%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT187_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:37:11 PM UTC 2026
% Result : Theorem 5.77s 2.01s
% Output : Refutation 8.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of formulae : 207 ( 12 unt; 0 typ; 22 def)
% Number of atoms : 942 ( 311 equ)
% Maximal formula atoms : 47 ( 4 avg)
% Number of connectives : 1246 ( 511 ~; 520 |; 192 &)
% ( 17 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 32 ( 30 usr; 19 prp; 0-5 aty)
% Number of functors : 100 ( 100 usr; 11 con; 0-7 aty)
% Number of variables : 169 ( 0 sgn 145 !; 24 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_8,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).
tff(func_def_1,type,
arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_2,type,
arrow_319942042_below: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_3,type,
arrow_276188178_mkbot: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_4,type,
arrow_424895264_mktop: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_5,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_6,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).
tff(func_def_7,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).
tff(func_def_8,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_9,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_10,type,
product_prod_case:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_11,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_12,type,
product_scomp:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( fun(X0,product_prod(X1,X2)) * fun(X1,fun(X2,X3)) ) > fun(X0,X3) ) ).
tff(func_def_13,type,
id_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_14,type,
converse:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > fun(product_prod(X1,X0),bool) ) ).
tff(func_def_15,type,
inv_image:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X1,X0) ) > fun(product_prod(X1,X1),bool) ) ).
tff(func_def_16,type,
lex_prod:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(product_prod(X1,X1),bool) ) > fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) ) ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
l: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_21,type,
x: arrow_411405190le_alt ).
tff(func_def_22,type,
y: arrow_411405190le_alt ).
tff(func_def_23,type,
sK5: arrow_411405190le_alt ).
tff(func_def_24,type,
sK6: arrow_411405190le_alt ).
tff(func_def_25,type,
sK7: ( arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_411405190le_alt ).
tff(func_def_26,type,
sK8: arrow_411405190le_alt > arrow_411405190le_alt ).
tff(func_def_27,type,
sK9: arrow_411405190le_alt > arrow_411405190le_alt ).
tff(func_def_28,type,
sK10: arrow_411405190le_alt ).
tff(func_def_29,type,
sK11: arrow_411405190le_alt ).
tff(func_def_30,type,
sK12:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_31,type,
sK13:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X0 ) ).
tff(func_def_32,type,
sK14:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X2 ) ).
tff(func_def_33,type,
sK15:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_34,type,
sK16:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_35,type,
sK17:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).
tff(func_def_36,type,
sK18:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).
tff(func_def_37,type,
sK19:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X1 ) ).
tff(func_def_38,type,
sK20:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X0 ) ).
tff(func_def_39,type,
sK21:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X0 ) ).
tff(func_def_40,type,
sK22:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_41,type,
sK23:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_42,type,
sK24:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_43,type,
sK25:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X1 ) ).
tff(func_def_44,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X0 ) ).
tff(func_def_45,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X0 ) ).
tff(func_def_46,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X1 ) ).
tff(func_def_47,type,
sK29:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_48,type,
sK30:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_49,type,
sK31:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_50,type,
sK32:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_51,type,
sK33:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_52,type,
sK34:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_53,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).
tff(func_def_54,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).
tff(func_def_55,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).
tff(func_def_56,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).
tff(func_def_57,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).
tff(func_def_58,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).
tff(func_def_59,type,
sK41:
!>[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_60,type,
sK42:
!>[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_61,type,
sK43:
!>[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_62,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).
tff(func_def_63,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).
tff(func_def_64,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_65,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_66,type,
sK48:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_67,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_68,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_69,type,
sK51:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_70,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_71,type,
sK53:
!>[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_72,type,
sK54:
!>[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_73,type,
sK55:
!>[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_74,type,
sK56:
!>[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_75,type,
sK57:
!>[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_76,type,
sK58:
!>[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_77,type,
sK59:
!>[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_78,type,
sK60:
!>[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_79,type,
sK61:
!>[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_80,type,
sK62:
!>[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_81,type,
sK63:
!>[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_82,type,
sK64:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_83,type,
sK65:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_84,type,
sK66:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_85,type,
sK67:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_86,type,
sK68:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_87,type,
sK69:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_88,type,
sK70:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_89,type,
sK71:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_90,type,
sK72:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_91,type,
sK73:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_92,type,
sK74:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_93,type,
sK75:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_94,type,
sK76:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_95,type,
sK77: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_96,type,
sK78:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_97,type,
sK79:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * product_prod(X0,X1) ) > X0 ) ).
tff(pred_def_1,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_2,type,
refl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_3,type,
antisym:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_4,type,
irrefl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_5,type,
sym:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_6,type,
total_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_7,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_8,type,
pp: bool > $o ).
tff(pred_def_9,type,
sP0: arrow_411405190le_alt > $o ).
tff(pred_def_10,type,
sP1: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_11,type,
sP2: ( arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_12,type,
sP3: ( arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(f93,axiom,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
=> ! [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ) )
& ! [X0: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X0),l)
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 != X1 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),l) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f94,conjecture,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| ( X0 = x )
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) ) )
& ( ( X1 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ( X0 = x )
| ! [X2: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ) )
& ( ( X0 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| ( X2 = y )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) ) ) )
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 = X1 )
| ( ( X0 = x )
& ( X1 = y ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( X0 != x )
& ( X1 != x ) )
| ( ( X1 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
& ( X0 != x ) )
| ( ( X0 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
& ( X1 != x ) )
| ( ( X1 = x )
& ( X0 = y ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),l)
& ( X1 != x )
& ( X0 != x ) )
| ( ( X0 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ( X1 != x ) )
| ( ( X1 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
& ( X0 != x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f95,negated_conjecture,
~ ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| ( X0 = x )
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) ) )
& ( ( X1 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ( X0 = x )
| ! [X2: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ) )
& ( ( X0 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| ( X2 = y )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) ) ) )
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 = X1 )
| ( ( X0 = x )
& ( X1 = y ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( X0 != x )
& ( X1 != x ) )
| ( ( X1 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
& ( X0 != x ) )
| ( ( X0 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
& ( X1 != x ) )
| ( ( X1 = x )
& ( X0 = y ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),l)
& ( X1 != x )
& ( X0 != x ) )
| ( ( X0 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ( X1 != x ) )
| ( ( X1 = x )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
& ( X0 != x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
tff(f96,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
=> ! [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) ) )
& ! [X3: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( ( X4 != X5 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X5),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X4),l) ) ) ),
inference(rectify,[],[f93]) ).
tff(f97,plain,
~ ( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| ( X0 = x )
| ( X1 = x )
| ! [X2: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ( X2 = x )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
& ( ( X2 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) ) )
& ( ( X1 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ( X0 = x )
| ! [X3: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X3),l)
| ( x = X3 )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),l) ) )
& ( ( X0 != x )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ( X1 = x )
| ! [X4: arrow_411405190le_alt] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),l)
| ( x = X4 )
| ( y = X4 )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X4),l) )
& ( ( x != X4 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) ) ) )
& ! [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 = X6 )
| ( ( x = X5 )
& ( y = X6 ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X6),l)
& ( x != X5 )
& ( x != X6 ) )
| ( ( x = X6 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),y),l)
& ( x != X5 ) )
| ( ( x = X5 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X6),l)
& ( x != X6 ) )
| ( ( x = X6 )
& ( y = X5 ) )
| ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),l)
& ( x != X6 )
& ( x != X5 ) )
| ( ( x = X5 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),y),l)
& ( x != X6 ) )
| ( ( x = X6 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X5),l)
& ( x != X5 ) ) ) ),
inference(rectify,[],[f95]) ).
tff(f99,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ! [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l) )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l) )
& ! [X3: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X5),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X4),l)
| ( X4 = X5 ) ) ),
inference(ennf_transformation,[],[f96]) ).
tff(f100,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ! [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l) )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l) )
& ! [X3: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X5),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X4),l)
| ( X4 = X5 ) ) ),
inference(flattening,[],[f99]) ).
tff(f101,plain,
( ? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( x != X0 )
& ( x != X1 )
& ? [X2: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
& ( x != X2 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
| ( ( x = X2 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) ) )
| ( ( x = X1 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
& ( x != X0 )
& ? [X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X3),l)
& ( x != X3 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),l) ) )
| ( ( x = X0 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
& ( x != X1 )
& ? [X4: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),l)
& ( x != X4 )
& ( y != X4 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X4),l) )
| ( ( x = X4 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) ) ) )
| ? [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
& ( ( x != X5 )
| ( y != X6 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X6),l)
| ( x = X5 )
| ( x = X6 ) )
& ( ( x != X6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),y),l)
| ( x = X5 ) )
& ( ( x != X5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X6),l)
| ( x = X6 ) )
& ( ( x != X6 )
| ( y != X5 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),l)
| ( x = X6 )
| ( x = X5 ) )
& ( ( x != X5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),y),l)
| ( x = X6 ) )
& ( ( x != X6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X5),l)
| ( x = X5 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
tff(f141,definition,
! [X1: arrow_411405190le_alt] :
( ? [X4: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),l)
& ( x != X4 )
& ( y != X4 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X4),l) )
| ( ( x = X4 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) )
| ~ sP0(X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f142,definition,
! [X2: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( x = X2 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) )
| ~ sP1(X2,X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
tff(f143,definition,
! [X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( x = X1 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
& ( x != X0 )
& ? [X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X3),l)
& ( x != X3 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),l) ) )
| ~ sP2(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
tff(f144,definition,
! [X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( x != X0 )
& ( x != X1 )
& ? [X2: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
& ( x != X2 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
| sP1(X2,X1,X0) ) )
| ~ sP3(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
tff(f145,definition,
( ? [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
& ( ( x != X5 )
| ( y != X6 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X6),l)
| ( x = X5 )
| ( x = X6 ) )
& ( ( x != X6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),y),l)
| ( x = X5 ) )
& ( ( x != X5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X6),l)
| ( x = X6 ) )
& ( ( x != X6 )
| ( y != X5 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),l)
| ( x = X6 )
| ( x = X5 ) )
& ( ( x != X5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),y),l)
| ( x = X6 ) )
& ( ( x != X6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X5),l)
| ( x = X5 ) ) )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
tff(f146,plain,
( ? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP3(X1,X0)
| sP2(X1,X0)
| ( ( x = X0 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
& ( x != X1 )
& sP0(X1) ) )
| sP4 ),
inference(definition_folding,[],[f101,f145,f144,f143,f142,f141]) ).
tff(f147,plain,
( ? [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
& ( ( x != X5 )
| ( y != X6 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X6),l)
| ( x = X5 )
| ( x = X6 ) )
& ( ( x != X6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),y),l)
| ( x = X5 ) )
& ( ( x != X5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X6),l)
| ( x = X6 ) )
& ( ( x != X6 )
| ( y != X5 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),l)
| ( x = X6 )
| ( x = X5 ) )
& ( ( x != X5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),y),l)
| ( x = X6 ) )
& ( ( x != X6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X5),l)
| ( x = X5 ) ) )
| ~ sP4 ),
inference(nnf_transformation,[],[f145]) ).
tff(f148,plain,
( ? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 != X1 )
& ( ( x != X0 )
| ( y != X1 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| ( x = X0 )
| ( x = X1 ) )
& ( ( x != X1 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ( x = X0 ) )
& ( ( x != X0 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l)
| ( x = X1 ) )
& ( ( x != X1 )
| ( y != 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),X0),l)
| ( x = X1 )
| ( x = X0 ) )
& ( ( x != X0 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
| ( x = X1 ) )
& ( ( x != X1 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
| ( x = X0 ) ) )
| ~ sP4 ),
inference(rectify,[],[f147]) ).
tff(f149,plain,
( ( ( sK5 != sK6 )
& ( ( x != sK5 )
| ( y != sK6 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK5),sK6),l)
| ( x = sK5 )
| ( x = sK6 ) )
& ( ( x != sK6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK5),y),l)
| ( x = sK5 ) )
& ( ( x != sK5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK6),l)
| ( x = sK6 ) )
& ( ( x != sK6 )
| ( y != sK5 ) )
& ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK6),sK5),l)
| ( x = sK6 )
| ( x = sK5 ) )
& ( ( x != sK5 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK6),y),l)
| ( x = sK6 ) )
& ( ( x != sK6 )
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK5),l)
| ( x = sK5 ) ) )
| ~ sP4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f148]) ).
tff(f150,plain,
! [X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( x != X0 )
& ( x != X1 )
& ? [X2: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
& ( x != X2 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l) )
| sP1(X2,X1,X0) ) )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f144]) ).
tff(f151,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),X1),X0),l)
& ( x != X1 )
& ( x != X0 )
& ? [X2: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l)
& ( x != X2 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l) )
| sP1(X2,X0,X1) ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f150]) ).
tff(f152,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),X1),X0),l)
& ( x != X1 )
& ( x != X0 )
& ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK7(X0,X1)),l)
& ( x != sK7(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),sK7(X0,X1)),l) )
| sP1(sK7(X0,X1),X0,X1) ) )
| ~ sP3(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f151]) ).
tff(f153,plain,
! [X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( x = X1 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
& ( x != X0 )
& ? [X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X3),l)
& ( x != X3 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),l) ) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f143]) ).
tff(f154,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ( x = X0 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ( x != X1 )
& ? [X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X2),l)
& ( x != X2 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l) ) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f153]) ).
tff(f155,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ( x = X0 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ( x != X1 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK8(X1)),l)
& ( x != sK8(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),sK8(X1)),l) )
| ~ sP2(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X1))],[f154]) ).
tff(f156,plain,
! [X2: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( x = X2 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) )
| ~ sP1(X2,X1,X0) ),
inference(nnf_transformation,[],[f142]) ).
tff(f157,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( ( ( x = X0 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),y),l) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f156]) ).
tff(f158,plain,
! [X1: arrow_411405190le_alt] :
( ? [X4: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),l)
& ( x != X4 )
& ( y != X4 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X4),l) )
| ( ( x = X4 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l) ) )
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f141]) ).
tff(f159,plain,
! [X0: arrow_411405190le_alt] :
( ? [X1: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
& ( x != X1 )
& ( y != X1 )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X1),l) )
| ( ( x = X1 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f158]) ).
tff(f160,plain,
! [X0: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK9(X0)),l)
& ( x != sK9(X0) )
& ( y != sK9(X0) )
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK9(X0)),l) )
| ( ( x = sK9(X0) )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f159]) ).
tff(f161,plain,
( sP3(sK11,sK10)
| sP2(sK11,sK10)
| ( ( x = sK10 )
& member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK11),l)
& ( x != sK11 )
& sP0(sK11) )
| sP4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f146]) ).
tff(f200,plain,
! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X4),l)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X5),l)
| ( X4 = X5 ) ),
inference(cnf_transformation,[],[f100]) ).
tff(f201,plain,
! [X3: arrow_411405190le_alt] : ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X3),l),
inference(cnf_transformation,[],[f100]) ).
tff(f202,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l) ),
inference(cnf_transformation,[],[f100]) ).
tff(f203,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK5),l)
| ( x != sK6 )
| ( x = sK5 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f204,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),sK6),y),l)
| ( x != sK5 )
| ( x = sK6 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f205,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),sK6),sK5),l)
| ( x = sK6 )
| ( x = sK5 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f206,plain,
( ( y != sK5 )
| ( x != sK6 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f207,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK6),l)
| ( x != sK5 )
| ( x = sK6 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f208,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),sK5),y),l)
| ( x != sK6 )
| ( x = sK5 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f209,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),sK5),sK6),l)
| ( x = sK5 )
| ( x = sK6 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f210,plain,
( ( y != sK6 )
| ( x != sK5 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f211,plain,
( ( sK5 != sK6 )
| ~ sP4 ),
inference(cnf_transformation,[],[f149]) ).
tff(f212,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),X1),sK7(X0,X1)),l)
| sP1(sK7(X0,X1),X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tff(f214,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),sK7(X0,X1)),l)
| sP1(sK7(X0,X1),X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tff(f217,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),X1),X0),l)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tff(f218,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),X1),sK8(X1)),l)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tff(f220,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK8(X1)),l)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tff(f222,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),X1),y),l)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tff(f224,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),y),l)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
tff(f225,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),y),l)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
tff(f228,plain,
! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK9(X0)),l)
| ( x = sK9(X0) )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f160]) ).
tff(f231,plain,
! [X0: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ( x != sK9(X0) )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f160]) ).
tff(f234,plain,
! [X0: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK9(X0)),l)
| ( x = sK9(X0) )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f160]) ).
tff(f235,plain,
( sP3(sK11,sK10)
| sP2(sK11,sK10)
| sP0(sK11)
| sP4 ),
inference(cnf_transformation,[],[f161]) ).
tff(f237,plain,
( sP3(sK11,sK10)
| sP2(sK11,sK10)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK11),l)
| sP4 ),
inference(cnf_transformation,[],[f161]) ).
tff(f323,definition,
( spl80_1
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl80_1])],[avatar_definition]) ).
tff(f325,plain,
( sP4
| ~ spl80_1 ),
inference(avatar_component_clause,[],[f323]) ).
tff(f327,definition,
( spl80_2
<=> sP0(sK11) ),
introduced(definition,[new_symbols(definition,[spl80_2])],[avatar_definition]) ).
tff(f329,plain,
( sP0(sK11)
| ~ spl80_2 ),
inference(avatar_component_clause,[],[f327]) ).
tff(f331,definition,
( spl80_3
<=> sP2(sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl80_3])],[avatar_definition]) ).
tff(f333,plain,
( sP2(sK11,sK10)
| ~ spl80_3 ),
inference(avatar_component_clause,[],[f331]) ).
tff(f335,definition,
( spl80_4
<=> sP3(sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl80_4])],[avatar_definition]) ).
tff(f337,plain,
( sP3(sK11,sK10)
| ~ spl80_4 ),
inference(avatar_component_clause,[],[f335]) ).
tff(f338,plain,
( spl80_1
| spl80_2
| spl80_3
| spl80_4 ),
inference(avatar_split_clause,[],[f235,f335,f331,f327,f323]) ).
tff(f345,definition,
( spl80_6
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK11),l) ),
introduced(definition,[new_symbols(definition,[spl80_6])],[avatar_definition]) ).
tff(f346,plain,
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK11),l)
| spl80_6 ),
inference(avatar_component_clause,[],[f345]) ).
tff(f347,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK11),l)
| ~ spl80_6 ),
inference(avatar_component_clause,[],[f345]) ).
tff(f348,plain,
( spl80_1
| spl80_6
| spl80_3
| spl80_4 ),
inference(avatar_split_clause,[],[f237,f335,f331,f345,f323]) ).
tff(f368,definition,
( spl80_10
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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),y),l) ),
introduced(definition,[new_symbols(definition,[spl80_10])],[avatar_definition]) ).
tff(f369,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),sK11),y),l)
| spl80_10 ),
inference(avatar_component_clause,[],[f368]) ).
tff(f393,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
| ( y = X0 )
| ~ sP1(X1,X2,X0) ),
inference(resolution,[],[f200,f224]) ).
tff(f397,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),sK6),y),l)
| ( y = sK6 )
| ( x != sK5 )
| ( x = sK6 )
| ~ sP4 ),
inference(resolution,[],[f200,f207]) ).
tff(f402,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK5),l)
| ( y = sK5 )
| ( x != sK6 )
| ( x = sK5 )
| ~ sP4 ),
inference(resolution,[],[f200,f208]) ).
tff(f403,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),sK5),sK6),l)
| ( sK5 = sK6 )
| ( x = sK6 )
| ( x = sK5 )
| ~ sP4 ),
inference(resolution,[],[f200,f205]) ).
tff(f425,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ~ sP1(X0,sK11,X1)
| spl80_10 ),
inference(resolution,[],[f369,f225]) ).
tff(f430,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),X1),X0),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l) ),
inference(resolution,[],[f202,f201]) ).
tff(f432,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK7(X1,X2)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X0),l)
| sP1(sK7(X1,X2),X1,X2)
| ~ sP3(X1,X2) ),
inference(resolution,[],[f202,f212]) ).
tff(f433,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK8(X1)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),l)
| ~ sP2(X2,X1) ),
inference(resolution,[],[f202,f218]) ).
tff(f437,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),sK9(X1)),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
| ( x = sK9(X1) )
| ~ sP0(X1) ),
inference(resolution,[],[f202,f228]) ).
tff(f524,plain,
! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
| ( x != sK9(X0) )
| ~ sP0(X0) ),
inference(resolution,[],[f430,f231]) ).
tff(f531,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),sK11),y),l)
| ~ spl80_6 ),
inference(resolution,[],[f430,f347]) ).
tff(f600,definition,
( spl80_15
<=> sP3(sK11,y) ),
introduced(definition,[new_symbols(definition,[spl80_15])],[avatar_definition]) ).
tff(f601,plain,
( sP3(sK11,y)
| ~ spl80_15 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f602,plain,
( ~ sP3(sK11,y)
| spl80_15 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f611,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),y),l)
| ~ sP2(X1,X0)
| ~ sP2(X2,X0) ),
inference(resolution,[],[f433,f220]) ).
tff(f617,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP2(X2,X0)
| ~ sP2(X1,X0) ),
inference(forward_subsumption_resolution,[],[f611,f222]) ).
tff(f619,plain,
! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
| ( x = sK9(X0) )
| ~ sP0(X0)
| ( x = sK9(X0) )
| ~ sP0(X0) ),
inference(resolution,[],[f437,f234]) ).
tff(f627,plain,
! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
| ( x = sK9(X0) )
| ~ sP0(X0) ),
inference(duplicate_literal_removal,[],[f619]) ).
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),y),X0),l)
| ~ sP0(X0) ),
inference(forward_subsumption_resolution,[],[f627,f524]) ).
tff(f633,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| sP1(sK7(X1,X0),X1,X0)
| ~ sP3(X1,X0)
| sP1(sK7(X1,X0),X1,X0)
| ~ sP3(X1,X0) ),
inference(resolution,[],[f432,f214]) ).
tff(f641,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),l)
| sP1(sK7(X1,X0),X1,X0)
| ~ sP3(X1,X0) ),
inference(duplicate_literal_removal,[],[f633]) ).
tff(f643,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP1(sK7(X1,X0),X1,X0)
| ~ sP3(X1,X0) ),
inference(forward_subsumption_resolution,[],[f641,f217]) ).
tff(f832,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP3(sK11,X0)
| spl80_10 ),
inference(resolution,[],[f643,f425]) ).
tff(f833,plain,
( $false
| ~ spl80_4
| spl80_10 ),
inference(resolution,[],[f832,f337]) ).
tff(f834,plain,
( ~ spl80_4
| spl80_10 ),
inference(avatar_contradiction_clause,[],[f833]) ).
tff(f839,plain,
( ! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),X0),l)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK11),l) )
| spl80_6 ),
inference(resolution,[],[f346,f202]) ).
tff(f853,plain,
( ! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),sK11),l)
| ( y = X0 )
| ~ sP1(X1,X2,X0) )
| spl80_6 ),
inference(resolution,[],[f839,f393]) ).
tff(f891,plain,
( ! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP1(X1,X2,X0)
| ( y = X0 )
| ~ sP3(sK11,X0) )
| spl80_6 ),
inference(resolution,[],[f853,f217]) ).
tff(f935,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP3(sK11,X0)
| ( y = X0 )
| ~ sP3(X1,X0) )
| spl80_6 ),
inference(resolution,[],[f891,f643]) ).
tff(f941,plain,
( ! [X0: arrow_411405190le_alt] :
( ( y = sK10 )
| ~ sP3(X0,sK10) )
| ~ spl80_4
| spl80_6 ),
inference(resolution,[],[f935,f337]) ).
tff(f943,definition,
( spl80_20
<=> ! [X0: arrow_411405190le_alt] : ~ sP3(X0,sK10) ),
introduced(definition,[new_symbols(definition,[spl80_20])],[avatar_definition]) ).
tff(f944,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP3(X0,sK10)
| ~ spl80_20 ),
inference(avatar_component_clause,[],[f943]) ).
tff(f946,definition,
( spl80_21
<=> ( y = sK10 ) ),
introduced(definition,[new_symbols(definition,[spl80_21])],[avatar_definition]) ).
tff(f948,plain,
( ( y = sK10 )
| ~ spl80_21 ),
inference(avatar_component_clause,[],[f946]) ).
tff(f949,plain,
( spl80_20
| spl80_21
| ~ spl80_4
| spl80_6 ),
inference(avatar_split_clause,[],[f941,f345,f335,f946,f943]) ).
tff(f961,plain,
( $false
| ~ spl80_3 ),
inference(forward_subsumption_resolution,[],[f333,f617]) ).
tff(f962,plain,
~ spl80_3,
inference(avatar_contradiction_clause,[],[f961]) ).
tff(f1003,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),sK5),sK6),l)
| ( sK5 = sK6 )
| ( x = sK6 )
| ( x = sK5 )
| ~ spl80_1 ),
inference(forward_subsumption_resolution,[],[f403,f325]) ).
tff(f1004,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK5),l)
| ( y = sK5 )
| ( x != sK6 )
| ( x = sK5 )
| ~ spl80_1 ),
inference(forward_subsumption_resolution,[],[f402,f325]) ).
tff(f1006,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),sK6),y),l)
| ( y = sK6 )
| ( x != sK5 )
| ( x = sK6 )
| ~ spl80_1 ),
inference(forward_subsumption_resolution,[],[f397,f325]) ).
tff(f1021,definition,
( spl80_22
<=> ( x = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl80_22])],[avatar_definition]) ).
tff(f1022,plain,
( ( x != sK6 )
| spl80_22 ),
inference(avatar_component_clause,[],[f1021]) ).
tff(f1023,plain,
( ( x = sK6 )
| ~ spl80_22 ),
inference(avatar_component_clause,[],[f1021]) ).
tff(f1025,definition,
( spl80_23
<=> ( x = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl80_23])],[avatar_definition]) ).
tff(f1026,plain,
( ( x = sK5 )
| ~ spl80_23 ),
inference(avatar_component_clause,[],[f1025]) ).
tff(f1027,plain,
( ( x != sK5 )
| spl80_23 ),
inference(avatar_component_clause,[],[f1025]) ).
tff(f1029,definition,
( spl80_24
<=> ( y = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl80_24])],[avatar_definition]) ).
tff(f1031,plain,
( ( y = sK6 )
| ~ spl80_24 ),
inference(avatar_component_clause,[],[f1029]) ).
tff(f1038,definition,
( spl80_26
<=> ( sK5 = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl80_26])],[avatar_definition]) ).
tff(f1040,plain,
( ( sK5 = sK6 )
| ~ spl80_26 ),
inference(avatar_component_clause,[],[f1038]) ).
tff(f1042,definition,
( spl80_27
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK5),sK6),l) ),
introduced(definition,[new_symbols(definition,[spl80_27])],[avatar_definition]) ).
tff(f1044,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),sK5),sK6),l)
| ~ spl80_27 ),
inference(avatar_component_clause,[],[f1042]) ).
tff(f1045,plain,
( spl80_23
| spl80_22
| spl80_26
| spl80_27
| ~ spl80_1 ),
inference(avatar_split_clause,[],[f1003,f323,f1042,f1038,f1021,f1025]) ).
tff(f1047,definition,
( spl80_28
<=> ( y = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl80_28])],[avatar_definition]) ).
tff(f1049,plain,
( ( y = sK5 )
| ~ spl80_28 ),
inference(avatar_component_clause,[],[f1047]) ).
tff(f1051,definition,
( spl80_29
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK5),l) ),
introduced(definition,[new_symbols(definition,[spl80_29])],[avatar_definition]) ).
tff(f1053,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),y),sK5),l)
| ~ spl80_29 ),
inference(avatar_component_clause,[],[f1051]) ).
tff(f1054,plain,
( spl80_23
| ~ spl80_22
| spl80_28
| spl80_29
| ~ spl80_1 ),
inference(avatar_split_clause,[],[f1004,f323,f1051,f1047,f1021,f1025]) ).
tff(f1061,definition,
( spl80_31
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK6),y),l) ),
introduced(definition,[new_symbols(definition,[spl80_31])],[avatar_definition]) ).
tff(f1063,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),sK6),y),l)
| ~ spl80_31 ),
inference(avatar_component_clause,[],[f1061]) ).
tff(f1064,plain,
( spl80_22
| ~ spl80_23
| spl80_24
| spl80_31
| ~ spl80_1 ),
inference(avatar_split_clause,[],[f1006,f323,f1061,f1029,f1025,f1021]) ).
tff(f1106,plain,
( ~ spl80_10
| ~ spl80_6 ),
inference(avatar_split_clause,[],[f531,f345,f368]) ).
tff(f1161,plain,
( ( x = sK5 )
| ( x = sK6 )
| ~ sP4
| ~ spl80_27 ),
inference(resolution,[],[f1044,f209]) ).
tff(f1178,plain,
( ( x != sK6 )
| ( x = sK5 )
| ~ sP4
| ~ spl80_29 ),
inference(resolution,[],[f1053,f203]) ).
tff(f1199,plain,
( ( x != sK5 )
| ( x = sK6 )
| ~ sP4
| ~ spl80_31 ),
inference(resolution,[],[f1063,f204]) ).
tff(f1527,plain,
( ~ sP0(sK11)
| ~ spl80_6 ),
inference(resolution,[],[f631,f347]) ).
tff(f1544,plain,
( $false
| ~ spl80_2
| ~ spl80_6 ),
inference(forward_subsumption_resolution,[],[f1527,f329]) ).
tff(f1545,plain,
( ~ spl80_2
| ~ spl80_6 ),
inference(avatar_contradiction_clause,[],[f1544]) ).
tff(f1548,plain,
( ( x = sK6 )
| ~ sP4
| spl80_23
| ~ spl80_27 ),
inference(forward_subsumption_resolution,[],[f1161,f1027]) ).
tff(f1550,plain,
( ~ sP4
| spl80_22
| spl80_23
| ~ spl80_27 ),
inference(forward_subsumption_resolution,[],[f1548,f1022]) ).
tff(f1552,plain,
( $false
| ~ spl80_1
| spl80_22
| spl80_23
| ~ spl80_27 ),
inference(forward_subsumption_resolution,[],[f1550,f325]) ).
tff(f1553,plain,
( ~ spl80_1
| spl80_22
| spl80_23
| ~ spl80_27 ),
inference(avatar_contradiction_clause,[],[f1552]) ).
tff(f1559,plain,
( ( x = sK6 )
| ~ sP4
| ~ spl80_23
| ~ spl80_31 ),
inference(forward_subsumption_resolution,[],[f1199,f1026]) ).
tff(f1594,plain,
( ~ sP4
| spl80_22
| ~ spl80_23
| ~ spl80_31 ),
inference(forward_subsumption_resolution,[],[f1559,f1022]) ).
tff(f1609,plain,
( $false
| ~ spl80_1
| spl80_22
| ~ spl80_23
| ~ spl80_31 ),
inference(forward_subsumption_resolution,[],[f1594,f325]) ).
tff(f1610,plain,
( ~ spl80_1
| spl80_22
| ~ spl80_23
| ~ spl80_31 ),
inference(avatar_contradiction_clause,[],[f1609]) ).
tff(f1702,plain,
( ( x != sK5 )
| ~ sP4
| ~ spl80_22 ),
inference(superposition,[],[f211,f1023]) ).
tff(f1723,plain,
( ( y != y )
| ( x != sK6 )
| ~ sP4
| ~ spl80_28 ),
inference(superposition,[],[f206,f1049]) ).
tff(f1742,plain,
( ( x != sK6 )
| ~ sP4
| ~ spl80_28 ),
inference(trivial_inequality_removal,[],[f1723]) ).
tff(f1745,plain,
( ~ sP4
| ~ spl80_22
| ~ spl80_28 ),
inference(forward_subsumption_resolution,[],[f1742,f1023]) ).
tff(f1746,plain,
( $false
| ~ spl80_1
| ~ spl80_22
| ~ spl80_28 ),
inference(forward_subsumption_resolution,[],[f1745,f325]) ).
tff(f1747,plain,
( ~ spl80_1
| ~ spl80_22
| ~ spl80_28 ),
inference(avatar_contradiction_clause,[],[f1746]) ).
tff(f1748,plain,
( ( x = sK5 )
| ~ sP4
| ~ spl80_22
| ~ spl80_29 ),
inference(forward_subsumption_resolution,[],[f1178,f1023]) ).
tff(f1763,plain,
( ~ sP4
| ~ spl80_22
| spl80_23
| ~ spl80_29 ),
inference(forward_subsumption_resolution,[],[f1748,f1027]) ).
tff(f1774,plain,
( $false
| ~ spl80_1
| ~ spl80_22
| spl80_23
| ~ spl80_29 ),
inference(forward_subsumption_resolution,[],[f1763,f325]) ).
tff(f1775,plain,
( ~ spl80_1
| ~ spl80_22
| spl80_23
| ~ spl80_29 ),
inference(avatar_contradiction_clause,[],[f1774]) ).
tff(f1793,plain,
( ~ sP4
| ~ spl80_22
| ~ spl80_23 ),
inference(forward_subsumption_resolution,[],[f1702,f1026]) ).
tff(f1800,plain,
( $false
| ~ spl80_1
| ~ spl80_22
| ~ spl80_23 ),
inference(forward_subsumption_resolution,[],[f1793,f325]) ).
tff(f1801,plain,
( ~ spl80_1
| ~ spl80_22
| ~ spl80_23 ),
inference(avatar_contradiction_clause,[],[f1800]) ).
tff(f1868,plain,
( ( y != y )
| ( x != sK5 )
| ~ sP4
| ~ spl80_24 ),
inference(superposition,[],[f210,f1031]) ).
tff(f1883,plain,
( ( x != sK5 )
| ~ sP4
| ~ spl80_24 ),
inference(trivial_inequality_removal,[],[f1868]) ).
tff(f1887,plain,
( ~ sP4
| ~ spl80_23
| ~ spl80_24 ),
inference(forward_subsumption_resolution,[],[f1883,f1026]) ).
tff(f1888,plain,
( $false
| ~ spl80_1
| ~ spl80_23
| ~ spl80_24 ),
inference(forward_subsumption_resolution,[],[f1887,f325]) ).
tff(f1889,plain,
( ~ spl80_1
| ~ spl80_23
| ~ spl80_24 ),
inference(avatar_contradiction_clause,[],[f1888]) ).
tff(f1939,plain,
( ~ sP3(sK11,y)
| spl80_6 ),
inference(resolution,[],[f346,f217]) ).
tff(f1974,plain,
( $false
| ~ spl80_4
| ~ spl80_20 ),
inference(resolution,[],[f944,f337]) ).
tff(f1975,plain,
( ~ spl80_4
| ~ spl80_20 ),
inference(avatar_contradiction_clause,[],[f1974]) ).
tff(f1983,plain,
( sP3(sK11,y)
| ~ spl80_4
| ~ spl80_21 ),
inference(superposition,[],[f337,f948]) ).
tff(f1985,plain,
( $false
| ~ spl80_4
| spl80_15
| ~ spl80_21 ),
inference(forward_subsumption_resolution,[],[f1983,f602]) ).
tff(f1986,plain,
( ~ spl80_4
| spl80_15
| ~ spl80_21 ),
inference(avatar_contradiction_clause,[],[f1985]) ).
tff(f1991,plain,
( $false
| spl80_6
| ~ spl80_15 ),
inference(forward_subsumption_resolution,[],[f1939,f601]) ).
tff(f1992,plain,
( spl80_6
| ~ spl80_15 ),
inference(avatar_contradiction_clause,[],[f1991]) ).
tff(f2018,plain,
( ( sK5 != sK5 )
| ~ sP4
| ~ spl80_26 ),
inference(superposition,[],[f211,f1040]) ).
tff(f2030,plain,
( ~ sP4
| ~ spl80_26 ),
inference(trivial_inequality_removal,[],[f2018]) ).
tff(f2033,plain,
( $false
| ~ spl80_1
| ~ spl80_26 ),
inference(forward_subsumption_resolution,[],[f2030,f325]) ).
tff(f2034,plain,
( ~ spl80_1
| ~ spl80_26 ),
inference(avatar_contradiction_clause,[],[f2033]) ).
cnf(s1,plain,
( spl80_1
| spl80_2
| spl80_3
| spl80_4 ),
inference(sat_conversion,[],[f338]) ).
cnf(s3,plain,
( spl80_1
| spl80_3
| spl80_4
| spl80_6 ),
inference(sat_conversion,[],[f348]) ).
cnf(s11,plain,
( ~ spl80_4
| spl80_10 ),
inference(sat_conversion,[],[f834]) ).
cnf(s14,plain,
( ~ spl80_4
| spl80_6
| spl80_20
| spl80_21 ),
inference(sat_conversion,[],[f949]) ).
cnf(s15,plain,
~ spl80_3,
inference(sat_conversion,[],[f962]) ).
cnf(s18,plain,
( ~ spl80_1
| spl80_22
| spl80_23
| spl80_26
| spl80_27 ),
inference(sat_conversion,[],[f1045]) ).
cnf(s19,plain,
( ~ spl80_1
| ~ spl80_22
| spl80_23
| spl80_28
| spl80_29 ),
inference(sat_conversion,[],[f1054]) ).
cnf(s21,plain,
( ~ spl80_1
| spl80_22
| ~ spl80_23
| spl80_24
| spl80_31 ),
inference(sat_conversion,[],[f1064]) ).
cnf(s31,plain,
( ~ spl80_6
| ~ spl80_10 ),
inference(sat_conversion,[],[f1106]) ).
cnf(s55,plain,
( ~ spl80_2
| ~ spl80_6 ),
inference(sat_conversion,[],[f1545]) ).
cnf(s56,plain,
( ~ spl80_1
| spl80_22
| spl80_23
| ~ spl80_27 ),
inference(sat_conversion,[],[f1553]) ).
cnf(s62,plain,
( ~ spl80_1
| spl80_22
| ~ spl80_23
| ~ spl80_31 ),
inference(sat_conversion,[],[f1610]) ).
cnf(s72,plain,
( ~ spl80_1
| ~ spl80_22
| ~ spl80_28 ),
inference(sat_conversion,[],[f1747]) ).
cnf(s74,plain,
( ~ spl80_1
| ~ spl80_22
| spl80_23
| ~ spl80_29 ),
inference(sat_conversion,[],[f1775]) ).
cnf(s79,plain,
( ~ spl80_1
| ~ spl80_22
| ~ spl80_23 ),
inference(sat_conversion,[],[f1801]) ).
cnf(s81,plain,
( ~ spl80_1
| ~ spl80_23
| ~ spl80_24 ),
inference(sat_conversion,[],[f1889]) ).
cnf(s90,plain,
( ~ spl80_4
| ~ spl80_20 ),
inference(sat_conversion,[],[f1975]) ).
cnf(s91,plain,
( ~ spl80_4
| spl80_15
| ~ spl80_21 ),
inference(sat_conversion,[],[f1986]) ).
cnf(s94,plain,
( spl80_6
| ~ spl80_15 ),
inference(sat_conversion,[],[f1992]) ).
cnf(s96,plain,
( ~ spl80_1
| ~ spl80_26 ),
inference(sat_conversion,[],[f2034]) ).
cnf(s98,plain,
( spl80_1
| spl80_4
| spl80_6 ),
inference(rat,[],[s3,s15]) ).
cnf(s100,plain,
( spl80_1
| spl80_2
| spl80_4 ),
inference(rat,[],[s1,s15]) ).
cnf(s101,plain,
~ spl80_4,
inference(rat,[],[s91,s14,s94,s31,s11,s90]) ).
cnf(s102,plain,
spl80_1,
inference(rat,[],[s55,s100,s98,s101]) ).
cnf(s103,plain,
~ spl80_26,
inference(rat,[],[s96,s102]) ).
cnf(s104,plain,
( spl80_23
| spl80_22 ),
inference(rat,[],[s56,s18,s103,s102]) ).
cnf(s105,plain,
spl80_22,
inference(rat,[],[s21,s62,s81,s104,s102]) ).
cnf(s106,plain,
~ spl80_23,
inference(rat,[],[s79,s102,s105]) ).
cnf(s107,plain,
~ spl80_28,
inference(rat,[],[s72,s102,s105]) ).
cnf(s108,plain,
~ spl80_29,
inference(rat,[],[s74,s105,s102,s106]) ).
cnf(s113,plain,
$false,
inference(rat,[],[s19,s105,s107,s102,s108,s106]) ).
tff(f2035,plain,
$false,
inference(avatar_sat_refutation,[],[s113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT187_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n020.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 23:58:49 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.47 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.77/2.01 % (3895221)Detected formulas, will run a generic FOF schedule.
% 5.77/2.01 % (3895229)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3549815511:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.77/2.01 % (3895228)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=214039140:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.77/2.01 % (3895230)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3316579347:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.77/2.01 % (3895231)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3606541120:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.77/2.01 % (3895233)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1974827527:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.77/2.01 % (3895232)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=352945242:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.77/2.01 % (3895231)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.77/2.01 % (3895230)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.77/2.01 % (3895234)dis-21_1_sil=8000:lcm=predicate:random_seed=1722536093:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.77/2.01 % (3895231)Instruction limit reached!
% 5.77/2.01 % (3895231)------------------------------
% 5.77/2.01 % (3895231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/2.01 % (3895231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/2.01 % (3895231)CaDiCaL version: 2.1.3
% 5.77/2.01 % (3895231)Termination reason: Instruction limit
% 5.77/2.01 % (3895231)Termination phase: Saturation
% 5.77/2.01 % (3895231)Time elapsed: 0.109 s
% 5.77/2.01 % (3895231)Peak memory usage: 89 MB
% 5.77/2.01 % (3895231)Instructions burned: 110 (million)
% 5.77/2.01 % (3895232)Instruction limit reached!
% 5.77/2.01 % (3895232)------------------------------
% 5.77/2.01 % (3895232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/2.01 % (3895232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/2.01 % (3895232)CaDiCaL version: 2.1.3
% 5.77/2.01 % (3895232)Termination reason: Instruction limit
% 5.77/2.01 % (3895232)Termination phase: Saturation
% 5.77/2.01 % (3895232)Time elapsed: 0.115 s
% 5.77/2.01 % (3895232)Peak memory usage: 88 MB
% 5.77/2.01 % (3895232)Instructions burned: 119 (million)
% 5.77/2.01 % (3895233)Instruction limit reached!
% 5.77/2.01 % (3895233)------------------------------
% 5.77/2.01 % (3895233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/2.01 % (3895233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/2.01 % (3895233)CaDiCaL version: 2.1.3
% 5.77/2.01 % (3895233)Termination reason: Instruction limit
% 5.77/2.01 % (3895233)Termination phase: Saturation
% 5.77/2.01 % (3895233)Time elapsed: 0.140 s
% 5.77/2.01 % (3895233)Peak memory usage: 89 MB
% 5.77/2.01 % (3895233)Instructions burned: 140 (million)
% 5.77/2.01 % (3895234)Instruction limit reached!
% 5.77/2.01 % (3895234)------------------------------
% 5.77/2.01 % (3895234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/2.01 % (3895234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/2.01 % (3895234)CaDiCaL version: 2.1.3
% 5.77/2.01 % (3895234)Termination reason: Instruction limit
% 5.77/2.01 % (3895234)Termination phase: Saturation
% 5.77/2.01 % (3895234)Time elapsed: 0.127 s
% 5.77/2.01 % (3895234)Peak memory usage: 90 MB
% 5.77/2.01 % (3895234)Instructions burned: 130 (million)
% 5.77/2.01 % Exception at run slice level
% 5.77/2.01 User error: GNN currently only supports monomorphic FOL.
% 5.77/2.01 % (3895242)lrs+10_1_sil=8000:sp=occurrence:random_seed=1188390757:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.77/2.01 % (3895243)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3684199402:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 5.77/2.01 % (3895244)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1612448138:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 5.77/2.01 % (3895245)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3130929968:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.77/2.01 % (3895242)Instruction limit reached!
% 5.77/2.01 % (3895242)------------------------------
% 5.77/2.01 % (3895242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/2.01 % (3895242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/2.01 % (3895242)CaDiCaL version: 2.1.3
% 5.77/2.01 % (3895242)Termination reason: Instruction limit
% 5.77/2.01 % (3895242)Termination phase: Saturation
% 5.77/2.01 % (3895242)Time elapsed: 0.141 s
% 5.77/2.01 % (3895242)Peak memory usage: 90 MB
% 5.77/2.01 % (3895242)Instructions burned: 285 (million)
% 5.77/2.01 % (3895246)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3974618919:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 5.77/2.01 % (3895246)First to succeed.
% 5.77/2.01 % (3895246)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3895221"
% 5.77/2.01 % (3895243)Instruction limit reached!
% 5.77/2.01 % (3895243)------------------------------
% 5.77/2.01 % (3895243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/2.01 % (3895243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/2.01 % (3895243)CaDiCaL version: 2.1.3
% 5.77/2.01 % (3895243)Termination reason: Instruction limit
% 5.77/2.01 % (3895243)Termination phase: Saturation
% 5.77/2.01 % (3895243)Time elapsed: 0.145 s
% 5.77/2.01 % (3895243)Peak memory usage: 89 MB
% 5.77/2.01 % (3895243)Instructions burned: 157 (million)
% 5.77/2.01 % Exception at run slice level
% 5.77/2.01 User error: GNN currently only supports monomorphic FOL.
% 5.77/2.01 % Exception at run slice level
% 5.77/2.01 User error: GNN currently only supports monomorphic FOL.
% 5.77/2.01 % (3895244)Also succeeded, but the first one will report.
% 5.77/2.01 % (3895245)Instruction limit reached!
% 5.77/2.01 % (3895245)------------------------------
% 5.77/2.01 % (3895245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/2.01 % (3895245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/2.01 % (3895245)CaDiCaL version: 2.1.3
% 5.77/2.01 % (3895245)Termination reason: Instruction limit
% 5.77/2.01 % (3895245)Termination phase: Saturation
% 5.77/2.01 % (3895245)Time elapsed: 0.206 s
% 5.77/2.01 % (3895245)Peak memory usage: 90 MB
% 5.77/2.01 % (3895245)Instructions burned: 248 (million)
% 5.77/2.01 % (3895251)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=773974179:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 5.77/2.01 % (3895246)Refutation found. Thanks to Tanya!
% 5.77/2.01 % SZS status Theorem for theBenchmark
% 5.77/2.01 % SZS output start Proof for theBenchmark
% See solution above
% 8.03/2.27 % (3895246)------------------------------
% 8.03/2.27 % (3895246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.03/2.27 % (3895246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.03/2.27 % (3895246)CaDiCaL version: 2.1.3
% 8.03/2.27 % (3895246)Termination reason: Refutation
% 8.03/2.27 % (3895246)Time elapsed: 0.077 s
% 8.03/2.27 % (3895246)Peak memory usage: 90 MB
% 8.03/2.27 % (3895246)Instructions burned: 151 (million)
% 8.03/2.27 % (3895246)------------------------------
% 8.03/2.27 % (3895246)------------------------------
% 8.03/2.27 % (3895221)Success in time 1.04 s
% 8.03/2.27 % Vampire exiting
%------------------------------------------------------------------------------