TSTP Solution File: SCT176_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT176_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:51:53 EDT 2024
% Result : Theorem 2.62s 0.73s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 392
% Syntax : Number of formulae : 1009 ( 185 unt; 116 typ; 0 def)
% Number of atoms : 2549 ( 487 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2775 (1119 ~;1121 |; 193 &)
% ( 206 <=>; 133 =>; 0 <=; 3 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 149 ( 98 >; 51 *; 0 +; 0 <<)
% Number of predicates : 188 ( 186 usr; 178 prp; 0-6 aty)
% Number of functors : 105 ( 105 usr; 10 con; 0-7 aty)
% Number of variables : 3481 (2972 !; 205 ?;3481 :)
% ( 304 !>; 0 ?*; 0 @-; 0 @+)
% 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,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_2,type,
order_215145569der_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(product_prod(X0,X0),bool),bool) ) ).
tff(func_def_3,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_5,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).
tff(func_def_6,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).
tff(func_def_7,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_8,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_9,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_10,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_11,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_12,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_13,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_14,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_15,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fTrue: bool ).
tff(func_def_18,type,
l: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_19,type,
sK2: arrow_411405190le_alt ).
tff(func_def_20,type,
sK3: arrow_411405190le_alt ).
tff(func_def_21,type,
sK4: arrow_411405190le_alt ).
tff(func_def_22,type,
sK5: arrow_411405190le_alt ).
tff(func_def_23,type,
sK6: arrow_411405190le_alt ).
tff(func_def_24,type,
sK7: arrow_411405190le_alt ).
tff(func_def_25,type,
sK8:
!>[X0: $tType] : X0 ).
tff(func_def_26,type,
sK9:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_27,type,
sK10:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_28,type,
sK11:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_29,type,
sK12:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_30,type,
sK13:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_31,type,
sK14:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_32,type,
sK15:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_33,type,
sK16:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_34,type,
sK17:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_35,type,
sK18:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_36,type,
sK19:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_37,type,
sK20:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_38,type,
sK21:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_39,type,
sK22:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_40,type,
sK23:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_41,type,
sK24:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_42,type,
sK25:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_43,type,
sK26:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_44,type,
sK27:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_45,type,
sK28:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_46,type,
sK29:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_47,type,
sK30:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_48,type,
sK31:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X0 ) ).
tff(func_def_49,type,
sK32:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X1 ) ).
tff(func_def_50,type,
sK33:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_51,type,
sK34:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X1 ) ).
tff(func_def_52,type,
sK35:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X0 ) ).
tff(func_def_53,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_54,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_55,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_56,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_57,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_58,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_59,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_60,type,
sK43:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_61,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_62,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_63,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X0 ) ).
tff(func_def_64,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X2 ) ).
tff(func_def_65,type,
sK48:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X0 ) ).
tff(func_def_66,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X2 ) ).
tff(func_def_67,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).
tff(func_def_68,type,
sK51:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).
tff(func_def_69,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X1 ) ).
tff(func_def_70,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X0 ) ).
tff(func_def_71,type,
sK54:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_72,type,
sK55:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_73,type,
sK56:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X0 ) ).
tff(func_def_74,type,
sK57:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_75,type,
sK58:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_76,type,
sK59:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_77,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_78,type,
sK61:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_79,type,
sK62:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).
tff(func_def_80,type,
sK63:
!>[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_81,type,
sK64:
!>[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_82,type,
sK65:
!>[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_83,type,
sK66:
!>[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_84,type,
sK67:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_85,type,
sK68:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_86,type,
sK69:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X4 ) ).
tff(func_def_87,type,
sK70:
!>[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_88,type,
sK71:
!>[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_89,type,
sK72:
!>[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_90,type,
sK73:
!>[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_91,type,
sK74:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).
tff(func_def_92,type,
sK75:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).
tff(func_def_93,type,
sK76:
!>[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_94,type,
sK77:
!>[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_95,type,
sK78:
!>[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_96,type,
sK79:
!>[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_97,type,
sK80:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X5 ) ).
tff(func_def_98,type,
sK81:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X4 ) ).
tff(func_def_99,type,
sK82:
!>[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_100,type,
sK83:
!>[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_101,type,
sK84:
!>[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_102,type,
sK85:
!>[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(pred_def_1,type,
top:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_3,type,
refl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_4,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_5,type,
irrefl:
!>[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,
trans:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_8,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_9,type,
pp: bool > $o ).
tff(f3742,plain,
$false,
inference(avatar_sat_refutation,[],[f459,f464,f469,f474,f479,f483,f487,f494,f498,f502,f507,f511,f515,f519,f523,f534,f538,f546,f551,f558,f562,f571,f576,f583,f587,f591,f595,f605,f612,f617,f623,f630,f639,f640,f648,f652,f662,f666,f674,f678,f683,f687,f691,f695,f710,f714,f718,f722,f726,f730,f734,f738,f742,f770,f774,f788,f804,f808,f813,f823,f828,f836,f841,f851,f856,f866,f900,f905,f910,f914,f918,f933,f992,f997,f1012,f1017,f1031,f1048,f1052,f1056,f1136,f1141,f1145,f1154,f1155,f1185,f1192,f1198,f1230,f1236,f1242,f1247,f1254,f1259,f1266,f1270,f1275,f1280,f1362,f1366,f1432,f1436,f1473,f1478,f1493,f1523,f1528,f1545,f1550,f1554,f1569,f1574,f1588,f1593,f1608,f1613,f1617,f1636,f1641,f1659,f1664,f1674,f1679,f1691,f1695,f1719,f1725,f1737,f1876,f1889,f2410,f2414,f2485,f2519,f2585,f2589,f2627,f2665,f2708,f2795,f2941,f2945,f2949,f2979,f2983,f2987,f2991,f2996,f3000,f3038,f3059,f3075,f3085,f3089,f3097,f3101,f3105,f3109,f3113,f3227,f3231,f3235,f3240,f3244,f3248,f3394,f3398,f3402,f3499,f3707,f3711,f3715,f3719,f3720,f3723,f3729,f3732,f3738,f3741]) ).
tff(f3741,plain,
( ~ spl86_1
| spl86_6 ),
inference(avatar_split_clause,[],[f309,f476,f452]) ).
tff(f452,plain,
( spl86_1
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_1])]) ).
tff(f476,plain,
( spl86_6
<=> trans(arrow_411405190le_alt,l) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_6])]) ).
tff(f309,plain,
( trans(arrow_411405190le_alt,l)
| ~ sP0 ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
( ( sP0
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
& ( sK5 != 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),sK7),sK7),l)
| ~ trans(arrow_411405190le_alt,l) )
& ( ( ! [X3: 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),X3),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),X3),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f218,f220,f219]) ).
tff(f219,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)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
& ( 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),sK5),sK6),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),sK6),sK5),l)
& ( sK5 != sK6 ) ) ),
introduced(choice_axiom,[]) ).
tff(f220,plain,
( ? [X2: arrow_411405190le_alt] : member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),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),sK7),sK7),l) ),
introduced(choice_axiom,[]) ).
tff(f218,plain,
( ( sP0
| ? [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)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
& ( X0 != 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),X2),X2),l)
| ~ trans(arrow_411405190le_alt,l) )
& ( ( ! [X3: 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),X3),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),X3),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) )
| ~ sP0 ) ),
inference(rectify,[],[f217]) ).
tff(f217,plain,
( ( sP0
| ? [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)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
& ( X0 != 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),X2),X2),l)
| ~ trans(arrow_411405190le_alt,l) )
& ( ( ! [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)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
| ( X0 = 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),X2),X2),l)
& trans(arrow_411405190le_alt,l) )
| ~ sP0 ) ),
inference(flattening,[],[f216]) ).
tff(f216,plain,
( ( sP0
| ? [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)
& ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
& ( X0 != 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),X2),X2),l)
| ~ trans(arrow_411405190le_alt,l) )
& ( ( ! [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)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
| ( X0 = 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),X2),X2),l)
& trans(arrow_411405190le_alt,l) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f207]) ).
tff(f207,plain,
( sP0
<=> ( ! [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)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
| ( X0 = 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),X2),X2),l)
& trans(arrow_411405190le_alt,l) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f3738,plain,
( ~ spl86_34
| ~ spl86_46 ),
inference(avatar_contradiction_clause,[],[f3733]) ).
tff(f3733,plain,
( $false
| ~ spl86_34
| ~ spl86_46 ),
inference(resolution,[],[f705,f638]) ).
tff(f638,plain,
( ! [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),X5),l)
| ~ spl86_34 ),
inference(avatar_component_clause,[],[f637]) ).
tff(f637,plain,
( spl86_34
<=> ! [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),X5),l) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_34])]) ).
tff(f705,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),sK4),sK4),l)
| ~ spl86_46 ),
inference(avatar_component_clause,[],[f703]) ).
tff(f703,plain,
( spl86_46
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK4),sK4),l) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_46])]) ).
tff(f3732,plain,
( ~ spl86_1
| ~ spl86_2 ),
inference(avatar_split_clause,[],[f316,f456,f452]) ).
tff(f456,plain,
( spl86_2
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_2])]) ).
tff(f316,plain,
( ~ sP1
| ~ sP0 ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
( ( ~ sP1
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(nnf_transformation,[],[f209]) ).
tff(f209,plain,
( sP0
<~> sP1 ),
inference(definition_folding,[],[f159,f208,f207]) ).
tff(f208,plain,
( sP1
<=> ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
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)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
| ( X0 = 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),X2),X2),l)
& trans(arrow_411405190le_alt,l) )
<~> ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) ) ),
inference(flattening,[],[f158]) ).
tff(f158,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)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
| ( X0 = 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),X2),X2),l)
& trans(arrow_411405190le_alt,l) )
<~> ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) ) ),
inference(ennf_transformation,[],[f83]) ).
tff(f83,plain,
~ ( ( ! [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) ) )
& ! [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),X2),X2),l)
& trans(arrow_411405190le_alt,l) )
<=> ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( X3 != X4 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l) ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) ) ),
inference(rectify,[],[f82]) ).
tff(f82,negated_conjecture,
~ ( ( ! [X17: arrow_411405190le_alt,X18: arrow_411405190le_alt] :
( ( X17 != X18 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X17),X18),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),X18),X17),l) ) )
& ! [X17: 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),X17),X17),l)
& trans(arrow_411405190le_alt,l) )
<=> ( ! [X17: arrow_411405190le_alt,X18: arrow_411405190le_alt] :
( ( X17 != X18 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X18),X17),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),X17),X18),l) ) )
& ! [X17: 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),X17),X17),l)
& trans(arrow_411405190le_alt,l) ) ),
inference(negated_conjecture,[],[f81]) ).
tff(f81,conjecture,
( ( ! [X17: arrow_411405190le_alt,X18: arrow_411405190le_alt] :
( ( X17 != X18 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X17),X18),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),X18),X17),l) ) )
& ! [X17: 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),X17),X17),l)
& trans(arrow_411405190le_alt,l) )
<=> ( ! [X17: arrow_411405190le_alt,X18: arrow_411405190le_alt] :
( ( X17 != X18 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X18),X17),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),X17),X18),l) ) )
& ! [X17: 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),X17),X17),l)
& trans(arrow_411405190le_alt,l) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f3729,plain,
( ~ spl86_34
| ~ spl86_86 ),
inference(avatar_contradiction_clause,[],[f3724]) ).
tff(f3724,plain,
( $false
| ~ spl86_34
| ~ spl86_86 ),
inference(resolution,[],[f1149,f638]) ).
tff(f1149,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),sK7),sK7),l)
| ~ spl86_86 ),
inference(avatar_component_clause,[],[f1147]) ).
tff(f1147,plain,
( spl86_86
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK7),sK7),l) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_86])]) ).
tff(f3723,plain,
( spl86_87
| spl86_89
| ~ spl86_85
| spl86_88 ),
inference(avatar_split_clause,[],[f1186,f1182,f1143,f1189,f1151]) ).
tff(f1151,plain,
( spl86_87
<=> ( sK5 = sK6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_87])]) ).
tff(f1189,plain,
( spl86_89
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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(avatar_definition,[new_symbols(naming,[spl86_89])]) ).
tff(f1143,plain,
( spl86_85
<=> ! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X4),l)
| ( X3 = X4 )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),l) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_85])]) ).
tff(f1182,plain,
( spl86_88
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_88])]) ).
tff(f1186,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 )
| ~ spl86_85
| spl86_88 ),
inference(resolution,[],[f1184,f1144]) ).
tff(f1144,plain,
( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 ) )
| ~ spl86_85 ),
inference(avatar_component_clause,[],[f1143]) ).
tff(f1184,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)
| spl86_88 ),
inference(avatar_component_clause,[],[f1182]) ).
tff(f3720,plain,
( spl86_47
| spl86_83
| spl86_84
| ~ spl86_85 ),
inference(avatar_split_clause,[],[f1158,f1143,f1138,f1133,f707]) ).
tff(f707,plain,
( spl86_47
<=> ( sK2 = sK3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_47])]) ).
tff(f1133,plain,
( spl86_83
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK2),sK3),l) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_83])]) ).
tff(f1138,plain,
( spl86_84
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK3),sK2),l) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_84])]) ).
tff(f1158,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),sK2),sK3),l)
| ( sK2 = sK3 )
| spl86_84
| ~ spl86_85 ),
inference(resolution,[],[f1144,f1140]) ).
tff(f1140,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),sK3),sK2),l)
| spl86_84 ),
inference(avatar_component_clause,[],[f1138]) ).
tff(f3719,plain,
( spl86_175
| ~ spl86_12
| ~ spl86_78 ),
inference(avatar_split_clause,[],[f1018,f1015,f505,f3717]) ).
tff(f3717,plain,
( spl86_175
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(X0,fun(X1,bool))] :
( pp(product_prod_rec(X0,X1,bool,X2,X3))
| ~ member(X1,sK35(X1,X0,X2,X3),aa(X0,fun(X1,bool),X2,sK34(X1,X0,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_175])]) ).
tff(f505,plain,
( spl86_12
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_12])]) ).
tff(f1015,plain,
( spl86_78
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X1,X0),X2: fun(X1,fun(X0,bool))] :
( pp(product_prod_rec(X1,X0,bool,X2,X3))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_78])]) ).
tff(f1018,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: product_prod(X0,X1)] :
( pp(product_prod_rec(X0,X1,bool,X2,X3))
| ~ member(X1,sK35(X1,X0,X2,X3),aa(X0,fun(X1,bool),X2,sK34(X1,X0,X2,X3))) )
| ~ spl86_12
| ~ spl86_78 ),
inference(resolution,[],[f1016,f506]) ).
tff(f506,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) )
| ~ spl86_12 ),
inference(avatar_component_clause,[],[f505]) ).
tff(f1016,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)))
| pp(product_prod_rec(X1,X0,bool,X2,X3)) )
| ~ spl86_78 ),
inference(avatar_component_clause,[],[f1015]) ).
tff(f3715,plain,
( spl86_174
| ~ spl86_13
| ~ spl86_76 ),
inference(avatar_split_clause,[],[f998,f995,f509,f3713]) ).
tff(f3713,plain,
( spl86_174
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(X0,fun(X1,bool))] :
( ~ pp(product_prod_rec(X0,X1,bool,X2,X3))
| member(X1,sK32(X0,X1,X3,X2),aa(X0,fun(X1,bool),X2,sK31(X0,X1,X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_174])]) ).
tff(f509,plain,
( spl86_13
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_13])]) ).
tff(f995,plain,
( spl86_76
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: product_prod(X0,X1)] :
( ~ pp(product_prod_rec(X0,X1,bool,X3,X2))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_76])]) ).
tff(f998,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,fun(X1,bool)),X3: product_prod(X0,X1)] :
( ~ pp(product_prod_rec(X0,X1,bool,X2,X3))
| member(X1,sK32(X0,X1,X3,X2),aa(X0,fun(X1,bool),X2,sK31(X0,X1,X3,X2))) )
| ~ spl86_13
| ~ spl86_76 ),
inference(resolution,[],[f996,f510]) ).
tff(f510,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| member(X0,X2,X1) )
| ~ spl86_13 ),
inference(avatar_component_clause,[],[f509]) ).
tff(f996,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)))
| ~ pp(product_prod_rec(X0,X1,bool,X3,X2)) )
| ~ spl86_76 ),
inference(avatar_component_clause,[],[f995]) ).
tff(f3711,plain,
( spl86_173
| ~ spl86_12
| ~ spl86_63 ),
inference(avatar_split_clause,[],[f829,f826,f505,f3709]) ).
tff(f3709,plain,
( spl86_173
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2)))
| ~ member(X1,X3,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_173])]) ).
tff(f826,plain,
( spl86_63
<=> ! [X1: $tType,X0: $tType,X4: X0,X5: X1,X2: fun(product_prod(X0,X1),bool)] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),X4),X5))
| pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_63])]) ).
tff(f829,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: X1,X4: X0] :
( pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2)))
| ~ member(X1,X3,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),X4)) )
| ~ spl86_12
| ~ spl86_63 ),
inference(resolution,[],[f827,f506]) ).
tff(f827,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),X4),X5))
| pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) )
| ~ spl86_63 ),
inference(avatar_component_clause,[],[f826]) ).
tff(f3707,plain,
( spl86_172
| ~ spl86_12
| ~ spl86_61 ),
inference(avatar_split_clause,[],[f815,f811,f505,f3705]) ).
tff(f3705,plain,
( spl86_172
<=> ! [X1: $tType,X0: $tType,X4: X0,X3: X1,X2: fun(product_prod(X1,X0),bool)] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,X2),X3),X4))
| ~ member(product_prod(X1,X0),sK21(X1,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_172])]) ).
tff(f811,plain,
( spl86_61
<=> ! [X1: $tType,X0: $tType,X7: X1,X6: X0,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),X6),X7))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK21(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_61])]) ).
tff(f815,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
( pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,X2),X3),X4))
| ~ member(product_prod(X1,X0),sK21(X1,X0,X2),X2) )
| ~ spl86_12
| ~ spl86_61 ),
inference(resolution,[],[f812,f506]) ).
tff(f812,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( ~ pp(aa(product_prod(X0,X1),bool,X2,sK21(X0,X1,X2)))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),X6),X7)) )
| ~ spl86_61 ),
inference(avatar_component_clause,[],[f811]) ).
tff(f3499,plain,
( spl86_171
| ~ spl86_7
| ~ spl86_48 ),
inference(avatar_split_clause,[],[f754,f712,f481,f3497]) ).
tff(f3497,plain,
( spl86_171
<=> ! [X1: $tType,X2: X1,X0: bool] :
( member(X1,X2,combk(bool,X1,X0))
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_171])]) ).
tff(f481,plain,
( spl86_7
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_7])]) ).
tff(f712,plain,
( spl86_48
<=> ! [X0: $tType,X1: X0] : member(X0,X1,combk(bool,X0,fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_48])]) ).
tff(f754,plain,
( ! [X1: $tType,X2: X1,X0: bool] :
( member(X1,X2,combk(bool,X1,X0))
| ( fFalse = X0 ) )
| ~ spl86_7
| ~ spl86_48 ),
inference(superposition,[],[f713,f482]) ).
tff(f482,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = X0 ) )
| ~ spl86_7 ),
inference(avatar_component_clause,[],[f481]) ).
tff(f713,plain,
( ! [X0: $tType,X1: X0] : member(X0,X1,combk(bool,X0,fTrue))
| ~ spl86_48 ),
inference(avatar_component_clause,[],[f712]) ).
tff(f3402,plain,
( spl86_170
| ~ spl86_44
| ~ spl86_58 ),
inference(avatar_split_clause,[],[f791,f786,f689,f3400]) ).
tff(f3400,plain,
( spl86_170
<=> ! [X1: $tType,X3: $tType,X0: $tType,X4: fun(X1,fun(X0,X3)),X2: product_prod(X1,X0)] : ( product_prod_rec(X1,X0,X3,X4,X2) = aa(X0,X3,aa(X1,fun(X0,X3),X4,sK29(X1,X0,X2)),sK30(X1,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_170])]) ).
tff(f689,plain,
( spl86_44
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK29(X0,X1,X2)),sK30(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_44])]) ).
tff(f786,plain,
( spl86_58
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( product_prod_rec(X0,X2,X1,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_58])]) ).
tff(f791,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: product_prod(X1,X0),X4: fun(X1,fun(X0,X3))] : ( product_prod_rec(X1,X0,X3,X4,X2) = aa(X0,X3,aa(X1,fun(X0,X3),X4,sK29(X1,X0,X2)),sK30(X1,X0,X2)) )
| ~ spl86_44
| ~ spl86_58 ),
inference(superposition,[],[f787,f690]) ).
tff(f690,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK29(X0,X1,X2)),sK30(X0,X1,X2)) = X2 )
| ~ spl86_44 ),
inference(avatar_component_clause,[],[f689]) ).
tff(f787,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( product_prod_rec(X0,X2,X1,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) )
| ~ spl86_58 ),
inference(avatar_component_clause,[],[f786]) ).
tff(f3398,plain,
( spl86_169
| ~ spl86_43
| ~ spl86_58 ),
inference(avatar_split_clause,[],[f790,f786,f685,f3396]) ).
tff(f3396,plain,
( spl86_169
<=> ! [X1: $tType,X3: $tType,X0: $tType,X4: fun(X1,fun(X0,X3)),X2: product_prod(X1,X0)] : ( product_prod_rec(X1,X0,X3,X4,X2) = aa(X0,X3,aa(X1,fun(X0,X3),X4,sK27(X1,X0,X2)),sK28(X1,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_169])]) ).
tff(f685,plain,
( spl86_43
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK27(X0,X1,X2)),sK28(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_43])]) ).
tff(f790,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: product_prod(X1,X0),X4: fun(X1,fun(X0,X3))] : ( product_prod_rec(X1,X0,X3,X4,X2) = aa(X0,X3,aa(X1,fun(X0,X3),X4,sK27(X1,X0,X2)),sK28(X1,X0,X2)) )
| ~ spl86_43
| ~ spl86_58 ),
inference(superposition,[],[f787,f686]) ).
tff(f686,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK27(X0,X1,X2)),sK28(X0,X1,X2)) = X2 )
| ~ spl86_43 ),
inference(avatar_component_clause,[],[f685]) ).
tff(f3394,plain,
( spl86_168
| ~ spl86_42
| ~ spl86_58 ),
inference(avatar_split_clause,[],[f789,f786,f681,f3392]) ).
tff(f3392,plain,
( spl86_168
<=> ! [X1: $tType,X3: $tType,X0: $tType,X4: fun(X1,fun(X0,X3)),X2: product_prod(X1,X0)] : ( aa(X0,X3,aa(X1,fun(X0,X3),X4,sK25(X1,X0,X2)),sK26(X1,X0,X2)) = product_prod_rec(X1,X0,X3,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_168])]) ).
tff(f681,plain,
( spl86_42
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_42])]) ).
tff(f789,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: product_prod(X1,X0),X4: fun(X1,fun(X0,X3))] : ( aa(X0,X3,aa(X1,fun(X0,X3),X4,sK25(X1,X0,X2)),sK26(X1,X0,X2)) = product_prod_rec(X1,X0,X3,X4,X2) )
| ~ spl86_42
| ~ spl86_58 ),
inference(superposition,[],[f787,f682]) ).
tff(f682,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X2 )
| ~ spl86_42 ),
inference(avatar_component_clause,[],[f681]) ).
tff(f3248,plain,
( spl86_167
| ~ spl86_12
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73 ),
inference(avatar_split_clause,[],[f983,f916,f786,f693,f681,f505,f3246]) ).
tff(f3246,plain,
( spl86_167
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X0,product_prod(X1,X2)),X4: fun(X1,fun(X2,bool)),X5: X0] :
( pp(product_prod_rec(X1,X2,bool,X4,aa(X0,product_prod(X1,X2),X3,X5)))
| ~ member(X0,X5,product_scomp(X0,X1,X2,bool,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_167])]) ).
tff(f693,plain,
( spl86_45
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2,X3: fun(X2,fun(X0,X1))] : ( product_scomp(X0,X2,X0,X1,aa(X2,fun(X0,product_prod(X2,X0)),product_Pair(X2,X0),X4),X3) = aa(X2,fun(X0,X1),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_45])]) ).
tff(f916,plain,
( spl86_73
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: fun(X3,product_prod(X1,X2)),X4: fun(X1,fun(X2,X0)),X6: X3] : ( aa(X3,X0,product_scomp(X3,X1,X2,X0,X5,X4),X6) = aa(product_prod(X1,X2),X0,aa(fun(X1,fun(X2,X0)),fun(product_prod(X1,X2),X0),product_prod_case(X1,X2,X0),X4),aa(X3,product_prod(X1,X2),X5,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_73])]) ).
tff(f983,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,product_prod(X1,X2)),X4: fun(X1,fun(X2,bool)),X5: X0] :
( pp(product_prod_rec(X1,X2,bool,X4,aa(X0,product_prod(X1,X2),X3,X5)))
| ~ member(X0,X5,product_scomp(X0,X1,X2,bool,X3,X4)) )
| ~ spl86_12
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73 ),
inference(forward_demodulation,[],[f964,f974]) ).
tff(f974,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: product_prod(X1,X0),X4: fun(X1,fun(X0,X3))] : ( product_prod_rec(X1,X0,X3,X4,X2) = aa(product_prod(X1,X0),X3,aa(fun(X1,fun(X0,X3)),fun(product_prod(X1,X0),X3),product_prod_case(X1,X0,X3),X4),X2) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73 ),
inference(forward_demodulation,[],[f973,f789]) ).
tff(f973,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: product_prod(X1,X0),X4: fun(X1,fun(X0,X3))] : ( aa(X0,X3,aa(X1,fun(X0,X3),X4,sK25(X1,X0,X2)),sK26(X1,X0,X2)) = aa(product_prod(X1,X0),X3,aa(fun(X1,fun(X0,X3)),fun(product_prod(X1,X0),X3),product_prod_case(X1,X0,X3),X4),X2) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_73 ),
inference(forward_demodulation,[],[f949,f694]) ).
tff(f694,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2] : ( product_scomp(X0,X2,X0,X1,aa(X2,fun(X0,product_prod(X2,X0)),product_Pair(X2,X0),X4),X3) = aa(X2,fun(X0,X1),X3,X4) )
| ~ spl86_45 ),
inference(avatar_component_clause,[],[f693]) ).
tff(f949,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: product_prod(X1,X0),X4: fun(X1,fun(X0,X3))] : ( aa(X0,X3,product_scomp(X0,X1,X0,X3,aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK25(X1,X0,X2)),X4),sK26(X1,X0,X2)) = aa(product_prod(X1,X0),X3,aa(fun(X1,fun(X0,X3)),fun(product_prod(X1,X0),X3),product_prod_case(X1,X0,X3),X4),X2) )
| ~ spl86_42
| ~ spl86_73 ),
inference(superposition,[],[f917,f682]) ).
tff(f917,plain,
( ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X3,X4: fun(X1,fun(X2,X0)),X5: fun(X3,product_prod(X1,X2))] : ( aa(X3,X0,product_scomp(X3,X1,X2,X0,X5,X4),X6) = aa(product_prod(X1,X2),X0,aa(fun(X1,fun(X2,X0)),fun(product_prod(X1,X2),X0),product_prod_case(X1,X2,X0),X4),aa(X3,product_prod(X1,X2),X5,X6)) )
| ~ spl86_73 ),
inference(avatar_component_clause,[],[f916]) ).
tff(f964,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,product_prod(X1,X2)),X4: fun(X1,fun(X2,bool)),X5: X0] :
( pp(aa(product_prod(X1,X2),bool,aa(fun(X1,fun(X2,bool)),fun(product_prod(X1,X2),bool),product_prod_case(X1,X2,bool),X4),aa(X0,product_prod(X1,X2),X3,X5)))
| ~ member(X0,X5,product_scomp(X0,X1,X2,bool,X3,X4)) )
| ~ spl86_12
| ~ spl86_73 ),
inference(superposition,[],[f506,f917]) ).
tff(f3244,plain,
( spl86_166
| ~ spl86_13
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73 ),
inference(avatar_split_clause,[],[f982,f916,f786,f693,f681,f509,f3242]) ).
tff(f3242,plain,
( spl86_166
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X0,product_prod(X1,X2)),X4: fun(X1,fun(X2,bool)),X5: X0] :
( ~ pp(product_prod_rec(X1,X2,bool,X4,aa(X0,product_prod(X1,X2),X3,X5)))
| member(X0,X5,product_scomp(X0,X1,X2,bool,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_166])]) ).
tff(f982,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,product_prod(X1,X2)),X4: fun(X1,fun(X2,bool)),X5: X0] :
( ~ pp(product_prod_rec(X1,X2,bool,X4,aa(X0,product_prod(X1,X2),X3,X5)))
| member(X0,X5,product_scomp(X0,X1,X2,bool,X3,X4)) )
| ~ spl86_13
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73 ),
inference(forward_demodulation,[],[f963,f974]) ).
tff(f963,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X0,product_prod(X1,X2)),X4: fun(X1,fun(X2,bool)),X5: X0] :
( ~ pp(aa(product_prod(X1,X2),bool,aa(fun(X1,fun(X2,bool)),fun(product_prod(X1,X2),bool),product_prod_case(X1,X2,bool),X4),aa(X0,product_prod(X1,X2),X3,X5)))
| member(X0,X5,product_scomp(X0,X1,X2,bool,X3,X4)) )
| ~ spl86_13
| ~ spl86_73 ),
inference(superposition,[],[f510,f917]) ).
tff(f3240,plain,
( spl86_165
| ~ spl86_15
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73 ),
inference(avatar_split_clause,[],[f979,f916,f786,f693,f681,f517,f3238]) ).
tff(f3238,plain,
( spl86_165
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: $tType,X3: product_prod(X1,X2),X4: X0,X6: fun(X1,fun(X2,X5))] : ( aa(X0,X5,product_scomp(X0,X1,X2,X5,combk(product_prod(X1,X2),X0,X3),X6),X4) = product_prod_rec(X1,X2,X5,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_165])]) ).
tff(f517,plain,
( spl86_15
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_15])]) ).
tff(f979,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X1,X2),X6: fun(X1,fun(X2,X5)),X4: X0] : ( aa(X0,X5,product_scomp(X0,X1,X2,X5,combk(product_prod(X1,X2),X0,X3),X6),X4) = product_prod_rec(X1,X2,X5,X6,X3) )
| ~ spl86_15
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73 ),
inference(forward_demodulation,[],[f952,f974]) ).
tff(f952,plain,
( ! [X5: $tType,X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X1,X2),X6: fun(X1,fun(X2,X5)),X4: X0] : ( aa(X0,X5,product_scomp(X0,X1,X2,X5,combk(product_prod(X1,X2),X0,X3),X6),X4) = aa(product_prod(X1,X2),X5,aa(fun(X1,fun(X2,X5)),fun(product_prod(X1,X2),X5),product_prod_case(X1,X2,X5),X6),X3) )
| ~ spl86_15
| ~ spl86_73 ),
inference(superposition,[],[f917,f518]) ).
tff(f518,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 )
| ~ spl86_15 ),
inference(avatar_component_clause,[],[f517]) ).
tff(f3235,plain,
( spl86_164
| ~ spl86_15
| ~ spl86_61 ),
inference(avatar_split_clause,[],[f818,f811,f517,f3233]) ).
tff(f3233,plain,
( spl86_164
<=> ! [X1: $tType,X0: $tType,X4: X1,X3: X0,X2: bool] :
( ~ pp(X2)
| pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,combk(bool,product_prod(X0,X1),X2)),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_164])]) ).
tff(f818,plain,
( ! [X1: $tType,X0: $tType,X2: bool,X3: X0,X4: X1] :
( ~ pp(X2)
| pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,combk(bool,product_prod(X0,X1),X2)),X3),X4)) )
| ~ spl86_15
| ~ spl86_61 ),
inference(superposition,[],[f812,f518]) ).
tff(f3231,plain,
( spl86_163
| ~ spl86_7
| ~ spl86_37 ),
inference(avatar_split_clause,[],[f655,f650,f481,f3229]) ).
tff(f3229,plain,
( spl86_163
<=> ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
| ( X1 = X2 )
| ( fFalse = sK33(X0,bool,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_163])]) ).
tff(f650,plain,
( spl86_37
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK33(X0,X1,X2,X3)) != aa(X1,X0,X2,sK33(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_37])]) ).
tff(f655,plain,
( ! [X0: $tType,X2: fun(bool,X0),X1: fun(bool,X0)] :
( ( aa(bool,X0,X2,fTrue) != aa(bool,X0,X1,fTrue) )
| ( X1 = X2 )
| ( fFalse = sK33(X0,bool,X1,X2) ) )
| ~ spl86_7
| ~ spl86_37 ),
inference(superposition,[],[f651,f482]) ).
tff(f651,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( aa(X1,X0,X3,sK33(X0,X1,X2,X3)) != aa(X1,X0,X2,sK33(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl86_37 ),
inference(avatar_component_clause,[],[f650]) ).
tff(f3227,plain,
( spl86_162
| ~ spl86_7
| ~ spl86_32 ),
inference(avatar_split_clause,[],[f624,f620,f481,f3225]) ).
tff(f3225,plain,
( spl86_162
<=> ! [X0: bool] :
( ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,X0))) )
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_162])]) ).
tff(f620,plain,
( spl86_32
<=> ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_32])]) ).
tff(f624,plain,
( ! [X0: bool] :
( ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,X0))) )
| ( fFalse = X0 ) )
| ~ spl86_7
| ~ spl86_32 ),
inference(superposition,[],[f622,f482]) ).
tff(f622,plain,
( ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue))) )
| ~ spl86_32 ),
inference(avatar_component_clause,[],[f620]) ).
tff(f3113,plain,
( spl86_161
| ~ spl86_63
| ~ spl86_76 ),
inference(avatar_split_clause,[],[f1000,f995,f826,f3111]) ).
tff(f3111,plain,
( spl86_161
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( ~ pp(product_prod_rec(X0,X1,bool,product_curry(X0,X1,bool,X2),X3))
| pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_161])]) ).
tff(f1000,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
( ~ pp(product_prod_rec(X0,X1,bool,product_curry(X0,X1,bool,X2),X3))
| pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) )
| ~ spl86_63
| ~ spl86_76 ),
inference(resolution,[],[f996,f827]) ).
tff(f3109,plain,
( spl86_160
| ~ spl86_17
| ~ spl86_119 ),
inference(avatar_split_clause,[],[f2924,f1615,f532,f3107]) ).
tff(f3107,plain,
( spl86_160
<=> ! [X1: $tType,X2: fun(product_prod(X1,X1),bool),X0: bool] :
( pp(X0)
| total_on(X1,combk(bool,X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_160])]) ).
tff(f532,plain,
( spl86_17
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| member(X0,sK17(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_17])]) ).
tff(f1615,plain,
( spl86_119
<=> ! [X0: $tType,X2: X0,X1: bool] :
( pp(X1)
| ~ member(X0,X2,combk(bool,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_119])]) ).
tff(f2924,plain,
( ! [X1: $tType,X2: fun(product_prod(X1,X1),bool),X0: bool] :
( pp(X0)
| total_on(X1,combk(bool,X1,X0),X2) )
| ~ spl86_17
| ~ spl86_119 ),
inference(resolution,[],[f1616,f533]) ).
tff(f533,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( member(X0,sK17(X0,X1,X2),X2)
| total_on(X0,X2,X1) )
| ~ spl86_17 ),
inference(avatar_component_clause,[],[f532]) ).
tff(f1616,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( ~ member(X0,X2,combk(bool,X0,X1))
| pp(X1) )
| ~ spl86_119 ),
inference(avatar_component_clause,[],[f1615]) ).
tff(f3105,plain,
( spl86_159
| ~ spl86_15
| ~ spl86_68 ),
inference(avatar_split_clause,[],[f876,f864,f517,f3103]) ).
tff(f3103,plain,
( spl86_159
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: X1] : ( aa(X1,X2,aa(X0,fun(X1,X2),product_curry(X0,X1,X2,combk(X2,product_prod(X0,X1),X3)),X4),X5) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_159])]) ).
tff(f864,plain,
( spl86_68
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(product_prod(X1,X2),X0),X4: X1,X3: X2] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X5),X4),X3) = aa(product_prod(X1,X2),X0,X5,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_68])]) ).
tff(f876,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: X1] : ( aa(X1,X2,aa(X0,fun(X1,X2),product_curry(X0,X1,X2,combk(X2,product_prod(X0,X1),X3)),X4),X5) = X3 )
| ~ spl86_15
| ~ spl86_68 ),
inference(superposition,[],[f865,f518]) ).
tff(f865,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X1,X5: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X5),X4),X3) = aa(product_prod(X1,X2),X0,X5,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X3)) )
| ~ spl86_68 ),
inference(avatar_component_clause,[],[f864]) ).
tff(f3101,plain,
( spl86_158
| ~ spl86_15
| ~ spl86_37 ),
inference(avatar_split_clause,[],[f657,f650,f517,f3099]) ).
tff(f3099,plain,
( spl86_158
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ( aa(X0,X1,X3,sK33(X1,X0,combk(X1,X0,X2),X3)) != X2 )
| ( combk(X1,X0,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_158])]) ).
tff(f657,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ( aa(X0,X1,X3,sK33(X1,X0,combk(X1,X0,X2),X3)) != X2 )
| ( combk(X1,X0,X2) = X3 ) )
| ~ spl86_15
| ~ spl86_37 ),
inference(superposition,[],[f651,f518]) ).
tff(f3097,plain,
( spl86_157
| ~ spl86_15
| ~ spl86_37 ),
inference(avatar_split_clause,[],[f654,f650,f517,f3095]) ).
tff(f3095,plain,
( spl86_157
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,X1),X2: X1] :
( ( aa(X0,X1,X3,sK33(X1,X0,X3,combk(X1,X0,X2))) != X2 )
| ( combk(X1,X0,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_157])]) ).
tff(f654,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,X1)] :
( ( aa(X0,X1,X3,sK33(X1,X0,X3,combk(X1,X0,X2))) != X2 )
| ( combk(X1,X0,X2) = X3 ) )
| ~ spl86_15
| ~ spl86_37 ),
inference(superposition,[],[f651,f518]) ).
tff(f3089,plain,
( spl86_156
| ~ spl86_11
| ~ spl86_20
| ~ spl86_61 ),
inference(avatar_split_clause,[],[f819,f811,f549,f500,f3087]) ).
tff(f3087,plain,
( spl86_156
<=> ! [X1: $tType,X0: $tType,X3: X0,X2: X1] : pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,combk(bool,product_prod(X1,X0),fTrue)),X2),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_156])]) ).
tff(f500,plain,
( spl86_11
<=> ! [X0: $tType,X1: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_11])]) ).
tff(f549,plain,
( spl86_20
<=> ! [X0: $tType] : ( top_top(fun(X0,bool)) = combk(bool,X0,fTrue) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_20])]) ).
tff(f819,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: X0] : pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,combk(bool,product_prod(X1,X0),fTrue)),X2),X3))
| ~ spl86_11
| ~ spl86_20
| ~ spl86_61 ),
inference(forward_demodulation,[],[f814,f550]) ).
tff(f550,plain,
( ! [X0: $tType] : ( top_top(fun(X0,bool)) = combk(bool,X0,fTrue) )
| ~ spl86_20 ),
inference(avatar_component_clause,[],[f549]) ).
tff(f814,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: X0] : pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,top_top(fun(product_prod(X1,X0),bool))),X2),X3))
| ~ spl86_11
| ~ spl86_61 ),
inference(resolution,[],[f812,f501]) ).
tff(f501,plain,
( ! [X0: $tType,X1: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X1))
| ~ spl86_11 ),
inference(avatar_component_clause,[],[f500]) ).
tff(f3085,plain,
( spl86_155
| ~ spl86_8
| ~ spl86_21 ),
inference(avatar_split_clause,[],[f564,f556,f485,f3083]) ).
tff(f3083,plain,
( spl86_155
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X0] :
( ( aa(X0,fun(X1,X2),top_top(fun(X0,fun(X1,X2))),X3) = top_top(fun(X1,X2)) )
| ~ top(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_155])]) ).
tff(f485,plain,
( spl86_8
<=> ! [X1: $tType,X0: $tType] :
( top(fun(X0,X1))
| ~ top(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_8])]) ).
tff(f556,plain,
( spl86_21
<=> ! [X1: $tType,X0: $tType,X2: X0] :
( ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
| ~ top(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_21])]) ).
tff(f564,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0] :
( ( aa(X0,fun(X1,X2),top_top(fun(X0,fun(X1,X2))),X3) = top_top(fun(X1,X2)) )
| ~ top(X2) )
| ~ spl86_8
| ~ spl86_21 ),
inference(resolution,[],[f557,f486]) ).
tff(f486,plain,
( ! [X1: $tType,X0: $tType] :
( top(fun(X0,X1))
| ~ top(X1) )
| ~ spl86_8 ),
inference(avatar_component_clause,[],[f485]) ).
tff(f557,plain,
( ! [X1: $tType,X0: $tType,X2: X0] :
( ~ top(X1)
| ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) ) )
| ~ spl86_21 ),
inference(avatar_component_clause,[],[f556]) ).
tff(f3075,plain,
( spl86_154
| ~ spl86_13
| ~ spl86_33 ),
inference(avatar_split_clause,[],[f634,f628,f509,f3073]) ).
tff(f3073,plain,
( spl86_154
<=> ! [X0: $tType,X2: fun(product_prod(X0,X0),bool),X1: fun(X0,bool)] :
( ~ total_on(X0,X1,X2)
| ~ irrefl(X0,X2)
| ~ trans(X0,X2)
| member(fun(product_prod(X0,X0),bool),X2,order_215145569der_on(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_154])]) ).
tff(f628,plain,
( spl86_33
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_33])]) ).
tff(f634,plain,
( ! [X0: $tType,X2: fun(product_prod(X0,X0),bool),X1: fun(X0,bool)] :
( ~ total_on(X0,X1,X2)
| ~ irrefl(X0,X2)
| ~ trans(X0,X2)
| member(fun(product_prod(X0,X0),bool),X2,order_215145569der_on(X0,X1)) )
| ~ spl86_13
| ~ spl86_33 ),
inference(resolution,[],[f629,f510]) ).
tff(f629,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) )
| ~ spl86_33 ),
inference(avatar_component_clause,[],[f628]) ).
tff(f3059,plain,
( spl86_153
| ~ spl86_7
| ~ spl86_24 ),
inference(avatar_split_clause,[],[f578,f574,f481,f3057]) ).
tff(f3057,plain,
( spl86_153
<=> ! [X0: fun(bool,bool)] :
( ~ member(bool,fTrue,X0)
| ( combk(bool,bool,fTrue) = X0 )
| ( fFalse = sK9(bool,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_153])]) ).
tff(f574,plain,
( spl86_24
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fTrue) = X1 )
| ~ member(X0,sK9(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_24])]) ).
tff(f578,plain,
( ! [X0: fun(bool,bool)] :
( ~ member(bool,fTrue,X0)
| ( combk(bool,bool,fTrue) = X0 )
| ( fFalse = sK9(bool,X0) ) )
| ~ spl86_7
| ~ spl86_24 ),
inference(superposition,[],[f575,f482]) ).
tff(f575,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ~ member(X0,sK9(X0,X1),X1)
| ( combk(bool,X0,fTrue) = X1 ) )
| ~ spl86_24 ),
inference(avatar_component_clause,[],[f574]) ).
tff(f3038,plain,
( spl86_152
| ~ spl86_7
| ~ spl86_22 ),
inference(avatar_split_clause,[],[f567,f560,f481,f3036]) ).
tff(f3036,plain,
( spl86_152
<=> ! [X0: fun(product_prod(bool,bool),bool),X1: fun(bool,bool)] :
( ( fTrue != sK17(bool,X0,X1) )
| total_on(bool,X1,X0)
| ( fFalse = sK18(bool,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_152])]) ).
tff(f560,plain,
( spl86_22
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ( sK17(X0,X1,X2) != sK18(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_22])]) ).
tff(f567,plain,
( ! [X0: fun(product_prod(bool,bool),bool),X1: fun(bool,bool)] :
( ( fTrue != sK17(bool,X0,X1) )
| total_on(bool,X1,X0)
| ( fFalse = sK18(bool,X0,X1) ) )
| ~ spl86_7
| ~ spl86_22 ),
inference(superposition,[],[f561,f482]) ).
tff(f561,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ( sK17(X0,X1,X2) != sK18(X0,X1,X2) )
| total_on(X0,X2,X1) )
| ~ spl86_22 ),
inference(avatar_component_clause,[],[f560]) ).
tff(f3000,plain,
( spl86_151
| ~ spl86_42
| ~ spl86_58 ),
inference(avatar_split_clause,[],[f795,f786,f681,f2998]) ).
tff(f2998,plain,
( spl86_151
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( product_prod_rec(X1,X0,product_prod(X1,X0),product_Pair(X1,X0),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_151])]) ).
tff(f795,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( product_prod_rec(X1,X0,product_prod(X1,X0),product_Pair(X1,X0),X2) = X2 )
| ~ spl86_42
| ~ spl86_58 ),
inference(superposition,[],[f787,f682]) ).
tff(f2996,plain,
( spl86_150
| ~ spl86_9
| ~ spl86_32 ),
inference(avatar_split_clause,[],[f625,f620,f492,f2993]) ).
tff(f2993,plain,
( spl86_150
<=> ( arrow_1985332922le_Lin = order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_150])]) ).
tff(f492,plain,
( spl86_9
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_9])]) ).
tff(f625,plain,
( ( arrow_1985332922le_Lin = order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue)) )
| ~ spl86_9
| ~ spl86_32 ),
inference(superposition,[],[f622,f493]) ).
tff(f493,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 )
| ~ spl86_9 ),
inference(avatar_component_clause,[],[f492]) ).
tff(f2991,plain,
( spl86_149
| ~ spl86_12
| ~ spl86_29 ),
inference(avatar_split_clause,[],[f606,f603,f505,f2989]) ).
tff(f2989,plain,
( spl86_149
<=> ! [X0: $tType,X2: fun(product_prod(X0,X0),bool),X1: fun(X0,bool)] :
( total_on(X0,X1,X2)
| ~ member(fun(product_prod(X0,X0),bool),X2,order_215145569der_on(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_149])]) ).
tff(f603,plain,
( spl86_29
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_29])]) ).
tff(f606,plain,
( ! [X0: $tType,X2: fun(product_prod(X0,X0),bool),X1: fun(X0,bool)] :
( total_on(X0,X1,X2)
| ~ member(fun(product_prod(X0,X0),bool),X2,order_215145569der_on(X0,X1)) )
| ~ spl86_12
| ~ spl86_29 ),
inference(resolution,[],[f604,f506]) ).
tff(f604,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| total_on(X0,X2,X1) )
| ~ spl86_29 ),
inference(avatar_component_clause,[],[f603]) ).
tff(f2987,plain,
( spl86_3
| spl86_148
| ~ spl86_15
| ~ spl86_100
| ~ spl86_143 ),
inference(avatar_split_clause,[],[f2969,f2939,f1278,f517,f2985,f461]) ).
tff(f461,plain,
( spl86_3
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_3])]) ).
tff(f2985,plain,
( spl86_148
<=> ! [X1: bool] :
( ~ pp(X1)
| ( fTrue = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_148])]) ).
tff(f1278,plain,
( spl86_100
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,bool),X4: fun(X0,fun(X2,X1)),X3: product_prod(X0,X2)] :
( ~ pp(aa(X1,bool,X5,product_prod_rec(X0,X2,X1,X4,X3)))
| pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_100])]) ).
tff(f2939,plain,
( spl86_143
<=> ! [X0: $tType,X2: X0,X1: bool] :
( ( fTrue = X1 )
| ( fFalse = aa(X0,bool,combk(bool,X0,X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_143])]) ).
tff(f2969,plain,
( ! [X1: bool] :
( ~ pp(X1)
| pp(fFalse)
| ( fTrue = X1 ) )
| ~ spl86_15
| ~ spl86_100
| ~ spl86_143 ),
inference(forward_demodulation,[],[f2957,f518]) ).
tff(f2957,plain,
( ! [X0: $tType,X3: $tType,X2: $tType,X1: bool,X4: fun(X3,fun(X2,X0)),X5: product_prod(X3,X2)] :
( pp(fFalse)
| ~ pp(aa(X0,bool,combk(bool,X0,X1),product_prod_rec(X3,X2,X0,X4,X5)))
| ( fTrue = X1 ) )
| ~ spl86_100
| ~ spl86_143 ),
inference(superposition,[],[f1279,f2940]) ).
tff(f2940,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( ( fFalse = aa(X0,bool,combk(bool,X0,X1),X2) )
| ( fTrue = X1 ) )
| ~ spl86_143 ),
inference(avatar_component_clause,[],[f2939]) ).
tff(f1279,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5))))
| ~ pp(aa(X1,bool,X5,product_prod_rec(X0,X2,X1,X4,X3))) )
| ~ spl86_100 ),
inference(avatar_component_clause,[],[f1278]) ).
tff(f2983,plain,
( spl86_147
| ~ spl86_7
| ~ spl86_18 ),
inference(avatar_split_clause,[],[f540,f536,f481,f2981]) ).
tff(f2981,plain,
( spl86_147
<=> ! [X0: fun(product_prod(bool,bool),bool),X1: fun(bool,bool)] :
( member(bool,fTrue,X1)
| total_on(bool,X1,X0)
| ( fFalse = sK18(bool,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_147])]) ).
tff(f536,plain,
( spl86_18
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| member(X0,sK18(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_18])]) ).
tff(f540,plain,
( ! [X0: fun(product_prod(bool,bool),bool),X1: fun(bool,bool)] :
( member(bool,fTrue,X1)
| total_on(bool,X1,X0)
| ( fFalse = sK18(bool,X0,X1) ) )
| ~ spl86_7
| ~ spl86_18 ),
inference(superposition,[],[f537,f482]) ).
tff(f537,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( member(X0,sK18(X0,X1,X2),X2)
| total_on(X0,X2,X1) )
| ~ spl86_18 ),
inference(avatar_component_clause,[],[f536]) ).
tff(f2979,plain,
( spl86_146
| ~ spl86_7
| ~ spl86_17 ),
inference(avatar_split_clause,[],[f539,f532,f481,f2977]) ).
tff(f2977,plain,
( spl86_146
<=> ! [X0: fun(product_prod(bool,bool),bool),X1: fun(bool,bool)] :
( member(bool,fTrue,X1)
| total_on(bool,X1,X0)
| ( fFalse = sK17(bool,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_146])]) ).
tff(f539,plain,
( ! [X0: fun(product_prod(bool,bool),bool),X1: fun(bool,bool)] :
( member(bool,fTrue,X1)
| total_on(bool,X1,X0)
| ( fFalse = sK17(bool,X0,X1) ) )
| ~ spl86_7
| ~ spl86_17 ),
inference(superposition,[],[f533,f482]) ).
tff(f2949,plain,
( spl86_145
| ~ spl86_12
| ~ spl86_27 ),
inference(avatar_split_clause,[],[f599,f589,f505,f2947]) ).
tff(f2947,plain,
( spl86_145
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| ~ member(fun(product_prod(X0,X0),bool),X1,order_215145569der_on(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_145])]) ).
tff(f589,plain,
( spl86_27
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_27])]) ).
tff(f599,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| ~ member(fun(product_prod(X0,X0),bool),X1,order_215145569der_on(X0,X2)) )
| ~ spl86_12
| ~ spl86_27 ),
inference(resolution,[],[f590,f506]) ).
tff(f590,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| irrefl(X0,X1) )
| ~ spl86_27 ),
inference(avatar_component_clause,[],[f589]) ).
tff(f2945,plain,
( spl86_144
| ~ spl86_12
| ~ spl86_26 ),
inference(avatar_split_clause,[],[f596,f585,f505,f2943]) ).
tff(f2943,plain,
( spl86_144
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ member(fun(product_prod(X0,X0),bool),X1,order_215145569der_on(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_144])]) ).
tff(f585,plain,
( spl86_26
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_26])]) ).
tff(f596,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ member(fun(product_prod(X0,X0),bool),X1,order_215145569der_on(X0,X2)) )
| ~ spl86_12
| ~ spl86_26 ),
inference(resolution,[],[f586,f506]) ).
tff(f586,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| trans(X0,X1) )
| ~ spl86_26 ),
inference(avatar_component_clause,[],[f585]) ).
tff(f2941,plain,
( spl86_143
| ~ spl86_7
| ~ spl86_15 ),
inference(avatar_split_clause,[],[f528,f517,f481,f2939]) ).
tff(f528,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( ( fTrue = X1 )
| ( fFalse = aa(X0,bool,combk(bool,X0,X1),X2) ) )
| ~ spl86_7
| ~ spl86_15 ),
inference(superposition,[],[f518,f482]) ).
tff(f2795,plain,
spl86_142,
inference(avatar_split_clause,[],[f422,f2793]) ).
tff(f2793,plain,
( spl86_142
<=> ! [X1: $tType,X3: $tType,X0: $tType,X2: $tType,X4: $tType,X5: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),sK74(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),aa(X1,fun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),sK75(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),aa(X2,fun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),sK76(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),aa(X3,fun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),sK77(X0,X1,X2,X3,X4,X5,X6)),aa(X5,product_prod(X4,X5),aa(X4,fun(X5,product_prod(X4,X5)),product_Pair(X4,X5),sK78(X0,X1,X2,X3,X4,X5,X6)),sK79(X0,X1,X2,X3,X4,X5,X6)))))) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_142])]) ).
tff(f422,plain,
! [X5: $tType,X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),sK74(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),aa(X1,fun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),sK75(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),aa(X2,fun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),sK76(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),aa(X3,fun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),sK77(X0,X1,X2,X3,X4,X5,X6)),aa(X5,product_prod(X4,X5),aa(X4,fun(X5,product_prod(X4,X5)),product_Pair(X4,X5),sK78(X0,X1,X2,X3,X4,X5,X6)),sK79(X0,X1,X2,X3,X4,X5,X6)))))) = X6 ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),sK74(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),aa(X1,fun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),sK75(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),aa(X2,fun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),sK76(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),aa(X3,fun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),sK77(X0,X1,X2,X3,X4,X5,X6)),aa(X5,product_prod(X4,X5),aa(X4,fun(X5,product_prod(X4,X5)),product_Pair(X4,X5),sK78(X0,X1,X2,X3,X4,X5,X6)),sK79(X0,X1,X2,X3,X4,X5,X6)))))) = X6 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75,sK76,sK77,sK78,sK79])],[f205,f297]) ).
tff(f297,plain,
! [X5: $tType,X4: $tType,X3: $tType,X2: $tType,X1: $tType,X0: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] :
( ? [X7: X0,X8: X1,X9: X2,X10: X3,X11: X4,X12: X5] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X7),aa(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),aa(X1,fun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),X8),aa(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),aa(X2,fun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),X9),aa(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),aa(X3,fun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),X10),aa(X5,product_prod(X4,X5),aa(X4,fun(X5,product_prod(X4,X5)),product_Pair(X4,X5),X11),X12))))) = X6 )
=> ( aa(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),sK74(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),aa(X1,fun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),sK75(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),aa(X2,fun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),sK76(X0,X1,X2,X3,X4,X5,X6)),aa(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),aa(X3,fun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),sK77(X0,X1,X2,X3,X4,X5,X6)),aa(X5,product_prod(X4,X5),aa(X4,fun(X5,product_prod(X4,X5)),product_Pair(X4,X5),sK78(X0,X1,X2,X3,X4,X5,X6)),sK79(X0,X1,X2,X3,X4,X5,X6)))))) = X6 ) ),
introduced(choice_axiom,[]) ).
tff(f205,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] :
? [X7: X0,X8: X1,X9: X2,X10: X3,X11: X4,X12: X5] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X7),aa(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),aa(X1,fun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),X8),aa(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),aa(X2,fun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),X9),aa(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),aa(X3,fun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),X10),aa(X5,product_prod(X4,X5),aa(X4,fun(X5,product_prod(X4,X5)),product_Pair(X4,X5),X11),X12))))) = X6 ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] :
~ ! [X7: X0,X8: X1,X9: X2,X10: X3,X11: X4,X12: X5] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X7),aa(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),aa(X1,fun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),X8),aa(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),aa(X2,fun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),X9),aa(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),aa(X3,fun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),X10),aa(X5,product_prod(X4,X5),aa(X4,fun(X5,product_prod(X4,X5)),product_Pair(X4,X5),X11),X12))))) != X6 ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X4: $tType,X37: $tType,X39: $tType,X32: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))))] :
~ ! [X33: X0,X34: X1,X35: X2,X36: X4,X38: X37,X40: X39] : ( aa(product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),X33),aa(product_prod(X2,product_prod(X4,product_prod(X37,X39))),product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))),aa(X1,fun(product_prod(X2,product_prod(X4,product_prod(X37,X39))),product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),product_Pair(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))),X34),aa(product_prod(X4,product_prod(X37,X39)),product_prod(X2,product_prod(X4,product_prod(X37,X39))),aa(X2,fun(product_prod(X4,product_prod(X37,X39)),product_prod(X2,product_prod(X4,product_prod(X37,X39)))),product_Pair(X2,product_prod(X4,product_prod(X37,X39))),X35),aa(product_prod(X37,X39),product_prod(X4,product_prod(X37,X39)),aa(X4,fun(product_prod(X37,X39),product_prod(X4,product_prod(X37,X39))),product_Pair(X4,product_prod(X37,X39)),X36),aa(X39,product_prod(X37,X39),aa(X37,fun(X39,product_prod(X37,X39)),product_Pair(X37,X39),X38),X40))))) != X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_prod__cases6) ).
tff(f2708,plain,
spl86_141,
inference(avatar_split_clause,[],[f413,f2706]) ).
tff(f2706,plain,
( spl86_141
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: $tType,X3: $tType,X5: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),sK62(X0,X1,X2,X3,X4,X5)),aa(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),aa(X1,fun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),sK63(X0,X1,X2,X3,X4,X5)),aa(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),aa(X2,fun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),sK64(X0,X1,X2,X3,X4,X5)),aa(X4,product_prod(X3,X4),aa(X3,fun(X4,product_prod(X3,X4)),product_Pair(X3,X4),sK65(X0,X1,X2,X3,X4,X5)),sK66(X0,X1,X2,X3,X4,X5))))) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_141])]) ).
tff(f413,plain,
! [X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X5: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),sK62(X0,X1,X2,X3,X4,X5)),aa(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),aa(X1,fun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),sK63(X0,X1,X2,X3,X4,X5)),aa(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),aa(X2,fun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),sK64(X0,X1,X2,X3,X4,X5)),aa(X4,product_prod(X3,X4),aa(X3,fun(X4,product_prod(X3,X4)),product_Pair(X3,X4),sK65(X0,X1,X2,X3,X4,X5)),sK66(X0,X1,X2,X3,X4,X5))))) = X5 ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),sK62(X0,X1,X2,X3,X4,X5)),aa(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),aa(X1,fun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),sK63(X0,X1,X2,X3,X4,X5)),aa(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),aa(X2,fun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),sK64(X0,X1,X2,X3,X4,X5)),aa(X4,product_prod(X3,X4),aa(X3,fun(X4,product_prod(X3,X4)),product_Pair(X3,X4),sK65(X0,X1,X2,X3,X4,X5)),sK66(X0,X1,X2,X3,X4,X5))))) = X5 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63,sK64,sK65,sK66])],[f199,f291]) ).
tff(f291,plain,
! [X4: $tType,X3: $tType,X2: $tType,X1: $tType,X0: $tType,X5: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] :
( ? [X6: X0,X7: X1,X8: X2,X9: X3,X10: X4] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X6),aa(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),aa(X1,fun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),X7),aa(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),aa(X2,fun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),X8),aa(X4,product_prod(X3,X4),aa(X3,fun(X4,product_prod(X3,X4)),product_Pair(X3,X4),X9),X10)))) = X5 )
=> ( aa(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),sK62(X0,X1,X2,X3,X4,X5)),aa(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),aa(X1,fun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),sK63(X0,X1,X2,X3,X4,X5)),aa(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),aa(X2,fun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),sK64(X0,X1,X2,X3,X4,X5)),aa(X4,product_prod(X3,X4),aa(X3,fun(X4,product_prod(X3,X4)),product_Pair(X3,X4),sK65(X0,X1,X2,X3,X4,X5)),sK66(X0,X1,X2,X3,X4,X5))))) = X5 ) ),
introduced(choice_axiom,[]) ).
tff(f199,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] :
? [X6: X0,X7: X1,X8: X2,X9: X3,X10: X4] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X6),aa(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),aa(X1,fun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),X7),aa(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),aa(X2,fun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),X8),aa(X4,product_prod(X3,X4),aa(X3,fun(X4,product_prod(X3,X4)),product_Pair(X3,X4),X9),X10)))) = X5 ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] :
~ ! [X6: X0,X7: X1,X8: X2,X9: X3,X10: X4] : ( aa(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X6),aa(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),aa(X1,fun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),X7),aa(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),aa(X2,fun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),X8),aa(X4,product_prod(X3,X4),aa(X3,fun(X4,product_prod(X3,X4)),product_Pair(X3,X4),X9),X10)))) != X5 ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X4: $tType,X37: $tType,X32: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37))))] :
~ ! [X33: X0,X34: X1,X35: X2,X36: X4,X38: X37] : ( aa(product_prod(X1,product_prod(X2,product_prod(X4,X37))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X4,X37))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37)))),X33),aa(product_prod(X2,product_prod(X4,X37)),product_prod(X1,product_prod(X2,product_prod(X4,X37))),aa(X1,fun(product_prod(X2,product_prod(X4,X37)),product_prod(X1,product_prod(X2,product_prod(X4,X37)))),product_Pair(X1,product_prod(X2,product_prod(X4,X37))),X34),aa(product_prod(X4,X37),product_prod(X2,product_prod(X4,X37)),aa(X2,fun(product_prod(X4,X37),product_prod(X2,product_prod(X4,X37))),product_Pair(X2,product_prod(X4,X37)),X35),aa(X37,product_prod(X4,X37),aa(X4,fun(X37,product_prod(X4,X37)),product_Pair(X4,X37),X36),X38)))) != X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_prod__cases5) ).
tff(f2665,plain,
spl86_140,
inference(avatar_split_clause,[],[f450,f2663]) ).
tff(f2663,plain,
( spl86_140
<=> ! [X1: $tType,X3: $tType,X5: $tType,X0: $tType,X4: $tType,X2: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),product_curry(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X7),sK80(X0,X1,X2,X3,X4,X5,X7))),sK81(X0,X1,X2,X3,X4,X5,X7))),sK82(X0,X1,X2,X3,X4,X5,X7))),sK83(X0,X1,X2,X3,X4,X5,X7))),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7)))
| pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_140])]) ).
tff(f450,plain,
! [X5: $tType,X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),product_curry(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X7),sK80(X0,X1,X2,X3,X4,X5,X7))),sK81(X0,X1,X2,X3,X4,X5,X7))),sK82(X0,X1,X2,X3,X4,X5,X7))),sK83(X0,X1,X2,X3,X4,X5,X7))),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7)))
| pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6)) ),
inference(forward_demodulation,[],[f449,f386]) ).
tff(f386,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X1,X5: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X5),X4),X3) = aa(product_prod(X1,X2),X0,X5,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X3)) ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X1,X5: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X5),X4),X3) = aa(product_prod(X1,X2),X0,X5,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X3)) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X14: X2,X15: X1,X43: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X43),X15),X14) = aa(product_prod(X1,X2),X0,X43,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_curry__conv) ).
tff(f449,plain,
! [X5: $tType,X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( ~ pp(aa(product_prod(X1,X0),bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),product_curry(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X7),sK80(X0,X1,X2,X3,X4,X5,X7))),sK81(X0,X1,X2,X3,X4,X5,X7))),sK82(X0,X1,X2,X3,X4,X5,X7))),sK83(X0,X1,X2,X3,X4,X5,X7)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7))))
| pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6)) ),
inference(forward_demodulation,[],[f448,f386]) ).
tff(f448,plain,
! [X5: $tType,X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),product_curry(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X7),sK80(X0,X1,X2,X3,X4,X5,X7))),sK81(X0,X1,X2,X3,X4,X5,X7))),sK82(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK83(X0,X1,X2,X3,X4,X5,X7)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7)))))
| pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6)) ),
inference(forward_demodulation,[],[f447,f386]) ).
tff(f447,plain,
! [X5: $tType,X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( ~ pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),product_curry(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X7),sK80(X0,X1,X2,X3,X4,X5,X7))),sK81(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK82(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK83(X0,X1,X2,X3,X4,X5,X7)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7))))))
| pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6)) ),
inference(forward_demodulation,[],[f446,f386]) ).
tff(f446,plain,
! [X5: $tType,X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( ~ pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),product_curry(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X7),sK80(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),sK81(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK82(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK83(X0,X1,X2,X3,X4,X5,X7)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7)))))))
| pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6)) ),
inference(forward_demodulation,[],[f423,f386]) ).
tff(f423,plain,
! [X5: $tType,X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6))
| ~ pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),sK80(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),sK81(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK82(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK83(X0,X1,X2,X3,X4,X5,X7)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7)))))))) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6))
| ~ pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),sK80(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),sK81(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK82(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK83(X0,X1,X2,X3,X4,X5,X7)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7)))))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81,sK82,sK83,sK84,sK85])],[f206,f299]) ).
tff(f299,plain,
! [X5: $tType,X4: $tType,X3: $tType,X2: $tType,X1: $tType,X0: $tType,X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( ? [X8: X5,X9: X4,X10: X3,X11: X2,X12: X1,X13: X0] : ~ pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X8),aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X9),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X10),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X11),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X12),X13)))))))
=> ~ pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),sK80(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),sK81(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK82(X0,X1,X2,X3,X4,X5,X7)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK83(X0,X1,X2,X3,X4,X5,X7)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK84(X0,X1,X2,X3,X4,X5,X7)),sK85(X0,X1,X2,X3,X4,X5,X7)))))))) ),
introduced(choice_axiom,[]) ).
tff(f206,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6))
| ? [X8: X5,X9: X4,X10: X3,X11: X2,X12: X1,X13: X0] : ~ pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X8),aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X9),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X10),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X11),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X12),X13))))))) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X7: fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool)] :
( ! [X8: X5,X9: X4,X10: X3,X11: X2,X12: X1,X13: X0] : pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),aa(X5,fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X8),aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X9),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X10),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X11),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X12),X13)))))))
=> pp(aa(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool,X7,X6)) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X39: $tType,X37: $tType,X4: $tType,X2: $tType,X1: $tType,X0: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),X8: fun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),bool)] :
( ! [X33: X0,X34: X1,X35: X2,X36: X4,X38: X37,X40: X39] : pp(aa(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),bool,X8,aa(product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),X33),aa(product_prod(X2,product_prod(X4,product_prod(X37,X39))),product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))),aa(X1,fun(product_prod(X2,product_prod(X4,product_prod(X37,X39))),product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),product_Pair(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39)))),X34),aa(product_prod(X4,product_prod(X37,X39)),product_prod(X2,product_prod(X4,product_prod(X37,X39))),aa(X2,fun(product_prod(X4,product_prod(X37,X39)),product_prod(X2,product_prod(X4,product_prod(X37,X39)))),product_Pair(X2,product_prod(X4,product_prod(X37,X39))),X35),aa(product_prod(X37,X39),product_prod(X4,product_prod(X37,X39)),aa(X4,fun(product_prod(X37,X39),product_prod(X4,product_prod(X37,X39))),product_Pair(X4,product_prod(X37,X39)),X36),aa(X39,product_prod(X37,X39),aa(X37,fun(X39,product_prod(X37,X39)),product_Pair(X37,X39),X38),X40)))))))
=> pp(aa(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,product_prod(X37,X39))))),bool,X8,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_prod__induct6) ).
tff(f2627,plain,
spl86_139,
inference(avatar_split_clause,[],[f425,f2625]) ).
tff(f2625,plain,
( spl86_139
<=> ! [X1: $tType,X0: $tType,X5: X0,X3: fun(product_prod(X0,X0),bool),X4: X1,X7: X0,X6: X1,X2: fun(product_prod(X1,X1),bool)] :
( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_139])]) ).
tff(f425,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
( ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ( ( ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| ( X5 != X7 ) )
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) )
& ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
& ( X5 = X7 ) )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ) ),
inference(flattening,[],[f301]) ).
tff(f301,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
( ( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ( ( ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| ( X5 != X7 ) )
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) )
& ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
& ( X5 = X7 ) )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ) ),
inference(nnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X4: X1,X5: X0,X6: X1,X7: X0] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
<=> ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
& ( X5 = X7 ) )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType,X1: $tType,X31: fun(product_prod(X1,X1),bool),X16: fun(product_prod(X0,X0),bool),X12: X1,X13: X0,X14: X1,X15: X0] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X15),X14)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X13),X12)),lex_prod(X0,X1,X16,X31))
<=> ( ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X14),X12),X31)
& ( X13 = X15 ) )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X15),X13),X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_in__lex__prod) ).
tff(f2589,plain,
( spl86_138
| spl86_3
| ~ spl86_104 ),
inference(avatar_split_clause,[],[f2106,f1434,f461,f2587]) ).
tff(f2587,plain,
( spl86_138
<=> ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ( X0 = X1 )
| ( fFalse = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_138])]) ).
tff(f1434,plain,
( spl86_104
<=> ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fFalse = X1 )
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_104])]) ).
tff(f2106,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(X0)
| ( X0 = X1 )
| ( fFalse = X1 ) )
| spl86_3
| ~ spl86_104 ),
inference(superposition,[],[f463,f1435]) ).
tff(f1435,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fFalse = X1 )
| ( fFalse = X0 ) )
| ~ spl86_104 ),
inference(avatar_component_clause,[],[f1434]) ).
tff(f463,plain,
( ~ pp(fFalse)
| spl86_3 ),
inference(avatar_component_clause,[],[f461]) ).
tff(f2585,plain,
spl86_137,
inference(avatar_split_clause,[],[f445,f2583]) ).
tff(f2583,plain,
( spl86_137
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: $tType,X3: $tType,X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool)] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X6),sK69(X0,X1,X2,X3,X4,X6))),sK70(X0,X1,X2,X3,X4,X6))),sK71(X0,X1,X2,X3,X4,X6))),sK72(X0,X1,X2,X3,X4,X6)),sK73(X0,X1,X2,X3,X4,X6)))
| pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_137])]) ).
tff(f445,plain,
! [X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X6),sK69(X0,X1,X2,X3,X4,X6))),sK70(X0,X1,X2,X3,X4,X6))),sK71(X0,X1,X2,X3,X4,X6))),sK72(X0,X1,X2,X3,X4,X6)),sK73(X0,X1,X2,X3,X4,X6)))
| pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5)) ),
inference(forward_demodulation,[],[f444,f386]) ).
tff(f444,plain,
! [X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] :
( ~ pp(aa(product_prod(X1,X0),bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X6),sK69(X0,X1,X2,X3,X4,X6))),sK70(X0,X1,X2,X3,X4,X6))),sK71(X0,X1,X2,X3,X4,X6)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK72(X0,X1,X2,X3,X4,X6)),sK73(X0,X1,X2,X3,X4,X6))))
| pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5)) ),
inference(forward_demodulation,[],[f443,f386]) ).
tff(f443,plain,
! [X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] :
( ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X6),sK69(X0,X1,X2,X3,X4,X6))),sK70(X0,X1,X2,X3,X4,X6)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK71(X0,X1,X2,X3,X4,X6)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK72(X0,X1,X2,X3,X4,X6)),sK73(X0,X1,X2,X3,X4,X6)))))
| pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5)) ),
inference(forward_demodulation,[],[f442,f386]) ).
tff(f442,plain,
! [X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] :
( ~ pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool),product_curry(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X6),sK69(X0,X1,X2,X3,X4,X6)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK70(X0,X1,X2,X3,X4,X6)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK71(X0,X1,X2,X3,X4,X6)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK72(X0,X1,X2,X3,X4,X6)),sK73(X0,X1,X2,X3,X4,X6))))))
| pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5)) ),
inference(forward_demodulation,[],[f421,f386]) ).
tff(f421,plain,
! [X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool),X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] :
( pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5))
| ~ pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),sK69(X0,X1,X2,X3,X4,X6)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK70(X0,X1,X2,X3,X4,X6)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK71(X0,X1,X2,X3,X4,X6)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK72(X0,X1,X2,X3,X4,X6)),sK73(X0,X1,X2,X3,X4,X6))))))) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool)] :
( pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5))
| ~ pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),sK69(X0,X1,X2,X3,X4,X6)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK70(X0,X1,X2,X3,X4,X6)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK71(X0,X1,X2,X3,X4,X6)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK72(X0,X1,X2,X3,X4,X6)),sK73(X0,X1,X2,X3,X4,X6))))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70,sK71,sK72,sK73])],[f204,f295]) ).
tff(f295,plain,
! [X4: $tType,X3: $tType,X2: $tType,X1: $tType,X0: $tType,X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool)] :
( ? [X7: X4,X8: X3,X9: X2,X10: X1,X11: X0] : ~ pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X7),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X8),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X9),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X10),X11))))))
=> ~ pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),sK69(X0,X1,X2,X3,X4,X6)),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK70(X0,X1,X2,X3,X4,X6)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK71(X0,X1,X2,X3,X4,X6)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK72(X0,X1,X2,X3,X4,X6)),sK73(X0,X1,X2,X3,X4,X6))))))) ),
introduced(choice_axiom,[]) ).
tff(f204,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool)] :
( pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5))
| ? [X7: X4,X8: X3,X9: X2,X10: X1,X11: X0] : ~ pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X7),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X8),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X9),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X10),X11)))))) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X6: fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool)] :
( ! [X7: X4,X8: X3,X9: X2,X10: X1,X11: X0] : pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),aa(X4,fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X7),aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X8),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X9),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X10),X11))))))
=> pp(aa(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool,X6,X5)) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X37: $tType,X4: $tType,X2: $tType,X1: $tType,X0: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37)))),X8: fun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37)))),bool)] :
( ! [X33: X0,X34: X1,X35: X2,X36: X4,X38: X37] : pp(aa(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37)))),bool,X8,aa(product_prod(X1,product_prod(X2,product_prod(X4,X37))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37)))),aa(X0,fun(product_prod(X1,product_prod(X2,product_prod(X4,X37))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37)))),X33),aa(product_prod(X2,product_prod(X4,X37)),product_prod(X1,product_prod(X2,product_prod(X4,X37))),aa(X1,fun(product_prod(X2,product_prod(X4,X37)),product_prod(X1,product_prod(X2,product_prod(X4,X37)))),product_Pair(X1,product_prod(X2,product_prod(X4,X37))),X34),aa(product_prod(X4,X37),product_prod(X2,product_prod(X4,X37)),aa(X2,fun(product_prod(X4,X37),product_prod(X2,product_prod(X4,X37))),product_Pair(X2,product_prod(X4,X37)),X35),aa(X37,product_prod(X4,X37),aa(X4,fun(X37,product_prod(X4,X37)),product_Pair(X4,X37),X36),X38))))))
=> pp(aa(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X4,X37)))),bool,X8,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_prod__induct5) ).
tff(f2519,plain,
spl86_136,
inference(avatar_split_clause,[],[f384,f2517]) ).
tff(f2517,plain,
( spl86_136
<=> ! [X1: $tType,X2: $tType,X3: $tType,X0: $tType,X4: product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ( aa(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),aa(X0,fun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),sK42(X0,X1,X2,X3,X4)),aa(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),aa(X1,fun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),sK43(X0,X1,X2,X3,X4)),aa(X3,product_prod(X2,X3),aa(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),sK44(X0,X1,X2,X3,X4)),sK45(X0,X1,X2,X3,X4)))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_136])]) ).
tff(f384,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X4: product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ( aa(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),aa(X0,fun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),sK42(X0,X1,X2,X3,X4)),aa(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),aa(X1,fun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),sK43(X0,X1,X2,X3,X4)),aa(X3,product_prod(X2,X3),aa(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),sK44(X0,X1,X2,X3,X4)),sK45(X0,X1,X2,X3,X4)))) = X4 ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ( aa(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),aa(X0,fun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),sK42(X0,X1,X2,X3,X4)),aa(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),aa(X1,fun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),sK43(X0,X1,X2,X3,X4)),aa(X3,product_prod(X2,X3),aa(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),sK44(X0,X1,X2,X3,X4)),sK45(X0,X1,X2,X3,X4)))) = X4 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43,sK44,sK45])],[f189,f272]) ).
tff(f272,plain,
! [X3: $tType,X2: $tType,X1: $tType,X0: $tType,X4: product_prod(X0,product_prod(X1,product_prod(X2,X3)))] :
( ? [X5: X0,X6: X1,X7: X2,X8: X3] : ( aa(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),aa(X0,fun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),aa(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),aa(X1,fun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),aa(X3,product_prod(X2,X3),aa(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) = X4 )
=> ( aa(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),aa(X0,fun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),sK42(X0,X1,X2,X3,X4)),aa(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),aa(X1,fun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),sK43(X0,X1,X2,X3,X4)),aa(X3,product_prod(X2,X3),aa(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),sK44(X0,X1,X2,X3,X4)),sK45(X0,X1,X2,X3,X4)))) = X4 ) ),
introduced(choice_axiom,[]) ).
tff(f189,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X0,product_prod(X1,product_prod(X2,X3)))] :
? [X5: X0,X6: X1,X7: X2,X8: X3] : ( aa(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),aa(X0,fun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),aa(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),aa(X1,fun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),aa(X3,product_prod(X2,X3),aa(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) = X4 ),
inference(ennf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X0,product_prod(X1,product_prod(X2,X3)))] :
~ ! [X5: X0,X6: X1,X7: X2,X8: X3] : ( aa(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),aa(X0,fun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),aa(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),aa(X1,fun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),aa(X3,product_prod(X2,X3),aa(X2,fun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) != X4 ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X4: $tType,X32: product_prod(X0,product_prod(X1,product_prod(X2,X4)))] :
~ ! [X33: X0,X34: X1,X35: X2,X36: X4] : ( aa(product_prod(X1,product_prod(X2,X4)),product_prod(X0,product_prod(X1,product_prod(X2,X4))),aa(X0,fun(product_prod(X1,product_prod(X2,X4)),product_prod(X0,product_prod(X1,product_prod(X2,X4)))),product_Pair(X0,product_prod(X1,product_prod(X2,X4))),X33),aa(product_prod(X2,X4),product_prod(X1,product_prod(X2,X4)),aa(X1,fun(product_prod(X2,X4),product_prod(X1,product_prod(X2,X4))),product_Pair(X1,product_prod(X2,X4)),X34),aa(X4,product_prod(X2,X4),aa(X2,fun(X4,product_prod(X2,X4)),product_Pair(X2,X4),X35),X36))) != X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_prod__cases4) ).
tff(f2485,plain,
spl86_135,
inference(avatar_split_clause,[],[f424,f2483]) ).
tff(f2483,plain,
( spl86_135
<=> ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X4: X1,X6: X1,X5: X0,X3: fun(product_prod(X0,X0),bool),X7: X0] :
( ( X5 = X7 )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_135])]) ).
tff(f424,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
( ( X5 = X7 )
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3)
| ~ member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2)) ),
inference(cnf_transformation,[],[f302]) ).
tff(f2414,plain,
spl86_134,
inference(avatar_split_clause,[],[f436,f2412]) ).
tff(f2412,plain,
( spl86_134
<=> ! [X1: $tType,X0: $tType,X6: X1,X4: X1,X7: X0,X3: fun(product_prod(X0,X0),bool),X2: fun(product_prod(X1,X1),bool)] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X4)),lex_prod(X0,X1,X3,X2))
| ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_134])]) ).
tff(f436,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X4)),lex_prod(X0,X1,X3,X2))
| ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2) ),
inference(equality_resolution,[],[f427]) ).
tff(f427,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),X6),X4),X2)
| ( X5 != X7 ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f2410,plain,
spl86_133,
inference(avatar_split_clause,[],[f426,f2408]) ).
tff(f2408,plain,
( spl86_133
<=> ! [X1: $tType,X0: $tType,X5: X0,X6: X1,X4: X1,X7: X0,X3: fun(product_prod(X0,X0),bool),X2: fun(product_prod(X1,X1),bool)] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_133])]) ).
tff(f426,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool),X6: X1,X7: X0,X4: X1,X5: X0] :
( member(product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1)),aa(product_prod(X0,X1),fun(product_prod(X0,X1),product_prod(product_prod(X0,X1),product_prod(X0,X1))),product_Pair(product_prod(X0,X1),product_prod(X0,X1)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X7),X6)),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4)),lex_prod(X0,X1,X3,X2))
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X7),X5),X3) ),
inference(cnf_transformation,[],[f302]) ).
tff(f1889,plain,
spl86_132,
inference(avatar_split_clause,[],[f434,f1887]) ).
tff(f1887,plain,
( spl86_132
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,fun(X1,X0)),X6: product_prod(X2,X1)] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X6) )
| ( aa(X1,X0,aa(X2,fun(X1,X0),X5,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) != aa(X1,X0,aa(X2,fun(X1,X0),X4,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_132])]) ).
tff(f434,plain,
! [X1: $tType,X0: $tType,X2: $tType,X6: product_prod(X2,X1),X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0))] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X6) )
| ( aa(X1,X0,aa(X2,fun(X1,X0),X5,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) != aa(X1,X0,aa(X2,fun(X1,X0),X4,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) ) ),
inference(equality_resolution,[],[f420]) ).
tff(f420,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X6: product_prod(X2,X1),X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0))] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X3) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) )
| ( X3 != X6 )
| ( aa(X1,X0,aa(X2,fun(X1,X0),X5,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) != aa(X1,X0,aa(X2,fun(X1,X0),X4,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0)),X6: product_prod(X2,X1)] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X3) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) )
| ( X3 != X6 )
| ( ( aa(X1,X0,aa(X2,fun(X1,X0),X5,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) != aa(X1,X0,aa(X2,fun(X1,X0),X4,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) )
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) = X6 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f203,f293]) ).
tff(f293,plain,
! [X2: $tType,X1: $tType,X0: $tType,X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0)),X6: product_prod(X2,X1)] :
( ? [X7: X2,X8: X1] :
( ( aa(X1,X0,aa(X2,fun(X1,X0),X5,X7),X8) != aa(X1,X0,aa(X2,fun(X1,X0),X4,X7),X8) )
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X7),X8) = X6 ) )
=> ( ( aa(X1,X0,aa(X2,fun(X1,X0),X5,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) != aa(X1,X0,aa(X2,fun(X1,X0),X4,sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) )
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) = X6 ) ) ),
introduced(choice_axiom,[]) ).
tff(f203,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0)),X6: product_prod(X2,X1)] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X3) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) )
| ( X3 != X6 )
| ? [X7: X2,X8: X1] :
( ( aa(X1,X0,aa(X2,fun(X1,X0),X5,X7),X8) != aa(X1,X0,aa(X2,fun(X1,X0),X4,X7),X8) )
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X7),X8) = X6 ) ) ),
inference(flattening,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0)),X6: product_prod(X2,X1)] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X3) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) )
| ( X3 != X6 )
| ? [X7: X2,X8: X1] :
( ( aa(X1,X0,aa(X2,fun(X1,X0),X5,X7),X8) != aa(X1,X0,aa(X2,fun(X1,X0),X4,X7),X8) )
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X7),X8) = X6 ) ) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0)),X6: product_prod(X2,X1)] :
( ! [X7: X2,X8: X1] :
( ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X7),X8) = X6 )
=> ( aa(X1,X0,aa(X2,fun(X1,X0),X5,X7),X8) = aa(X1,X0,aa(X2,fun(X1,X0),X4,X7),X8) ) )
=> ( ( X3 = X6 )
=> ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X3) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) ) ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X47: product_prod(X0,X1),X48: fun(X0,fun(X1,X2)),X43: fun(X0,fun(X1,X2)),X49: product_prod(X0,X1)] :
( ! [X21: X0,X22: X1] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X21),X22) = X49 )
=> ( aa(X1,X2,aa(X0,fun(X1,X2),X43,X21),X22) = aa(X1,X2,aa(X0,fun(X1,X2),X48,X21),X22) ) )
=> ( ( X47 = X49 )
=> ( aa(product_prod(X0,X1),X2,aa(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2),product_prod_case(X0,X1,X2),X43),X47) = aa(product_prod(X0,X1),X2,aa(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2),product_prod_case(X0,X1,X2),X48),X49) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_split__cong) ).
tff(f1876,plain,
spl86_131,
inference(avatar_split_clause,[],[f439,f1874]) ).
tff(f1874,plain,
( spl86_131
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X4: product_prod(X3,product_prod(X2,product_prod(X1,X0))),X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,X5),sK58(X0,X1,X2,X3,X5))),sK59(X0,X1,X2,X3,X5))),sK60(X0,X1,X2,X3,X5)),sK61(X0,X1,X2,X3,X5)))
| pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_131])]) ).
tff(f439,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X4: product_prod(X3,product_prod(X2,product_prod(X1,X0))),X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,X5),sK58(X0,X1,X2,X3,X5))),sK59(X0,X1,X2,X3,X5))),sK60(X0,X1,X2,X3,X5)),sK61(X0,X1,X2,X3,X5)))
| pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,X4)) ),
inference(forward_demodulation,[],[f438,f386]) ).
tff(f438,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X4: product_prod(X3,product_prod(X2,product_prod(X1,X0))),X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( ~ pp(aa(product_prod(X1,X0),bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,X5),sK58(X0,X1,X2,X3,X5))),sK59(X0,X1,X2,X3,X5)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK60(X0,X1,X2,X3,X5)),sK61(X0,X1,X2,X3,X5))))
| pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,X4)) ),
inference(forward_demodulation,[],[f437,f386]) ).
tff(f437,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X4: product_prod(X3,product_prod(X2,product_prod(X1,X0))),X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,aa(X3,fun(product_prod(X2,product_prod(X1,X0)),bool),product_curry(X3,product_prod(X2,product_prod(X1,X0)),bool,X5),sK58(X0,X1,X2,X3,X5)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK59(X0,X1,X2,X3,X5)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK60(X0,X1,X2,X3,X5)),sK61(X0,X1,X2,X3,X5)))))
| pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,X4)) ),
inference(forward_demodulation,[],[f407,f386]) ).
tff(f407,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X4: product_prod(X3,product_prod(X2,product_prod(X1,X0))),X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,X4))
| ~ pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK58(X0,X1,X2,X3,X5)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK59(X0,X1,X2,X3,X5)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK60(X0,X1,X2,X3,X5)),sK61(X0,X1,X2,X3,X5)))))) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X3,product_prod(X2,product_prod(X1,X0))),X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,X4))
| ~ pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK58(X0,X1,X2,X3,X5)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK59(X0,X1,X2,X3,X5)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK60(X0,X1,X2,X3,X5)),sK61(X0,X1,X2,X3,X5)))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60,sK61])],[f198,f286]) ).
tff(f286,plain,
! [X3: $tType,X2: $tType,X1: $tType,X0: $tType,X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( ? [X6: X3,X7: X2,X8: X1,X9: X0] : ~ pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X6),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X7),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X8),X9)))))
=> ~ pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),sK58(X0,X1,X2,X3,X5)),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK59(X0,X1,X2,X3,X5)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK60(X0,X1,X2,X3,X5)),sK61(X0,X1,X2,X3,X5)))))) ),
introduced(choice_axiom,[]) ).
tff(f198,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X3,product_prod(X2,product_prod(X1,X0))),X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,X4))
| ? [X6: X3,X7: X2,X8: X1,X9: X0] : ~ pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X6),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X7),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X8),X9))))) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X3,product_prod(X2,product_prod(X1,X0))),X5: fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool)] :
( ! [X6: X3,X7: X2,X8: X1,X9: X0] : pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,aa(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),aa(X3,fun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X6),aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X7),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X8),X9)))))
=> pp(aa(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool,X5,X4)) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X4: $tType,X2: $tType,X1: $tType,X0: $tType,X6: product_prod(X0,product_prod(X1,product_prod(X2,X4))),X8: fun(product_prod(X0,product_prod(X1,product_prod(X2,X4))),bool)] :
( ! [X33: X0,X34: X1,X35: X2,X36: X4] : pp(aa(product_prod(X0,product_prod(X1,product_prod(X2,X4))),bool,X8,aa(product_prod(X1,product_prod(X2,X4)),product_prod(X0,product_prod(X1,product_prod(X2,X4))),aa(X0,fun(product_prod(X1,product_prod(X2,X4)),product_prod(X0,product_prod(X1,product_prod(X2,X4)))),product_Pair(X0,product_prod(X1,product_prod(X2,X4))),X33),aa(product_prod(X2,X4),product_prod(X1,product_prod(X2,X4)),aa(X1,fun(product_prod(X2,X4),product_prod(X1,product_prod(X2,X4))),product_Pair(X1,product_prod(X2,X4)),X34),aa(X4,product_prod(X2,X4),aa(X2,fun(X4,product_prod(X2,X4)),product_Pair(X2,X4),X35),X36)))))
=> pp(aa(product_prod(X0,product_prod(X1,product_prod(X2,X4))),bool,X8,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_prod__induct4) ).
tff(f1737,plain,
spl86_130,
inference(avatar_split_clause,[],[f435,f1735]) ).
tff(f1735,plain,
( spl86_130
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,fun(X1,X0)),X6: product_prod(X2,X1)] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X6) )
| ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) = X6 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_130])]) ).
tff(f435,plain,
! [X1: $tType,X0: $tType,X2: $tType,X6: product_prod(X2,X1),X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0))] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X6) )
| ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) = X6 ) ),
inference(equality_resolution,[],[f419]) ).
tff(f419,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X6: product_prod(X2,X1),X4: fun(X2,fun(X1,X0)),X5: fun(X2,fun(X1,X0))] :
( ( aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X5),X3) = aa(product_prod(X2,X1),X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X4),X6) )
| ( X3 != X6 )
| ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK67(X0,X1,X2,X4,X5,X6)),sK68(X0,X1,X2,X4,X5,X6)) = X6 ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f1725,plain,
( spl86_129
| ~ spl86_68
| ~ spl86_128 ),
inference(avatar_split_clause,[],[f1721,f1717,f864,f1723]) ).
tff(f1723,plain,
( spl86_129
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: fun(product_prod(X2,product_prod(X1,X0)),bool),X3: product_prod(X2,product_prod(X1,X0))] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,X4),sK39(X0,X1,X2,X4))),sK40(X0,X1,X2,X4)),sK41(X0,X1,X2,X4)))
| pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_129])]) ).
tff(f1717,plain,
( spl86_128
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(product_prod(X2,product_prod(X1,X0)),bool),X3: product_prod(X2,product_prod(X1,X0))] :
( pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3))
| ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK39(X0,X1,X2,X4)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK40(X0,X1,X2,X4)),sK41(X0,X1,X2,X4))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_128])]) ).
tff(f1721,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)),X4: fun(product_prod(X2,product_prod(X1,X0)),bool)] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),product_curry(X1,X0,bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,X4),sK39(X0,X1,X2,X4))),sK40(X0,X1,X2,X4)),sK41(X0,X1,X2,X4)))
| pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3)) )
| ~ spl86_68
| ~ spl86_128 ),
inference(forward_demodulation,[],[f1720,f865]) ).
tff(f1720,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)),X4: fun(product_prod(X2,product_prod(X1,X0)),bool)] :
( ~ pp(aa(product_prod(X1,X0),bool,aa(X2,fun(product_prod(X1,X0),bool),product_curry(X2,product_prod(X1,X0),bool,X4),sK39(X0,X1,X2,X4)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK40(X0,X1,X2,X4)),sK41(X0,X1,X2,X4))))
| pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3)) )
| ~ spl86_68
| ~ spl86_128 ),
inference(forward_demodulation,[],[f1718,f865]) ).
tff(f1718,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)),X4: fun(product_prod(X2,product_prod(X1,X0)),bool)] :
( pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3))
| ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK39(X0,X1,X2,X4)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK40(X0,X1,X2,X4)),sK41(X0,X1,X2,X4))))) )
| ~ spl86_128 ),
inference(avatar_component_clause,[],[f1717]) ).
tff(f1719,plain,
spl86_128,
inference(avatar_split_clause,[],[f383,f1717]) ).
tff(f383,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)),X4: fun(product_prod(X2,product_prod(X1,X0)),bool)] :
( pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3))
| ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK39(X0,X1,X2,X4)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK40(X0,X1,X2,X4)),sK41(X0,X1,X2,X4))))) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)),X4: fun(product_prod(X2,product_prod(X1,X0)),bool)] :
( pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3))
| ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK39(X0,X1,X2,X4)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK40(X0,X1,X2,X4)),sK41(X0,X1,X2,X4))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40,sK41])],[f188,f270]) ).
tff(f270,plain,
! [X2: $tType,X1: $tType,X0: $tType,X4: fun(product_prod(X2,product_prod(X1,X0)),bool)] :
( ? [X5: X2,X6: X1,X7: X0] : ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7))))
=> ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),sK39(X0,X1,X2,X4)),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK40(X0,X1,X2,X4)),sK41(X0,X1,X2,X4))))) ),
introduced(choice_axiom,[]) ).
tff(f188,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)),X4: fun(product_prod(X2,product_prod(X1,X0)),bool)] :
( pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3))
| ? [X5: X2,X6: X1,X7: X0] : ~ pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)))) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)),X4: fun(product_prod(X2,product_prod(X1,X0)),bool)] :
( ! [X5: X2,X6: X1,X7: X0] : pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,aa(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),aa(X2,fun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7))))
=> pp(aa(product_prod(X2,product_prod(X1,X0)),bool,X4,X3)) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X6: product_prod(X0,product_prod(X1,X2)),X8: fun(product_prod(X0,product_prod(X1,X2)),bool)] :
( ! [X33: X0,X34: X1,X35: X2] : pp(aa(product_prod(X0,product_prod(X1,X2)),bool,X8,aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X33),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X34),X35))))
=> pp(aa(product_prod(X0,product_prod(X1,X2)),bool,X8,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prod__induct3) ).
tff(f1695,plain,
spl86_127,
inference(avatar_split_clause,[],[f337,f1693]) ).
tff(f1693,plain,
( spl86_127
<=> ! [X0: $tType,X6: X0,X7: X0,X5: X0,X1: fun(product_prod(X0,X0),bool)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ~ trans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_127])]) ).
tff(f337,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X6: X0,X7: X0,X5: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ~ trans(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( trans(X0,X1)
| ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK14(X0,X1)),sK16(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1)),sK16(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK14(X0,X1)),sK15(X0,X1)),X1) ) )
& ( ! [X5: X0,X6: X0,X7: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1) )
| ~ trans(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f234,f235]) ).
tff(f235,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
=> ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK14(X0,X1)),sK16(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1)),sK16(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK14(X0,X1)),sK15(X0,X1)),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f234,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( trans(X0,X1)
| ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) )
& ( ! [X5: X0,X6: X0,X7: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X7),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1) )
| ~ trans(X0,X1) ) ),
inference(rectify,[],[f233]) ).
tff(f233,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( trans(X0,X1)
| ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) )
& ( ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
| ~ trans(X0,X1) ) ),
inference(nnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
<=> ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
inference(flattening,[],[f165]) ).
tff(f165,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
<=> ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
inference(ennf_transformation,[],[f96]) ).
tff(f96,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
<=> ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1) ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType,X16: fun(product_prod(X0,X0),bool)] :
( trans(X0,X16)
<=> ! [X17: X0,X18: X0,X19: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X17),X18),X16)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X18),X19),X16)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X17),X19),X16) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_trans__def) ).
tff(f1691,plain,
( spl86_126
| ~ spl86_10
| ~ spl86_20
| ~ spl86_56 ),
inference(avatar_split_clause,[],[f779,f768,f549,f496,f1689]) ).
tff(f1689,plain,
( spl86_126
<=> ! [X0: $tType,X1: fun(X0,bool)] : total_on(X0,X1,combk(bool,product_prod(X0,X0),fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_126])]) ).
tff(f496,plain,
( spl86_10
<=> ! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_10])]) ).
tff(f768,plain,
( spl86_56
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK17(X0,X1,X2)),sK18(X0,X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_56])]) ).
tff(f779,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : total_on(X0,X1,combk(bool,product_prod(X0,X0),fTrue))
| ~ spl86_10
| ~ spl86_20
| ~ spl86_56 ),
inference(forward_demodulation,[],[f775,f550]) ).
tff(f775,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : total_on(X0,X1,top_top(fun(product_prod(X0,X0),bool)))
| ~ spl86_10
| ~ spl86_56 ),
inference(resolution,[],[f769,f497]) ).
tff(f497,plain,
( ! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool)))
| ~ spl86_10 ),
inference(avatar_component_clause,[],[f496]) ).
tff(f769,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK17(X0,X1,X2)),sK18(X0,X1,X2)),X1)
| total_on(X0,X2,X1) )
| ~ spl86_56 ),
inference(avatar_component_clause,[],[f768]) ).
tff(f1679,plain,
( spl86_125
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_124 ),
inference(avatar_split_clause,[],[f1675,f1672,f916,f786,f693,f681,f1677]) ).
tff(f1677,plain,
( spl86_125
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,product_prod_rec(X0,X1,fun(X2,bool),X4,X5),X3))
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_125])]) ).
tff(f1672,plain,
( spl86_124
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3))
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_124])]) ).
tff(f1675,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,product_prod_rec(X0,X1,fun(X2,bool),X4,X5),X3))
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)) = X5 ) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_124 ),
inference(forward_demodulation,[],[f1673,f974]) ).
tff(f1673,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3))
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)) = X5 ) )
| ~ spl86_124 ),
inference(avatar_component_clause,[],[f1672]) ).
tff(f1674,plain,
spl86_124,
inference(avatar_split_clause,[],[f405,f1672]) ).
tff(f405,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3))
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)) = X5 ) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3))
| ( ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)),X3))
& ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)) = X5 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57])],[f197,f284]) ).
tff(f284,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( ? [X6: X0,X7: X1] :
( ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,X6),X7),X3))
& ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7) = X5 ) )
=> ( ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)),X3))
& ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)) = X5 ) ) ),
introduced(choice_axiom,[]) ).
tff(f197,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3))
| ? [X6: X0,X7: X1] :
( ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,X6),X7),X3))
& ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7) = X5 ) ) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( ! [X6: X0,X7: X1] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7) = X5 )
=> pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,X6),X7),X3)) )
=> pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3)) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X6: X2,X20: fun(X0,fun(X1,fun(X2,bool))),X47: product_prod(X0,X1)] :
( ! [X33: X0,X34: X1] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X33),X34) = X47 )
=> pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X20,X33),X34),X6)) )
=> pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X20),X47),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_splitI2_H) ).
tff(f1664,plain,
( spl86_123
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_122 ),
inference(avatar_split_clause,[],[f1660,f1657,f916,f786,f693,f681,f1662]) ).
tff(f1662,plain,
( spl86_123
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ~ pp(aa(X2,bool,product_prod_rec(X1,X0,fun(X2,bool),X5,X4),X3))
| ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_123])]) ).
tff(f1657,plain,
( spl86_122
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)) = X4 )
| ~ pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_122])]) ).
tff(f1660,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ~ pp(aa(X2,bool,product_prod_rec(X1,X0,fun(X2,bool),X5,X4),X3))
| ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_122 ),
inference(forward_demodulation,[],[f1658,f974]) ).
tff(f1658,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)) = X4 )
| ~ pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3)) )
| ~ spl86_122 ),
inference(avatar_component_clause,[],[f1657]) ).
tff(f1659,plain,
spl86_122,
inference(avatar_split_clause,[],[f399,f1657]) ).
tff(f399,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)) = X4 )
| ~ pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3)) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ( pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)),X3))
& ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ~ pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53])],[f194,f280]) ).
tff(f280,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ? [X6: X1,X7: X0] :
( pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,X6),X7),X3))
& ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7) = X4 ) )
=> ( pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)),X3))
& ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f194,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ? [X6: X1,X7: X0] :
( pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,X6),X7),X3))
& ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7) = X4 ) )
| ~ pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3)) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3))
=> ~ ! [X6: X1,X7: X0] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7) = X4 )
=> ~ pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,X6),X7),X3)) ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X46: X2,X47: product_prod(X0,X1),X20: fun(X0,fun(X1,fun(X2,bool)))] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X20),X47),X46))
=> ~ ! [X21: X0,X22: X1] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X21),X22) = X47 )
=> ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X20,X21),X22),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_splitE_H) ).
tff(f1641,plain,
( spl86_121
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_120 ),
inference(avatar_split_clause,[],[f1637,f1634,f916,f786,f693,f681,f1639]) ).
tff(f1639,plain,
( spl86_121
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,product_prod_rec(X0,X1,fun(X2,bool),X4,X5),X3))
| ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_121])]) ).
tff(f1634,plain,
( spl86_120
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3))
| ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_120])]) ).
tff(f1637,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,product_prod_rec(X0,X1,fun(X2,bool),X4,X5),X3))
| ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)),X3)) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_120 ),
inference(forward_demodulation,[],[f1635,f974]) ).
tff(f1635,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3))
| ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)),X3)) )
| ~ spl86_120 ),
inference(avatar_component_clause,[],[f1634]) ).
tff(f1636,plain,
spl86_120,
inference(avatar_split_clause,[],[f406,f1634]) ).
tff(f406,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X0,fun(X1,fun(X2,bool))),X5: product_prod(X0,X1)] :
( pp(aa(X2,bool,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X4),X5),X3))
| ~ pp(aa(X2,bool,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X4,sK56(X0,X1,X2,X3,X4,X5)),sK57(X0,X1,X2,X3,X4,X5)),X3)) ),
inference(cnf_transformation,[],[f285]) ).
tff(f1617,plain,
( spl86_119
| ~ spl86_12
| ~ spl86_15 ),
inference(avatar_split_clause,[],[f530,f517,f505,f1615]) ).
tff(f530,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( pp(X1)
| ~ member(X0,X2,combk(bool,X0,X1)) )
| ~ spl86_12
| ~ spl86_15 ),
inference(superposition,[],[f506,f518]) ).
tff(f1613,plain,
( spl86_118
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_117 ),
inference(avatar_split_clause,[],[f1609,f1606,f916,f786,f693,f681,f1611]) ).
tff(f1611,plain,
( spl86_118
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ~ pp(aa(X2,bool,product_prod_rec(X1,X0,fun(X2,bool),X5,X4),X3))
| pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_118])]) ).
tff(f1606,plain,
( spl86_117
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)),X3))
| ~ pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_117])]) ).
tff(f1609,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( ~ pp(aa(X2,bool,product_prod_rec(X1,X0,fun(X2,bool),X5,X4),X3))
| pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)),X3)) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_117 ),
inference(forward_demodulation,[],[f1607,f974]) ).
tff(f1607,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)),X3))
| ~ pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3)) )
| ~ spl86_117 ),
inference(avatar_component_clause,[],[f1606]) ).
tff(f1608,plain,
spl86_117,
inference(avatar_split_clause,[],[f400,f1606]) ).
tff(f400,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: product_prod(X1,X0),X5: fun(X1,fun(X0,fun(X2,bool)))] :
( pp(aa(X2,bool,aa(X0,fun(X2,bool),aa(X1,fun(X0,fun(X2,bool)),X5,sK52(X0,X1,X2,X3,X4,X5)),sK53(X0,X1,X2,X3,X4,X5)),X3))
| ~ pp(aa(X2,bool,aa(product_prod(X1,X0),fun(X2,bool),aa(fun(X1,fun(X0,fun(X2,bool))),fun(product_prod(X1,X0),fun(X2,bool)),product_prod_case(X1,X0,fun(X2,bool)),X5),X4),X3)) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1593,plain,
( spl86_116
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_115 ),
inference(avatar_split_clause,[],[f1589,f1586,f916,f786,f693,f681,f1591]) ).
tff(f1591,plain,
( spl86_116
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,product_prod_rec(X2,X1,fun(X0,bool),X3,X5))
| ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_116])]) ).
tff(f1586,plain,
( spl86_115
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5))
| ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)) = X5 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_115])]) ).
tff(f1589,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,product_prod_rec(X2,X1,fun(X0,bool),X3,X5))
| ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)) = X5 ) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_115 ),
inference(forward_demodulation,[],[f1587,f974]) ).
tff(f1587,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5))
| ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)) = X5 ) )
| ~ spl86_115 ),
inference(avatar_component_clause,[],[f1586]) ).
tff(f1588,plain,
spl86_115,
inference(avatar_split_clause,[],[f403,f1586]) ).
tff(f403,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5))
| ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)) = X5 ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5))
| ( ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)))
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)) = X5 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f196,f282]) ).
tff(f282,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( ? [X6: X2,X7: X1] :
( ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,X6),X7))
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X6),X7) = X5 ) )
=> ( ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)))
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5)) = X5 ) ) ),
introduced(choice_axiom,[]) ).
tff(f196,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5))
| ? [X6: X2,X7: X1] :
( ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,X6),X7))
& ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X6),X7) = X5 ) ) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( ! [X6: X2,X7: X1] :
( ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X6),X7) = X5 )
=> member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,X6),X7)) )
=> member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5)) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X20: fun(X0,fun(X1,fun(X2,bool))),X46: X2,X47: product_prod(X0,X1)] :
( ! [X33: X0,X34: X1] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X33),X34) = X47 )
=> member(X2,X46,aa(X1,fun(X2,bool),aa(X0,fun(X1,fun(X2,bool)),X20,X33),X34)) )
=> member(X2,X46,aa(product_prod(X0,X1),fun(X2,bool),aa(fun(X0,fun(X1,fun(X2,bool))),fun(product_prod(X0,X1),fun(X2,bool)),product_prod_case(X0,X1,fun(X2,bool)),X20),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_mem__splitI2) ).
tff(f1574,plain,
( spl86_114
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_113 ),
inference(avatar_split_clause,[],[f1570,f1567,f916,f786,f693,f681,f1572]) ).
tff(f1572,plain,
( spl86_114
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: X1,X4: fun(X0,fun(X2,fun(X1,bool))),X3: product_prod(X0,X2)] :
( ~ member(X1,X5,product_prod_rec(X0,X2,fun(X1,bool),X4,X3))
| ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_114])]) ).
tff(f1567,plain,
( spl86_113
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)) = X3 )
| ~ member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_113])]) ).
tff(f1570,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( ~ member(X1,X5,product_prod_rec(X0,X2,fun(X1,bool),X4,X3))
| ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_113 ),
inference(forward_demodulation,[],[f1568,f974]) ).
tff(f1568,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)) = X3 )
| ~ member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3)) )
| ~ spl86_113 ),
inference(avatar_component_clause,[],[f1567]) ).
tff(f1569,plain,
spl86_113,
inference(avatar_split_clause,[],[f397,f1567]) ).
tff(f397,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)) = X3 )
| ~ member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3)) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( ( member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)))
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ~ member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51])],[f193,f278]) ).
tff(f278,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( ? [X6: X0,X7: X2] :
( member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,X6),X7))
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 ) )
=> ( member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)))
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
tff(f193,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( ? [X6: X0,X7: X2] :
( member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,X6),X7))
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 ) )
| ~ member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3)) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3))
=> ~ ! [X6: X0,X7: X2] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 )
=> ~ member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,X6),X7)) ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X47: product_prod(X1,X2),X20: fun(X1,fun(X2,fun(X0,bool))),X46: X0] :
( member(X0,X46,aa(product_prod(X1,X2),fun(X0,bool),aa(fun(X1,fun(X2,fun(X0,bool))),fun(product_prod(X1,X2),fun(X0,bool)),product_prod_case(X1,X2,fun(X0,bool)),X20),X47))
=> ~ ! [X21: X1,X22: X2] :
( ( aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X21),X22) = X47 )
=> ~ member(X0,X46,aa(X2,fun(X0,bool),aa(X1,fun(X2,fun(X0,bool)),X20,X21),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_mem__splitE) ).
tff(f1554,plain,
( spl86_112
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_110 ),
inference(avatar_split_clause,[],[f1546,f1543,f916,f786,f693,f681,f1552]) ).
tff(f1552,plain,
( spl86_112
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,product_prod_rec(X2,X1,fun(X0,bool),X3,X5))
| ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_112])]) ).
tff(f1543,plain,
( spl86_110
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5))
| ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_110])]) ).
tff(f1546,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,product_prod_rec(X2,X1,fun(X0,bool),X3,X5))
| ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5))) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_110 ),
inference(forward_demodulation,[],[f1544,f974]) ).
tff(f1544,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5))
| ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5))) )
| ~ spl86_110 ),
inference(avatar_component_clause,[],[f1543]) ).
tff(f1550,plain,
( spl86_111
| ~ spl86_13
| ~ spl86_15 ),
inference(avatar_split_clause,[],[f529,f517,f509,f1548]) ).
tff(f1548,plain,
( spl86_111
<=> ! [X0: $tType,X2: X0,X1: bool] :
( ~ pp(X1)
| member(X0,X2,combk(bool,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_111])]) ).
tff(f529,plain,
( ! [X0: $tType,X2: X0,X1: bool] :
( ~ pp(X1)
| member(X0,X2,combk(bool,X0,X1)) )
| ~ spl86_13
| ~ spl86_15 ),
inference(superposition,[],[f510,f518]) ).
tff(f1545,plain,
spl86_110,
inference(avatar_split_clause,[],[f404,f1543]) ).
tff(f404,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,fun(X0,bool))),X4: X0,X5: product_prod(X2,X1)] :
( member(X0,X4,aa(product_prod(X2,X1),fun(X0,bool),aa(fun(X2,fun(X1,fun(X0,bool))),fun(product_prod(X2,X1),fun(X0,bool)),product_prod_case(X2,X1,fun(X0,bool)),X3),X5))
| ~ member(X0,X4,aa(X1,fun(X0,bool),aa(X2,fun(X1,fun(X0,bool)),X3,sK54(X0,X1,X2,X3,X4,X5)),sK55(X0,X1,X2,X3,X4,X5))) ),
inference(cnf_transformation,[],[f283]) ).
tff(f1528,plain,
( spl86_109
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_108 ),
inference(avatar_split_clause,[],[f1524,f1521,f916,f786,f693,f681,f1526]) ).
tff(f1526,plain,
( spl86_109
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: X1,X4: fun(X0,fun(X2,fun(X1,bool))),X3: product_prod(X0,X2)] :
( ~ member(X1,X5,product_prod_rec(X0,X2,fun(X1,bool),X4,X3))
| member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_109])]) ).
tff(f1521,plain,
( spl86_108
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)))
| ~ member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_108])]) ).
tff(f1524,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( ~ member(X1,X5,product_prod_rec(X0,X2,fun(X1,bool),X4,X3))
| member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5))) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_108 ),
inference(forward_demodulation,[],[f1522,f974]) ).
tff(f1522,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)))
| ~ member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3)) )
| ~ spl86_108 ),
inference(avatar_component_clause,[],[f1521]) ).
tff(f1523,plain,
spl86_108,
inference(avatar_split_clause,[],[f398,f1521]) ).
tff(f398,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,fun(X1,bool))),X5: X1] :
( member(X1,X5,aa(X2,fun(X1,bool),aa(X0,fun(X2,fun(X1,bool)),X4,sK50(X0,X1,X2,X3,X4,X5)),sK51(X0,X1,X2,X3,X4,X5)))
| ~ member(X1,X5,aa(product_prod(X0,X2),fun(X1,bool),aa(fun(X0,fun(X2,fun(X1,bool))),fun(product_prod(X0,X2),fun(X1,bool)),product_prod_case(X0,X2,fun(X1,bool)),X4),X3)) ),
inference(cnf_transformation,[],[f279]) ).
tff(f1493,plain,
spl86_107,
inference(avatar_split_clause,[],[f374,f1491]) ).
tff(f1491,plain,
( spl86_107
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: product_prod(X0,product_prod(X1,X2))] : ( aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),sK36(X0,X1,X2,X3)),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_107])]) ).
tff(f374,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,product_prod(X1,X2))] : ( aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),sK36(X0,X1,X2,X3)),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) = X3 ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,product_prod(X1,X2))] : ( aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),sK36(X0,X1,X2,X3)),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) = X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37,sK38])],[f179,f268]) ).
tff(f268,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: product_prod(X0,product_prod(X1,X2))] :
( ? [X4: X0,X5: X1,X6: X2] : ( aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = X3 )
=> ( aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),sK36(X0,X1,X2,X3)),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sK37(X0,X1,X2,X3)),sK38(X0,X1,X2,X3))) = X3 ) ),
introduced(choice_axiom,[]) ).
tff(f179,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,product_prod(X1,X2))] :
? [X4: X0,X5: X1,X6: X2] : ( aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = X3 ),
inference(ennf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,product_prod(X1,X2))] :
~ ! [X4: X0,X5: X1,X6: X2] : ( aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) != X3 ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X32: product_prod(X0,product_prod(X1,X2))] :
~ ! [X33: X0,X34: X1,X35: X2] : ( aa(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),aa(X0,fun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X33),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X34),X35)) != X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod__cases3) ).
tff(f1478,plain,
( spl86_106
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_105 ),
inference(avatar_split_clause,[],[f1474,f1471,f916,f786,f693,f681,f1476]) ).
tff(f1476,plain,
( spl86_106
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,bool),X4: fun(X0,fun(X2,X1)),X3: product_prod(X0,X2)] :
( ~ pp(aa(X1,bool,X5,product_prod_rec(X0,X2,X1,X4,X3)))
| ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_106])]) ).
tff(f1471,plain,
( spl86_105
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)) = X3 )
| ~ pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_105])]) ).
tff(f1474,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( ~ pp(aa(X1,bool,X5,product_prod_rec(X0,X2,X1,X4,X3)))
| ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_105 ),
inference(forward_demodulation,[],[f1472,f974]) ).
tff(f1472,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)) = X3 )
| ~ pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3))) )
| ~ spl86_105 ),
inference(avatar_component_clause,[],[f1471]) ).
tff(f1473,plain,
spl86_105,
inference(avatar_split_clause,[],[f395,f1471]) ).
tff(f395,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)) = X3 )
| ~ pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3))) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( ( pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5))))
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ~ pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49])],[f192,f276]) ).
tff(f276,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( ? [X6: X0,X7: X2] :
( pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,X6),X7)))
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 ) )
=> ( pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5))))
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
tff(f192,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( ? [X6: X0,X7: X2] :
( pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,X6),X7)))
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 ) )
| ~ pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3))) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3)))
=> ~ ! [X6: X0,X7: X2] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 )
=> ~ pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,X6),X7))) ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X46: product_prod(X1,X2),X8: fun(X1,fun(X2,X0)),X50: fun(X0,bool)] :
( pp(aa(X0,bool,X50,aa(product_prod(X1,X2),X0,aa(fun(X1,fun(X2,X0)),fun(product_prod(X1,X2),X0),product_prod_case(X1,X2,X0),X8),X46)))
=> ~ ! [X21: X1,X22: X2] :
( ( aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X21),X22) = X46 )
=> ~ pp(aa(X0,bool,X50,aa(X2,X0,aa(X1,fun(X2,X0),X8,X21),X22))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_splitE2) ).
tff(f1436,plain,
( spl86_104
| ~ spl86_7 ),
inference(avatar_split_clause,[],[f488,f481,f1434]) ).
tff(f488,plain,
( ! [X0: bool,X1: bool] :
( ( X0 = X1 )
| ( fFalse = X1 )
| ( fFalse = X0 ) )
| ~ spl86_7 ),
inference(superposition,[],[f482,f482]) ).
tff(f1432,plain,
spl86_103,
inference(avatar_split_clause,[],[f344,f1430]) ).
tff(f1430,plain,
( spl86_103
<=> ! [X0: $tType,X5: X0,X2: fun(X0,bool),X6: X0,X1: fun(product_prod(X0,X0),bool)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2)
| ~ member(X0,X5,X2)
| ~ total_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_103])]) ).
tff(f344,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool),X6: X0,X5: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2)
| ~ member(X0,X5,X2)
| ~ total_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK18(X0,X1,X2)),sK17(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK17(X0,X1,X2)),sK18(X0,X1,X2)),X1)
& ( sK17(X0,X1,X2) != sK18(X0,X1,X2) )
& member(X0,sK18(X0,X1,X2),X2)
& member(X0,sK17(X0,X1,X2),X2) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2) )
| ~ member(X0,X5,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f239,f241,f240]) ).
tff(f240,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ? [X3: X0] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& ( X3 != X4 )
& member(X0,X4,X2) )
& member(X0,X3,X2) )
=> ( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),sK17(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK17(X0,X1,X2)),X4),X1)
& ( sK17(X0,X1,X2) != X4 )
& member(X0,X4,X2) )
& member(X0,sK17(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
tff(f241,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),sK17(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK17(X0,X1,X2)),X4),X1)
& ( sK17(X0,X1,X2) != X4 )
& member(X0,X4,X2) )
=> ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK18(X0,X1,X2)),sK17(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK17(X0,X1,X2)),sK18(X0,X1,X2)),X1)
& ( sK17(X0,X1,X2) != sK18(X0,X1,X2) )
& member(X0,sK18(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
tff(f239,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ? [X3: X0] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& ( X3 != X4 )
& member(X0,X4,X2) )
& member(X0,X3,X2) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2) )
| ~ member(X0,X5,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(rectify,[],[f238]) ).
tff(f238,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ? [X3: X0] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& ( X3 != X4 )
& member(X0,X4,X2) )
& member(X0,X3,X2) ) )
& ( ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) ) ),
inference(flattening,[],[f169]) ).
tff(f169,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) ) ),
inference(ennf_transformation,[],[f99]) ).
tff(f99,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( member(X0,X3,X2)
=> ! [X4: X0] :
( member(X0,X4,X2)
=> ( ( X3 != X4 )
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1) ) ) ) ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType,X16: fun(product_prod(X0,X0),bool),X44: fun(X0,bool)] :
( total_on(X0,X44,X16)
<=> ! [X17: X0] :
( member(X0,X17,X44)
=> ! [X45: X0] :
( member(X0,X45,X44)
=> ( ( X17 != X45 )
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X45),X17),X16)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X17),X45),X16) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_total__on__def) ).
tff(f1366,plain,
spl86_102,
inference(avatar_split_clause,[],[f409,f1364]) ).
tff(f1364,plain,
( spl86_102
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: X0,X3: fun(product_prod(X1,X1),bool),X2: fun(X0,X1)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X4),inv_image(X1,X0,X3,X2))
| ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),aa(X0,X1,X2,X5)),aa(X0,X1,X2,X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_102])]) ).
tff(f409,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(product_prod(X1,X1),bool),X4: X0,X5: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X4),inv_image(X1,X0,X3,X2))
| ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),aa(X0,X1,X2,X5)),aa(X0,X1,X2,X4)),X3) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,X1),X3: fun(product_prod(X1,X1),bool),X4: X0,X5: X0] :
( ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X4),inv_image(X1,X0,X3,X2))
| ~ member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),aa(X0,X1,X2,X5)),aa(X0,X1,X2,X4)),X3) )
& ( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),aa(X0,X1,X2,X5)),aa(X0,X1,X2,X4)),X3)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X4),inv_image(X1,X0,X3,X2)) ) ),
inference(nnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,X1),X3: fun(product_prod(X1,X1),bool),X4: X0,X5: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X4),inv_image(X1,X0,X3,X2))
<=> member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),aa(X0,X1,X2,X5)),aa(X0,X1,X2,X4)),X3) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X0: $tType,X1: $tType,X43: fun(X0,X1),X16: fun(product_prod(X1,X1),bool),X5: X0,X6: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),inv_image(X1,X0,X16,X43))
<=> member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),aa(X0,X1,X43,X6)),aa(X0,X1,X43,X5)),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_in__inv__image) ).
tff(f1362,plain,
spl86_101,
inference(avatar_split_clause,[],[f408,f1360]) ).
tff(f1360,plain,
( spl86_101
<=> ! [X1: $tType,X0: $tType,X5: X0,X4: X0,X3: fun(product_prod(X1,X1),bool),X2: fun(X0,X1)] :
( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),aa(X0,X1,X2,X5)),aa(X0,X1,X2,X4)),X3)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X4),inv_image(X1,X0,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_101])]) ).
tff(f408,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,X1),X3: fun(product_prod(X1,X1),bool),X4: X0,X5: X0] :
( member(product_prod(X1,X1),aa(X1,product_prod(X1,X1),aa(X1,fun(X1,product_prod(X1,X1)),product_Pair(X1,X1),aa(X0,X1,X2,X5)),aa(X0,X1,X2,X4)),X3)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X4),inv_image(X1,X0,X3,X2)) ),
inference(cnf_transformation,[],[f288]) ).
tff(f1280,plain,
( spl86_100
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_99 ),
inference(avatar_split_clause,[],[f1276,f1273,f916,f786,f693,f681,f1278]) ).
tff(f1273,plain,
( spl86_99
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5))))
| ~ pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_99])]) ).
tff(f1276,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( ~ pp(aa(X1,bool,X5,product_prod_rec(X0,X2,X1,X4,X3)))
| pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5)))) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_99 ),
inference(forward_demodulation,[],[f1274,f974]) ).
tff(f1274,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5))))
| ~ pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3))) )
| ~ spl86_99 ),
inference(avatar_component_clause,[],[f1273]) ).
tff(f1275,plain,
spl86_99,
inference(avatar_split_clause,[],[f396,f1273]) ).
tff(f396,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,fun(X2,X1)),X5: fun(X1,bool)] :
( pp(aa(X1,bool,X5,aa(X2,X1,aa(X0,fun(X2,X1),X4,sK48(X0,X1,X2,X3,X4,X5)),sK49(X0,X1,X2,X3,X4,X5))))
| ~ pp(aa(X1,bool,X5,aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X4),X3))) ),
inference(cnf_transformation,[],[f277]) ).
tff(f1270,plain,
spl86_98,
inference(avatar_split_clause,[],[f343,f1268]) ).
tff(f1268,plain,
( spl86_98
<=> ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_98])]) ).
tff(f343,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2) ) )
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(nnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) )
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(flattening,[],[f167]) ).
tff(f167,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) )
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(ennf_transformation,[],[f98]) ).
tff(f98,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
=> ( ( X0 != X1 )
=> ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) ) ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt,X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7,arrow_1985332922le_Lin)
=> ( ( X5 != 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),X6),X5),X7)
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X5),X6),X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_notin__Lin__iff) ).
tff(f1266,plain,
spl86_97,
inference(avatar_split_clause,[],[f342,f1264]) ).
tff(f1264,plain,
( spl86_97
<=> ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_97])]) ).
tff(f342,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X0 = X1 )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f237]) ).
tff(f1259,plain,
( spl86_96
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_95 ),
inference(avatar_split_clause,[],[f1255,f1252,f916,f786,f693,f681,f1257]) ).
tff(f1257,plain,
( spl86_96
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X1,X0),X2: fun(X1,fun(X0,bool))] :
( pp(product_prod_rec(X1,X0,bool,X2,X3))
| ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_96])]) ).
tff(f1252,plain,
( spl86_95
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X1,X0),X2: fun(X1,fun(X0,bool))] :
( pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3))
| ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_95])]) ).
tff(f1255,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( pp(product_prod_rec(X1,X0,bool,X2,X3))
| ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)) = X3 ) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_95 ),
inference(forward_demodulation,[],[f1253,f974]) ).
tff(f1253,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3))
| ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)) = X3 ) )
| ~ spl86_95 ),
inference(avatar_component_clause,[],[f1252]) ).
tff(f1254,plain,
spl86_95,
inference(avatar_split_clause,[],[f372,f1252]) ).
tff(f372,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3))
| ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)) = X3 ) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3))
| ( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)))
& ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)) = X3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35])],[f178,f266]) ).
tff(f266,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( ? [X4: X1,X5: X0] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X4),X5))
& ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5) = X3 ) )
=> ( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)))
& ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
tff(f178,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3))
| ? [X4: X1,X5: X0] :
( ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X4),X5))
& ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5) = X3 ) ) ),
inference(ennf_transformation,[],[f115]) ).
tff(f115,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( ! [X4: X1,X5: X0] :
( ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5) = X3 )
=> pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,X4),X5)) )
=> pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3)) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X1: $tType,X0: $tType,X20: fun(X0,fun(X1,bool)),X47: product_prod(X0,X1)] :
( ! [X33: X0,X34: X1] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X33),X34) = X47 )
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),X20,X33),X34)) )
=> pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X20),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_splitI2) ).
tff(f1247,plain,
( spl86_94
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_93 ),
inference(avatar_split_clause,[],[f1243,f1240,f916,f786,f693,f681,f1245]) ).
tff(f1245,plain,
( spl86_94
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: product_prod(X0,X1)] :
( ~ pp(product_prod_rec(X0,X1,bool,X3,X2))
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_94])]) ).
tff(f1240,plain,
( spl86_93
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: product_prod(X0,X1)] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 )
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_93])]) ).
tff(f1243,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( ~ pp(product_prod_rec(X0,X1,bool,X3,X2))
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 ) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_93 ),
inference(forward_demodulation,[],[f1241,f974]) ).
tff(f1241,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 )
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2)) )
| ~ spl86_93 ),
inference(avatar_component_clause,[],[f1240]) ).
tff(f1242,plain,
spl86_93,
inference(avatar_split_clause,[],[f369,f1240]) ).
tff(f369,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 )
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2)) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( ( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)))
& ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 ) )
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f176,f262]) ).
tff(f262,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( ? [X4: X0,X5: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,X4),X5))
& ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5) = X2 ) )
=> ( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)))
& ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f176,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( ? [X4: X0,X5: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,X4),X5))
& ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5) = X2 ) )
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2)) ),
inference(ennf_transformation,[],[f113]) ).
tff(f113,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2))
=> ~ ! [X4: X0,X5: X1] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5) = X2 )
=> ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,X4),X5)) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType,X1: $tType,X47: product_prod(X0,X1),X20: fun(X0,fun(X1,bool))] :
( pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X20),X47))
=> ~ ! [X21: X0,X22: X1] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X21),X22) = X47 )
=> ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X20,X21),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_splitE) ).
tff(f1236,plain,
spl86_92,
inference(avatar_split_clause,[],[f382,f1234]) ).
tff(f1234,plain,
( spl86_92
<=> ! [X1: $tType,X0: $tType,X4: fun(X0,fun(X1,bool)),X3: X0,X2: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X4,X3),X2))
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_92])]) ).
tff(f382,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X4,X3),X2))
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2))) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X4,X3),X2))
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2))) ),
inference(ennf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: fun(X0,fun(X1,bool))] :
( pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),X4,X3),X2)) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType,X1: $tType,X14: X1,X15: X0,X43: fun(X0,fun(X1,bool))] :
( pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X43),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X15),X14)))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),X43,X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_splitD) ).
tff(f1230,plain,
spl86_91,
inference(avatar_split_clause,[],[f377,f1228]) ).
tff(f1228,plain,
( spl86_91
<=> ! [X1: $tType,X0: $tType,X4: fun(X0,fun(X1,bool)),X3: X0,X2: X1] :
( pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X4,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_91])]) ).
tff(f377,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: fun(X0,fun(X1,bool))] :
( pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X4,X3),X2)) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: fun(X0,fun(X1,bool))] :
( pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X4,X3),X2)) ),
inference(ennf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X4,X3),X2))
=> pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X4),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2))) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType,X1: $tType,X14: X1,X15: X0,X41: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X41,X15),X14))
=> pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X41),aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X15),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_prod__caseI) ).
tff(f1198,plain,
spl86_90,
inference(avatar_split_clause,[],[f389,f1196]) ).
tff(f1196,plain,
( spl86_90
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X0,fun(X2,X1)),X4: X0,X3: X2] : ( aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) = aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X5),aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_90])]) ).
tff(f389,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) = aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X5),aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) = aa(product_prod(X0,X2),X1,aa(fun(X0,fun(X2,X1)),fun(product_prod(X0,X2),X1),product_prod_case(X0,X2,X1),X5),aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X14: X2,X15: X1,X41: fun(X1,fun(X2,X0))] : ( aa(X2,X0,aa(X1,fun(X2,X0),X41,X15),X14) = aa(product_prod(X1,X2),X0,aa(fun(X1,fun(X2,X0)),fun(product_prod(X1,X2),X0),product_prod_case(X1,X2,X0),X41),aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_prod_Osimps_I2_J) ).
tff(f1192,plain,
( ~ spl86_6
| spl86_86
| ~ spl86_89
| spl86_1 ),
inference(avatar_split_clause,[],[f314,f452,f1189,f1147,f476]) ).
tff(f314,plain,
( sP0
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK7),sK7),l)
| ~ trans(arrow_411405190le_alt,l) ),
inference(cnf_transformation,[],[f221]) ).
tff(f1185,plain,
( ~ spl86_6
| spl86_86
| ~ spl86_88
| spl86_1 ),
inference(avatar_split_clause,[],[f313,f452,f1182,f1147,f476]) ).
tff(f313,plain,
( sP0
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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)
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK7),sK7),l)
| ~ trans(arrow_411405190le_alt,l) ),
inference(cnf_transformation,[],[f221]) ).
tff(f1155,plain,
( ~ spl86_2
| spl86_85 ),
inference(avatar_split_clause,[],[f305,f1143,f456]) ).
tff(f305,plain,
! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 )
| ~ sP1 ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
( ( sP1
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK3),sK2),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),sK2),sK3),l)
& ( sK2 != sK3 ) )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK4),sK4),l)
| ~ trans(arrow_411405190le_alt,l) )
& ( ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f212,f214,f213]) ).
tff(f213,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)
& ( 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),sK3),sK2),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),sK2),sK3),l)
& ( sK2 != sK3 ) ) ),
introduced(choice_axiom,[]) ).
tff(f214,plain,
( ? [X2: arrow_411405190le_alt] : member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),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),sK4),sK4),l) ),
introduced(choice_axiom,[]) ).
tff(f212,plain,
( ( sP1
| ? [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)
& ( X0 != 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),X2),X2),l)
| ~ trans(arrow_411405190le_alt,l) )
& ( ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) )
| ~ sP1 ) ),
inference(rectify,[],[f211]) ).
tff(f211,plain,
( ( sP1
| ? [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
& ( X3 != X4 ) )
| ? [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),X5),l)
| ~ trans(arrow_411405190le_alt,l) )
& ( ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) )
| ~ sP1 ) ),
inference(flattening,[],[f210]) ).
tff(f210,plain,
( ( sP1
| ? [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
& ( X3 != X4 ) )
| ? [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),X5),l)
| ~ trans(arrow_411405190le_alt,l) )
& ( ( ! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X3),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),X3),X4),l)
| ( X3 = X4 ) )
& ! [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),X5),l)
& trans(arrow_411405190le_alt,l) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f208]) ).
tff(f1154,plain,
( ~ spl86_6
| spl86_86
| ~ spl86_87
| spl86_1 ),
inference(avatar_split_clause,[],[f312,f452,f1151,f1147,f476]) ).
tff(f312,plain,
( sP0
| ( sK5 != 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),sK7),sK7),l)
| ~ trans(arrow_411405190le_alt,l) ),
inference(cnf_transformation,[],[f221]) ).
tff(f1145,plain,
( ~ spl86_1
| spl86_85 ),
inference(avatar_split_clause,[],[f311,f1143,f452]) ).
tff(f311,plain,
! [X3: 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),X3),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),X3),l)
| ( X3 = X4 )
| ~ sP0 ),
inference(cnf_transformation,[],[f221]) ).
tff(f1141,plain,
( ~ spl86_6
| spl86_46
| ~ spl86_84
| spl86_2 ),
inference(avatar_split_clause,[],[f308,f456,f1138,f703,f476]) ).
tff(f308,plain,
( sP1
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK3),sK2),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),sK4),sK4),l)
| ~ trans(arrow_411405190le_alt,l) ),
inference(cnf_transformation,[],[f215]) ).
tff(f1136,plain,
( ~ spl86_6
| spl86_46
| ~ spl86_83
| spl86_2 ),
inference(avatar_split_clause,[],[f307,f456,f1133,f703,f476]) ).
tff(f307,plain,
( sP1
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK2),sK3),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),sK4),sK4),l)
| ~ trans(arrow_411405190le_alt,l) ),
inference(cnf_transformation,[],[f215]) ).
tff(f1056,plain,
spl86_82,
inference(avatar_split_clause,[],[f388,f1054]) ).
tff(f1054,plain,
( spl86_82
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X5,X4)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_82])]) ).
tff(f388,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X5,X4)),X3) ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X5,X4)),X3) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X2: $tType,X0: $tType,X1: $tType,X5: X1,X6: X2,X43: fun(X2,X0)] : ( product_apfst(X2,X0,X1,X43,aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X6),X5)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),aa(X2,X0,X43,X6)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_apfst__conv) ).
tff(f1052,plain,
spl86_81,
inference(avatar_split_clause,[],[f387,f1050]) ).
tff(f1050,plain,
( spl86_81
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: X0,X5: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),aa(X2,X1,X5,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_81])]) ).
tff(f387,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),aa(X2,X1,X5,X3)) ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),aa(X2,X1,X5,X3)) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X5: X2,X6: X0,X43: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X43,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X5)) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),aa(X2,X1,X43,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_apsnd__conv) ).
tff(f1048,plain,
( spl86_80
| ~ spl86_10
| ~ spl86_20
| ~ spl86_51 ),
inference(avatar_split_clause,[],[f750,f724,f549,f496,f1046]) ).
tff(f1046,plain,
( spl86_80
<=> ! [X0: $tType] : trans(X0,combk(bool,product_prod(X0,X0),fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_80])]) ).
tff(f724,plain,
( spl86_51
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK12(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_51])]) ).
tff(f750,plain,
( ! [X0: $tType] : trans(X0,combk(bool,product_prod(X0,X0),fTrue))
| ~ spl86_10
| ~ spl86_20
| ~ spl86_51 ),
inference(forward_demodulation,[],[f747,f550]) ).
tff(f747,plain,
( ! [X0: $tType] : trans(X0,top_top(fun(product_prod(X0,X0),bool)))
| ~ spl86_10
| ~ spl86_51 ),
inference(resolution,[],[f725,f497]) ).
tff(f725,plain,
( ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK12(X0,X1)),X1)
| trans(X0,X1) )
| ~ spl86_51 ),
inference(avatar_component_clause,[],[f724]) ).
tff(f1031,plain,
spl86_79,
inference(avatar_split_clause,[],[f431,f1029]) ).
tff(f1029,plain,
( spl86_79
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: fun(X0,X1),X3: product_prod(X0,X2)] : ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK46(X0,X1,X2,X3,X4,product_apfst(X0,X1,X2,X4,X3))),sK47(X0,X1,X2,X3,X4,product_apfst(X0,X1,X2,X4,X3))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_79])]) ).
tff(f431,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,X1)] : ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK46(X0,X1,X2,X3,X4,product_apfst(X0,X1,X2,X4,X3))),sK47(X0,X1,X2,X3,X4,product_apfst(X0,X1,X2,X4,X3))) = X3 ),
inference(equality_resolution,[],[f393]) ).
tff(f393,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,X1),X5: product_prod(X1,X2)] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK46(X0,X1,X2,X3,X4,X5)),sK47(X0,X1,X2,X3,X4,X5)) = X3 )
| ( product_apfst(X0,X1,X2,X4,X3) != X5 ) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,X1),X5: product_prod(X1,X2)] :
( ( ( aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X4,sK46(X0,X1,X2,X3,X4,X5))),sK47(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK46(X0,X1,X2,X3,X4,X5)),sK47(X0,X1,X2,X3,X4,X5)) = X3 ) )
| ( product_apfst(X0,X1,X2,X4,X3) != X5 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47])],[f191,f274]) ).
tff(f274,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: product_prod(X0,X2),X4: fun(X0,X1),X5: product_prod(X1,X2)] :
( ? [X6: X0,X7: X2] :
( ( aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X4,X6)),X7) = X5 )
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 ) )
=> ( ( aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X4,sK46(X0,X1,X2,X3,X4,X5))),sK47(X0,X1,X2,X3,X4,X5)) = X5 )
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),sK46(X0,X1,X2,X3,X4,X5)),sK47(X0,X1,X2,X3,X4,X5)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
tff(f191,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,X1),X5: product_prod(X1,X2)] :
( ? [X6: X0,X7: X2] :
( ( aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X4,X6)),X7) = X5 )
& ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 ) )
| ( product_apfst(X0,X1,X2,X4,X3) != X5 ) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,X2),X4: fun(X0,X1),X5: product_prod(X1,X2)] :
( ( product_apfst(X0,X1,X2,X4,X3) = X5 )
=> ~ ! [X6: X0,X7: X2] :
( ( aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7) = X3 )
=> ( aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),aa(X0,X1,X4,X6)),X7) != X5 ) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X2: $tType,X0: $tType,X1: $tType,X47: product_prod(X2,X1),X43: fun(X2,X0),X49: product_prod(X0,X1)] :
( ( product_apfst(X2,X0,X1,X43,X47) = X49 )
=> ~ ! [X21: X2,X22: X1] :
( ( aa(X1,product_prod(X2,X1),aa(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X21),X22) = X47 )
=> ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),aa(X2,X0,X43,X21)),X22) != X49 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_apfst__convE) ).
tff(f1017,plain,
( spl86_78
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_77 ),
inference(avatar_split_clause,[],[f1013,f1010,f916,f786,f693,f681,f1015]) ).
tff(f1010,plain,
( spl86_77
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X1,X0),X2: fun(X1,fun(X0,bool))] :
( pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_77])]) ).
tff(f1013,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( pp(product_prod_rec(X1,X0,bool,X2,X3))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3))) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_77 ),
inference(forward_demodulation,[],[f1011,f974]) ).
tff(f1011,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3))) )
| ~ spl86_77 ),
inference(avatar_component_clause,[],[f1010]) ).
tff(f1012,plain,
spl86_77,
inference(avatar_split_clause,[],[f373,f1010]) ).
tff(f373,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,fun(X0,bool)),X3: product_prod(X1,X0)] :
( pp(aa(product_prod(X1,X0),bool,aa(fun(X1,fun(X0,bool)),fun(product_prod(X1,X0),bool),product_prod_case(X1,X0,bool),X2),X3))
| ~ pp(aa(X0,bool,aa(X1,fun(X0,bool),X2,sK34(X0,X1,X2,X3)),sK35(X0,X1,X2,X3))) ),
inference(cnf_transformation,[],[f267]) ).
tff(f997,plain,
( spl86_76
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_75 ),
inference(avatar_split_clause,[],[f993,f990,f916,f786,f693,f681,f995]) ).
tff(f990,plain,
( spl86_75
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: product_prod(X0,X1)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)))
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_75])]) ).
tff(f993,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( ~ pp(product_prod_rec(X0,X1,bool,X3,X2))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3))) )
| ~ spl86_42
| ~ spl86_45
| ~ spl86_58
| ~ spl86_73
| ~ spl86_75 ),
inference(forward_demodulation,[],[f991,f974]) ).
tff(f991,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)))
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2)) )
| ~ spl86_75 ),
inference(avatar_component_clause,[],[f990]) ).
tff(f992,plain,
spl86_75,
inference(avatar_split_clause,[],[f370,f990]) ).
tff(f370,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK31(X0,X1,X2,X3)),sK32(X0,X1,X2,X3)))
| ~ pp(aa(product_prod(X0,X1),bool,aa(fun(X0,fun(X1,bool)),fun(product_prod(X0,X1),bool),product_prod_case(X0,X1,bool),X3),X2)) ),
inference(cnf_transformation,[],[f263]) ).
tff(f933,plain,
( spl86_74
| ~ spl86_10
| ~ spl86_20
| ~ spl86_38 ),
inference(avatar_split_clause,[],[f668,f660,f549,f496,f931]) ).
tff(f931,plain,
( spl86_74
<=> ! [X0: $tType] : ~ irrefl(X0,combk(bool,product_prod(X0,X0),fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_74])]) ).
tff(f660,plain,
( spl86_38
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X3: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_38])]) ).
tff(f668,plain,
( ! [X0: $tType] : ~ irrefl(X0,combk(bool,product_prod(X0,X0),fTrue))
| ~ spl86_10
| ~ spl86_20
| ~ spl86_38 ),
inference(forward_demodulation,[],[f667,f550]) ).
tff(f667,plain,
( ! [X0: $tType] : ~ irrefl(X0,top_top(fun(product_prod(X0,X0),bool)))
| ~ spl86_10
| ~ spl86_38 ),
inference(resolution,[],[f661,f497]) ).
tff(f661,plain,
( ! [X0: $tType,X3: X0,X1: fun(product_prod(X0,X0),bool)] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) )
| ~ spl86_38 ),
inference(avatar_component_clause,[],[f660]) ).
tff(f918,plain,
spl86_73,
inference(avatar_split_clause,[],[f415,f916]) ).
tff(f415,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: X3,X4: fun(X1,fun(X2,X0)),X5: fun(X3,product_prod(X1,X2))] : ( aa(X3,X0,product_scomp(X3,X1,X2,X0,X5,X4),X6) = aa(product_prod(X1,X2),X0,aa(fun(X1,fun(X2,X0)),fun(product_prod(X1,X2),X0),product_prod_case(X1,X2,X0),X4),aa(X3,product_prod(X1,X2),X5,X6)) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: fun(X1,fun(X2,X0)),X5: fun(X3,product_prod(X1,X2)),X6: X3] : ( aa(X3,X0,product_scomp(X3,X1,X2,X0,X5,X4),X6) = aa(product_prod(X1,X2),X0,aa(fun(X1,fun(X2,X0)),fun(product_prod(X1,X2),X0),product_prod_case(X1,X2,X0),X4),aa(X3,product_prod(X1,X2),X5,X6)) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X1: $tType,X2: $tType,X4: $tType,X0: $tType,X48: fun(X2,fun(X4,X1)),X43: fun(X0,product_prod(X2,X4)),X51: X0] : ( aa(X0,X1,product_scomp(X0,X2,X4,X1,X43,X48),X51) = aa(product_prod(X2,X4),X1,aa(fun(X2,fun(X4,X1)),fun(product_prod(X2,X4),X1),product_prod_case(X2,X4,X1),X48),aa(X0,product_prod(X2,X4),X43,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_scomp__def) ).
tff(f914,plain,
spl86_72,
inference(avatar_split_clause,[],[f402,f912]) ).
tff(f912,plain,
( spl86_72
<=> ! [X1: $tType,X0: $tType,X3: X0,X4: X1,X5: X0,X2: X1] :
( ( X2 = X4 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_72])]) ).
tff(f402,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( X2 = X4 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) ) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( ( X2 = X4 )
& ( X3 = X5 ) )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) ) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) )
=> ~ ( ( X3 = X5 )
=> ( X2 != X4 ) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X1: $tType,X24: X1,X25: X0,X26: X1,X27: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X27),X26) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X25),X24) )
=> ~ ( ( X25 = X27 )
=> ( X24 != X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_Pair__inject) ).
tff(f910,plain,
spl86_71,
inference(avatar_split_clause,[],[f401,f908]) ).
tff(f908,plain,
( spl86_71
<=> ! [X1: $tType,X0: $tType,X2: X1,X4: X1,X5: X0,X3: X0] :
( ( X3 = X5 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_71])]) ).
tff(f401,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( X3 = X5 )
| ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2) != aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X5),X4) ) ),
inference(cnf_transformation,[],[f195]) ).
tff(f905,plain,
spl86_70,
inference(avatar_split_clause,[],[f381,f903]) ).
tff(f903,plain,
( spl86_70
<=> ! [X1: $tType,X0: $tType,X4: fun(product_prod(X0,X1),bool),X3: X0,X2: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X4),X3),X2))
| ~ pp(aa(product_prod(X0,X1),bool,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_70])]) ).
tff(f381,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X4),X3),X2))
| ~ pp(aa(product_prod(X0,X1),bool,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2))) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X4),X3),X2))
| ~ pp(aa(product_prod(X0,X1),bool,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2))) ),
inference(ennf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X4),X3),X2)) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType,X1: $tType,X14: X1,X15: X0,X43: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X43,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X15),X14)))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X43),X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_curryI) ).
tff(f900,plain,
spl86_69,
inference(avatar_split_clause,[],[f379,f898]) ).
tff(f898,plain,
( spl86_69
<=> ! [X1: $tType,X0: $tType,X4: fun(product_prod(X0,X1),bool),X3: X0,X2: X1] :
( pp(aa(product_prod(X0,X1),bool,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X4),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_69])]) ).
tff(f379,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X4),X3),X2)) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X4),X3),X2)) ),
inference(ennf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: fun(product_prod(X0,X1),bool)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X4),X3),X2))
=> pp(aa(product_prod(X0,X1),bool,X4,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2))) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType,X1: $tType,X14: X1,X15: X0,X43: fun(product_prod(X0,X1),bool)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X43),X15),X14))
=> pp(aa(product_prod(X0,X1),bool,X43,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X15),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_curryE) ).
tff(f866,plain,
spl86_68,
inference(avatar_split_clause,[],[f386,f864]) ).
tff(f856,plain,
( spl86_67
| ~ spl86_66 ),
inference(avatar_split_clause,[],[f852,f849,f854]) ).
tff(f854,plain,
( spl86_67
<=> ! [X1: $tType,X0: $tType,X8: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),sK23(X0,X1,X2)),sK24(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_67])]) ).
tff(f849,plain,
( spl86_66
<=> ! [X1: $tType,X0: $tType,X8: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK23(X0,X1,X2)),sK24(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_66])]) ).
tff(f852,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X8: product_prod(X0,X1)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),sK23(X0,X1,X2)),sK24(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) )
| ~ spl86_66 ),
inference(forward_demodulation,[],[f850,f386]) ).
tff(f850,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X8: product_prod(X0,X1)] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK23(X0,X1,X2)),sK24(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) )
| ~ spl86_66 ),
inference(avatar_component_clause,[],[f849]) ).
tff(f851,plain,
spl86_66,
inference(avatar_split_clause,[],[f358,f849]) ).
tff(f358,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X8: product_prod(X0,X1)] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK23(X0,X1,X2)),sK24(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2)))
| ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK23(X0,X1,X2)),sK24(X0,X1,X2))))
| ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24])],[f252,f254,f253]) ).
tff(f253,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
=> pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f254,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
=> pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK23(X0,X1,X2)),sK24(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f252,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ? [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(rectify,[],[f251]) ).
tff(f251,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ! [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ? [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)))
| ! [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
inference(nnf_transformation,[],[f103]) ).
tff(f103,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
<=> ? [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType,X1: $tType,X8: fun(product_prod(X0,X1),bool)] :
( ? [X9: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X8,X9))
<=> ? [X10: X0,X11: X1] : pp(aa(product_prod(X0,X1),bool,X8,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X10),X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_split__paired__Ex) ).
tff(f841,plain,
( spl86_65
| ~ spl86_64 ),
inference(avatar_split_clause,[],[f837,f834,f839]) ).
tff(f839,plain,
( spl86_65
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),sK19(X0,X1,X2)),sK20(X0,X1,X2)))
| pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_65])]) ).
tff(f834,plain,
( spl86_64
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK19(X0,X1,X2)),sK20(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_64])]) ).
tff(f837,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),sK19(X0,X1,X2)),sK20(X0,X1,X2)))
| pp(aa(product_prod(X0,X1),bool,X2,X3)) )
| ~ spl86_64 ),
inference(forward_demodulation,[],[f835,f386]) ).
tff(f835,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
( pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK19(X0,X1,X2)),sK20(X0,X1,X2)))) )
| ~ spl86_64 ),
inference(avatar_component_clause,[],[f834]) ).
tff(f836,plain,
spl86_64,
inference(avatar_split_clause,[],[f357,f834]) ).
tff(f357,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
( pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK19(X0,X1,X2)),sK20(X0,X1,X2)))) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK19(X0,X1,X2)),sK20(X0,X1,X2)))) )
& ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK21(X0,X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21])],[f247,f249,f248]) ).
tff(f248,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)))
=> ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK19(X0,X1,X2)),sK20(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f249,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8))
=> ~ pp(aa(product_prod(X0,X1),bool,X2,sK21(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f247,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ! [X6: X0,X7: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ? [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(rectify,[],[f246]) ).
tff(f246,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
| ? [X4: X0,X5: X1] : ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
& ( ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)))
| ? [X3: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
inference(nnf_transformation,[],[f102]) ).
tff(f102,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ! [X3: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X2,X3))
<=> ! [X4: X0,X5: X1] : pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0: $tType,X1: $tType,X8: fun(product_prod(X0,X1),bool)] :
( ! [X9: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X8,X9))
<=> ! [X10: X0,X11: X1] : pp(aa(product_prod(X0,X1),bool,X8,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X10),X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_split__paired__All) ).
tff(f828,plain,
( spl86_63
| ~ spl86_62 ),
inference(avatar_split_clause,[],[f824,f821,f826]) ).
tff(f821,plain,
( spl86_62
<=> ! [X1: $tType,X0: $tType,X4: X0,X5: X1,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_62])]) ).
tff(f824,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),X4),X5))
| pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2))) )
| ~ spl86_62 ),
inference(forward_demodulation,[],[f822,f386]) ).
tff(f822,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) )
| ~ spl86_62 ),
inference(avatar_component_clause,[],[f821]) ).
tff(f823,plain,
spl86_62,
inference(avatar_split_clause,[],[f359,f821]) ).
tff(f359,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,sK22(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) ),
inference(cnf_transformation,[],[f255]) ).
tff(f813,plain,
( spl86_61
| ~ spl86_60 ),
inference(avatar_split_clause,[],[f809,f806,f811]) ).
tff(f806,plain,
( spl86_60
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK21(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_60])]) ).
tff(f809,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X2),X6),X7))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK21(X0,X1,X2))) )
| ~ spl86_60 ),
inference(forward_demodulation,[],[f807,f386]) ).
tff(f807,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK21(X0,X1,X2))) )
| ~ spl86_60 ),
inference(avatar_component_clause,[],[f806]) ).
tff(f808,plain,
spl86_60,
inference(avatar_split_clause,[],[f356,f806]) ).
tff(f356,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6),X7)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK21(X0,X1,X2))) ),
inference(cnf_transformation,[],[f250]) ).
tff(f804,plain,
( spl86_59
| ~ spl86_34
| ~ spl86_52 ),
inference(avatar_split_clause,[],[f755,f728,f637,f801]) ).
tff(f801,plain,
( spl86_59
<=> irrefl(arrow_411405190le_alt,l) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_59])]) ).
tff(f728,plain,
( spl86_52
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK13(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_52])]) ).
tff(f755,plain,
( irrefl(arrow_411405190le_alt,l)
| ~ spl86_34
| ~ spl86_52 ),
inference(resolution,[],[f729,f638]) ).
tff(f729,plain,
( ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK13(X0,X1)),X1)
| irrefl(X0,X1) )
| ~ spl86_52 ),
inference(avatar_component_clause,[],[f728]) ).
tff(f788,plain,
spl86_58,
inference(avatar_split_clause,[],[f385,f786]) ).
tff(f385,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( product_prod_rec(X0,X2,X1,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) ),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: X0,X5: fun(X0,fun(X2,X1))] : ( product_prod_rec(X0,X2,X1,X5,aa(X2,product_prod(X0,X2),aa(X0,fun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X3)) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X4),X3) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X14: X2,X15: X1,X41: fun(X1,fun(X2,X0))] : ( product_prod_rec(X1,X2,X0,X41,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X15),X14)) = aa(X2,X0,aa(X1,fun(X2,X0),X41,X15),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_prod_Orecs) ).
tff(f774,plain,
spl86_57,
inference(avatar_split_clause,[],[f349,f772]) ).
tff(f772,plain,
( spl86_57
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK18(X0,X1,X2)),sK17(X0,X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_57])]) ).
tff(f349,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK18(X0,X1,X2)),sK17(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f242]) ).
tff(f770,plain,
spl86_56,
inference(avatar_split_clause,[],[f348,f768]) ).
tff(f348,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK17(X0,X1,X2)),sK18(X0,X1,X2)),X1) ),
inference(cnf_transformation,[],[f242]) ).
tff(f742,plain,
spl86_55,
inference(avatar_split_clause,[],[f340,f740]) ).
tff(f740,plain,
( spl86_55
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK14(X0,X1)),sK16(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_55])]) ).
tff(f340,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK14(X0,X1)),sK16(X0,X1)),X1) ),
inference(cnf_transformation,[],[f236]) ).
tff(f738,plain,
spl86_54,
inference(avatar_split_clause,[],[f339,f736]) ).
tff(f736,plain,
( spl86_54
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1)),sK16(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_54])]) ).
tff(f339,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK15(X0,X1)),sK16(X0,X1)),X1) ),
inference(cnf_transformation,[],[f236]) ).
tff(f734,plain,
spl86_53,
inference(avatar_split_clause,[],[f338,f732]) ).
tff(f732,plain,
( spl86_53
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK14(X0,X1)),sK15(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_53])]) ).
tff(f338,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK14(X0,X1)),sK15(X0,X1)),X1) ),
inference(cnf_transformation,[],[f236]) ).
tff(f730,plain,
spl86_52,
inference(avatar_split_clause,[],[f336,f728]) ).
tff(f336,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK13(X0,X1)),X1) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK13(X0,X1)),X1) )
& ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f230,f231]) ).
tff(f231,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK13(X0,X1)),sK13(X0,X1)),X1) ),
introduced(choice_axiom,[]) ).
tff(f230,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
& ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ) ),
inference(rectify,[],[f229]) ).
tff(f229,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
& ( ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
| ~ irrefl(X0,X1) ) ),
inference(nnf_transformation,[],[f95]) ).
tff(f95,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
<=> ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType,X16: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X16)
<=> ! [X17: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X17),X17),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_irrefl__def) ).
tff(f726,plain,
spl86_51,
inference(avatar_split_clause,[],[f334,f724]) ).
tff(f334,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK12(X0,X1)),X1) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK12(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK12(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK11(X0,X1)),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f164,f227]) ).
tff(f227,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) )
=> ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK12(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK12(X0,X1)),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK11(X0,X1)),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f164,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
inference(flattening,[],[f163]) ).
tff(f163,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ? [X2: X0,X3: X0,X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1) ) ),
inference(ennf_transformation,[],[f93]) ).
tff(f93,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ! [X2: X0,X3: X0,X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3),X1)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X4),X1) ) )
=> trans(X0,X1) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType,X16: fun(product_prod(X0,X0),bool)] :
( ! [X21: X0,X22: X0,X23: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X21),X22),X16)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X22),X23),X16)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X21),X23),X16) ) )
=> trans(X0,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_transI) ).
tff(f722,plain,
spl86_50,
inference(avatar_split_clause,[],[f333,f720]) ).
tff(f720,plain,
( spl86_50
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK12(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_50])]) ).
tff(f333,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK11(X0,X1)),sK12(X0,X1)),X1) ),
inference(cnf_transformation,[],[f228]) ).
tff(f718,plain,
spl86_49,
inference(avatar_split_clause,[],[f332,f716]) ).
tff(f716,plain,
( spl86_49
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK11(X0,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_49])]) ).
tff(f332,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK10(X0,X1)),sK11(X0,X1)),X1) ),
inference(cnf_transformation,[],[f228]) ).
tff(f714,plain,
( spl86_48
| ~ spl86_10
| ~ spl86_20 ),
inference(avatar_split_clause,[],[f553,f549,f496,f712]) ).
tff(f553,plain,
( ! [X0: $tType,X1: X0] : member(X0,X1,combk(bool,X0,fTrue))
| ~ spl86_10
| ~ spl86_20 ),
inference(superposition,[],[f497,f550]) ).
tff(f710,plain,
( ~ spl86_6
| spl86_46
| ~ spl86_47
| spl86_2 ),
inference(avatar_split_clause,[],[f306,f456,f707,f703,f476]) ).
tff(f306,plain,
( sP1
| ( sK2 != sK3 )
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),sK4),sK4),l)
| ~ trans(arrow_411405190le_alt,l) ),
inference(cnf_transformation,[],[f215]) ).
tff(f695,plain,
spl86_45,
inference(avatar_split_clause,[],[f375,f693]) ).
tff(f375,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2] : ( product_scomp(X0,X2,X0,X1,aa(X2,fun(X0,product_prod(X2,X0)),product_Pair(X2,X0),X4),X3) = aa(X2,fun(X0,X1),X3,X4) ),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,fun(X0,X1)),X4: X2] : ( product_scomp(X0,X2,X0,X1,aa(X2,fun(X0,product_prod(X2,X0)),product_Pair(X2,X0),X4),X3) = aa(X2,fun(X0,X1),X3,X4) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X43: fun(X2,fun(X0,X1)),X6: X2] : ( product_scomp(X0,X2,X0,X1,aa(X2,fun(X0,product_prod(X2,X0)),product_Pair(X2,X0),X6),X43) = aa(X2,fun(X0,X1),X43,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Pair__scomp) ).
tff(f691,plain,
spl86_44,
inference(avatar_split_clause,[],[f362,f689]) ).
tff(f362,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK29(X0,X1,X2)),sK30(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK29(X0,X1,X2)),sK30(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f106,f260]) ).
tff(f260,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 )
=> ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK29(X0,X1,X2)),sK30(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f106,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType,X1: $tType,X42: product_prod(X0,X1)] :
? [X21: X0,X22: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X21),X22) = X42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_surj__pair) ).
tff(f687,plain,
spl86_43,
inference(avatar_split_clause,[],[f361,f685]) ).
tff(f361,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK27(X0,X1,X2)),sK28(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK27(X0,X1,X2)),sK28(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f172,f258]) ).
tff(f258,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 )
=> ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK27(X0,X1,X2)),sK28(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f172,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 ),
inference(ennf_transformation,[],[f105]) ).
tff(f105,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
~ ! [X3: X0,X4: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) != X2 ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X0: $tType,X1: $tType,X32: product_prod(X0,X1)] :
~ ! [X33: X0,X34: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X33),X34) != X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_prod_Oexhaust) ).
tff(f683,plain,
spl86_42,
inference(avatar_split_clause,[],[f360,f681]) ).
tff(f360,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f171,f256]) ).
tff(f256,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 )
=> ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK25(X0,X1,X2)),sK26(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f171,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 ),
inference(ennf_transformation,[],[f104]) ).
tff(f104,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
~ ! [X3: X0,X4: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) != X2 ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType,X1: $tType,X42: product_prod(X0,X1)] :
~ ! [X21: X0,X22: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X21),X22) != X42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_PairE) ).
tff(f678,plain,
spl86_41,
inference(avatar_split_clause,[],[f366,f676]) ).
tff(f676,plain,
( spl86_41
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(product_prod(X2,X1),X0)] : ( aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),product_curry(X2,X1,X0,X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_41])]) ).
tff(f366,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(product_prod(X2,X1),X0)] : ( aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),product_curry(X2,X1,X0,X3)) = X3 ),
inference(cnf_transformation,[],[f110]) ).
tff(f110,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(product_prod(X2,X1),X0)] : ( aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),product_curry(X2,X1,X0,X3)) = X3 ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X43: fun(product_prod(X0,X1),X2)] : ( aa(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2),product_prod_case(X0,X1,X2),product_curry(X0,X1,X2,X43)) = X43 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_split__curry) ).
tff(f674,plain,
spl86_40,
inference(avatar_split_clause,[],[f365,f672]) ).
tff(f672,plain,
( spl86_40
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X2,fun(X1,X0))] : ( product_curry(X2,X1,X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_40])]) ).
tff(f365,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,fun(X1,X0))] : ( product_curry(X2,X1,X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X3)) = X3 ),
inference(cnf_transformation,[],[f109]) ).
tff(f109,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,fun(X1,X0))] : ( product_curry(X2,X1,X0,aa(fun(X2,fun(X1,X0)),fun(product_prod(X2,X1),X0),product_prod_case(X2,X1,X0),X3)) = X3 ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X43: fun(X0,fun(X1,X2))] : ( product_curry(X0,X1,X2,aa(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2),product_prod_case(X0,X1,X2),X43)) = X43 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_curry__split) ).
tff(f666,plain,
spl86_39,
inference(avatar_split_clause,[],[f414,f664]) ).
tff(f664,plain,
( spl86_39
<=> ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X4: product_prod(X3,X2),X5: fun(X3,X0),X6: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X6,product_apfst(X3,X0,X2,X5,X4)) = product_apfst(X3,X0,X1,X5,product_apsnd(X2,X1,X3,X6,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_39])]) ).
tff(f414,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(X2,X1),X4: product_prod(X3,X2),X5: fun(X3,X0)] : ( product_apsnd(X2,X1,X0,X6,product_apfst(X3,X0,X2,X5,X4)) = product_apfst(X3,X0,X1,X5,product_apsnd(X2,X1,X3,X6,X4)) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X3,X2),X5: fun(X3,X0),X6: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X6,product_apfst(X3,X0,X2,X5,X4)) = product_apfst(X3,X0,X1,X5,product_apsnd(X2,X1,X3,X6,X4)) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X4: $tType,X47: product_prod(X4,X2),X48: fun(X4,X0),X43: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X43,product_apfst(X4,X0,X2,X48,X47)) = product_apfst(X4,X0,X1,X48,product_apsnd(X2,X1,X4,X43,X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_apsnd__apfst__commute) ).
tff(f662,plain,
spl86_38,
inference(avatar_split_clause,[],[f335,f660]) ).
tff(f335,plain,
! [X0: $tType,X3: X0,X1: fun(product_prod(X0,X0),bool)] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
tff(f652,plain,
spl86_37,
inference(avatar_split_clause,[],[f371,f650]) ).
tff(f371,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK33(X0,X1,X2,X3)) != aa(X1,X0,X2,sK33(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK33(X0,X1,X2,X3)) != aa(X1,X0,X2,sK33(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f177,f264]) ).
tff(f264,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK33(X0,X1,X2,X3)) != aa(X1,X0,X2,sK33(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f177,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f114]) ).
tff(f114,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X1: $tType,X0: $tType,X48: fun(X0,X1),X43: fun(X0,X1)] :
( ! [X21: X0] : ( aa(X0,X1,X43,X21) = aa(X0,X1,X48,X21) )
=> ( X43 = X48 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_ext) ).
tff(f648,plain,
( spl86_35
| ~ spl86_36
| ~ spl86_7 ),
inference(avatar_split_clause,[],[f490,f481,f645,f642]) ).
tff(f642,plain,
( spl86_35
<=> ! [X0: bool] : ( fFalse = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_35])]) ).
tff(f645,plain,
( spl86_36
<=> ( fTrue = fFalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_36])]) ).
tff(f490,plain,
( ! [X0: bool] :
( ( fTrue != fFalse )
| ( fFalse = X0 ) )
| ~ spl86_7 ),
inference(equality_factoring,[],[f482]) ).
tff(f640,plain,
( ~ spl86_1
| spl86_34 ),
inference(avatar_split_clause,[],[f310,f637,f452]) ).
tff(f310,plain,
! [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),X5),l)
| ~ sP0 ),
inference(cnf_transformation,[],[f221]) ).
tff(f639,plain,
( ~ spl86_2
| spl86_34 ),
inference(avatar_split_clause,[],[f304,f637,f456]) ).
tff(f304,plain,
! [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),X5),l)
| ~ sP1 ),
inference(cnf_transformation,[],[f215]) ).
tff(f630,plain,
spl86_33,
inference(avatar_split_clause,[],[f355,f628]) ).
tff(f355,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) )
& ( ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) )
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
inference(flattening,[],[f244]) ).
tff(f244,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) )
& ( ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) )
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
inference(nnf_transformation,[],[f101]) ).
tff(f101,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
<=> ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType,X16: fun(product_prod(X0,X0),bool),X44: fun(X0,bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X44),X16))
<=> ( total_on(X0,X44,X16)
& irrefl(X0,X16)
& trans(X0,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_strict__linear__order__on__def) ).
tff(f623,plain,
( spl86_32
| ~ spl86_20
| ~ spl86_31 ),
inference(avatar_split_clause,[],[f618,f614,f549,f620]) ).
tff(f614,plain,
( spl86_31
<=> ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_31])]) ).
tff(f618,plain,
( ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue))) )
| ~ spl86_20
| ~ spl86_31 ),
inference(forward_demodulation,[],[f616,f550]) ).
tff(f616,plain,
( ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)))) )
| ~ spl86_31 ),
inference(avatar_component_clause,[],[f614]) ).
tff(f617,plain,
spl86_31,
inference(avatar_split_clause,[],[f321,f614]) ).
tff(f321,plain,
arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)))),
inference(cnf_transformation,[],[f59]) ).
tff(f59,axiom,
arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Lin__def) ).
tff(f612,plain,
spl86_30,
inference(avatar_split_clause,[],[f364,f610]) ).
tff(f610,plain,
( spl86_30
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,product_prod(X1,X0))] : ( product_scomp(X2,X1,X0,product_prod(X1,X0),X3,product_Pair(X1,X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_30])]) ).
tff(f364,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,product_prod(X1,X0))] : ( product_scomp(X2,X1,X0,product_prod(X1,X0),X3,product_Pair(X1,X0)) = X3 ),
inference(cnf_transformation,[],[f108]) ).
tff(f108,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,product_prod(X1,X0))] : ( product_scomp(X2,X1,X0,product_prod(X1,X0),X3,product_Pair(X1,X0)) = X3 ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X6: fun(X0,product_prod(X1,X2))] : ( product_scomp(X0,X1,X2,product_prod(X1,X2),X6,product_Pair(X1,X2)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_scomp__Pair) ).
tff(f605,plain,
spl86_29,
inference(avatar_split_clause,[],[f354,f603]) ).
tff(f354,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
inference(cnf_transformation,[],[f245]) ).
tff(f595,plain,
spl86_28,
inference(avatar_split_clause,[],[f368,f593]) ).
tff(f593,plain,
( spl86_28
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X0),bool),X2: fun(product_prod(X1,X1),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_28])]) ).
tff(f368,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(flattening,[],[f174]) ).
tff(f174,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(ennf_transformation,[],[f112]) ).
tff(f112,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(X0,X3)
=> ( trans(X1,X2)
=> trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2)) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType,X1: $tType,X28: fun(product_prod(X1,X1),bool),X29: fun(product_prod(X0,X0),bool)] :
( trans(X0,X29)
=> ( trans(X1,X28)
=> trans(product_prod(X0,X1),lex_prod(X0,X1,X29,X28)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_trans__lex__prod) ).
tff(f591,plain,
spl86_27,
inference(avatar_split_clause,[],[f353,f589]) ).
tff(f353,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
inference(cnf_transformation,[],[f245]) ).
tff(f587,plain,
spl86_26,
inference(avatar_split_clause,[],[f352,f585]) ).
tff(f352,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
inference(cnf_transformation,[],[f245]) ).
tff(f583,plain,
( spl86_25
| ~ spl86_4
| ~ spl86_15
| ~ spl86_20
| ~ spl86_21 ),
inference(avatar_split_clause,[],[f566,f556,f549,f517,f466,f580]) ).
tff(f580,plain,
( spl86_25
<=> ( fTrue = top_top(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_25])]) ).
tff(f466,plain,
( spl86_4
<=> top(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_4])]) ).
tff(f566,plain,
( ( fTrue = top_top(bool) )
| ~ spl86_4
| ~ spl86_15
| ~ spl86_20
| ~ spl86_21 ),
inference(forward_demodulation,[],[f565,f518]) ).
tff(f565,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,bool,combk(bool,X0,fTrue),X1) = top_top(bool) )
| ~ spl86_4
| ~ spl86_20
| ~ spl86_21 ),
inference(forward_demodulation,[],[f563,f550]) ).
tff(f563,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,bool,top_top(fun(X0,bool)),X1) = top_top(bool) )
| ~ spl86_4
| ~ spl86_21 ),
inference(resolution,[],[f557,f468]) ).
tff(f468,plain,
( top(bool)
| ~ spl86_4 ),
inference(avatar_component_clause,[],[f466]) ).
tff(f576,plain,
( spl86_24
| ~ spl86_20
| ~ spl86_23 ),
inference(avatar_split_clause,[],[f572,f569,f549,f574]) ).
tff(f569,plain,
( spl86_23
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ member(X0,sK9(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_23])]) ).
tff(f572,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fTrue) = X1 )
| ~ member(X0,sK9(X0,X1),X1) )
| ~ spl86_20
| ~ spl86_23 ),
inference(forward_demodulation,[],[f570,f550]) ).
tff(f570,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ member(X0,sK9(X0,X1),X1) )
| ~ spl86_23 ),
inference(avatar_component_clause,[],[f569]) ).
tff(f571,plain,
spl86_23,
inference(avatar_split_clause,[],[f331,f569]) ).
tff(f331,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ member(X0,sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ member(X0,sK9(X0,X1),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f162,f225]) ).
tff(f225,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : ~ member(X0,X2,X1)
=> ~ member(X0,sK9(X0,X1),X1) ),
introduced(choice_axiom,[]) ).
tff(f162,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ? [X2: X0] : ~ member(X0,X2,X1) ),
inference(ennf_transformation,[],[f92]) ).
tff(f92,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ! [X2: X0] : member(X0,X2,X1)
=> ( top_top(fun(X0,bool)) = X1 ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType,X44: fun(X0,bool)] :
( ! [X21: X0] : member(X0,X21,X44)
=> ( top_top(fun(X0,bool)) = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_UNIV__eq__I) ).
tff(f562,plain,
spl86_22,
inference(avatar_split_clause,[],[f347,f560]) ).
tff(f347,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ( sK17(X0,X1,X2) != sK18(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f242]) ).
tff(f558,plain,
spl86_21,
inference(avatar_split_clause,[],[f330,f556]) ).
tff(f330,plain,
! [X1: $tType,X0: $tType,X2: X0] :
( ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
| ~ top(X1) ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X0] : ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
| ~ top(X1) ),
inference(ennf_transformation,[],[f91]) ).
tff(f91,plain,
! [X0: $tType,X1: $tType] :
( top(X1)
=> ! [X2: X0] : ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X1: $tType,X0: $tType] :
( top(X0)
=> ! [X6: X1] : ( aa(X1,X0,top_top(fun(X1,X0)),X6) = top_top(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_top__apply) ).
tff(f551,plain,
( spl86_20
| ~ spl86_9
| ~ spl86_19 ),
inference(avatar_split_clause,[],[f547,f544,f492,f549]) ).
tff(f544,plain,
( spl86_19
<=> ! [X0: $tType] : ( top_top(fun(X0,bool)) = collect(X0,combk(bool,X0,fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_19])]) ).
tff(f547,plain,
( ! [X0: $tType] : ( top_top(fun(X0,bool)) = combk(bool,X0,fTrue) )
| ~ spl86_9
| ~ spl86_19 ),
inference(forward_demodulation,[],[f545,f493]) ).
tff(f545,plain,
( ! [X0: $tType] : ( top_top(fun(X0,bool)) = collect(X0,combk(bool,X0,fTrue)) )
| ~ spl86_19 ),
inference(avatar_component_clause,[],[f544]) ).
tff(f546,plain,
spl86_19,
inference(avatar_split_clause,[],[f322,f544]) ).
tff(f322,plain,
! [X0: $tType] : ( top_top(fun(X0,bool)) = collect(X0,combk(bool,X0,fTrue)) ),
inference(cnf_transformation,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] : ( top_top(fun(X0,bool)) = collect(X0,combk(bool,X0,fTrue)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_UNIV__def) ).
tff(f538,plain,
spl86_18,
inference(avatar_split_clause,[],[f346,f536]) ).
tff(f346,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| member(X0,sK18(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f242]) ).
tff(f534,plain,
spl86_17,
inference(avatar_split_clause,[],[f345,f532]) ).
tff(f345,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| member(X0,sK17(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f242]) ).
tff(f523,plain,
spl86_16,
inference(avatar_split_clause,[],[f367,f521]) ).
tff(f521,plain,
( spl86_16
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X0),bool),X2: fun(X1,X0)] :
( trans(X1,inv_image(X0,X1,X3,X2))
| ~ trans(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_16])]) ).
tff(f367,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
( trans(X1,inv_image(X0,X1,X3,X2))
| ~ trans(X0,X3) ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
( trans(X1,inv_image(X0,X1,X3,X2))
| ~ trans(X0,X3) ),
inference(ennf_transformation,[],[f111]) ).
tff(f111,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(product_prod(X0,X0),bool)] :
( trans(X0,X3)
=> trans(X1,inv_image(X0,X1,X3,X2)) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType,X1: $tType,X43: fun(X1,X0),X16: fun(product_prod(X0,X0),bool)] :
( trans(X0,X16)
=> trans(X1,inv_image(X0,X1,X16,X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_trans__inv__image) ).
tff(f519,plain,
spl86_15,
inference(avatar_split_clause,[],[f363,f517]) ).
tff(f363,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f107]) ).
tff(f107,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X1: $tType,X0: $tType,X54: X1,X55: X0] : ( aa(X1,X0,combk(X0,X1,X55),X54) = X55 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f515,plain,
( spl86_14
| ~ spl86_5
| ~ spl86_7 ),
inference(avatar_split_clause,[],[f489,f481,f471,f513]) ).
tff(f513,plain,
( spl86_14
<=> ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_14])]) ).
tff(f471,plain,
( spl86_5
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_5])]) ).
tff(f489,plain,
( ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) )
| ~ spl86_5
| ~ spl86_7 ),
inference(superposition,[],[f473,f482]) ).
tff(f473,plain,
( pp(fTrue)
| ~ spl86_5 ),
inference(avatar_component_clause,[],[f471]) ).
tff(f511,plain,
spl86_13,
inference(avatar_split_clause,[],[f351,f509]) ).
tff(f351,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f100]) ).
tff(f100,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( member(X0,X2,X1)
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X44: fun(X0,bool),X6: X0] :
( member(X0,X6,X44)
<=> pp(aa(X0,bool,X44,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_mem__def) ).
tff(f507,plain,
spl86_12,
inference(avatar_split_clause,[],[f350,f505]) ).
tff(f350,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f243]) ).
tff(f502,plain,
spl86_11,
inference(avatar_split_clause,[],[f328,f500]) ).
tff(f328,plain,
! [X0: $tType,X1: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X1)),
inference(cnf_transformation,[],[f89]) ).
tff(f89,plain,
! [X0: $tType,X1: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X1)),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType,X6: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_top1I) ).
tff(f498,plain,
spl86_10,
inference(avatar_split_clause,[],[f326,f496]) ).
tff(f326,plain,
! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
inference(cnf_transformation,[],[f87]) ).
tff(f87,plain,
! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType,X6: X0] : member(X0,X6,top_top(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_UNIV__I) ).
tff(f494,plain,
spl86_9,
inference(avatar_split_clause,[],[f325,f492]) ).
tff(f325,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f86]) ).
tff(f86,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType,X8: fun(X0,bool)] : ( collect(X0,X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Collect__def) ).
tff(f487,plain,
spl86_8,
inference(avatar_split_clause,[],[f329,f485]) ).
tff(f329,plain,
! [X1: $tType,X0: $tType] :
( top(fun(X0,X1))
| ~ top(X1) ),
inference(cnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType,X1: $tType] :
( top(fun(X0,X1))
| ~ top(X1) ),
inference(ennf_transformation,[],[f90]) ).
tff(f90,plain,
! [X0: $tType,X1: $tType] :
( top(X1)
=> top(fun(X0,X1)) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X52: $tType,X53: $tType] :
( top(X53)
=> top(fun(X52,X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
tff(f483,plain,
spl86_7,
inference(avatar_split_clause,[],[f323,f481]) ).
tff(f323,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f84]) ).
tff(f84,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X55: bool] :
( ( fFalse = X55 )
| ( fTrue = X55 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
tff(f479,plain,
( ~ spl86_2
| spl86_6 ),
inference(avatar_split_clause,[],[f303,f476,f456]) ).
tff(f303,plain,
( trans(arrow_411405190le_alt,l)
| ~ sP1 ),
inference(cnf_transformation,[],[f215]) ).
tff(f474,plain,
spl86_5,
inference(avatar_split_clause,[],[f319,f471]) ).
tff(f319,plain,
pp(fTrue),
inference(cnf_transformation,[],[f77]) ).
tff(f77,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f469,plain,
spl86_4,
inference(avatar_split_clause,[],[f318,f466]) ).
tff(f318,plain,
top(bool),
inference(cnf_transformation,[],[f75]) ).
tff(f75,axiom,
top(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
tff(f464,plain,
~ spl86_3,
inference(avatar_split_clause,[],[f317,f461]) ).
tff(f317,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f76]) ).
tff(f76,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
tff(f459,plain,
( spl86_1
| spl86_2 ),
inference(avatar_split_clause,[],[f315,f456,f452]) ).
tff(f315,plain,
( sP1
| sP0 ),
inference(cnf_transformation,[],[f222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT176_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 00:18:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (25299)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (25303)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (25302)WARNING: value z3 for option sas not known
% 0.14/0.38 % (25300)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (25301)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (25302)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (25304)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (25305)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (25306)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % Exception at run slice level
% 0.14/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % (25306)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % (25307)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.40 % (25307)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.40 % Exception at run slice level
% 0.21/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.40 % (25308)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.40 % (25309)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.41 % (25308)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41 % (25310)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.96/0.70 % (25304)First to succeed.
% 2.62/0.72 % (25304)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25299"
% 2.62/0.73 % (25304)Refutation found. Thanks to Tanya!
% 2.62/0.73 % SZS status Theorem for theBenchmark
% 2.62/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/0.73 % (25304)------------------------------
% 2.62/0.73 % (25304)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.62/0.73 % (25304)Termination reason: Refutation
% 2.62/0.73
% 2.62/0.73 % (25304)Memory used [KB]: 5114
% 2.62/0.73 % (25304)Time elapsed: 0.348 s
% 2.62/0.73 % (25304)Instructions burned: 958 (million)
% 2.62/0.73 % (25299)Success in time 0.375 s
%------------------------------------------------------------------------------