TSTP Solution File: SCT193_5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SCT193_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:23:38 EDT 2023
% Result : Theorem 0.24s 0.66s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 196
% Syntax : Number of formulae : 541 ( 49 unt; 123 typ; 0 def)
% Number of atoms : 1502 ( 382 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1709 ( 625 ~; 764 |; 191 &)
% ( 63 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 178 ( 105 >; 73 *; 0 +; 0 <<)
% Number of predicates : 47 ( 45 usr; 34 prp; 0-6 aty)
% Number of functors : 108 ( 108 usr; 9 con; 0-7 aty)
% Number of variables : 1352 (;1016 !; 37 ?;1352 :)
% ( 299 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
arrow_159774573e_indi: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_9,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,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_6,type,
order_215145569der_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(product_prod(X0,X0),bool),bool) ) ).
tff(func_def_7,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_8,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_9,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).
tff(func_def_10,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).
tff(func_def_11,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_12,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_13,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_14,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_15,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_16,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_17,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_18,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_19,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_20,type,
fFalse: bool ).
tff(func_def_21,type,
fTrue: bool ).
tff(func_def_22,type,
f: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_23,type,
p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_24,type,
a: arrow_411405190le_alt ).
tff(func_def_25,type,
b: arrow_411405190le_alt ).
tff(func_def_26,type,
i: arrow_159774573e_indi ).
tff(func_def_27,type,
sK4: arrow_159774573e_indi ).
tff(func_def_28,type,
sK5: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > arrow_159774573e_indi ).
tff(func_def_29,type,
sK6:
!>[X0: $tType] : X0 ).
tff(func_def_30,type,
sK7:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_31,type,
sK8:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_32,type,
sK9:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_33,type,
sK10:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_34,type,
sK11:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_35,type,
sK12:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_36,type,
sK13:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_37,type,
sK14:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_38,type,
sK15:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_39,type,
sK16:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_40,type,
sK17:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_41,type,
sK18:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_42,type,
sK19:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_43,type,
sK20:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_44,type,
sK21:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_45,type,
sK22:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_46,type,
sK23:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_47,type,
sK24:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_48,type,
sK25:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_49,type,
sK26:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_50,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X0 ) ).
tff(func_def_51,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X1 ) ).
tff(func_def_52,type,
sK29:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_53,type,
sK30:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X1 ) ).
tff(func_def_54,type,
sK31:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X0 ) ).
tff(func_def_55,type,
sK32:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_56,type,
sK33:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_57,type,
sK34:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_58,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_59,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_60,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_61,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_62,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_63,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_64,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_65,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X0 ) ).
tff(func_def_66,type,
sK43:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X2 ) ).
tff(func_def_67,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X0 ) ).
tff(func_def_68,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X2 ) ).
tff(func_def_69,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).
tff(func_def_70,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).
tff(func_def_71,type,
sK48:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X1 ) ).
tff(func_def_72,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X0 ) ).
tff(func_def_73,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_74,type,
sK51:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_75,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X0 ) ).
tff(func_def_76,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_77,type,
sK54:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_78,type,
sK55:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_79,type,
sK56:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_80,type,
sK57:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_81,type,
sK58:
!>[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_82,type,
sK59:
!>[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_83,type,
sK60:
!>[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_84,type,
sK61:
!>[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_85,type,
sK62:
!>[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_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,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X4 ) ).
tff(func_def_89,type,
sK66:
!>[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_90,type,
sK67:
!>[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_91,type,
sK68:
!>[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_92,type,
sK69:
!>[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_93,type,
sK70:
!>[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_94,type,
sK71:
!>[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_95,type,
sK72:
!>[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_96,type,
sK73:
!>[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_97,type,
sK74:
!>[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_98,type,
sK75:
!>[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_99,type,
sK76:
!>[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_100,type,
sK77:
!>[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_101,type,
sK78:
!>[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_102,type,
sK79:
!>[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_103,type,
sK80:
!>[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_104,type,
sK81:
!>[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_105,type,
sK82: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(pred_def_1,type,
top:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_3,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_4,type,
irrefl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_5,type,
total_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_6,type,
trans:
!>[X0: $tType] : ( 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,
sP0: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_10,type,
sP1: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).
tff(pred_def_11,type,
sP2: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_12,type,
sP3: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).
tff(f3604,plain,
$false,
inference(avatar_sat_refutation,[],[f697,f699,f701,f703,f714,f722,f818,f865,f1063,f1110,f1118,f1182,f1192,f1345,f1394,f1399,f1409,f1605,f1756,f1844,f1941,f1998,f2055,f2116,f2173,f2481,f2513,f2979,f2982,f2997,f2999,f3020,f3022,f3519,f3575,f3577]) ).
tff(f3577,plain,
( ~ spl83_4
| ~ spl83_5
| ~ spl83_21 ),
inference(avatar_contradiction_clause,[],[f3576]) ).
tff(f3576,plain,
( $false
| ~ spl83_4
| ~ spl83_5
| ~ spl83_21 ),
inference(subsumption_resolution,[],[f3523,f716]) ).
tff(f716,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),X1),X1),f(p))
| ~ spl83_5 ),
inference(resolution,[],[f713,f379]) ).
tff(f379,plain,
! [X0: $tType,X3: X0,X1: fun(product_prod(X0,X0),bool)] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK11(X0,X1)),X1) )
& ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f263,f264]) ).
tff(f264,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK11(X0,X1)),X1) ),
introduced(choice_axiom,[]) ).
tff(f263,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
& ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ) ),
inference(rectify,[],[f262]) ).
tff(f262,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
& ( ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
| ~ irrefl(X0,X1) ) ),
inference(nnf_transformation,[],[f111]) ).
tff(f111,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
<=> ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X0: $tType,X5: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X5)
<=> ! [X6: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X6),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_0_irrefl__def) ).
tff(f713,plain,
( irrefl(arrow_411405190le_alt,f(p))
| ~ spl83_5 ),
inference(avatar_component_clause,[],[f711]) ).
tff(f711,plain,
( spl83_5
<=> irrefl(arrow_411405190le_alt,f(p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_5])]) ).
tff(f3523,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),b),b),f(p))
| ~ spl83_4
| ~ spl83_21 ),
inference(resolution,[],[f1842,f896]) ).
tff(f896,plain,
( ! [X56: 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),X56),a),f(p))
| 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),X56),b),f(p)) )
| ~ spl83_4 ),
inference(subsumption_resolution,[],[f668,f696]) ).
tff(f696,plain,
( trans(arrow_411405190le_alt,f(p))
| ~ spl83_4 ),
inference(avatar_component_clause,[],[f694]) ).
tff(f694,plain,
( spl83_4
<=> trans(arrow_411405190le_alt,f(p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_4])]) ).
tff(f668,plain,
! [X56: 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),X56),b),f(p))
| ~ 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),X56),a),f(p))
| ~ trans(arrow_411405190le_alt,f(p)) ),
inference(resolution,[],[f351,f478]) ).
tff(f478,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: fun(product_prod(X0,X0),bool)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
| ~ trans(X0,X4) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
| ~ trans(X0,X4) ),
inference(flattening,[],[f218]) ).
tff(f218,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
| ~ trans(X0,X4) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
( trans(X0,X4)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4) ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType,X20: X0,X14: X0,X15: X0,X5: fun(product_prod(X0,X0),bool)] :
( trans(X0,X5)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X15),X14),X5)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X14),X20),X5)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X15),X20),X5) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_8_transD) ).
tff(f351,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),a),b),f(p)),
inference(cnf_transformation,[],[f91]) ).
tff(f91,axiom,
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),a),b),f(p)),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_2) ).
tff(f1842,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),b),a),f(p))
| ~ spl83_21 ),
inference(avatar_component_clause,[],[f1841]) ).
tff(f1841,plain,
( spl83_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),b),a),f(p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_21])]) ).
tff(f3575,plain,
( ~ spl83_4
| ~ spl83_5
| ~ spl83_21 ),
inference(avatar_contradiction_clause,[],[f3574]) ).
tff(f3574,plain,
( $false
| ~ spl83_4
| ~ spl83_5
| ~ spl83_21 ),
inference(subsumption_resolution,[],[f3520,f716]) ).
tff(f3520,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),a),a),f(p))
| ~ spl83_4
| ~ spl83_21 ),
inference(resolution,[],[f1842,f897]) ).
tff(f897,plain,
( ! [X55: 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),b),X55),f(p))
| 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),a),X55),f(p)) )
| ~ spl83_4 ),
inference(subsumption_resolution,[],[f667,f696]) ).
tff(f667,plain,
! [X55: 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),a),X55),f(p))
| ~ 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),b),X55),f(p))
| ~ trans(arrow_411405190le_alt,f(p)) ),
inference(resolution,[],[f351,f478]) ).
tff(f3519,plain,
( spl83_21
| spl83_8
| ~ spl83_16 ),
inference(avatar_split_clause,[],[f2583,f1391,f815,f1841]) ).
tff(f815,plain,
( spl83_8
<=> ( a = b ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_8])]) ).
tff(f1391,plain,
( spl83_16
<=> 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),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_16])]) ).
tff(f2583,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),b),a),f(p))
| spl83_8
| ~ spl83_16 ),
inference(subsumption_resolution,[],[f2549,f816]) ).
tff(f816,plain,
( ( a != b )
| spl83_8 ),
inference(avatar_component_clause,[],[f815]) ).
tff(f2549,plain,
( ( a = b )
| 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),b),a),f(p))
| ~ spl83_16 ),
inference(resolution,[],[f736,f1393]) ).
tff(f1393,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),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ spl83_16 ),
inference(avatar_component_clause,[],[f1391]) ).
tff(f736,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),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ( 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),f(p)) ),
inference(subsumption_resolution,[],[f735,f355]) ).
tff(f355,plain,
! [X0: arrow_159774573e_indi] : trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
inference(cnf_transformation,[],[f97]) ).
tff(f97,plain,
! [X0: arrow_159774573e_indi] :
( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
& trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X52: arrow_159774573e_indi] :
( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52))
& trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52)) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_1) ).
tff(f735,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),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ( 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),f(p))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK5(p))) ),
inference(subsumption_resolution,[],[f730,f357]) ).
tff(f357,plain,
! [X0: arrow_159774573e_indi] : total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
inference(cnf_transformation,[],[f97]) ).
tff(f730,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),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ( X0 = X1 )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK5(p)))
| 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),f(p))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK5(p))) ),
inference(resolution,[],[f358,f356]) ).
tff(f356,plain,
! [X0: arrow_159774573e_indi] : irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
inference(cnf_transformation,[],[f97]) ).
tff(f358,plain,
! [X2: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: arrow_411405190le_alt] :
( ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(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),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X1 = X2 )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(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),X2),f(X0))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0))) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [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),X1),X2),f(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),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X1 = X2 ) )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f253,f254]) ).
tff(f254,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ? [X3: arrow_159774573e_indi] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3)) )
=> ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0)))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK5(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f253,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [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),X1),X2),f(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),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X1 = X2 ) )
| ? [X3: arrow_159774573e_indi] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3)) ) ),
inference(rectify,[],[f183]) ).
tff(f183,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X2: arrow_411405190le_alt,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),X2),X3),f(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),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X2 = X3 ) )
| ? [X1: arrow_159774573e_indi] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
inference(flattening,[],[f182]) ).
tff(f182,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X2: arrow_411405190le_alt,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),X2),X3),f(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),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X2 = X3 ) )
| ? [X1: arrow_159774573e_indi] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
inference(ennf_transformation,[],[f98]) ).
tff(f98,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X1: arrow_159774573e_indi] :
( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
& trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) )
=> ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( X2 != 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),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
=> 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),X2),X3),f(X0)) ) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X57: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X28: arrow_159774573e_indi] :
( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X57,X28))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X57,X28))
& trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X57,X28)) )
=> ! [X58: arrow_411405190le_alt,X59: arrow_411405190le_alt] :
( ( X58 != X59 )
=> ( 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),X58),X59),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X57,i))
=> 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),X58),X59),f(X57)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_0) ).
tff(f3022,plain,
spl83_31,
inference(avatar_contradiction_clause,[],[f3021]) ).
tff(f3021,plain,
( $false
| spl83_31 ),
inference(subsumption_resolution,[],[f3016,f369]) ).
tff(f369,plain,
! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
inference(cnf_transformation,[],[f103]) ).
tff(f103,plain,
! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: $tType,X7: X0] : member(X0,X7,top_top(fun(X0,bool))),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_2_UNIV__I) ).
tff(f3016,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),sK16(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),top_top(fun(arrow_411405190le_alt,bool)))),sK15(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),top_top(fun(arrow_411405190le_alt,bool)))),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| spl83_31 ),
inference(resolution,[],[f2971,f396]) ).
tff(f396,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK16(X0,X1,X2)),sK15(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK16(X0,X1,X2)),sK15(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),sK16(X0,X1,X2)),X1)
& ( sK15(X0,X1,X2) != sK16(X0,X1,X2) )
& member(X0,sK16(X0,X1,X2),X2)
& member(X0,sK15(X0,X1,X2),X2) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2) )
| ~ member(X0,X5,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f272,f274,f273]) ).
tff(f273,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ? [X3: X0] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& ( X3 != X4 )
& member(X0,X4,X2) )
& member(X0,X3,X2) )
=> ( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),sK15(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),X4),X1)
& ( sK15(X0,X1,X2) != X4 )
& member(X0,X4,X2) )
& member(X0,sK15(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
tff(f274,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),sK15(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),X4),X1)
& ( sK15(X0,X1,X2) != X4 )
& member(X0,X4,X2) )
=> ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK16(X0,X1,X2)),sK15(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),sK16(X0,X1,X2)),X1)
& ( sK15(X0,X1,X2) != sK16(X0,X1,X2) )
& member(X0,sK16(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
tff(f272,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ? [X3: X0] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& ( X3 != X4 )
& member(X0,X4,X2) )
& member(X0,X3,X2) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2) )
| ~ member(X0,X5,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(rectify,[],[f271]) ).
tff(f271,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ? [X3: X0] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& ( X3 != X4 )
& member(X0,X4,X2) )
& member(X0,X3,X2) ) )
& ( ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) ) ),
inference(flattening,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) ) ),
inference(ennf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( member(X0,X3,X2)
=> ! [X4: X0] :
( member(X0,X4,X2)
=> ( ( X3 != X4 )
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1) ) ) ) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X5: fun(product_prod(X0,X0),bool),X16: fun(X0,bool)] :
( total_on(X0,X16,X5)
<=> ! [X6: X0] :
( member(X0,X6,X16)
=> ! [X17: X0] :
( member(X0,X17,X16)
=> ( ( X6 != X17 )
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X17),X6),X5)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X17),X5) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_6_total__on__def) ).
tff(f2971,plain,
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| spl83_31 ),
inference(avatar_component_clause,[],[f2969]) ).
tff(f2969,plain,
( spl83_31
<=> total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_31])]) ).
tff(f3020,plain,
spl83_31,
inference(avatar_contradiction_clause,[],[f3019]) ).
tff(f3019,plain,
( $false
| spl83_31 ),
inference(subsumption_resolution,[],[f3015,f369]) ).
tff(f3015,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),sK15(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),top_top(fun(arrow_411405190le_alt,bool)))),sK16(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),top_top(fun(arrow_411405190le_alt,bool)))),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| spl83_31 ),
inference(resolution,[],[f2971,f395]) ).
tff(f395,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1,X2)),sK16(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f275]) ).
tff(f2999,plain,
spl83_30,
inference(avatar_contradiction_clause,[],[f2998]) ).
tff(f2998,plain,
( $false
| spl83_30 ),
inference(subsumption_resolution,[],[f2993,f369]) ).
tff(f2993,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),sK12(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))),sK14(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| spl83_30 ),
inference(resolution,[],[f2967,f384]) ).
tff(f384,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK14(X0,X1)),X1) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( trans(X0,X1)
| ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK14(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK14(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK13(X0,X1)),X1) ) )
& ( ! [X5: X0,X6: X0,X7: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1) )
| ~ trans(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f267,f268]) ).
tff(f268,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
=> ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK14(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK14(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK12(X0,X1)),sK13(X0,X1)),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f267,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( trans(X0,X1)
| ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) )
& ( ! [X5: X0,X6: X0,X7: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1) )
| ~ trans(X0,X1) ) ),
inference(rectify,[],[f266]) ).
tff(f266,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( trans(X0,X1)
| ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) )
& ( ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
| ~ trans(X0,X1) ) ),
inference(nnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
<=> ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
inference(flattening,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
<=> ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
inference(ennf_transformation,[],[f112]) ).
tff(f112,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
<=> ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType,X5: fun(product_prod(X0,X0),bool)] :
( trans(X0,X5)
<=> ! [X6: X0,X18: X0,X19: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X18),X5)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X18),X19),X5)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X19),X5) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_7_trans__def) ).
tff(f2967,plain,
( ~ trans(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| spl83_30 ),
inference(avatar_component_clause,[],[f2965]) ).
tff(f2965,plain,
( spl83_30
<=> trans(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_30])]) ).
tff(f2997,plain,
spl83_30,
inference(avatar_contradiction_clause,[],[f2996]) ).
tff(f2996,plain,
( $false
| spl83_30 ),
inference(subsumption_resolution,[],[f2990,f369]) ).
tff(f2990,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),sK8(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))),sK10(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| spl83_30 ),
inference(resolution,[],[f2967,f378]) ).
tff(f378,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK10(X0,X1)),X1) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK10(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK9(X0,X1)),sK10(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK9(X0,X1)),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f190,f260]) ).
tff(f260,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
=> ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK10(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK9(X0,X1)),sK10(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK8(X0,X1)),sK9(X0,X1)),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f190,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
inference(flattening,[],[f189]) ).
tff(f189,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
inference(ennf_transformation,[],[f110]) ).
tff(f110,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1) ) )
=> trans(X0,X1) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType,X5: fun(product_prod(X0,X0),bool)] :
( ! [X28: X0,X29: X0,X30: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X28),X29),X5)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X29),X30),X5)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X28),X30),X5) ) )
=> trans(X0,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_15_transI) ).
tff(f2982,plain,
spl83_29,
inference(avatar_contradiction_clause,[],[f2981]) ).
tff(f2981,plain,
( $false
| spl83_29 ),
inference(subsumption_resolution,[],[f2980,f360]) ).
tff(f360,plain,
top(bool),
inference(cnf_transformation,[],[f83]) ).
tff(f83,axiom,
top(bool),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',arity_HOL_Obool___Orderings_Otop) ).
tff(f2980,plain,
( ~ top(bool)
| spl83_29 ),
inference(resolution,[],[f2963,f371]) ).
tff(f371,plain,
! [X1: $tType,X0: $tType] :
( top(fun(X0,X1))
| ~ top(X1) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType,X1: $tType] :
( top(fun(X0,X1))
| ~ top(X1) ),
inference(ennf_transformation,[],[f105]) ).
tff(f105,plain,
! [X0: $tType,X1: $tType] :
( top(X1)
=> top(fun(X0,X1)) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X53: $tType,X54: $tType] :
( top(X54)
=> top(fun(X53,X54)) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',arity_fun___Orderings_Otop) ).
tff(f2963,plain,
( ~ top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))
| spl83_29 ),
inference(avatar_component_clause,[],[f2961]) ).
tff(f2961,plain,
( spl83_29
<=> top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_29])]) ).
tff(f2979,plain,
( ~ spl83_29
| ~ spl83_30
| ~ spl83_31
| spl83_32
| ~ spl83_33 ),
inference(avatar_split_clause,[],[f734,f2976,f2973,f2969,f2965,f2961]) ).
tff(f2973,plain,
( spl83_32
<=> ! [X4: arrow_411405190le_alt,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),X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),top_top(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),i))
| 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),X4),f(top_top(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))))
| ( X3 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_32])]) ).
tff(f2976,plain,
( spl83_33
<=> irrefl(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_33])]) ).
tff(f734,plain,
! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ~ irrefl(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| ~ 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),X4),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),top_top(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),i))
| ( X3 = X4 )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| 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),X4),f(top_top(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))))
| ~ trans(arrow_411405190le_alt,top_top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)))
| ~ top(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ),
inference(superposition,[],[f358,f372]) ).
tff(f372,plain,
! [X1: $tType,X0: $tType,X2: X0] :
( ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
| ~ top(X1) ),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X0] : ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
| ~ top(X1) ),
inference(ennf_transformation,[],[f106]) ).
tff(f106,plain,
! [X0: $tType,X1: $tType] :
( top(X1)
=> ! [X2: X0] : ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X1: $tType,X0: $tType] :
( top(X0)
=> ! [X7: X1] : ( aa(X1,X0,top_top(fun(X1,X0)),X7) = top_top(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_10_top__apply) ).
tff(f2513,plain,
( spl83_8
| spl83_28 ),
inference(avatar_split_clause,[],[f648,f2511,f815]) ).
tff(f2511,plain,
( spl83_28
<=> ! [X30: arrow_411405190le_alt,X31: arrow_411405190le_alt] :
( sP2(f(p),b,a,X30,X31)
| ~ 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),X31),b),f(p))
| ~ 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),a),X31),f(p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_28])]) ).
tff(f648,plain,
! [X31: arrow_411405190le_alt,X30: arrow_411405190le_alt] :
( sP2(f(p),b,a,X30,X31)
| ~ 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),a),X31),f(p))
| ~ 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),X31),b),f(p))
| ( a = b ) ),
inference(resolution,[],[f351,f476]) ).
tff(f476,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,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),X2),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),X2),X4),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),X4),X1),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP2(X0,X1,X2,X3,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),X2),X1),X0)
& ( X1 != 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),X2),X4),X0)
& ( X2 != X4 )
& ( X1 = X3 ) ) )
& ( X2 != 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),X4),X1),X0)
& ( X2 = X3 ) )
| ( X1 = 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),X2),X1),X0)
| ( X1 = 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),X2),X4),X0)
| ( X2 = X4 )
| ( X1 != X3 ) ) )
| ( X2 = 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),X4),X1),X0)
| ( X2 != X3 ) )
& ( X1 != X2 ) )
| ~ sP2(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f313]) ).
tff(f313,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP2(X2,X0,X1,X3,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),X0),X2)
& ( X0 != 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),X1),X4),X2)
& ( X1 != X4 )
& ( X0 = X3 ) ) )
& ( X1 != 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),X4),X0),X2)
& ( X1 = X3 ) )
| ( 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),X1),X0),X2)
| ( X0 = 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),X1),X4),X2)
| ( X1 = X4 )
| ( X0 != X3 ) ) )
| ( X1 = 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),X4),X0),X2)
| ( X1 != X3 ) )
& ( X0 != X1 ) )
| ~ sP2(X2,X0,X1,X3,X4) ) ),
inference(flattening,[],[f312]) ).
tff(f312,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP2(X2,X0,X1,X3,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),X0),X2)
& ( X0 != 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),X1),X4),X2)
& ( X1 != X4 )
& ( X0 = X3 ) ) )
& ( X1 != 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),X4),X0),X2)
& ( X1 = X3 ) )
| ( 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),X1),X0),X2)
| ( X0 = 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),X1),X4),X2)
| ( X1 = X4 )
| ( X0 != X3 ) ) )
| ( X1 = 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),X4),X0),X2)
| ( X1 != X3 ) )
& ( X0 != X1 ) )
| ~ sP2(X2,X0,X1,X3,X4) ) ),
inference(nnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X2,X0,X1,X3,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),X0),X2)
| ( X0 = 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),X1),X4),X2)
| ( X1 = X4 )
| ( X0 != X3 ) ) )
| ( X1 = 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),X4),X0),X2)
| ( X1 != X3 ) )
& ( X0 != X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f2481,plain,
( spl83_8
| spl83_27 ),
inference(avatar_split_clause,[],[f640,f2479,f815]) ).
tff(f2479,plain,
( spl83_27
<=> ! [X14: arrow_411405190le_alt,X15: arrow_411405190le_alt] :
( sP0(f(p),b,a,X14,X15)
| ~ 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),a),X15),f(p))
| ~ 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),X15),b),f(p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_27])]) ).
tff(f640,plain,
! [X14: arrow_411405190le_alt,X15: arrow_411405190le_alt] :
( sP0(f(p),b,a,X14,X15)
| ~ 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),X15),b),f(p))
| ~ 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),a),X15),f(p))
| ( a = b ) ),
inference(resolution,[],[f351,f455]) ).
tff(f455,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,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),X2),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),X4),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),X2),X4),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP0(X0,X1,X2,X3,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),X2),X1),X0)
& ( X2 != 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),X4),X1),X0)
& ( X1 != X4 )
& ( X2 = X3 ) ) )
& ( X1 != 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),X2),X4),X0)
& ( X1 = X3 ) )
| ( X1 = 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),X2),X1),X0)
| ( X2 = 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),X4),X1),X0)
| ( X1 = X4 )
| ( X2 != X3 ) ) )
| ( X1 = 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),X2),X4),X0)
| ( X1 != X3 ) )
& ( X1 != X2 ) )
| ~ sP0(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f308]) ).
tff(f308,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( sP0(X2,X0,X1,X4,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),X1),X0),X2)
& ( X1 != 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),X3),X0),X2)
& ( X0 != X3 )
& ( X1 = X4 ) ) )
& ( X0 != 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),X3),X2)
& ( X0 = X4 ) )
| ( 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),X1),X0),X2)
| ( X1 = 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),X3),X0),X2)
| ( X0 = X3 )
| ( X1 != X4 ) ) )
| ( X0 = 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),X3),X2)
| ( X0 != X4 ) )
& ( X0 != X1 ) )
| ~ sP0(X2,X0,X1,X4,X3) ) ),
inference(flattening,[],[f307]) ).
tff(f307,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( sP0(X2,X0,X1,X4,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),X1),X0),X2)
& ( X1 != 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),X3),X0),X2)
& ( X0 != X3 )
& ( X1 = X4 ) ) )
& ( X0 != 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),X3),X2)
& ( X0 = X4 ) )
| ( 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),X1),X0),X2)
| ( X1 = 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),X3),X0),X2)
| ( X0 = X3 )
| ( X1 != X4 ) ) )
| ( X0 = 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),X3),X2)
| ( X0 != X4 ) )
& ( X0 != X1 ) )
| ~ sP0(X2,X0,X1,X4,X3) ) ),
inference(nnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( sP0(X2,X0,X1,X4,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),X1),X0),X2)
| ( X1 = 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),X3),X0),X2)
| ( X0 = X3 )
| ( X1 != X4 ) ) )
| ( X0 = 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),X3),X2)
| ( X0 != X4 ) )
& ( X0 != X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f2173,plain,
( spl83_26
| spl83_8 ),
inference(avatar_split_clause,[],[f612,f815,f2171]) ).
tff(f2171,plain,
( spl83_26
<=> ! [X14: $tType,X17: fun(product_prod(X14,X14),bool),X16: X14,X15: X14] : ~ member(product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(product_prod(arrow_411405190le_alt,X14),product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(product_prod(arrow_411405190le_alt,X14),fun(product_prod(arrow_411405190le_alt,X14),product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14))),product_Pair(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(X14,product_prod(arrow_411405190le_alt,X14),aa(arrow_411405190le_alt,fun(X14,product_prod(arrow_411405190le_alt,X14)),product_Pair(arrow_411405190le_alt,X14),a),X15)),aa(X14,product_prod(arrow_411405190le_alt,X14),aa(arrow_411405190le_alt,fun(X14,product_prod(arrow_411405190le_alt,X14)),product_Pair(arrow_411405190le_alt,X14),b),X16)),lex_prod(arrow_411405190le_alt,X14,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_26])]) ).
tff(f612,plain,
! [X14: $tType,X16: X14,X17: fun(product_prod(X14,X14),bool),X15: X14] :
( ( a = b )
| ~ member(product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(product_prod(arrow_411405190le_alt,X14),product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(product_prod(arrow_411405190le_alt,X14),fun(product_prod(arrow_411405190le_alt,X14),product_prod(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14))),product_Pair(product_prod(arrow_411405190le_alt,X14),product_prod(arrow_411405190le_alt,X14)),aa(X14,product_prod(arrow_411405190le_alt,X14),aa(arrow_411405190le_alt,fun(X14,product_prod(arrow_411405190le_alt,X14)),product_Pair(arrow_411405190le_alt,X14),a),X15)),aa(X14,product_prod(arrow_411405190le_alt,X14),aa(arrow_411405190le_alt,fun(X14,product_prod(arrow_411405190le_alt,X14)),product_Pair(arrow_411405190le_alt,X14),b),X16)),lex_prod(arrow_411405190le_alt,X14,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X17)) ),
inference(resolution,[],[f350,f526]) ).
tff(f526,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
( ( X5 = X7 )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ),
inference(cnf_transformation,[],[f347]) ).
tff(f347,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
( ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ( ( ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| ( X5 != X7 ) )
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) )
& ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
& ( X5 = X7 ) )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ) ),
inference(flattening,[],[f346]) ).
tff(f346,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
( ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ( ( ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| ( X5 != X7 ) )
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) )
& ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
& ( X5 = X7 ) )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ) ),
inference(nnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
<=> ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
& ( X5 = X7 ) )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType,X1: $tType,X47: fun(product_prod(X1,X1),bool),X5: fun(product_prod(X0,X0),bool),X12: X1,X13: X0,X14: X1,X15: X0] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X15),X14)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X13),X12)),lex_prod(X0,X1,X5,X47))
<=> ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X14),X12),X47)
& ( X13 = X15 ) )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X15),X13),X5) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_56_in__lex__prod) ).
tff(f350,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),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
inference(cnf_transformation,[],[f95]) ).
tff(f95,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),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
inference(flattening,[],[f94]) ).
tff(f94,negated_conjecture,
~ 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),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
inference(negated_conjecture,[],[f93]) ).
tff(f93,conjecture,
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),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_4) ).
tff(f2116,plain,
( spl83_8
| spl83_25 ),
inference(avatar_split_clause,[],[f646,f2114,f815]) ).
tff(f2114,plain,
( spl83_25
<=> ! [X27: arrow_411405190le_alt,X26: arrow_411405190le_alt] :
( sP2(f(p),b,a,X26,X27)
| ( a = X26 )
| ~ 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),a),X27),f(p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_25])]) ).
tff(f646,plain,
! [X26: arrow_411405190le_alt,X27: arrow_411405190le_alt] :
( sP2(f(p),b,a,X26,X27)
| ~ 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),a),X27),f(p))
| ( a = X26 )
| ( a = b ) ),
inference(resolution,[],[f351,f475]) ).
tff(f475,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,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),X2),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),X2),X4),X0)
| ( X2 = X3 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f2055,plain,
( spl83_8
| spl83_24 ),
inference(avatar_split_clause,[],[f644,f2053,f815]) ).
tff(f2053,plain,
( spl83_24
<=> ! [X22: arrow_411405190le_alt,X23: arrow_411405190le_alt] :
( sP2(f(p),b,a,X22,X23)
| ~ 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),X23),b),f(p))
| ( b = X22 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_24])]) ).
tff(f644,plain,
! [X22: arrow_411405190le_alt,X23: arrow_411405190le_alt] :
( sP2(f(p),b,a,X22,X23)
| ( b = X22 )
| ~ 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),X23),b),f(p))
| ( a = b ) ),
inference(resolution,[],[f351,f472]) ).
tff(f472,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,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),X2),X1),X0)
| ( X1 = 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),X4),X1),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f1998,plain,
( spl83_8
| spl83_23 ),
inference(avatar_split_clause,[],[f638,f1996,f815]) ).
tff(f1996,plain,
( spl83_23
<=> ! [X11: arrow_411405190le_alt,X10: arrow_411405190le_alt] :
( sP0(f(p),b,a,X10,X11)
| ( b = X10 )
| ~ 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),X11),b),f(p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_23])]) ).
tff(f638,plain,
! [X10: arrow_411405190le_alt,X11: arrow_411405190le_alt] :
( sP0(f(p),b,a,X10,X11)
| ~ 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),X11),b),f(p))
| ( b = X10 )
| ( a = b ) ),
inference(resolution,[],[f351,f454]) ).
tff(f454,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,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),X2),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),X4),X1),X0)
| ( X1 = X3 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f1941,plain,
( spl83_8
| spl83_22 ),
inference(avatar_split_clause,[],[f636,f1939,f815]) ).
tff(f1939,plain,
( spl83_22
<=> ! [X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( sP0(f(p),b,a,X6,X7)
| ~ 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),a),X7),f(p))
| ( a = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_22])]) ).
tff(f636,plain,
! [X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( sP0(f(p),b,a,X6,X7)
| ( a = 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),a),X7),f(p))
| ( a = b ) ),
inference(resolution,[],[f351,f451]) ).
tff(f451,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,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),X2),X1),X0)
| ( X2 = 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),X2),X4),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f1844,plain,
( ~ spl83_20
| ~ spl83_21 ),
inference(avatar_split_clause,[],[f629,f1841,f1837]) ).
tff(f1837,plain,
( spl83_20
<=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f(p),arrow_1985332922le_Lin) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_20])]) ).
tff(f629,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),b),a),f(p))
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f(p),arrow_1985332922le_Lin) ),
inference(resolution,[],[f351,f390]) ).
tff(f390,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),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),X0),X2)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ~ 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),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),X0),X2)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(flattening,[],[f199]) ).
tff(f199,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ~ 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),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),X0),X2)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(ennf_transformation,[],[f117]) ).
tff(f117,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
=> ( 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),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),X1),X2) ) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X14: arrow_411405190le_alt,X15: arrow_411405190le_alt,X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X22,arrow_1985332922le_Lin)
=> ( 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),X15),X14),X22)
=> ~ 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),X14),X15),X22) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_24_Lin__irrefl) ).
tff(f1756,plain,
( spl83_8
| spl83_19 ),
inference(avatar_split_clause,[],[f634,f1754,f815]) ).
tff(f1754,plain,
( spl83_19
<=> ! [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),a),b),arrow_276188178_mkbot(f(p),X3))
| ( b = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_19])]) ).
tff(f634,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),a),b),arrow_276188178_mkbot(f(p),X3))
| ( a = b )
| ( b = X3 ) ),
inference(resolution,[],[f351,f433]) ).
tff(f433,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( 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),X2),arrow_276188178_mkbot(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),X3),X2),X1)
| ( X2 = X3 )
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,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),X2),arrow_276188178_mkbot(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),X3),X2),X1)
& ( X0 != X3 ) )
| ( ( X2 = X3 )
& ( X0 = X3 ) )
| ( X0 = 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),X3),X2),X1)
| ( X0 = X3 ) )
& ( ( X2 != X3 )
| ( X0 != X3 ) )
& ( X0 != 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),X3),X2),arrow_276188178_mkbot(X1,X0)) ) ),
inference(flattening,[],[f301]) ).
tff(f301,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,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),X2),arrow_276188178_mkbot(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),X3),X2),X1)
& ( X0 != X3 ) )
| ( ( X2 = X3 )
& ( X0 = X3 ) )
| ( X0 = 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),X3),X2),X1)
| ( X0 = X3 ) )
& ( ( X2 != X3 )
| ( X0 != X3 ) )
& ( X0 != 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),X3),X2),arrow_276188178_mkbot(X1,X0)) ) ),
inference(nnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,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),X2),arrow_276188178_mkbot(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),X3),X2),X1)
| ( X0 = X3 ) )
& ( ( X2 != X3 )
| ( X0 != X3 ) )
& ( X0 != X2 ) ) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,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),X2),arrow_276188178_mkbot(X1,X0))
<=> ( ( ( X0 != 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),X3),X2),X1) )
& ( ( X0 = X3 )
=> ( X2 != X3 ) )
& ( X0 != X2 ) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X21: arrow_411405190le_alt,X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X23: arrow_411405190le_alt,X7: 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),X7),X23),arrow_276188178_mkbot(X22,X21))
<=> ( ( ( X7 != X21 )
=> 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),X7),X23),X22) )
& ( ( X7 = X21 )
=> ( X7 != X23 ) )
& ( X21 != X23 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_11_in__mkbot) ).
tff(f1605,plain,
( spl83_8
| spl83_18 ),
inference(avatar_split_clause,[],[f632,f1603,f815]) ).
tff(f1603,plain,
( spl83_18
<=> ! [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),a),b),arrow_424895264_mktop(f(p),X1))
| ( a = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_18])]) ).
tff(f632,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),a),b),arrow_424895264_mktop(f(p),X1))
| ( a = b )
| ( a = X1 ) ),
inference(resolution,[],[f351,f426]) ).
tff(f426,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( 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),X2),arrow_424895264_mktop(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),X3),X2),X1)
| ( X2 = X3 )
| ( X0 = X3 ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,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),X2),arrow_424895264_mktop(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),X3),X2),X1)
& ( X0 != X2 ) )
| ( ( X2 = X3 )
& ( X0 = X2 ) )
| ( X0 = 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),X3),X2),X1)
| ( X0 = X2 ) )
& ( ( X2 != X3 )
| ( X0 != X2 ) )
& ( X0 != 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),X3),X2),arrow_424895264_mktop(X1,X0)) ) ),
inference(flattening,[],[f299]) ).
tff(f299,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,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),X2),arrow_424895264_mktop(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),X3),X2),X1)
& ( X0 != X2 ) )
| ( ( X2 = X3 )
& ( X0 = X2 ) )
| ( X0 = 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),X3),X2),X1)
| ( X0 = X2 ) )
& ( ( X2 != X3 )
| ( X0 != X2 ) )
& ( X0 != 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),X3),X2),arrow_424895264_mktop(X1,X0)) ) ),
inference(nnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,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),X2),arrow_424895264_mktop(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),X3),X2),X1)
| ( X0 = X2 ) )
& ( ( X2 != X3 )
| ( X0 != X2 ) )
& ( X0 != X3 ) ) ),
inference(ennf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,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),X2),arrow_424895264_mktop(X1,X0))
<=> ( ( ( X0 != 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),X3),X2),X1) )
& ( ( X0 = X2 )
=> ( X2 != X3 ) )
& ( X0 != X3 ) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X21: arrow_411405190le_alt,X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X23: arrow_411405190le_alt,X7: 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),X7),X23),arrow_424895264_mktop(X22,X21))
<=> ( ( ( X21 != X23 )
=> 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),X7),X23),X22) )
& ( ( X21 = X23 )
=> ( X7 != X23 ) )
& ( X7 != X21 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_39_in__mktop) ).
tff(f1409,plain,
~ spl83_17,
inference(avatar_contradiction_clause,[],[f1408]) ).
tff(f1408,plain,
( $false
| ~ spl83_17 ),
inference(subsumption_resolution,[],[f1407,f369]) ).
tff(f1407,plain,
( ~ member(arrow_411405190le_alt,b,top_top(fun(arrow_411405190le_alt,bool)))
| ~ spl83_17 ),
inference(subsumption_resolution,[],[f1400,f369]) ).
tff(f1400,plain,
( ~ member(arrow_411405190le_alt,a,top_top(fun(arrow_411405190le_alt,bool)))
| ~ member(arrow_411405190le_alt,b,top_top(fun(arrow_411405190le_alt,bool)))
| ~ spl83_17 ),
inference(resolution,[],[f1398,f357]) ).
tff(f1398,plain,
( ! [X11: fun(arrow_411405190le_alt,bool)] :
( ~ total_on(arrow_411405190le_alt,X11,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ member(arrow_411405190le_alt,a,X11)
| ~ member(arrow_411405190le_alt,b,X11) )
| ~ spl83_17 ),
inference(avatar_component_clause,[],[f1397]) ).
tff(f1397,plain,
( spl83_17
<=> ! [X11: fun(arrow_411405190le_alt,bool)] :
( ~ member(arrow_411405190le_alt,a,X11)
| ~ total_on(arrow_411405190le_alt,X11,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ member(arrow_411405190le_alt,b,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_17])]) ).
tff(f1399,plain,
( spl83_17
| spl83_8
| spl83_16 ),
inference(avatar_split_clause,[],[f609,f1391,f815,f1397]) ).
tff(f609,plain,
! [X11: fun(arrow_411405190le_alt,bool)] :
( 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),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ( a = b )
| ~ member(arrow_411405190le_alt,a,X11)
| ~ member(arrow_411405190le_alt,b,X11)
| ~ total_on(arrow_411405190le_alt,X11,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
inference(resolution,[],[f350,f391]) ).
tff(f391,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool),X6: X0,X5: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2)
| ~ member(X0,X5,X2)
| ~ total_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f275]) ).
tff(f1394,plain,
( ~ spl83_15
| spl83_8
| spl83_16 ),
inference(avatar_split_clause,[],[f598,f1391,f815,f1387]) ).
tff(f1387,plain,
( spl83_15
<=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),arrow_1985332922le_Lin) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_15])]) ).
tff(f598,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),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ( a = b )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),arrow_1985332922le_Lin) ),
inference(resolution,[],[f350,f388]) ).
tff(f388,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),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),X0),X2)
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ( ~ 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),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),X1),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),X1),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),X0),X2) ) )
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(nnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ~ 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),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),X1),X2) )
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(flattening,[],[f197]) ).
tff(f197,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ~ 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),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),X1),X2) )
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(ennf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
=> ( ( 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),X1),X0),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),X1),X2) ) ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X23: arrow_411405190le_alt,X7: arrow_411405190le_alt,X22: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X22,arrow_1985332922le_Lin)
=> ( ( X7 != X23 )
=> ( ~ 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),X7),X23),X22)
<=> 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),X23),X7),X22) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_23_notin__Lin__iff) ).
tff(f1345,plain,
( ~ spl83_5
| spl83_14
| ~ spl83_4 ),
inference(avatar_split_clause,[],[f708,f694,f1343,f711]) ).
tff(f1343,plain,
( spl83_14
<=> ! [X9: fun(arrow_411405190le_alt,bool)] :
( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X9),f(p)))
| ~ total_on(arrow_411405190le_alt,X9,f(p)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_14])]) ).
tff(f708,plain,
( ! [X9: fun(arrow_411405190le_alt,bool)] :
( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X9),f(p)))
| ~ total_on(arrow_411405190le_alt,X9,f(p))
| ~ irrefl(arrow_411405190le_alt,f(p)) )
| ~ spl83_4 ),
inference(resolution,[],[f696,f402]) ).
tff(f402,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) )
& ( ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) )
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
inference(flattening,[],[f277]) ).
tff(f277,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) )
& ( ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) )
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
inference(nnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
<=> ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType,X5: fun(product_prod(X0,X0),bool),X16: fun(X0,bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X16),X5))
<=> ( total_on(X0,X16,X5)
& irrefl(X0,X5)
& trans(X0,X5) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_9_strict__linear__order__on__def) ).
tff(f1192,plain,
( spl83_8
| spl83_13 ),
inference(avatar_split_clause,[],[f643,f1190,f815]) ).
tff(f1190,plain,
( spl83_13
<=> ! [X20: arrow_411405190le_alt,X21: arrow_411405190le_alt] :
( sP2(f(p),b,a,X20,X21)
| ( a = X20 )
| ( b = X20 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_13])]) ).
tff(f643,plain,
! [X21: arrow_411405190le_alt,X20: arrow_411405190le_alt] :
( sP2(f(p),b,a,X20,X21)
| ( b = X20 )
| ( a = X20 )
| ( a = b ) ),
inference(resolution,[],[f351,f471]) ).
tff(f471,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,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),X2),X1),X0)
| ( X1 = X3 )
| ( X2 = X3 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f1182,plain,
( spl83_8
| spl83_12 ),
inference(avatar_split_clause,[],[f635,f1180,f815]) ).
tff(f1180,plain,
( spl83_12
<=> ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( sP0(f(p),b,a,X4,X5)
| ( b = X4 )
| ( a = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_12])]) ).
tff(f635,plain,
! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( sP0(f(p),b,a,X4,X5)
| ( a = X4 )
| ( b = X4 )
| ( a = b ) ),
inference(resolution,[],[f351,f450]) ).
tff(f450,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,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),X2),X1),X0)
| ( X2 = X3 )
| ( X1 = X3 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f1118,plain,
( spl83_11
| spl83_8 ),
inference(avatar_split_clause,[],[f903,f815,f1116]) ).
tff(f1116,plain,
( spl83_11
<=> ! [X40: arrow_411405190le_alt] : sP2(f(p),b,a,X40,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_11])]) ).
tff(f903,plain,
! [X40: arrow_411405190le_alt] :
( ( a = b )
| sP2(f(p),b,a,X40,a) ),
inference(global_subsumption,[],[f354,f353,f352,f357,f356,f355,f358,f589,f590,f591,f592,f595,f597,f604,f624,f626,f622,f627,f641,f642,f649,f650,f652,f657,f661,f663,f667,f668,f736,f737,f732,f738,f734,f794,f773,f755,f743,f678,f676,f675,f665,f664,f662,f660,f655,f647,f645,f639,f637,f633,f631,f629,f619,f618,f616,f614,f607,f605,f603,f602,f601,f600,f351,f350,f598,f606,f609,f612,f632,f634,f635,f636,f638,f640,f643,f644,f646,f648,f651,f902,f656]) ).
tff(f656,plain,
! [X40: arrow_411405190le_alt] :
( sP2(f(p),b,a,X40,a)
| ( a = X40 )
| ( a = b ) ),
inference(resolution,[],[f351,f557]) ).
tff(f557,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X4,X3,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),X4),X1),X0)
| ( X3 = X4 )
| ( X1 = X4 ) ),
inference(equality_resolution,[],[f473]) ).
tff(f473,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,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),X2),X1),X0)
| ( X2 != X4 )
| ( X2 = X3 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f902,plain,
! [X36: arrow_411405190le_alt] :
( sP0(f(p),b,a,X36,b)
| ( a = b ) ),
inference(global_subsumption,[],[f354,f353,f352,f357,f356,f355,f358,f589,f590,f591,f592,f595,f597,f604,f624,f626,f622,f627,f641,f642,f649,f650,f652,f656,f657,f661,f663,f667,f668,f736,f737,f732,f738,f734,f794,f773,f755,f743,f678,f676,f675,f665,f664,f662,f660,f655,f647,f645,f639,f637,f633,f631,f629,f619,f618,f616,f614,f607,f605,f603,f602,f601,f600,f351,f350,f598,f606,f609,f612,f632,f634,f635,f636,f638,f640,f643,f644,f646,f648,f651]) ).
tff(f651,plain,
! [X36: arrow_411405190le_alt] :
( sP0(f(p),b,a,X36,b)
| ( b = X36 )
| ( a = b ) ),
inference(resolution,[],[f351,f542]) ).
tff(f542,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( sP0(X0,X4,X2,X3,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),X2),X4),X0)
| ( X3 = X4 )
| ( X2 = X4 ) ),
inference(equality_resolution,[],[f452]) ).
tff(f452,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,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),X2),X1),X0)
| ( X1 != X4 )
| ( X1 = X3 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f606,plain,
! [X8: arrow_411405190le_alt] :
( ( a = b )
| ( a = X8 )
| ~ sP2(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X8,a,X8,b) ),
inference(resolution,[],[f350,f568]) ).
tff(f568,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X2),X4),X0)
| ( X2 = X4 )
| ( X2 = X3 )
| ~ sP2(X0,X3,X2,X3,X4) ),
inference(equality_resolution,[],[f461]) ).
tff(f461,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X2),X4),X0)
| ( X2 = X4 )
| ( X1 != X3 )
| ( X2 = X3 )
| ~ sP2(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f314]) ).
tff(f600,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),a),b),arrow_424895264_mktop(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X0))
| ( b = X0 ) ),
inference(resolution,[],[f350,f422]) ).
tff(f422,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( 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),X2),X1)
| ( X0 = 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),X3),X2),arrow_424895264_mktop(X1,X0)) ),
inference(cnf_transformation,[],[f300]) ).
tff(f601,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),a),b),arrow_276188178_mkbot(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X1))
| ( a = X1 ) ),
inference(resolution,[],[f350,f429]) ).
tff(f429,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( 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),X2),X1)
| ( X0 = 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),X3),X2),arrow_276188178_mkbot(X1,X0)) ),
inference(cnf_transformation,[],[f302]) ).
tff(f602,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ~ sP0(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,a,X2,X3)
| ( b = X2 )
| ( a = X2 ) ),
inference(resolution,[],[f350,f441]) ).
tff(f441,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X2),X1),X0)
| ( X2 = X3 )
| ( X1 = X3 )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f309]) ).
tff(f603,plain,
! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( ~ sP2(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,a,X4,X5)
| ( a = X4 )
| ( b = X4 ) ),
inference(resolution,[],[f350,f462]) ).
tff(f462,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X2),X1),X0)
| ( X1 = X3 )
| ( X2 = X3 )
| ~ sP2(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f314]) ).
tff(f605,plain,
! [X7: arrow_411405190le_alt] : ~ sP0(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X7,a,X7,b),
inference(resolution,[],[f350,f554]) ).
tff(f554,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X2),X4),X0)
| ~ sP0(X0,X3,X2,X3,X4) ),
inference(equality_resolution,[],[f439]) ).
tff(f439,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X2),X4),X0)
| ( X1 != X3 )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f309]) ).
tff(f607,plain,
! [X9: arrow_411405190le_alt] : ~ sP2(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,X9,X9,a),
inference(resolution,[],[f350,f569]) ).
tff(f569,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X4),X1),X0)
| ~ sP2(X0,X1,X3,X3,X4) ),
inference(equality_resolution,[],[f460]) ).
tff(f460,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X4),X1),X0)
| ( X2 != X3 )
| ~ sP2(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f314]) ).
tff(f614,plain,
! [X22: $tType,X24: X22,X25: fun(product_prod(X22,X22),bool),X23: X22] :
( member(product_prod(X22,X22),aa(X22,product_prod(X22,X22),aa(X22,fun(X22,product_prod(X22,X22)),product_Pair(X22,X22),X23),X24),X25)
| ~ member(product_prod(product_prod(arrow_411405190le_alt,X22),product_prod(arrow_411405190le_alt,X22)),aa(product_prod(arrow_411405190le_alt,X22),product_prod(product_prod(arrow_411405190le_alt,X22),product_prod(arrow_411405190le_alt,X22)),aa(product_prod(arrow_411405190le_alt,X22),fun(product_prod(arrow_411405190le_alt,X22),product_prod(product_prod(arrow_411405190le_alt,X22),product_prod(arrow_411405190le_alt,X22))),product_Pair(product_prod(arrow_411405190le_alt,X22),product_prod(arrow_411405190le_alt,X22)),aa(X22,product_prod(arrow_411405190le_alt,X22),aa(arrow_411405190le_alt,fun(X22,product_prod(arrow_411405190le_alt,X22)),product_Pair(arrow_411405190le_alt,X22),a),X23)),aa(X22,product_prod(arrow_411405190le_alt,X22),aa(arrow_411405190le_alt,fun(X22,product_prod(arrow_411405190le_alt,X22)),product_Pair(arrow_411405190le_alt,X22),b),X24)),lex_prod(arrow_411405190le_alt,X22,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X25)) ),
inference(resolution,[],[f350,f527]) ).
tff(f527,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ),
inference(cnf_transformation,[],[f347]) ).
tff(f616,plain,
! [X10: 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),a),X10),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ 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),X10),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
inference(subsumption_resolution,[],[f608,f355]) ).
tff(f608,plain,
! [X10: 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),X10),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ 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),a),X10),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
inference(resolution,[],[f350,f381]) ).
tff(f381,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X6: X0,X7: X0,X5: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ~ trans(X0,X1) ),
inference(cnf_transformation,[],[f269]) ).
tff(f618,plain,
! [X18: $tType,X21: fun(product_prod(X18,X18),bool),X19: X18,X20: X18] :
( ~ member(product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X20),product_apfst(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),arrow_411405190le_alt,aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X19),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),a),b))),lex_prod(X18,arrow_411405190le_alt,X21,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)))
| member(product_prod(X18,X18),aa(X18,product_prod(X18,X18),aa(X18,fun(X18,product_prod(X18,X18)),product_Pair(X18,X18),X19),X20),X21) ),
inference(forward_demodulation,[],[f617,f490]) ).
tff(f490,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X5,X4)),X3) ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X5,X4)),X3) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X2: $tType,X0: $tType,X1: $tType,X23: X1,X7: X2,X43: fun(X2,X0)] : ( product_apfst(X2,X0,X1,X43,aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X7),X23)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),aa(X2,X0,X43,X7)),X23) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_72_apfst__conv) ).
tff(f617,plain,
! [X18: $tType,X21: fun(product_prod(X18,X18),bool),X19: X18,X20: X18] :
( ~ member(product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X20),aa(arrow_411405190le_alt,product_prod(product_prod(X18,arrow_411405190le_alt),arrow_411405190le_alt),aa(product_prod(X18,arrow_411405190le_alt),fun(arrow_411405190le_alt,product_prod(product_prod(X18,arrow_411405190le_alt),arrow_411405190le_alt)),product_Pair(product_prod(X18,arrow_411405190le_alt),arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X19),a)),b)),lex_prod(X18,arrow_411405190le_alt,X21,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)))
| member(product_prod(X18,X18),aa(X18,product_prod(X18,X18),aa(X18,fun(X18,product_prod(X18,X18)),product_Pair(X18,X18),X19),X20),X21) ),
inference(forward_demodulation,[],[f613,f489]) ).
tff(f489,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),aa(X2,X1,X5,X3)) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),aa(X2,X1,X5,X3)) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X23: X2,X7: X0,X43: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X43,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X7),X23)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),aa(X2,X1,X43,X23)) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_51_apsnd__conv) ).
tff(f613,plain,
! [X18: $tType,X21: fun(product_prod(X18,X18),bool),X19: X18,X20: X18] :
( member(product_prod(X18,X18),aa(X18,product_prod(X18,X18),aa(X18,fun(X18,product_prod(X18,X18)),product_Pair(X18,X18),X19),X20),X21)
| ~ member(product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),aa(product_prod(X18,arrow_411405190le_alt),product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),aa(product_prod(X18,arrow_411405190le_alt),fun(product_prod(X18,arrow_411405190le_alt),product_prod(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt))),product_Pair(product_prod(X18,arrow_411405190le_alt),product_prod(X18,arrow_411405190le_alt)),aa(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X19),a)),aa(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt),aa(X18,fun(arrow_411405190le_alt,product_prod(X18,arrow_411405190le_alt)),product_Pair(X18,arrow_411405190le_alt),X20),b)),lex_prod(X18,arrow_411405190le_alt,X21,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))) ),
inference(resolution,[],[f350,f527]) ).
tff(f619,plain,
~ pp(aa(arrow_411405190le_alt,bool,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,bool),product_curry(arrow_411405190le_alt,arrow_411405190le_alt,bool,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),a),b)),
inference(forward_demodulation,[],[f615,f488]) ).
tff(f488,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X1,X5: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X5),X4),X3) = aa(product_prod(X1,X2),X0,X5,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X3)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X1,X5: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X5),X4),X3) = aa(product_prod(X1,X2),X0,X5,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X3)) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X14: X2,X15: X1,X43: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X43),X15),X14) = aa(product_prod(X1,X2),X0,X43,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X15),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_41_curry__conv) ).
tff(f615,plain,
~ pp(aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),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),a),b))),
inference(resolution,[],[f350,f398]) ).
tff(f398,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( member(X0,X2,X1)
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X16: fun(X0,bool),X7: X0] :
( member(X0,X7,X16)
<=> pp(aa(X0,bool,X16,X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_76_mem__def) ).
tff(f631,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),a),b),arrow_424895264_mktop(f(p),X0))
| ( b = X0 )
| ( a = X0 ) ),
inference(resolution,[],[f351,f425]) ).
tff(f425,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( 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),X2),arrow_424895264_mktop(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),X3),X2),X1)
| ( X0 = X2 )
| ( X0 = X3 ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f633,plain,
! [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),a),b),arrow_276188178_mkbot(f(p),X2))
| ( a = X2 )
| ( b = X2 ) ),
inference(resolution,[],[f351,f432]) ).
tff(f432,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( 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),X2),arrow_276188178_mkbot(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),X3),X2),X1)
| ( X0 = X3 )
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f637,plain,
! [X8: arrow_411405190le_alt,X9: 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),a),X8),f(p))
| sP0(f(p),X8,a,X9,b)
| ( a = X9 )
| ( a = X8 ) ),
inference(resolution,[],[f351,f451]) ).
tff(f639,plain,
! [X12: arrow_411405190le_alt,X13: 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),X12),b),f(p))
| sP0(f(p),b,X12,X13,a)
| ( b = X13 )
| ( b = X12 ) ),
inference(resolution,[],[f351,f454]) ).
tff(f645,plain,
! [X24: arrow_411405190le_alt,X25: 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),X24),b),f(p))
| sP2(f(p),b,X24,X25,a)
| ( b = X25 )
| ( b = X24 ) ),
inference(resolution,[],[f351,f472]) ).
tff(f647,plain,
! [X28: arrow_411405190le_alt,X29: 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),a),X28),f(p))
| sP2(f(p),X28,a,X29,b)
| ( a = X29 )
| ( a = X28 ) ),
inference(resolution,[],[f351,f475]) ).
tff(f655,plain,
! [X39: arrow_411405190le_alt] :
( sP0(f(p),X39,a,X39,b)
| ( a = X39 ) ),
inference(resolution,[],[f351,f551]) ).
tff(f551,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( sP0(X0,X3,X2,X3,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),X2),X4),X0)
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f443]) ).
tff(f443,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,X4)
| ( X1 != 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),X2),X4),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f660,plain,
! [X43: arrow_411405190le_alt] :
( sP2(f(p),b,X43,X43,a)
| ( b = X43 ) ),
inference(resolution,[],[f351,f566]) ).
tff(f566,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X3,X3,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),X4),X1),X0)
| ( X1 = X3 ) ),
inference(equality_resolution,[],[f464]) ).
tff(f464,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,X4)
| ( X2 != 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),X4),X1),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f662,plain,
! [X45: arrow_411405190le_alt] :
( sP0(f(p),b,X45,X45,a)
| ( b = X45 ) ),
inference(resolution,[],[f351,f582]) ).
tff(f582,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X3,X3,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),X4),X1),X0)
| ( X1 = X3 ) ),
inference(duplicate_literal_removal,[],[f544]) ).
tff(f544,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X3,X3,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),X4),X1),X0)
| ( X1 = X3 )
| ( X1 = X3 ) ),
inference(equality_resolution,[],[f448]) ).
tff(f448,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,X4)
| ( X2 != 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),X4),X1),X0)
| ( X1 = X3 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f664,plain,
! [X47: arrow_411405190le_alt] :
( sP2(f(p),X47,a,X47,b)
| ( a = X47 ) ),
inference(resolution,[],[f351,f586]) ).
tff(f586,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( sP2(X0,X3,X2,X3,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),X2),X4),X0)
| ( X2 = X3 ) ),
inference(duplicate_literal_removal,[],[f559]) ).
tff(f559,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( sP2(X0,X3,X2,X3,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),X2),X4),X0)
| ( X2 = X3 )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f469]) ).
tff(f469,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,X4)
| ( X1 != 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),X2),X4),X0)
| ( X2 = X3 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f665,plain,
! [X48: $tType,X50: X48,X51: fun(product_prod(X48,X48),bool),X49: X48] : member(product_prod(product_prod(arrow_411405190le_alt,X48),product_prod(arrow_411405190le_alt,X48)),aa(product_prod(arrow_411405190le_alt,X48),product_prod(product_prod(arrow_411405190le_alt,X48),product_prod(arrow_411405190le_alt,X48)),aa(product_prod(arrow_411405190le_alt,X48),fun(product_prod(arrow_411405190le_alt,X48),product_prod(product_prod(arrow_411405190le_alt,X48),product_prod(arrow_411405190le_alt,X48))),product_Pair(product_prod(arrow_411405190le_alt,X48),product_prod(arrow_411405190le_alt,X48)),aa(X48,product_prod(arrow_411405190le_alt,X48),aa(arrow_411405190le_alt,fun(X48,product_prod(arrow_411405190le_alt,X48)),product_Pair(arrow_411405190le_alt,X48),a),X49)),aa(X48,product_prod(arrow_411405190le_alt,X48),aa(arrow_411405190le_alt,fun(X48,product_prod(arrow_411405190le_alt,X48)),product_Pair(arrow_411405190le_alt,X48),b),X50)),lex_prod(arrow_411405190le_alt,X48,f(p),X51)),
inference(resolution,[],[f351,f528]) ).
tff(f528,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ),
inference(cnf_transformation,[],[f347]) ).
tff(f675,plain,
! [X52: $tType,X54: fun(product_prod(X52,X52),bool),X53: X52] : member(product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),product_apfst(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),arrow_411405190le_alt,aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),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),a),b))),lex_prod(X52,arrow_411405190le_alt,X54,f(p))),
inference(forward_demodulation,[],[f674,f490]) ).
tff(f674,plain,
! [X52: $tType,X54: fun(product_prod(X52,X52),bool),X53: X52] : member(product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),aa(arrow_411405190le_alt,product_prod(product_prod(X52,arrow_411405190le_alt),arrow_411405190le_alt),aa(product_prod(X52,arrow_411405190le_alt),fun(arrow_411405190le_alt,product_prod(product_prod(X52,arrow_411405190le_alt),arrow_411405190le_alt)),product_Pair(product_prod(X52,arrow_411405190le_alt),arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),a)),b)),lex_prod(X52,arrow_411405190le_alt,X54,f(p))),
inference(forward_demodulation,[],[f666,f489]) ).
tff(f666,plain,
! [X52: $tType,X54: fun(product_prod(X52,X52),bool),X53: X52] : member(product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),aa(product_prod(X52,arrow_411405190le_alt),product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),aa(product_prod(X52,arrow_411405190le_alt),fun(product_prod(X52,arrow_411405190le_alt),product_prod(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt))),product_Pair(product_prod(X52,arrow_411405190le_alt),product_prod(X52,arrow_411405190le_alt)),aa(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),a)),aa(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt),aa(X52,fun(arrow_411405190le_alt,product_prod(X52,arrow_411405190le_alt)),product_Pair(X52,arrow_411405190le_alt),X53),b)),lex_prod(X52,arrow_411405190le_alt,X54,f(p))),
inference(resolution,[],[f351,f578]) ).
tff(f578,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X4)),lex_prod(X0,X1,X3,X2))
| ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2) ),
inference(equality_resolution,[],[f529]) ).
tff(f529,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| ( X5 != X7 ) ),
inference(cnf_transformation,[],[f347]) ).
tff(f676,plain,
pp(aa(arrow_411405190le_alt,bool,aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,bool),product_curry(arrow_411405190le_alt,arrow_411405190le_alt,bool,f(p)),a),b)),
inference(forward_demodulation,[],[f671,f488]) ).
tff(f671,plain,
pp(aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool,f(p),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),a),b))),
inference(resolution,[],[f351,f397]) ).
tff(f397,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f276]) ).
tff(f678,plain,
! [X59: product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X60: fun(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),bool)] :
( ~ total_on(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),f(p),X60)
| member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,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),a),aa(arrow_411405190le_alt,product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(arrow_411405190le_alt,product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt)),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt),X59),b)),X60)
| ( 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),a),b) = X59 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X59,f(p))
| member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_apfst(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,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),a),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(arrow_411405190le_alt,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt))),product_Pair(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),b),X59)),X60) ),
inference(forward_demodulation,[],[f677,f490]) ).
tff(f677,plain,
! [X59: product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X60: fun(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),bool)] :
( member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_apsnd(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,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),a),aa(arrow_411405190le_alt,product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(arrow_411405190le_alt,product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt)),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),arrow_411405190le_alt),X59),b)),X60)
| member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt))),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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),a),b)),X59),X60)
| ( 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),a),b) = X59 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X59,f(p))
| ~ total_on(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),f(p),X60) ),
inference(forward_demodulation,[],[f672,f489]) ).
tff(f672,plain,
! [X59: product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X60: fun(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),bool)] :
( member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt))),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),X59),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),a),b)),X60)
| member(product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),aa(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_prod(arrow_411405190le_alt,arrow_411405190le_alt))),product_Pair(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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),a),b)),X59),X60)
| ( 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),a),b) = X59 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),X59,f(p))
| ~ total_on(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),f(p),X60) ),
inference(resolution,[],[f351,f391]) ).
tff(f743,plain,
! [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),a),X4),arrow_319942042_below(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X4,b))
| ~ sP1(b,X4,a,X4,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
inference(resolution,[],[f605,f436]) ).
tff(f436,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP0(X4,X3,X2,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),X2),X3),arrow_319942042_below(X4,X1,X0))
| ~ sP1(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ( 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),X2),X3),arrow_319942042_below(X4,X1,X0))
| ~ sP0(X4,X3,X2,X1,X0) )
& ( sP0(X4,X3,X2,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),X2),X3),arrow_319942042_below(X4,X1,X0)) ) )
| ~ sP1(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f305]) ).
tff(f305,plain,
! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ( 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),arrow_319942042_below(X2,X4,X3))
| ~ sP0(X2,X0,X1,X4,X3) )
& ( sP0(X2,X0,X1,X4,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),X1),X0),arrow_319942042_below(X2,X4,X3)) ) )
| ~ sP1(X3,X4,X1,X0,X2) ),
inference(nnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( 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),arrow_319942042_below(X2,X4,X3))
<=> sP0(X2,X0,X1,X4,X3) )
| ~ sP1(X3,X4,X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f755,plain,
! [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),X4),b),arrow_1158827142_above(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),a,X4))
| ~ sP3(a,X4,X4,b,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
inference(resolution,[],[f607,f457]) ).
tff(f457,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP2(X4,X3,X2,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),X2),X3),arrow_1158827142_above(X4,X0,X1))
| ~ sP3(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ( 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),X2),X3),arrow_1158827142_above(X4,X0,X1))
| ~ sP2(X4,X3,X2,X1,X0) )
& ( sP2(X4,X3,X2,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),X2),X3),arrow_1158827142_above(X4,X0,X1)) ) )
| ~ sP3(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f310]) ).
tff(f310,plain,
! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ( 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),arrow_1158827142_above(X2,X4,X3))
| ~ sP2(X2,X0,X1,X3,X4) )
& ( sP2(X2,X0,X1,X3,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),X0),arrow_1158827142_above(X2,X4,X3)) ) )
| ~ sP3(X4,X3,X1,X0,X2) ),
inference(nnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( 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),arrow_1158827142_above(X2,X4,X3))
<=> sP2(X2,X0,X1,X3,X4) )
| ~ sP3(X4,X3,X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f773,plain,
! [X8: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( ( b = X7 )
| ( a = X7 )
| ~ 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),a),b),arrow_319942042_below(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X7,X8))
| ~ sP1(X8,X7,a,b,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
inference(resolution,[],[f602,f436]) ).
tff(f794,plain,
! [X8: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( ( a = X7 )
| ( b = X7 )
| ~ 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),a),b),arrow_1158827142_above(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X8,X7))
| ~ sP3(X8,X7,a,b,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
inference(resolution,[],[f603,f457]) ).
tff(f738,plain,
! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ irrefl(arrow_411405190le_alt,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),X2),X0)
| ( X1 = X2 )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),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),X2),f(combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0)))
| ~ trans(arrow_411405190le_alt,X0) ),
inference(forward_demodulation,[],[f733,f409]) ).
tff(f409,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X1: $tType,X0: $tType,X55: X1,X56: X0] : ( aa(X1,X0,combk(X0,X1,X56),X55) = X56 ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',help_COMBK_1_1_U) ).
tff(f733,plain,
! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ irrefl(arrow_411405190le_alt,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),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0),i))
| ( X1 = X2 )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),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),X2),f(combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,X0)))
| ~ trans(arrow_411405190le_alt,X0) ),
inference(superposition,[],[f358,f409]) ).
tff(f732,plain,
! [X8: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8)))
| ( X6 = X7 )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8)))
| 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),X7),f(X8))
| ~ 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),X7),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,i))
| 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),sK11(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8)))),sK11(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8)))),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,sK5(X8))) ),
inference(resolution,[],[f358,f380]) ).
tff(f380,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK11(X0,X1)),X1) ),
inference(cnf_transformation,[],[f265]) ).
tff(f737,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X5: fun(arrow_411405190le_alt,bool)] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))
| ( X2 = 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),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,i))
| 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),X2),X3),f(X4))
| ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X5),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))) ),
inference(subsumption_resolution,[],[f731,f399]) ).
tff(f399,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
inference(cnf_transformation,[],[f278]) ).
tff(f731,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X5: fun(arrow_411405190le_alt,bool)] :
( ~ 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),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,i))
| ( X2 = X3 )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(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),X2),X3),f(X4))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))
| ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X5),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4,sK5(X4)))) ),
inference(resolution,[],[f358,f400]) ).
tff(f400,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
inference(cnf_transformation,[],[f278]) ).
tff(f663,plain,
! [X46: arrow_411405190le_alt] :
( sP2(f(p),b,a,X46,a)
| ( a = b ) ),
inference(resolution,[],[f351,f585]) ).
tff(f585,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X4,X3,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),X4),X1),X0)
| ( X1 = X4 ) ),
inference(duplicate_literal_removal,[],[f556]) ).
tff(f556,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X4,X3,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),X4),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),X4),X1),X0)
| ( X1 = X4 ) ),
inference(equality_resolution,[],[f474]) ).
tff(f474,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,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),X2),X1),X0)
| ( X2 != 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),X4),X1),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f661,plain,
! [X44: arrow_411405190le_alt] :
( sP0(f(p),b,a,X44,b)
| ( a = b ) ),
inference(resolution,[],[f351,f581]) ).
tff(f581,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( sP0(X0,X4,X2,X3,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),X2),X4),X0)
| ( X2 = X4 ) ),
inference(duplicate_literal_removal,[],[f541]) ).
tff(f541,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( sP0(X0,X4,X2,X3,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),X2),X4),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),X2),X4),X0)
| ( X2 = X4 ) ),
inference(equality_resolution,[],[f453]) ).
tff(f453,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,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),X2),X1),X0)
| ( X1 != 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),X2),X4),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f657,plain,
! [X41: arrow_411405190le_alt] :
( sP2(f(p),X41,a,X41,b)
| ~ 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),b),X41),f(p))
| ( a = X41 ) ),
inference(resolution,[],[f351,f558]) ).
tff(f558,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( sP2(X0,X3,X2,X3,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),X2),X4),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),X4),X3),X0)
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f470]) ).
tff(f470,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,X4)
| ( X1 != 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),X2),X4),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),X4),X1),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f652,plain,
! [X37: arrow_411405190le_alt] :
( sP0(f(p),b,X37,X37,a)
| ~ 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),X37),a),f(p))
| ( b = X37 ) ),
inference(resolution,[],[f351,f543]) ).
tff(f543,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X3,X3,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),X4),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),X3),X4),X0)
| ( X1 = X3 ) ),
inference(equality_resolution,[],[f449]) ).
tff(f449,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3,X4)
| ( X2 != 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),X4),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),X2),X4),X0)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f650,plain,
! [X34: arrow_411405190le_alt,X35: arrow_411405190le_alt] :
( sP2(f(p),X34,a,X35,b)
| ~ 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),a),X34),f(p))
| ~ 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),b),X34),f(p))
| ( a = X34 ) ),
inference(resolution,[],[f351,f476]) ).
tff(f649,plain,
! [X32: arrow_411405190le_alt,X33: arrow_411405190le_alt] :
( sP2(f(p),b,X32,X33,a)
| ~ 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),X32),b),f(p))
| ~ 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),X32),a),f(p))
| ( b = X32 ) ),
inference(resolution,[],[f351,f476]) ).
tff(f642,plain,
! [X18: arrow_411405190le_alt,X19: arrow_411405190le_alt] :
( sP0(f(p),X18,a,X19,b)
| ~ 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),a),X18),f(p))
| ~ 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),b),X18),f(p))
| ( a = X18 ) ),
inference(resolution,[],[f351,f455]) ).
tff(f641,plain,
! [X16: arrow_411405190le_alt,X17: arrow_411405190le_alt] :
( sP0(f(p),b,X16,X17,a)
| ~ 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),X16),b),f(p))
| ~ 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),X16),a),f(p))
| ( b = X16 ) ),
inference(resolution,[],[f351,f455]) ).
tff(f627,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),b),a),f(p))
| ( a = b )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f(p),arrow_1985332922le_Lin) ),
inference(resolution,[],[f351,f389]) ).
tff(f389,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X0),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),X1),X2)
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f270]) ).
tff(f622,plain,
! [X0: fun(arrow_411405190le_alt,bool),X1: arrow_159774573e_indi] :
( ~ member(arrow_411405190le_alt,sK7(arrow_411405190le_alt,X0),X0)
| total_on(arrow_411405190le_alt,X0,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X1)) ),
inference(superposition,[],[f357,f375]) ).
tff(f375,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ member(X0,sK7(X0,X1),X1) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ member(X0,sK7(X0,X1),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f188,f258]) ).
tff(f258,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : ~ member(X0,X2,X1)
=> ~ member(X0,sK7(X0,X1),X1) ),
introduced(choice_axiom,[]) ).
tff(f188,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ? [X2: X0] : ~ member(X0,X2,X1) ),
inference(ennf_transformation,[],[f109]) ).
tff(f109,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ! [X2: X0] : member(X0,X2,X1)
=> ( top_top(fun(X0,bool)) = X1 ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType,X16: fun(X0,bool)] :
( ! [X28: X0] : member(X0,X28,X16)
=> ( top_top(fun(X0,bool)) = X16 ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_18_UNIV__eq__I) ).
tff(f626,plain,
! [X2: arrow_411405190le_alt,X3: arrow_159774573e_indi,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),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,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),X2),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
| ( X1 = X2 ) ),
inference(subsumption_resolution,[],[f625,f369]) ).
tff(f625,plain,
! [X2: arrow_411405190le_alt,X3: arrow_159774573e_indi,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),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,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),X2),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
| ( X1 = X2 )
| ~ member(arrow_411405190le_alt,X2,top_top(fun(arrow_411405190le_alt,bool))) ),
inference(subsumption_resolution,[],[f621,f369]) ).
tff(f621,plain,
! [X2: arrow_411405190le_alt,X3: arrow_159774573e_indi,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),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,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),X2),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3))
| ( X1 = X2 )
| ~ member(arrow_411405190le_alt,X1,top_top(fun(arrow_411405190le_alt,bool)))
| ~ member(arrow_411405190le_alt,X2,top_top(fun(arrow_411405190le_alt,bool))) ),
inference(resolution,[],[f357,f391]) ).
tff(f624,plain,
! [X0: arrow_159774573e_indi] : pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))),
inference(subsumption_resolution,[],[f623,f355]) ).
tff(f623,plain,
! [X0: arrow_159774573e_indi] :
( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
inference(subsumption_resolution,[],[f620,f356]) ).
tff(f620,plain,
! [X0: arrow_159774573e_indi] :
( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
inference(resolution,[],[f357,f402]) ).
tff(f604,plain,
! [X6: arrow_411405190le_alt] :
( ( a = b )
| ( b = X6 )
| ~ sP0(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,X6,X6,a) ),
inference(resolution,[],[f350,f553]) ).
tff(f553,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X4),X1),X0)
| ( X1 = X4 )
| ( X1 = X3 )
| ~ sP0(X0,X1,X3,X3,X4) ),
inference(equality_resolution,[],[f440]) ).
tff(f440,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X4),X1),X0)
| ( X1 = X4 )
| ( X2 != X3 )
| ( X1 = X3 )
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f309]) ).
tff(f597,plain,
! [X2: arrow_411405190le_alt,X3: arrow_159774573e_indi] : ~ 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),X2),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X3)),
inference(resolution,[],[f356,f379]) ).
tff(f595,plain,
! [X14: arrow_159774573e_indi,X13: fun(arrow_411405190le_alt,bool)] :
( ~ total_on(arrow_411405190le_alt,X13,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14))
| pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X13),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14))) ),
inference(subsumption_resolution,[],[f593,f356]) ).
tff(f593,plain,
! [X14: arrow_159774573e_indi,X13: fun(arrow_411405190le_alt,bool)] :
( pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,X13),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14)))
| ~ total_on(arrow_411405190le_alt,X13,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X14)) ),
inference(resolution,[],[f355,f402]) ).
tff(f592,plain,
! [X10: $tType,X11: arrow_159774573e_indi,X12: fun(X10,arrow_411405190le_alt)] : trans(X10,inv_image(arrow_411405190le_alt,X10,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X11),X12)),
inference(resolution,[],[f355,f413]) ).
tff(f413,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
( trans(X1,inv_image(X0,X1,X3,X2))
| ~ trans(X0,X3) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
( trans(X1,inv_image(X0,X1,X3,X2))
| ~ trans(X0,X3) ),
inference(ennf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
( trans(X0,X3)
=> trans(X1,inv_image(X0,X1,X3,X2)) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType,X1: $tType,X43: fun(X1,X0),X5: fun(product_prod(X0,X0),bool)] :
( trans(X0,X5)
=> trans(X1,inv_image(X0,X1,X5,X43)) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_47_trans__inv__image) ).
tff(f591,plain,
! [X7: $tType,X8: fun(product_prod(X7,X7),bool),X9: arrow_159774573e_indi] :
( ~ trans(X7,X8)
| trans(product_prod(X7,arrow_411405190le_alt),lex_prod(X7,arrow_411405190le_alt,X8,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X9))) ),
inference(resolution,[],[f355,f414]) ).
tff(f414,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(flattening,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(ennf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(X0,X3)
=> ( trans(X1,X2)
=> trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2)) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType,X1: $tType,X44: fun(product_prod(X1,X1),bool),X45: fun(product_prod(X0,X0),bool)] :
( trans(X0,X45)
=> ( trans(X1,X44)
=> trans(product_prod(X0,X1),lex_prod(X0,X1,X45,X44)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',fact_49_trans__lex__prod) ).
tff(f590,plain,
! [X4: $tType,X6: fun(product_prod(X4,X4),bool),X5: arrow_159774573e_indi] :
( ~ trans(X4,X6)
| trans(product_prod(arrow_411405190le_alt,X4),lex_prod(arrow_411405190le_alt,X4,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X5),X6)) ),
inference(resolution,[],[f355,f414]) ).
tff(f589,plain,
! [X2: arrow_159774573e_indi,X3: 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),X0),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,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),X3),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,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),X1),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X2)) ),
inference(resolution,[],[f355,f478]) ).
tff(f352,plain,
( trans(arrow_411405190le_alt,f(p))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
( ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
& irrefl(arrow_411405190le_alt,f(p))
& trans(arrow_411405190le_alt,f(p)) )
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f181,f251]) ).
tff(f251,plain,
( ? [X0: arrow_159774573e_indi] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) )
=> ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ) ),
introduced(choice_axiom,[]) ).
tff(f181,plain,
( ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
& irrefl(arrow_411405190le_alt,f(p))
& trans(arrow_411405190le_alt,f(p)) )
| ? [X0: arrow_159774573e_indi] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ) ),
inference(ennf_transformation,[],[f96]) ).
tff(f96,plain,
( ! [X0: arrow_159774573e_indi] :
( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
& trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) )
=> ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
& irrefl(arrow_411405190le_alt,f(p))
& trans(arrow_411405190le_alt,f(p)) ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
( ! [X28: arrow_159774573e_indi] :
( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X28))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X28))
& trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X28)) )
=> ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
& irrefl(arrow_411405190le_alt,f(p))
& trans(arrow_411405190le_alt,f(p)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205',conj_3) ).
tff(f353,plain,
( irrefl(arrow_411405190le_alt,f(p))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
inference(cnf_transformation,[],[f252]) ).
tff(f354,plain,
( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
inference(cnf_transformation,[],[f252]) ).
tff(f1110,plain,
( spl83_8
| spl83_10 ),
inference(avatar_split_clause,[],[f902,f1108,f815]) ).
tff(f1108,plain,
( spl83_10
<=> ! [X36: arrow_411405190le_alt] : sP0(f(p),b,a,X36,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_10])]) ).
tff(f1063,plain,
( spl83_9
| spl83_8 ),
inference(avatar_split_clause,[],[f606,f815,f1061]) ).
tff(f1061,plain,
( spl83_9
<=> ! [X8: arrow_411405190le_alt] :
( ( a = X8 )
| ~ sP2(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),X8,a,X8,b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_9])]) ).
tff(f865,plain,
( ~ spl83_5
| ~ spl83_8 ),
inference(avatar_contradiction_clause,[],[f864]) ).
tff(f864,plain,
( $false
| ~ spl83_5
| ~ spl83_8 ),
inference(subsumption_resolution,[],[f820,f716]) ).
tff(f820,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),a),a),f(p))
| ~ spl83_8 ),
inference(backward_demodulation,[],[f351,f817]) ).
tff(f817,plain,
( ( a = b )
| ~ spl83_8 ),
inference(avatar_component_clause,[],[f815]) ).
tff(f818,plain,
( spl83_7
| spl83_8 ),
inference(avatar_split_clause,[],[f604,f815,f812]) ).
tff(f812,plain,
( spl83_7
<=> ! [X6: arrow_411405190le_alt] :
( ( b = X6 )
| ~ sP0(aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i),b,X6,X6,a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_7])]) ).
tff(f722,plain,
( ~ spl83_1
| ~ spl83_2
| ~ spl83_3
| spl83_6 ),
inference(avatar_split_clause,[],[f354,f719,f690,f686,f682]) ).
tff(f682,plain,
( spl83_1
<=> trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_1])]) ).
tff(f686,plain,
( spl83_2
<=> irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_2])]) ).
tff(f690,plain,
( spl83_3
<=> total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_3])]) ).
tff(f719,plain,
( spl83_6
<=> total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl83_6])]) ).
tff(f714,plain,
( ~ spl83_1
| ~ spl83_2
| ~ spl83_3
| spl83_5 ),
inference(avatar_split_clause,[],[f353,f711,f690,f686,f682]) ).
tff(f703,plain,
spl83_3,
inference(avatar_contradiction_clause,[],[f702]) ).
tff(f702,plain,
( $false
| spl83_3 ),
inference(subsumption_resolution,[],[f692,f357]) ).
tff(f692,plain,
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| spl83_3 ),
inference(avatar_component_clause,[],[f690]) ).
tff(f701,plain,
spl83_2,
inference(avatar_contradiction_clause,[],[f700]) ).
tff(f700,plain,
( $false
| spl83_2 ),
inference(subsumption_resolution,[],[f688,f356]) ).
tff(f688,plain,
( ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| spl83_2 ),
inference(avatar_component_clause,[],[f686]) ).
tff(f699,plain,
spl83_1,
inference(avatar_contradiction_clause,[],[f698]) ).
tff(f698,plain,
( $false
| spl83_1 ),
inference(subsumption_resolution,[],[f684,f355]) ).
tff(f684,plain,
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK4))
| spl83_1 ),
inference(avatar_component_clause,[],[f682]) ).
tff(f697,plain,
( ~ spl83_1
| ~ spl83_2
| ~ spl83_3
| spl83_4 ),
inference(avatar_split_clause,[],[f352,f694,f690,f686,f682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SCT193_5 : TPTP v8.1.2. Released v6.0.0.
% 0.15/0.17 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.38 % Computer : n022.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Thu Aug 24 16:02:41 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.17/0.38 This is a TF1_THM_EQU_NAR problem
% 0.17/0.38 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.X8HJaWz3eT/Vampire---4.8_32205
% 0.17/0.38 % (32318)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.43 % (32321)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.24/0.45 % (32322)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.24/0.45 % (32323)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.24/0.45 % (32320)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.24/0.45 % (32324)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.24/0.46 % (32322)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.24/0.46 % (32319)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.24/0.47 % (32325)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.24/0.47 % (32319)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.24/0.65 % (32321)First to succeed.
% 0.24/0.66 % (32321)Refutation found. Thanks to Tanya!
% 0.24/0.66 % SZS status Theorem for Vampire---4
% 0.24/0.66 % SZS output start Proof for Vampire---4
% See solution above
% 0.24/0.66 % (32321)------------------------------
% 0.24/0.66 % (32321)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.66 % (32321)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.66 % (32321)Termination reason: Refutation
% 0.24/0.66
% 0.24/0.66 % (32321)Memory used [KB]: 15479
% 0.24/0.66 % (32321)Time elapsed: 0.230 s
% 0.24/0.66 % (32321)------------------------------
% 0.24/0.66 % (32321)------------------------------
% 0.24/0.66 % (32318)Success in time 0.279 s
% 0.24/0.66 % Vampire---4.8 exiting
%------------------------------------------------------------------------------