar_component_clause,[],[f990]) ).
tff(f995,definition,
( spl91_32
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),sK89(sK83,sK84)),l) ),
introduced(definition,[new_symbols(definition,[spl91_32])],[avatar_definition]) ).
tff(f997,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),sK89(sK83,sK84)),l)
| ~ spl91_32 ),
inference(avatar_component_clause,[],[f995]) ).
tff(f1115,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP86(X2,X1)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l) ),
inference(resolution,[],[f334,f372]) ).
tff(f1116,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP90(X2,X1)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l) ),
inference(resolution,[],[f334,f348]) ).
tff(f1123,plain,
( ! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK84),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) )
| ~ spl91_30 ),
inference(resolution,[],[f334,f975]) ).
tff(f1163,plain,
( ! [X0: arrow_411405190le_alt] :
( ~ sP86(sK84,X0)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) )
| ~ spl91_30 ),
inference(resolution,[],[f1123,f372]) ).
tff(f1165,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),y),l)
| ~ sP85(sK84,x)
| ~ spl91_30 ),
inference(resolution,[],[f1123,f550]) ).
tff(f1181,plain,
( ~ sP85(sK84,x)
| ~ spl91_30 ),
inference(forward_subsumption_resolution,[],[f1165,f336]) ).
tff(f1217,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| ~ spl91_22
| ~ spl91_30 ),
inference(resolution,[],[f1163,f935]) ).
tff(f1402,definition,
( spl91_54
<=> ( sK83 = sK88(sK83) ) ),
introduced(definition,[new_symbols(definition,[spl91_54])],[avatar_definition]) ).
tff(f1403,plain,
( ( sK83 != sK88(sK83) )
| spl91_54 ),
inference(avatar_component_clause,[],[f1402]) ).
tff(f1404,plain,
( ( sK83 = sK88(sK83) )
| ~ spl91_54 ),
inference(avatar_component_clause,[],[f1402]) ).
tff(f1406,definition,
( spl91_55
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK88(sK83)),y),l) ),
introduced(definition,[new_symbols(definition,[spl91_55])],[avatar_definition]) ).
tff(f1407,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK88(sK83)),y),l)
| spl91_55 ),
inference(avatar_component_clause,[],[f1406]) ).
tff(f1408,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK88(sK83)),y),l)
| ~ spl91_55 ),
inference(avatar_component_clause,[],[f1406]) ).
tff(f1486,plain,
( ! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK88(sK83)),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) )
| ~ spl91_55 ),
inference(resolution,[],[f1408,f334]) ).
tff(f1605,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),y),l)
| ~ spl91_26
| ~ spl91_55 ),
inference(resolution,[],[f955,f1486]) ).
tff(f1607,plain,
( $false
| ~ spl91_26
| ~ spl91_55 ),
inference(forward_subsumption_resolution,[],[f1605,f336]) ).
tff(f1608,plain,
( ~ spl91_26
| ~ spl91_55 ),
inference(avatar_contradiction_clause,[],[f1607]) ).
tff(f1625,plain,
( ( x != sK81 )
| ~ spl91_7
| spl91_14 ),
inference(forward_demodulation,[],[f521,f486]) ).
tff(f1761,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK82),l)
| ( y = sK82 )
| spl91_12 ),
inference(resolution,[],[f511,f335]) ).
tff(f1766,plain,
( ( y = sK82 )
| spl91_9
| spl91_12 ),
inference(forward_subsumption_resolution,[],[f1761,f496]) ).
tff(f1769,plain,
( $false
| spl91_5
| spl91_9
| spl91_12 ),
inference(forward_subsumption_resolution,[],[f1766,f477]) ).
tff(f1770,plain,
( spl91_5
| spl91_9
| spl91_12 ),
inference(avatar_contradiction_clause,[],[f1769]) ).
tff(f1777,plain,
( $false
| ~ spl91_4
| ~ spl91_7
| spl91_14 ),
inference(forward_subsumption_resolution,[],[f1625,f472]) ).
tff(f1778,plain,
( ~ spl91_4
| ~ spl91_7
| spl91_14 ),
inference(avatar_contradiction_clause,[],[f1777]) ).
tff(f1791,plain,
( sP90(sK87(sK84),sK84)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| sP86(sK84,sK83)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),y),l)
| ~ spl91_3 ),
inference(resolution,[],[f469,f351]) ).
tff(f1793,plain,
( sP90(sK87(sK84),sK84)
| ( x = sK84 )
| sP86(sK84,sK83)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),y),l)
| ~ spl91_3 ),
inference(resolution,[],[f469,f353]) ).
tff(f1795,plain,
( sP90(sK87(sK84),sK84)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK88(sK83)),l)
| sP86(sK84,sK83)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),y),l)
| ~ spl91_3 ),
inference(resolution,[],[f469,f355]) ).
tff(f1800,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK88(sK83)),l)
| sP86(sK84,sK83)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK84),l)
| ~ spl91_3 ),
inference(resolution,[],[f469,f366]) ).
tff(f1801,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK88(sK83)),l)
| sP86(sK84,sK83)
| ( x = sK83 )
| ~ spl91_3 ),
inference(resolution,[],[f469,f369]) ).
tff(f1802,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| sP86(sK84,sK83)
| ( x = sK83 )
| ~ spl91_3 ),
inference(resolution,[],[f469,f373]) ).
tff(f1803,plain,
( ( x = sK84 )
| sP86(sK84,sK83)
| ( x = sK83 )
| ~ spl91_3 ),
inference(resolution,[],[f469,f374]) ).
tff(f1804,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| sP86(sK84,sK83)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK84),l)
| ~ spl91_3 ),
inference(resolution,[],[f469,f376]) ).
tff(f1805,plain,
( ( x = sK84 )
| sP86(sK84,sK83)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK84),l)
| ~ spl91_3 ),
inference(resolution,[],[f469,f377]) ).
tff(f1856,plain,
( sP85(x,sK83)
| ~ spl91_3
| ~ spl91_23 ),
inference(superposition,[],[f469,f939]) ).
tff(f2031,plain,
( ! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK83),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) )
| ~ spl91_24 ),
inference(resolution,[],[f944,f334]) ).
tff(f2263,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK88(sK83)),y),l)
| ( sK83 = sK88(sK83) )
| ~ sP85(x,sK83)
| ~ spl91_24 ),
inference(resolution,[],[f2031,f842]) ).
tff(f2266,plain,
( ( sK83 = sK88(sK83) )
| ~ sP85(x,sK83)
| ~ spl91_24
| spl91_55 ),
inference(forward_subsumption_resolution,[],[f2263,f1407]) ).
tff(f2270,plain,
( ~ sP85(x,sK83)
| ~ spl91_24
| spl91_54
| spl91_55 ),
inference(forward_subsumption_resolution,[],[f2266,f1403]) ).
tff(f2271,plain,
( $false
| ~ spl91_3
| ~ spl91_23
| ~ spl91_24
| spl91_54
| spl91_55 ),
inference(forward_subsumption_resolution,[],[f2270,f1856]) ).
tff(f2272,plain,
( ~ spl91_3
| ~ spl91_23
| ~ spl91_24
| spl91_54
| spl91_55 ),
inference(avatar_contradiction_clause,[],[f2271]) ).
tff(f2388,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| ~ spl91_54
| spl91_55 ),
inference(superposition,[],[f1407,f1404]) ).
tff(f2406,plain,
( $false
| ~ spl91_24
| ~ spl91_54
| spl91_55 ),
inference(forward_subsumption_resolution,[],[f2388,f944]) ).
tff(f2407,plain,
( ~ spl91_24
| ~ spl91_54
| spl91_55 ),
inference(avatar_contradiction_clause,[],[f2406]) ).
tff(f2410,plain,
( spl91_21
| spl91_22
| spl91_23
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1805,f467,f937,f933,f929]) ).
tff(f2411,plain,
( spl91_25
| spl91_22
| spl91_23
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1803,f467,f937,f933,f947]) ).
tff(f2416,plain,
( spl91_30
| spl91_22
| spl91_23
| spl91_29
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1793,f467,f968,f937,f933,f973]) ).
tff(f2726,plain,
( sP85(sK84,x)
| ~ spl91_3
| ~ spl91_25 ),
inference(superposition,[],[f469,f949]) ).
tff(f2727,plain,
( sP86(sK84,x)
| ~ spl91_22
| ~ spl91_25 ),
inference(superposition,[],[f935,f949]) ).
tff(f2754,plain,
( $false
| ~ spl91_22
| ~ spl91_25 ),
inference(forward_subsumption_resolution,[],[f2727,f436]) ).
tff(f2755,plain,
( ~ spl91_22
| ~ spl91_25 ),
inference(avatar_contradiction_clause,[],[f2754]) ).
tff(f2780,plain,
( spl91_25
| spl91_22
| spl91_26
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1801,f467,f953,f933,f947]) ).
tff(f2782,plain,
( spl91_30
| spl91_22
| spl91_26
| spl91_29
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1795,f467,f968,f953,f933,f973]) ).
tff(f2783,plain,
( spl91_25
| spl91_22
| spl91_24
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1802,f467,f942,f933,f947]) ).
tff(f2785,plain,
( spl91_30
| spl91_22
| spl91_24
| spl91_29
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1791,f467,f968,f942,f933,f973]) ).
tff(f2850,plain,
( $false
| ~ spl91_3
| ~ spl91_25
| ~ spl91_30 ),
inference(forward_subsumption_resolution,[],[f2726,f1181]) ).
tff(f2851,plain,
( ~ spl91_3
| ~ spl91_25
| ~ spl91_30 ),
inference(avatar_contradiction_clause,[],[f2850]) ).
tff(f2858,plain,
( spl91_21
| spl91_22
| spl91_26
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1800,f467,f953,f933,f929]) ).
tff(f2859,plain,
( spl91_21
| spl91_22
| spl91_24
| ~ spl91_3 ),
inference(avatar_split_clause,[],[f1804,f467,f942,f933,f929]) ).
tff(f2864,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),sK89(sK83,sK84)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| ~ spl91_22 ),
inference(resolution,[],[f935,f344]) ).
tff(f2865,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),sK89(sK83,sK84)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| ~ spl91_22 ),
inference(resolution,[],[f935,f342]) ).
tff(f2866,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),sK89(sK83,sK84)),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),y),l)
| ~ spl91_22 ),
inference(resolution,[],[f935,f341]) ).
tff(f2867,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),sK89(sK83,sK84)),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),y),l)
| ~ spl91_22 ),
inference(resolution,[],[f935,f339]) ).
tff(f2868,plain,
( spl91_30
| ~ spl91_31
| ~ spl91_22 ),
inference(avatar_split_clause,[],[f2867,f933,f990,f973]) ).
tff(f2869,plain,
( spl91_30
| spl91_32
| ~ spl91_22 ),
inference(avatar_split_clause,[],[f2866,f933,f995,f973]) ).
tff(f2870,plain,
( ~ spl91_24
| ~ spl91_31
| ~ spl91_22 ),
inference(avatar_split_clause,[],[f2865,f933,f990,f942]) ).
tff(f2871,plain,
( ~ spl91_24
| spl91_32
| ~ spl91_22 ),
inference(avatar_split_clause,[],[f2864,f933,f995,f942]) ).
tff(f3090,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK81),l)
| ( y = sK81 )
| spl91_8 ),
inference(resolution,[],[f491,f335]) ).
tff(f3095,plain,
( spl91_10
| spl91_13
| spl91_8 ),
inference(avatar_split_clause,[],[f3090,f489,f514,f499]) ).
tff(f3106,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),y),l)
| ( y = sK84 )
| spl91_21 ),
inference(resolution,[],[f930,f335]) ).
tff(f3111,definition,
( spl91_94
<=> ( y = sK84 ) ),
introduced(definition,[new_symbols(definition,[spl91_94])],[avatar_definition]) ).
tff(f3113,plain,
( ( y = sK84 )
| ~ spl91_94 ),
inference(avatar_component_clause,[],[f3111]) ).
tff(f3115,plain,
( spl91_94
| spl91_30
| spl91_21 ),
inference(avatar_split_clause,[],[f3106,f929,f973,f3111]) ).
tff(f3223,plain,
( sP85(y,sK83)
| ~ spl91_3
| ~ spl91_94 ),
inference(superposition,[],[f469,f3113]) ).
tff(f3275,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| sP86(y,sK83)
| ( x = sK83 )
| ~ spl91_3
| ~ spl91_94 ),
inference(resolution,[],[f3223,f373]) ).
tff(f3284,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),y),l)
| ( x = sK83 )
| ~ spl91_3
| ~ spl91_94 ),
inference(forward_subsumption_resolution,[],[f3275,f372]) ).
tff(f3300,plain,
( ( x = sK83 )
| ~ spl91_3
| spl91_24
| ~ spl91_94 ),
inference(forward_subsumption_resolution,[],[f3284,f943]) ).
tff(f3323,plain,
( $false
| ~ spl91_3
| spl91_24
| spl91_25
| ~ spl91_94 ),
inference(forward_subsumption_resolution,[],[f3300,f948]) ).
tff(f3324,plain,
( ~ spl91_3
| spl91_24
| spl91_25
| ~ spl91_94 ),
inference(avatar_contradiction_clause,[],[f3323]) ).
tff(f3331,plain,
( $false
| ~ spl91_22
| spl91_24
| ~ spl91_30 ),
inference(forward_subsumption_resolution,[],[f1217,f943]) ).
tff(f3332,plain,
( ~ spl91_22
| spl91_24
| ~ spl91_30 ),
inference(avatar_contradiction_clause,[],[f3331]) ).
tff(f3594,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK82),sK81),l)
| ( sK81 = sK82 )
| spl91_6 ),
inference(resolution,[],[f482,f335]) ).
tff(f4727,plain,
( ! [X0: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK84),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK83),l) )
| ~ spl91_22 ),
inference(resolution,[],[f1115,f935]) ).
tff(f4761,plain,
( spl91_14
| spl91_11
| spl91_6 ),
inference(avatar_split_clause,[],[f3594,f480,f504,f519]) ).
tff(f4976,plain,
( ! [X0: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK89(sK83,sK84)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK84),l) )
| ~ spl91_32 ),
inference(resolution,[],[f997,f334]) ).
tff(f5173,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK84),sK83),l)
| ~ spl91_22 ),
inference(resolution,[],[f4727,f336]) ).
tff(f5177,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),sK84),l)
| ( sK83 = sK84 )
| ~ spl91_22 ),
inference(resolution,[],[f5173,f335]) ).
tff(f5182,definition,
( spl91_107
<=> ( sK83 = sK84 ) ),
introduced(definition,[new_symbols(definition,[spl91_107])],[avatar_definition]) ).
tff(f5184,plain,
( ( sK83 = sK84 )
| ~ spl91_107 ),
inference(avatar_component_clause,[],[f5182]) ).
tff(f5186,definition,
( spl91_108
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),sK84),l) ),
introduced(definition,[new_symbols(definition,[spl91_108])],[avatar_definition]) ).
tff(f5188,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),sK84),l)
| ~ spl91_108 ),
inference(avatar_component_clause,[],[f5186]) ).
tff(f5190,plain,
( spl91_107
| spl91_108
| ~ spl91_22 ),
inference(avatar_split_clause,[],[f5177,f933,f5186,f5182]) ).
tff(f5230,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK83),sK84),l)
| spl91_31
| ~ spl91_32 ),
inference(resolution,[],[f4976,f992]) ).
tff(f5231,plain,
( $false
| spl91_31
| ~ spl91_32
| ~ spl91_108 ),
inference(forward_subsumption_resolution,[],[f5230,f5188]) ).
tff(f5232,plain,
( spl91_31
| ~ spl91_32
| ~ spl91_108 ),
inference(avatar_contradiction_clause,[],[f5231]) ).
tff(f5237,plain,
( sP86(sK83,sK83)
| ~ spl91_22
| ~ spl91_107 ),
inference(superposition,[],[f935,f5184]) ).
tff(f5267,plain,
( $false
| ~ spl91_22
| ~ spl91_107 ),
inference(forward_subsumption_resolution,[],[f5237,f607]) ).
tff(f5268,plain,
( ~ spl91_22
| ~ spl91_107 ),
inference(avatar_contradiction_clause,[],[f5267]) ).
tff(f5317,plain,
( ! [X0: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK87(sK84)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK84),l) )
| ~ spl91_29 ),
inference(resolution,[],[f970,f1116]) ).
tff(f5575,plain,
( ! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK84),l)
| ~ sP90(sK87(sK84),X0) )
| ~ spl91_29 ),
inference(resolution,[],[f5317,f345]) ).
tff(f5576,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP90(sK87(sK84),X0)
| ~ spl91_21
| ~ spl91_29 ),
inference(forward_subsumption_resolution,[],[f5575,f931]) ).
tff(f5578,plain,
( $false
| ~ spl91_21
| ~ spl91_29 ),
inference(resolution,[],[f5576,f970]) ).
tff(f5579,plain,
( ~ spl91_21
| ~ spl91_29 ),
inference(avatar_contradiction_clause,[],[f5578]) ).
cnf(s2,plain,
( spl91_3
| ~ spl91_4
| ~ spl91_5 ),
inference(sat_conversion,[],[f478]) ).
cnf(s3,plain,
( spl91_3
| spl91_4
| ~ spl91_6
| spl91_7 ),
inference(sat_conversion,[],[f487]) ).
cnf(s4,plain,
( spl91_3
| spl91_4
| ~ spl91_7
| ~ spl91_8 ),
inference(sat_conversion,[],[f492]) ).
cnf(s5,plain,
( spl91_3
| ~ spl91_4
| spl91_7
| ~ spl91_9 ),
inference(sat_conversion,[],[f497]) ).
cnf(s6,plain,
( spl91_3
| ~ spl91_7
| ~ spl91_10 ),
inference(sat_conversion,[],[f502]) ).
cnf(s7,plain,
( spl91_3
| spl91_4
| spl91_7
| ~ spl91_11 ),
inference(sat_conversion,[],[f507]) ).
cnf(s8,plain,
( spl91_3
| ~ spl91_4
| spl91_7
| ~ spl91_12 ),
inference(sat_conversion,[],[f512]) ).
cnf(s9,plain,
( spl91_3
| spl91_4
| ~ spl91_7
| ~ spl91_13 ),
inference(sat_conversion,[],[f517]) ).
cnf(s10,plain,
( spl91_3
| ~ spl91_14 ),
inference(sat_conversion,[],[f522]) ).
cnf(s72,plain,
( ~ spl91_26
| ~ spl91_55 ),
inference(sat_conversion,[],[f1608]) ).
cnf(s80,plain,
( spl91_5
| spl91_9
| spl91_12 ),
inference(sat_conversion,[],[f1770]) ).
cnf(s82,plain,
( ~ spl91_4
| ~ spl91_7
| spl91_14 ),
inference(sat_conversion,[],[f1778]) ).
cnf(s115,plain,
( ~ spl91_3
| ~ spl91_23
| ~ spl91_24
| spl91_54
| spl91_55 ),
inference(sat_conversion,[],[f2272]) ).
cnf(s126,plain,
( ~ spl91_24
| ~ spl91_54
| spl91_55 ),
inference(sat_conversion,[],[f2407]) ).
cnf(s129,plain,
( ~ spl91_3
| spl91_21
| spl91_22
| spl91_23 ),
inference(sat_conversion,[],[f2410]) ).
cnf(s130,plain,
( ~ spl91_3
| spl91_22
| spl91_23
| spl91_25 ),
inference(sat_conversion,[],[f2411]) ).
cnf(s135,plain,
( ~ spl91_3
| spl91_22
| spl91_23
| spl91_29
| spl91_30 ),
inference(sat_conversion,[],[f2416]) ).
cnf(s155,plain,
( ~ spl91_22
| ~ spl91_25 ),
inference(sat_conversion,[],[f2755]) ).
cnf(s159,plain,
( ~ spl91_3
| spl91_22
| spl91_25
| spl91_26 ),
inference(sat_conversion,[],[f2780]) ).
cnf(s161,plain,
( ~ spl91_3
| spl91_22
| spl91_26
| spl91_29
| spl91_30 ),
inference(sat_conversion,[],[f2782]) ).
cnf(s162,plain,
( ~ spl91_3
| spl91_22
| spl91_24
| spl91_25 ),
inference(sat_conversion,[],[f2783]) ).
cnf(s164,plain,
( ~ spl91_3
| spl91_22
| spl91_24
| spl91_29
| spl91_30 ),
inference(sat_conversion,[],[f2785]) ).
cnf(s171,plain,
( ~ spl91_3
| ~ spl91_25
| ~ spl91_30 ),
inference(sat_conversion,[],[f2851]) ).
cnf(s173,plain,
( ~ spl91_3
| spl91_21
| spl91_22
| spl91_26 ),
inference(sat_conversion,[],[f2858]) ).
cnf(s174,plain,
( ~ spl91_3
| spl91_21
| spl91_22
| spl91_24 ),
inference(sat_conversion,[],[f2859]) ).
cnf(s177,plain,
( ~ spl91_22
| spl91_30
| ~ spl91_31 ),
inference(sat_conversion,[],[f2868]) ).
cnf(s178,plain,
( ~ spl91_22
| spl91_30
| spl91_32 ),
inference(sat_conversion,[],[f2869]) ).
cnf(s179,plain,
( ~ spl91_22
| ~ spl91_24
| ~ spl91_31 ),
inference(sat_conversion,[],[f2870]) ).
cnf(s180,plain,
( ~ spl91_22
| ~ spl91_24
| spl91_32 ),
inference(sat_conversion,[],[f2871]) ).
cnf(s187,plain,
( spl91_8
| spl91_10
| spl91_13 ),
inference(sat_conversion,[],[f3095]) ).
cnf(s189,plain,
( spl91_21
| spl91_30
| spl91_94 ),
inference(sat_conversion,[],[f3115]) ).
cnf(s200,plain,
( ~ spl91_3
| spl91_24
| spl91_25
| ~ spl91_94 ),
inference(sat_conversion,[],[f3324]) ).
cnf(s205,plain,
( ~ spl91_22
| spl91_24
| ~ spl91_30 ),
inference(sat_conversion,[],[f3332]) ).
cnf(s243,plain,
( spl91_6
| spl91_11
| spl91_14 ),
inference(sat_conversion,[],[f4761]) ).
cnf(s248,plain,
( ~ spl91_22
| spl91_107
| spl91_108 ),
inference(sat_conversion,[],[f5190]) ).
cnf(s249,plain,
( spl91_31
| ~ spl91_32
| ~ spl91_108 ),
inference(sat_conversion,[],[f5232]) ).
cnf(s250,plain,
( ~ spl91_22
| ~ spl91_107 ),
inference(sat_conversion,[],[f5268]) ).
cnf(s270,plain,
( ~ spl91_21
| ~ spl91_29 ),
inference(sat_conversion,[],[f5579]) ).
cnf(s273,plain,
( ~ spl91_7
| spl91_4
| spl91_3 ),
inference(rat,[],[s187,s4,s9,s6]) ).
cnf(s274,plain,
( spl91_4
| spl91_3 ),
inference(rat,[],[s243,s3,s7,s273,s10]) ).
cnf(s275,plain,
spl91_3,
inference(rat,[],[s80,s5,s8,s82,s2,s274,s10]) ).
cnf(s276,plain,
( ~ spl91_23
| spl91_55
| ~ spl91_24 ),
inference(rat,[],[s126,s115,s275]) ).
cnf(s277,plain,
( spl91_22
| spl91_21 ),
inference(rat,[],[s276,s72,s129,s173,s174,s275]) ).
cnf(s278,plain,
( ~ spl91_24
| ~ spl91_22 ),
inference(rat,[],[s249,s179,s180,s248,s250]) ).
cnf(s279,plain,
spl91_21,
inference(rat,[],[s189,s200,s205,s278,s155,s277,s275]) ).
cnf(s280,plain,
~ spl91_29,
inference(rat,[],[s270,s279]) ).
cnf(s281,plain,
( spl91_23
| spl91_22 ),
inference(rat,[],[s171,s130,s135,s280,s275]) ).
cnf(s282,plain,
( spl91_26
| spl91_22 ),
inference(rat,[],[s171,s159,s161,s280,s275]) ).
cnf(s283,plain,
~ spl91_24,
inference(rat,[],[s282,s72,s276,s281,s278]) ).
cnf(s286,plain,
~ spl91_22,
inference(rat,[],[s249,s177,s178,s248,s205,s250,s283]) ).
cnf(s287,plain,
spl91_30,
inference(rat,[],[s164,s283,s280,s275,s286]) ).
cnf(s289,plain,
spl91_25,
inference(rat,[],[s162,s283,s275,s286]) ).
cnf(s292,plain,
$false,
inference(rat,[],[s171,s275,s289,s287]) ).
tff(f5583,plain,
$false,
inference(avatar_sat_refutation,[],[s292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT187_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:03:18 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.44/0.80 % (3129057)Will run a generic schedule for satisfiability detection.
% 1.44/0.80 % (3129065)dis+10_1_sil=32000:sp=arity:random_seed=732466155:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.44/0.80 % (3129063)% WARNING: option uhcvi not known.
% 1.44/0.80 % (3129062)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4282779792_2999 on theBenchmark for (2999ds/0Mi)
% 1.44/0.80 % (3129063)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3063771765:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.44/0.80 % (3129064)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=947678460:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.44/0.80 % (3129066)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=981977684:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.44/0.80 % (3129067)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=841768425:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.44/0.80 % (3129068)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3663787916:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.44/0.80 % Exception at run slice level
% 1.44/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.44/0.80 % (3129065)Instruction limit reached!
% 1.44/0.80 % (3129065)------------------------------
% 1.44/0.80 % (3129065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.80 % (3129065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.80 % (3129065)CaDiCaL version: 2.1.3
% 1.44/0.80 % (3129065)Termination reason: Instruction limit
% 1.44/0.80 % (3129065)Termination phase: Saturation
% 1.44/0.80 % (3129065)Time elapsed: 0.035 s
% 1.44/0.80 % (3129065)Peak memory usage: 12 MB
% 1.44/0.80 % (3129065)Instructions burned: 104 (million)
% 1.44/0.80 % (3129076)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=108570834:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.44/0.80 % (3129077)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4116351927:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.44/0.80 % Exception at run slice level
% 1.44/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.44/0.80 % (3129080)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4154822795:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.44/0.80 % (3129066)Instruction limit reached!
% 1.44/0.80 % (3129066)------------------------------
% 1.44/0.80 % (3129066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.80 % (3129066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.80 % (3129066)CaDiCaL version: 2.1.3
% 1.44/0.80 % (3129066)Termination reason: Instruction limit
% 1.44/0.80 % (3129066)Termination phase: Saturation
% 1.44/0.80 % (3129066)Time elapsed: 0.070 s
% 1.44/0.80 % (3129066)Peak memory usage: 13 MB
% 1.44/0.80 % (3129066)Instructions burned: 116 (million)
% 1.44/0.80 % (3129067)Instruction limit reached!
% 1.44/0.80 % (3129067)------------------------------
% 1.44/0.80 % (3129067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.80 % (3129067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.80 % (3129067)CaDiCaL version: 2.1.3
% 1.44/0.80 % (3129067)Termination reason: Instruction limit
% 1.44/0.80 % (3129067)Termination phase: Saturation
% 1.44/0.80 % (3129067)Time elapsed: 0.079 s
% 1.44/0.80 % (3129067)Peak memory usage: 13 MB
% 1.44/0.80 % (3129067)Instructions burned: 131 (million)
% 1.44/0.80 % (3129077)Instruction limit reached!
% 1.44/0.80 % (3129077)------------------------------
% 1.44/0.80 % (3129077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.80 % (3129077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.80 % (3129077)CaDiCaL version: 2.1.3
% 1.44/0.80 % (3129077)Termination reason: Instruction limit
% 1.44/0.80 % (3129077)Termination phase: Saturation
% 1.44/0.80 % (3129077)Time elapsed: 0.042 s
% 1.44/0.80 % (3129077)Peak memory usage: 13 MB
% 1.44/0.80 % (3129077)Instructions burned: 133 (million)
% 1.44/0.80 % (3129082)ott-21_1_sil=16000:fs=off:random_seed=1654273317:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.44/0.80 % (3129084)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3980152966:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.44/0.80 % (3129068)Instruction limit reached!
% 1.44/0.80 % (3129068)------------------------------
% 1.44/0.80 % (3129068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.80 % (3129068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.80 % (3129068)CaDiCaL version: 2.1.3
% 1.44/0.80 % (3129068)Termination reason: Instruction limit
% 1.44/0.80 % (3129068)Termination phase: Saturation
% 1.44/0.80 % (3129068)Time elapsed: 0.095 s
% 1.44/0.80 % (3129068)Peak memory usage: 14 MB
% 1.44/0.80 % (3129068)Instructions burned: 159 (million)
% 1.44/0.80 % Exception at run slice level
% 1.44/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.44/0.80 % (3129083)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1360283575:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.44/0.80 % (3129088)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=916681098:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.44/0.80 % Exception at run slice level
% 1.44/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.44/0.80 % (3129087)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=971255020:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.44/0.80 % (3129091)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2502884726:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.44/0.80 % (3129082)Instruction limit reached!
% 1.44/0.80 % (3129082)------------------------------
% 1.44/0.80 % (3129082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.80 % (3129082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.80 % (3129082)CaDiCaL version: 2.1.3
% 1.44/0.80 % (3129082)Termination reason: Instruction limit
% 1.44/0.80 % (3129082)Termination phase: Saturation
% 1.44/0.80 % (3129082)Time elapsed: 0.105 s
% 1.44/0.80 % (3129082)Peak memory usage: 13 MB
% 1.44/0.80 % (3129082)Instructions burned: 181 (million)
% 1.44/0.80 % (3129094)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3352711926:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.44/0.80 % (3129080) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3129057-3129080"...
% 1.44/0.80 % (3129080)...printing done.
% 1.44/0.80 % (3129080)Refutation found. Thanks to Tanya!
% 1.44/0.80 % SZS status Theorem for theBenchmark
% 1.44/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/0.80 % (3129080)------------------------------
% 2.62/0.80 % (3129080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.62/0.80 % (3129080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/0.80 % (3129080)CaDiCaL version: 2.1.3
% 2.62/0.80 % (3129080)Termination reason: Refutation
% 2.62/0.80 % (3129080)Time elapsed: 0.258 s
% 2.62/0.80 % (3129080)Peak memory usage: 15 MB
% 2.62/0.80 % (3129080)Instructions burned: 440 (million)
% 2.62/0.80 % (3129057)Success in time 0.37 s
% 2.62/0.80 % Vampire exiting
%------------------------------------------------------------------------------