TSTP Solution File: SCT200_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT200_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 Apr 30 14:57:16 EDT 2024
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 305
% Syntax : Number of formulae : 730 ( 201 unt; 112 typ; 0 def)
% Number of atoms : 1687 ( 576 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1736 ( 667 ~; 676 |; 161 &)
% ( 157 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 188 ( 99 >; 89 *; 0 +; 0 <<)
% Number of predicates : 137 ( 135 usr; 122 prp; 0-5 aty)
% Number of functors : 96 ( 96 usr; 8 con; 0-7 aty)
% Number of variables : 2454 (2111 !; 52 ?;2454 :)
% ( 291 !>; 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,
arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_2,type,
arrow_319942042_below: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_3,type,
arrow_276188178_mkbot: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_4,type,
arrow_424895264_mktop: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_5,type,
comp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_6,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_7,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).
tff(func_def_8,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).
tff(func_def_9,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_10,type,
product_fst:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_11,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_12,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_13,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_14,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_15,type,
product_snd:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_16,type,
lex_prod:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(product_prod(X1,X1),bool) ) > fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) ) ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
r: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_21,type,
a: arrow_411405190le_alt ).
tff(func_def_22,type,
b: arrow_411405190le_alt ).
tff(func_def_23,type,
sK10: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_24,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_25,type,
sK12:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_26,type,
sK13:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_27,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_28,type,
sK15:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_29,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_30,type,
sK17:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_31,type,
sK18:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_32,type,
sK19:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_33,type,
sK20:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_34,type,
sK21:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_35,type,
sK22:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_36,type,
sK23:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,bool)) > X1 ) ).
tff(func_def_37,type,
sK24:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,bool)) > X0 ) ).
tff(func_def_38,type,
sK25:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X0 ) ).
tff(func_def_39,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X1 ) ).
tff(func_def_40,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_41,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X1 ) ).
tff(func_def_42,type,
sK29:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X0 ) ).
tff(func_def_43,type,
sK30:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_44,type,
sK31:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_45,type,
sK32:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_46,type,
sK33:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_47,type,
sK34:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_48,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_49,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_50,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_51,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_52,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_53,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X0 ) ).
tff(func_def_54,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X2 ) ).
tff(func_def_55,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X0 ) ).
tff(func_def_56,type,
sK43:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X2 ) ).
tff(func_def_57,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).
tff(func_def_58,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).
tff(func_def_59,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X1 ) ).
tff(func_def_60,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X0 ) ).
tff(func_def_61,type,
sK48:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_62,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_63,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X0 ) ).
tff(func_def_64,type,
sK51:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_65,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_66,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_67,type,
sK54:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_68,type,
sK55:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_69,type,
sK56:
!>[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_70,type,
sK57:
!>[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_71,type,
sK58:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).
tff(func_def_72,type,
sK59:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).
tff(func_def_73,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).
tff(func_def_74,type,
sK61:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_75,type,
sK62:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_76,type,
sK63:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X4 ) ).
tff(func_def_77,type,
sK64:
!>[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_78,type,
sK65:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X2 ) ).
tff(func_def_79,type,
sK66:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X1 ) ).
tff(func_def_80,type,
sK67:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X0 ) ).
tff(func_def_81,type,
sK68:
!>[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_82,type,
sK69:
!>[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_83,type,
sK70:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).
tff(func_def_84,type,
sK71:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).
tff(func_def_85,type,
sK72:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).
tff(func_def_86,type,
sK73:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).
tff(func_def_87,type,
sK74:
!>[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_88,type,
sK75:
!>[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_89,type,
sK76:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X3 ) ).
tff(func_def_90,type,
sK77:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X2 ) ).
tff(func_def_91,type,
sK78:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X1 ) ).
tff(func_def_92,type,
sK79:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X0 ) ).
tff(func_def_93,type,
sK80: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(pred_def_1,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_2,type,
refl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_3,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_5,type,
sP0: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_6,type,
sP1: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_7,type,
sP2: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_8,type,
sP3: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_9,type,
sP4: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).
tff(pred_def_10,type,
sP5: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_11,type,
sP6: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_12,type,
sP7: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_13,type,
sP8: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).
tff(pred_def_14,type,
sP9: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(f1765,plain,
$false,
inference(avatar_sat_refutation,[],[f601,f606,f611,f615,f619,f623,f627,f631,f635,f639,f643,f647,f652,f657,f662,f666,f670,f676,f680,f684,f688,f693,f697,f701,f705,f713,f717,f721,f725,f729,f735,f739,f743,f753,f757,f761,f765,f769,f773,f777,f798,f816,f820,f824,f828,f841,f852,f859,f863,f867,f871,f897,f927,f931,f935,f939,f943,f947,f951,f955,f985,f989,f993,f997,f1001,f1025,f1029,f1033,f1037,f1065,f1093,f1097,f1103,f1107,f1116,f1121,f1126,f1131,f1136,f1140,f1144,f1148,f1164,f1178,f1182,f1186,f1190,f1279,f1283,f1287,f1291,f1295,f1299,f1343,f1392,f1397,f1403,f1408,f1419,f1425,f1429,f1436,f1440,f1444,f1448,f1452,f1456,f1525,f1596,f1601,f1607,f1612,f1623,f1693,f1700,f1739,f1745,f1751,f1755,f1759,f1763,f1764]) ).
tff(f1764,plain,
( spl81_3
| ~ spl81_17
| ~ spl81_94 ),
inference(avatar_split_clause,[],[f1624,f1341,f668,f608]) ).
tff(f608,plain,
( spl81_3
<=> ( a = b ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_3])]) ).
tff(f668,plain,
( spl81_17
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( sP0(X0,X1,X3,X3)
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_17])]) ).
tff(f1341,plain,
( spl81_94
<=> ! [X0: arrow_411405190le_alt] : ~ sP0(r,b,a,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_94])]) ).
tff(f1624,plain,
( ( a = b )
| ~ spl81_17
| ~ spl81_94 ),
inference(resolution,[],[f1342,f669]) ).
tff(f669,plain,
( ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP0(X0,X1,X3,X3)
| ( X1 = X3 ) )
| ~ spl81_17 ),
inference(avatar_component_clause,[],[f668]) ).
tff(f1342,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP0(r,b,a,X0)
| ~ spl81_94 ),
inference(avatar_component_clause,[],[f1341]) ).
tff(f1763,plain,
spl81_121,
inference(avatar_split_clause,[],[f539,f1761]) ).
tff(f1761,plain,
( spl81_121
<=> ! [X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X10: fun(X1,X3),X8: X0,X6: fun(X4,X2),X9: fun(X0,X1),X7: fun(X2,X3),X5: X4] :
( ( aa(X0,X3,comp(X1,X3,X0,X10,X9),X8) = aa(X4,X3,comp(X2,X3,X4,X7,X6),X5) )
| ( aa(X1,X3,X10,aa(X0,X1,X9,X8)) != aa(X2,X3,X7,aa(X4,X2,X6,X5)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_121])]) ).
tff(f539,plain,
! [X4: $tType,X1: $tType,X0: $tType,X3: $tType,X2: $tType,X10: fun(X1,X3),X8: X0,X6: fun(X4,X2),X9: fun(X0,X1),X7: fun(X2,X3),X5: X4] :
( ( aa(X0,X3,comp(X1,X3,X0,X10,X9),X8) = aa(X4,X3,comp(X2,X3,X4,X7,X6),X5) )
| ( aa(X1,X3,X10,aa(X0,X1,X9,X8)) != aa(X2,X3,X7,aa(X4,X2,X6,X5)) ) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: X4,X6: fun(X4,X2),X7: fun(X2,X3),X8: X0,X9: fun(X0,X1),X10: fun(X1,X3)] :
( ( aa(X0,X3,comp(X1,X3,X0,X10,X9),X8) = aa(X4,X3,comp(X2,X3,X4,X7,X6),X5) )
| ( aa(X1,X3,X10,aa(X0,X1,X9,X8)) != aa(X2,X3,X7,aa(X4,X2,X6,X5)) ) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: X4,X6: fun(X4,X2),X7: fun(X2,X3),X8: X0,X9: fun(X0,X1),X10: fun(X1,X3)] :
( ( aa(X1,X3,X10,aa(X0,X1,X9,X8)) = aa(X2,X3,X7,aa(X4,X2,X6,X5)) )
=> ( aa(X0,X3,comp(X1,X3,X0,X10,X9),X8) = aa(X4,X3,comp(X2,X3,X4,X7,X6),X5) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X2: $tType,X1: $tType,X4: $tType,X0: $tType,X33: $tType,X52: X33,X53: fun(X33,X4),X54: fun(X4,X0),X7: X2,X42: fun(X2,X1),X37: fun(X1,X0)] :
( ( aa(X1,X0,X37,aa(X2,X1,X42,X7)) = aa(X4,X0,X54,aa(X33,X4,X53,X52)) )
=> ( aa(X2,X0,comp(X1,X0,X2,X37,X42),X7) = aa(X33,X0,comp(X4,X0,X33,X54,X53),X52) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_comp__cong) ).
tff(f1759,plain,
spl81_120,
inference(avatar_split_clause,[],[f520,f1757]) ).
tff(f1757,plain,
( spl81_120
<=> ! [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,[spl81_120])]) ).
tff(f520,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,[],[f181]) ).
tff(f181,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,[],[f62]) ).
tff(f62,axiom,
! [X1: $tType,X2: $tType,X4: $tType,X0: $tType,X42: fun(X2,fun(X4,X1)),X37: fun(X0,product_prod(X2,X4)),X45: X0] : ( aa(X0,X1,product_scomp(X0,X2,X4,X1,X37,X42),X45) = aa(product_prod(X2,X4),X1,aa(fun(X2,fun(X4,X1)),fun(product_prod(X2,X4),X1),product_prod_case(X2,X4,X1),X42),aa(X0,product_prod(X2,X4),X37,X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_scomp__def) ).
tff(f1755,plain,
spl81_119,
inference(avatar_split_clause,[],[f502,f1753]) ).
tff(f1753,plain,
( spl81_119
<=> ! [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,[spl81_119])]) ).
tff(f502,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,[],[f243]) ).
tff(f243,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,[],[f169]) ).
tff(f169,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,[],[f17]) ).
tff(f17,axiom,
! [X0: $tType,X1: $tType,X19: X1,X20: X0,X21: X1,X22: X0] :
( ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X22),X21) = aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X20),X19) )
=> ~ ( ( X20 = X22 )
=> ( X19 != X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Pair__inject) ).
tff(f1751,plain,
spl81_118,
inference(avatar_split_clause,[],[f501,f1749]) ).
tff(f1749,plain,
( spl81_118
<=> ! [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,[spl81_118])]) ).
tff(f501,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,[],[f243]) ).
tff(f1745,plain,
spl81_117,
inference(avatar_split_clause,[],[f477,f1743]) ).
tff(f1743,plain,
( spl81_117
<=> ! [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,[spl81_117])]) ).
tff(f477,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,[],[f232]) ).
tff(f232,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,[],[f149]) ).
tff(f149,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,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType,X1: $tType,X9: X1,X10: X0,X37: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X37,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X10),X9)))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X37),X10),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_curryI) ).
tff(f1739,plain,
spl81_116,
inference(avatar_split_clause,[],[f473,f1737]) ).
tff(f1737,plain,
( spl81_116
<=> ! [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,[spl81_116])]) ).
tff(f473,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,[],[f228]) ).
tff(f228,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,[],[f145]) ).
tff(f145,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,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X1: $tType,X9: X1,X10: X0,X37: fun(product_prod(X0,X1),bool)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),product_curry(X0,X1,bool,X37),X10),X9))
=> pp(aa(product_prod(X0,X1),bool,X37,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X10),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_curryE) ).
tff(f1700,plain,
( spl81_115
| ~ spl81_44
| ~ spl81_45
| ~ spl81_55
| ~ spl81_56
| ~ spl81_92
| ~ spl81_114 ),
inference(avatar_split_clause,[],[f1696,f1691,f1293,f937,f933,f826,f822,f1698]) ).
tff(f1698,plain,
( spl81_115
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X2,fun(X1,X0)),X3: 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),X3) = product_prod_rec(X2,X1,X0,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_115])]) ).
tff(f822,plain,
( spl81_44
<=> ! [X1: $tType,X0: $tType,X3: X0,X2: X1] : ( product_snd(X0,X1,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_44])]) ).
tff(f826,plain,
( spl81_45
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( product_fst(X1,X0,aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X3),X2)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_45])]) ).
tff(f933,plain,
( spl81_55
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),product_fst(X1,X0,X2)),product_snd(X1,X0,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_55])]) ).
tff(f937,plain,
( spl81_56
<=> ! [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),sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_56])]) ).
tff(f1293,plain,
( spl81_92
<=> ! [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,[spl81_92])]) ).
tff(f1691,plain,
( spl81_114
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: fun(X2,fun(X1,X0)),X3: 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),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X4,product_fst(X2,X1,X3)),product_snd(X2,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_114])]) ).
tff(f1696,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: 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),X3) = product_prod_rec(X2,X1,X0,X4,X3) )
| ~ spl81_44
| ~ spl81_45
| ~ spl81_55
| ~ spl81_56
| ~ spl81_92
| ~ spl81_114 ),
inference(forward_demodulation,[],[f1695,f1371]) ).
tff(f1371,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,sK17(X1,X0,X2)),sK18(X1,X0,X2)) )
| ~ spl81_44
| ~ spl81_45
| ~ spl81_55
| ~ spl81_56
| ~ spl81_92 ),
inference(forward_demodulation,[],[f1370,f965]) ).
tff(f965,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( product_fst(X1,X0,X2) = sK17(X1,X0,X2) )
| ~ spl81_45
| ~ spl81_56 ),
inference(superposition,[],[f827,f938]) ).
tff(f938,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),sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X2 )
| ~ spl81_56 ),
inference(avatar_component_clause,[],[f937]) ).
tff(f827,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( product_fst(X1,X0,aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X3),X2)) = X3 )
| ~ spl81_45 ),
inference(avatar_component_clause,[],[f826]) ).
tff(f1370,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,product_fst(X1,X0,X2)),sK18(X1,X0,X2)) )
| ~ spl81_44
| ~ spl81_55
| ~ spl81_56
| ~ spl81_92 ),
inference(forward_demodulation,[],[f1344,f966]) ).
tff(f966,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( product_snd(X1,X0,X2) = sK18(X1,X0,X2) )
| ~ spl81_44
| ~ spl81_56 ),
inference(superposition,[],[f823,f938]) ).
tff(f823,plain,
( ! [X1: $tType,X0: $tType,X2: X1,X3: X0] : ( product_snd(X0,X1,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)) = X2 )
| ~ spl81_44 ),
inference(avatar_component_clause,[],[f822]) ).
tff(f1344,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,product_fst(X1,X0,X2)),product_snd(X1,X0,X2)) = product_prod_rec(X1,X0,X3,X4,X2) )
| ~ spl81_55
| ~ spl81_92 ),
inference(superposition,[],[f1294,f934]) ).
tff(f934,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),product_fst(X1,X0,X2)),product_snd(X1,X0,X2)) = X2 )
| ~ spl81_55 ),
inference(avatar_component_clause,[],[f933]) ).
tff(f1294,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) )
| ~ spl81_92 ),
inference(avatar_component_clause,[],[f1293]) ).
tff(f1695,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: 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),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X4,sK17(X2,X1,X3)),sK18(X2,X1,X3)) )
| ~ spl81_44
| ~ spl81_45
| ~ spl81_56
| ~ spl81_114 ),
inference(forward_demodulation,[],[f1694,f965]) ).
tff(f1694,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: 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),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X4,product_fst(X2,X1,X3)),sK18(X2,X1,X3)) )
| ~ spl81_44
| ~ spl81_56
| ~ spl81_114 ),
inference(forward_demodulation,[],[f1692,f966]) ).
tff(f1692,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: 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),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X4,product_fst(X2,X1,X3)),product_snd(X2,X1,X3)) )
| ~ spl81_114 ),
inference(avatar_component_clause,[],[f1691]) ).
tff(f1693,plain,
spl81_114,
inference(avatar_split_clause,[],[f435,f1691]) ).
tff(f435,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: 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),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X4,product_fst(X2,X1,X3)),product_snd(X2,X1,X3)) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: 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),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X4,product_fst(X2,X1,X3)),product_snd(X2,X1,X3)) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X41: product_prod(X1,X2),X37: fun(X1,fun(X2,X0))] : ( aa(product_prod(X1,X2),X0,aa(fun(X1,fun(X2,X0)),fun(product_prod(X1,X2),X0),product_prod_case(X1,X2,X0),X37),X41) = aa(X2,X0,aa(X1,fun(X2,X0),X37,product_fst(X1,X2,X41)),product_snd(X1,X2,X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_prod__case__beta) ).
tff(f1623,plain,
spl81_113,
inference(avatar_split_clause,[],[f484,f1621]) ).
tff(f1621,plain,
( spl81_113
<=> ! [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,[spl81_113])]) ).
tff(f484,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,[],[f157]) ).
tff(f157,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,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X9: X2,X10: X1,X37: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X37),X10),X9) = aa(product_prod(X1,X2),X0,X37,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X10),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_curry__conv) ).
tff(f1612,plain,
( spl81_112
| ~ spl81_41
| ~ spl81_111 ),
inference(avatar_split_clause,[],[f1608,f1605,f796,f1610]) ).
tff(f1610,plain,
( spl81_112
<=> ! [X1: $tType,X0: $tType,X8: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(X1,bool,comp(product_prod(X0,X1),bool,X1,X2,aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK15(X0,X1,X2))),sK16(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_112])]) ).
tff(f796,plain,
( spl81_41
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X1,X0,X5,aa(X2,X1,X4,X3)) = aa(X2,X0,comp(X1,X0,X2,X5,X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_41])]) ).
tff(f1605,plain,
( spl81_111
<=> ! [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),sK15(X0,X1,X2)),sK16(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_111])]) ).
tff(f1608,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X8: product_prod(X0,X1)] :
( pp(aa(X1,bool,comp(product_prod(X0,X1),bool,X1,X2,aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK15(X0,X1,X2))),sK16(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) )
| ~ spl81_41
| ~ spl81_111 ),
inference(forward_demodulation,[],[f1606,f797]) ).
tff(f797,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X1,X0,X5,aa(X2,X1,X4,X3)) = aa(X2,X0,comp(X1,X0,X2,X5,X4),X3) )
| ~ spl81_41 ),
inference(avatar_component_clause,[],[f796]) ).
tff(f1606,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),sK15(X0,X1,X2)),sK16(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) )
| ~ spl81_111 ),
inference(avatar_component_clause,[],[f1605]) ).
tff(f1607,plain,
spl81_111,
inference(avatar_split_clause,[],[f391,f1605]) ).
tff(f391,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),sK15(X0,X1,X2)),sK16(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( pp(aa(product_prod(X0,X1),bool,X2,sK14(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),sK15(X0,X1,X2)),sK16(X0,X1,X2))))
| ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f283,f285,f284]) ).
tff(f284,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,sK14(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f285,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),sK15(X0,X1,X2)),sK16(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f283,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,[],[f282]) ).
tff(f282,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,[],[f116]) ).
tff(f116,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,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType,X1: $tType,X11: fun(product_prod(X0,X1),bool)] :
( ? [X12: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X11,X12))
<=> ? [X13: X0,X14: X1] : pp(aa(product_prod(X0,X1),bool,X11,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X13),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_split__paired__Ex) ).
tff(f1601,plain,
( spl81_110
| ~ spl81_41
| ~ spl81_109 ),
inference(avatar_split_clause,[],[f1597,f1594,f796,f1599]) ).
tff(f1599,plain,
( spl81_110
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X0,X1),X2: fun(product_prod(X0,X1),bool)] :
( ~ pp(aa(X1,bool,comp(product_prod(X0,X1),bool,X1,X2,aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK11(X0,X1,X2))),sK12(X0,X1,X2)))
| pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_110])]) ).
tff(f1594,plain,
( spl81_109
<=> ! [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),sK11(X0,X1,X2)),sK12(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_109])]) ).
tff(f1597,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X3: product_prod(X0,X1)] :
( ~ pp(aa(X1,bool,comp(product_prod(X0,X1),bool,X1,X2,aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),sK11(X0,X1,X2))),sK12(X0,X1,X2)))
| pp(aa(product_prod(X0,X1),bool,X2,X3)) )
| ~ spl81_41
| ~ spl81_109 ),
inference(forward_demodulation,[],[f1595,f797]) ).
tff(f1595,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),sK11(X0,X1,X2)),sK12(X0,X1,X2)))) )
| ~ spl81_109 ),
inference(avatar_component_clause,[],[f1594]) ).
tff(f1596,plain,
spl81_109,
inference(avatar_split_clause,[],[f390,f1594]) ).
tff(f390,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),sK11(X0,X1,X2)),sK12(X0,X1,X2)))) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,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),sK11(X0,X1,X2)),sK12(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,sK13(X0,X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f278,f280,f279]) ).
tff(f279,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),sK11(X0,X1,X2)),sK12(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f280,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,sK13(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f278,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,[],[f277]) ).
tff(f277,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,[],[f115]) ).
tff(f115,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,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType,X1: $tType,X11: fun(product_prod(X0,X1),bool)] :
( ! [X12: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X11,X12))
<=> ! [X13: X0,X14: X1] : pp(aa(product_prod(X0,X1),bool,X11,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X13),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_split__paired__All) ).
tff(f1525,plain,
( spl81_108
| ~ spl81_15
| ~ spl81_83 ),
inference(avatar_split_clause,[],[f1275,f1162,f659,f1523]) ).
tff(f1523,plain,
( spl81_108
<=> ! [X0: arrow_411405190le_alt] : ~ sP0(sK80,b,a,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_108])]) ).
tff(f659,plain,
( spl81_15
<=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK80,arrow_1985332922le_Lin) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_15])]) ).
tff(f1162,plain,
( spl81_83
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ sP0(X0,b,a,X1)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_83])]) ).
tff(f1275,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP0(sK80,b,a,X0)
| ~ spl81_15
| ~ spl81_83 ),
inference(resolution,[],[f1163,f661]) ).
tff(f661,plain,
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK80,arrow_1985332922le_Lin)
| ~ spl81_15 ),
inference(avatar_component_clause,[],[f659]) ).
tff(f1163,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ~ sP0(X0,b,a,X1) )
| ~ spl81_83 ),
inference(avatar_component_clause,[],[f1162]) ).
tff(f1456,plain,
spl81_107,
inference(avatar_split_clause,[],[f459,f1454]) ).
tff(f1454,plain,
( spl81_107
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP8(X0,X1,X2,X3,X4)
| ~ sP7(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X0),X4)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_107])]) ).
tff(f459,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP8(X0,X1,X2,X3,X4)
| ~ sP7(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X0),X4)
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f328]) ).
tff(f328,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( sP8(X0,X1,X2,X3,X4)
| ~ sP7(X4,X3,X2,X1,X0)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X0),X4)
& ( X1 = X3 ) )
| ( X2 = X3 ) )
& ( ( sP7(X4,X3,X2,X1,X0)
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X0),X4)
| ( X1 != X3 ) )
& ( X2 != X3 ) )
| ~ sP8(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f327]) ).
tff(f327,plain,
! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( sP8(X3,X4,X1,X0,X2)
| ~ sP7(X2,X0,X1,X4,X3)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
& ( X0 = X4 ) )
| ( X0 = X1 ) )
& ( ( sP7(X2,X0,X1,X4,X3)
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
| ( X0 != X4 ) )
& ( X0 != X1 ) )
| ~ sP8(X3,X4,X1,X0,X2) ) ),
inference(flattening,[],[f326]) ).
tff(f326,plain,
! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( sP8(X3,X4,X1,X0,X2)
| ~ sP7(X2,X0,X1,X4,X3)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
& ( X0 = X4 ) )
| ( X0 = X1 ) )
& ( ( sP7(X2,X0,X1,X4,X3)
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
| ( X0 != X4 ) )
& ( X0 != X1 ) )
| ~ sP8(X3,X4,X1,X0,X2) ) ),
inference(nnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP8(X3,X4,X1,X0,X2)
<=> ( sP7(X2,X0,X1,X4,X3)
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
| ( X0 != X4 ) )
& ( X0 != X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
tff(f1452,plain,
spl81_106,
inference(avatar_split_clause,[],[f454,f1450]) ).
tff(f1450,plain,
( spl81_106
<=> ! [X2: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_319942042_below(X0,X3,X4))
| ~ sP8(X4,X3,X2,X1,X0)
| ~ sP9(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_106])]) ).
tff(f454,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_319942042_below(X0,X3,X4))
| ~ sP8(X4,X3,X2,X1,X0)
| ~ sP9(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_319942042_below(X0,X3,X4))
| ~ sP8(X4,X3,X2,X1,X0) )
& ( sP8(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_319942042_below(X0,X3,X4)) ) )
| ~ sP9(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f324]) ).
tff(f324,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_319942042_below(X2,X4,X3))
| ~ sP8(X3,X4,X1,X0,X2) )
& ( sP8(X3,X4,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),X1),X0),arrow_319942042_below(X2,X4,X3)) ) )
| ~ sP9(X2,X0,X1,X4,X3) ),
inference(nnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_319942042_below(X2,X4,X3))
<=> sP8(X3,X4,X1,X0,X2) )
| ~ sP9(X2,X0,X1,X4,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
tff(f1448,plain,
spl81_105,
inference(avatar_split_clause,[],[f453,f1446]) ).
tff(f1446,plain,
( spl81_105
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP8(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_319942042_below(X0,X3,X4))
| ~ sP9(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_105])]) ).
tff(f453,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP8(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_319942042_below(X0,X3,X4))
| ~ sP9(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f325]) ).
tff(f1444,plain,
spl81_104,
inference(avatar_split_clause,[],[f442,f1442]) ).
tff(f1442,plain,
( spl81_104
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP4(X0,X1,X2,X3,X4)
| ~ sP3(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),X4)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_104])]) ).
tff(f442,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP4(X0,X1,X2,X3,X4)
| ~ sP3(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),X4)
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( sP4(X0,X1,X2,X3,X4)
| ~ sP3(X4,X3,X2,X1,X0)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),X4)
& ( X1 = X2 ) )
| ( X2 = X3 ) )
& ( ( sP3(X4,X3,X2,X1,X0)
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),X4)
| ( X1 != X2 ) )
& ( X2 != X3 ) )
| ~ sP4(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f316]) ).
tff(f316,plain,
! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( sP4(X4,X3,X1,X0,X2)
| ~ sP3(X2,X0,X1,X3,X4)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
& ( X1 = X3 ) )
| ( X0 = X1 ) )
& ( ( sP3(X2,X0,X1,X3,X4)
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
| ( X1 != X3 ) )
& ( X0 != X1 ) )
| ~ sP4(X4,X3,X1,X0,X2) ) ),
inference(flattening,[],[f315]) ).
tff(f315,plain,
! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( sP4(X4,X3,X1,X0,X2)
| ~ sP3(X2,X0,X1,X3,X4)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
& ( X1 = X3 ) )
| ( X0 = X1 ) )
& ( ( sP3(X2,X0,X1,X3,X4)
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
| ( X1 != X3 ) )
& ( X0 != X1 ) )
| ~ sP4(X4,X3,X1,X0,X2) ) ),
inference(nnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X4: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP4(X4,X3,X1,X0,X2)
<=> ( sP3(X2,X0,X1,X3,X4)
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
| ( X1 != X3 ) )
& ( X0 != X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
tff(f1440,plain,
spl81_103,
inference(avatar_split_clause,[],[f437,f1438]) ).
tff(f1438,plain,
( spl81_103
<=> ! [X2: arrow_411405190le_alt,X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_1158827142_above(X0,X4,X3))
| ~ sP4(X4,X3,X2,X1,X0)
| ~ sP5(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_103])]) ).
tff(f437,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_1158827142_above(X0,X4,X3))
| ~ sP4(X4,X3,X2,X1,X0)
| ~ sP5(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_1158827142_above(X0,X4,X3))
| ~ sP4(X4,X3,X2,X1,X0) )
& ( sP4(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_1158827142_above(X0,X4,X3)) ) )
| ~ sP5(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f313]) ).
tff(f313,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_1158827142_above(X2,X4,X3))
| ~ sP4(X4,X3,X1,X0,X2) )
& ( sP4(X4,X3,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),X1),X0),arrow_1158827142_above(X2,X4,X3)) ) )
| ~ sP5(X2,X0,X1,X3,X4) ),
inference(nnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_1158827142_above(X2,X4,X3))
<=> sP4(X4,X3,X1,X0,X2) )
| ~ sP5(X2,X0,X1,X3,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
tff(f1436,plain,
spl81_102,
inference(avatar_split_clause,[],[f436,f1434]) ).
tff(f1434,plain,
( spl81_102
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP4(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_1158827142_above(X0,X4,X3))
| ~ sP5(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_102])]) ).
tff(f436,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP4(X4,X3,X2,X1,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),arrow_1158827142_above(X0,X4,X3))
| ~ sP5(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f314]) ).
tff(f1429,plain,
( spl81_101
| ~ spl81_14
| ~ spl81_83 ),
inference(avatar_split_clause,[],[f1274,f1162,f654,f1427]) ).
tff(f1427,plain,
( spl81_101
<=> ! [X0: arrow_411405190le_alt] : ~ sP0(sK10,b,a,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_101])]) ).
tff(f654,plain,
( spl81_14
<=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK10,arrow_1985332922le_Lin) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_14])]) ).
tff(f1274,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP0(sK10,b,a,X0)
| ~ spl81_14
| ~ spl81_83 ),
inference(resolution,[],[f1163,f656]) ).
tff(f656,plain,
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK10,arrow_1985332922le_Lin)
| ~ spl81_14 ),
inference(avatar_component_clause,[],[f654]) ).
tff(f1425,plain,
( spl81_100
| ~ spl81_44
| ~ spl81_45
| ~ spl81_56
| ~ spl81_99 ),
inference(avatar_split_clause,[],[f1421,f1417,f937,f826,f822,f1423]) ).
tff(f1423,plain,
( spl81_100
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: product_prod(X1,X0)] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK18(X1,X0,X2)),sK17(X1,X0,X2)))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK24(X0,X1,X3)),sK23(X0,X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_100])]) ).
tff(f1417,plain,
( spl81_99
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool)),X2: product_prod(X1,X0)] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK24(X0,X1,X3)),sK23(X0,X1,X3)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,product_snd(X1,X0,X2)),product_fst(X1,X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_99])]) ).
tff(f1421,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0),X3: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK18(X1,X0,X2)),sK17(X1,X0,X2)))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK24(X0,X1,X3)),sK23(X0,X1,X3))) )
| ~ spl81_44
| ~ spl81_45
| ~ spl81_56
| ~ spl81_99 ),
inference(forward_demodulation,[],[f1420,f966]) ).
tff(f1420,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0),X3: fun(X0,fun(X1,bool))] :
( ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,product_snd(X1,X0,X2)),sK17(X1,X0,X2)))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK24(X0,X1,X3)),sK23(X0,X1,X3))) )
| ~ spl81_45
| ~ spl81_56
| ~ spl81_99 ),
inference(forward_demodulation,[],[f1418,f965]) ).
tff(f1418,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK24(X0,X1,X3)),sK23(X0,X1,X3)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,product_snd(X1,X0,X2)),product_fst(X1,X0,X2))) )
| ~ spl81_99 ),
inference(avatar_component_clause,[],[f1417]) ).
tff(f1419,plain,
spl81_99,
inference(avatar_split_clause,[],[f402,f1417]) ).
tff(f402,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X1,X0),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK24(X0,X1,X3)),sK23(X0,X1,X3)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,product_snd(X1,X0,X2)),product_fst(X1,X0,X2))) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK24(X0,X1,X3)),sK23(X0,X1,X3)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,product_snd(X1,X0,X2)),product_fst(X1,X0,X2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f214,f293]) ).
tff(f293,plain,
! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,bool))] :
( ? [X4: X1,X5: X0] : pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,X5),X4))
=> pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK24(X0,X1,X3)),sK23(X0,X1,X3))) ),
introduced(choice_axiom,[]) ).
tff(f214,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0),X3: fun(X0,fun(X1,bool))] :
( ? [X4: X1,X5: X0] : pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,X5),X4))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,product_snd(X1,X0,X2)),product_fst(X1,X0,X2))) ),
inference(ennf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0),X3: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,product_snd(X1,X0,X2)),product_fst(X1,X0,X2)))
=> ~ ! [X4: X1,X5: X0] : ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,X5),X4)) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType,X1: $tType,X41: product_prod(X1,X0),X11: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X11,product_snd(X1,X0,X41)),product_fst(X1,X0,X41)))
=> ~ ! [X28: X1,X29: X0] : ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X11,X29),X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_exE__realizer_H) ).
tff(f1408,plain,
( spl81_98
| ~ spl81_41
| ~ spl81_97 ),
inference(avatar_split_clause,[],[f1404,f1401,f796,f1406]) ).
tff(f1406,plain,
( spl81_98
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( ~ pp(aa(X1,bool,comp(product_prod(X0,X1),bool,X1,X2,aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4)),X5))
| pp(aa(product_prod(X0,X1),bool,X2,sK14(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_98])]) ).
tff(f1401,plain,
( spl81_97
<=> ! [X1: $tType,X0: $tType,X4: X0,X5: X1,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,sK14(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,[spl81_97])]) ).
tff(f1404,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( ~ pp(aa(X1,bool,comp(product_prod(X0,X1),bool,X1,X2,aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4)),X5))
| pp(aa(product_prod(X0,X1),bool,X2,sK14(X0,X1,X2))) )
| ~ spl81_41
| ~ spl81_97 ),
inference(forward_demodulation,[],[f1402,f797]) ).
tff(f1402,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,sK14(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))) )
| ~ spl81_97 ),
inference(avatar_component_clause,[],[f1401]) ).
tff(f1403,plain,
spl81_97,
inference(avatar_split_clause,[],[f392,f1401]) ).
tff(f392,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,sK14(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,[],[f286]) ).
tff(f1397,plain,
( spl81_96
| ~ spl81_41
| ~ spl81_95 ),
inference(avatar_split_clause,[],[f1393,f1390,f796,f1395]) ).
tff(f1395,plain,
( spl81_96
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(X1,bool,comp(product_prod(X0,X1),bool,X1,X2,aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6)),X7))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK13(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_96])]) ).
tff(f1390,plain,
( spl81_95
<=> ! [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,sK13(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_95])]) ).
tff(f1393,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X6: X0,X7: X1] :
( pp(aa(X1,bool,comp(product_prod(X0,X1),bool,X1,X2,aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X6)),X7))
| ~ pp(aa(product_prod(X0,X1),bool,X2,sK13(X0,X1,X2))) )
| ~ spl81_41
| ~ spl81_95 ),
inference(forward_demodulation,[],[f1391,f797]) ).
tff(f1391,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,sK13(X0,X1,X2))) )
| ~ spl81_95 ),
inference(avatar_component_clause,[],[f1390]) ).
tff(f1392,plain,
spl81_95,
inference(avatar_split_clause,[],[f389,f1390]) ).
tff(f389,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,sK13(X0,X1,X2))) ),
inference(cnf_transformation,[],[f281]) ).
tff(f1343,plain,
( spl81_94
| ~ spl81_13
| ~ spl81_83 ),
inference(avatar_split_clause,[],[f1273,f1162,f649,f1341]) ).
tff(f649,plain,
( spl81_13
<=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),r,arrow_1985332922le_Lin) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_13])]) ).
tff(f1273,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP0(r,b,a,X0)
| ~ spl81_13
| ~ spl81_83 ),
inference(resolution,[],[f1163,f651]) ).
tff(f651,plain,
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),r,arrow_1985332922le_Lin)
| ~ spl81_13 ),
inference(avatar_component_clause,[],[f649]) ).
tff(f1299,plain,
spl81_93,
inference(avatar_split_clause,[],[f532,f1297]) ).
tff(f1297,plain,
( spl81_93
<=> ! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X8: X3,X6: fun(X3,X0),X7: fun(X0,X1),X4: fun(X3,X2),X5: fun(X2,X1)] :
( ( aa(X0,X1,X7,aa(X3,X0,X6,X8)) = aa(X2,X1,X5,aa(X3,X2,X4,X8)) )
| ( comp(X0,X1,X3,X7,X6) != comp(X2,X1,X3,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_93])]) ).
tff(f532,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X8: X3,X6: fun(X3,X0),X7: fun(X0,X1),X4: fun(X3,X2),X5: fun(X2,X1)] :
( ( aa(X0,X1,X7,aa(X3,X0,X6,X8)) = aa(X2,X1,X5,aa(X3,X2,X4,X8)) )
| ( comp(X0,X1,X3,X7,X6) != comp(X2,X1,X3,X5,X4) ) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: fun(X3,X2),X5: fun(X2,X1),X6: fun(X3,X0),X7: fun(X0,X1)] :
( ! [X8: X3] : ( aa(X0,X1,X7,aa(X3,X0,X6,X8)) = aa(X2,X1,X5,aa(X3,X2,X4,X8)) )
| ( comp(X0,X1,X3,X7,X6) != comp(X2,X1,X3,X5,X4) ) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: fun(X3,X2),X5: fun(X2,X1),X6: fun(X3,X0),X7: fun(X0,X1)] :
( ( comp(X0,X1,X3,X7,X6) = comp(X2,X1,X3,X5,X4) )
=> ! [X8: X3] : ( aa(X0,X1,X7,aa(X3,X0,X6,X8)) = aa(X2,X1,X5,aa(X3,X2,X4,X8)) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X2: $tType,X1: $tType,X4: $tType,X0: $tType,X55: fun(X0,X4),X36: fun(X4,X1),X9: fun(X0,X2),X10: fun(X2,X1)] :
( ( comp(X2,X1,X0,X10,X9) = comp(X4,X1,X0,X36,X55) )
=> ! [X56: X0] : ( aa(X2,X1,X10,aa(X0,X2,X9,X56)) = aa(X4,X1,X36,aa(X0,X4,X55,X56)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_o__eq__elim) ).
tff(f1295,plain,
spl81_92,
inference(avatar_split_clause,[],[f483,f1293]) ).
tff(f483,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,[],[f156]) ).
tff(f156,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,[],[f19]) ).
tff(f19,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X9: X2,X10: X1,X23: fun(X1,fun(X2,X0))] : ( product_prod_rec(X1,X2,X0,X23,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X10),X9)) = aa(X2,X0,aa(X1,fun(X2,X0),X23,X10),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_prod_Orecs) ).
tff(f1291,plain,
spl81_91,
inference(avatar_split_clause,[],[f464,f1289]) ).
tff(f1289,plain,
( spl81_91
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP7(X0,X1,X2,X3,X4)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ~ sP6(X0,X1,X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_91])]) ).
tff(f464,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP7(X0,X1,X2,X3,X4)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ~ sP6(X0,X1,X4,X3,X2) ),
inference(cnf_transformation,[],[f331]) ).
tff(f331,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP7(X0,X1,X2,X3,X4)
| ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
& ( X2 != X3 ) )
| ~ sP6(X0,X1,X4,X3,X2) )
& ( X1 != X3 ) ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X2 = X3 ) )
& sP6(X0,X1,X4,X3,X2) )
| ( X1 = X3 )
| ~ sP7(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f330]) ).
tff(f330,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( sP7(X2,X0,X1,X4,X3)
| ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
& ( X1 != X4 ) )
| ~ sP6(X2,X0,X3,X4,X1) )
& ( X0 != X4 ) ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X1 = X4 ) )
& sP6(X2,X0,X3,X4,X1) )
| ( X0 = X4 )
| ~ sP7(X2,X0,X1,X4,X3) ) ),
inference(flattening,[],[f329]) ).
tff(f329,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( sP7(X2,X0,X1,X4,X3)
| ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
& ( X1 != X4 ) )
| ~ sP6(X2,X0,X3,X4,X1) )
& ( X0 != X4 ) ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X1 = X4 ) )
& sP6(X2,X0,X3,X4,X1) )
| ( X0 = X4 )
| ~ sP7(X2,X0,X1,X4,X3) ) ),
inference(nnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( sP7(X2,X0,X1,X4,X3)
<=> ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X1 = X4 ) )
& sP6(X2,X0,X3,X4,X1) )
| ( X0 = X4 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
tff(f1287,plain,
spl81_90,
inference(avatar_split_clause,[],[f461,f1285]) ).
tff(f1285,plain,
( spl81_90
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X2 = X3 )
| ( X1 = X3 )
| ~ sP7(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_90])]) ).
tff(f461,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X2 = X3 )
| ( X1 = X3 )
| ~ sP7(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f331]) ).
tff(f1283,plain,
spl81_89,
inference(avatar_split_clause,[],[f447,f1281]) ).
tff(f1281,plain,
( spl81_89
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP3(X0,X1,X2,X3,X4)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ~ sP2(X0,X4,X2,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_89])]) ).
tff(f447,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP3(X0,X1,X2,X3,X4)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ~ sP2(X0,X4,X2,X3,X1) ),
inference(cnf_transformation,[],[f320]) ).
tff(f320,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP3(X0,X1,X2,X3,X4)
| ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
& ( X1 != X3 ) )
| ~ sP2(X0,X4,X2,X3,X1) )
& ( X2 != X3 ) ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X3 ) )
& sP2(X0,X4,X2,X3,X1) )
| ( X2 = X3 )
| ~ sP3(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f319]) ).
tff(f319,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP3(X2,X0,X1,X3,X4)
| ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
& ( X0 != X3 ) )
| ~ sP2(X2,X4,X1,X3,X0) )
& ( X1 != X3 ) ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X0 = X3 ) )
& sP2(X2,X4,X1,X3,X0) )
| ( X1 = X3 )
| ~ sP3(X2,X0,X1,X3,X4) ) ),
inference(flattening,[],[f318]) ).
tff(f318,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP3(X2,X0,X1,X3,X4)
| ( ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
& ( X0 != X3 ) )
| ~ sP2(X2,X4,X1,X3,X0) )
& ( X1 != X3 ) ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X0 = X3 ) )
& sP2(X2,X4,X1,X3,X0) )
| ( X1 = X3 )
| ~ sP3(X2,X0,X1,X3,X4) ) ),
inference(nnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP3(X2,X0,X1,X3,X4)
<=> ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X0 = X3 ) )
& sP2(X2,X4,X1,X3,X0) )
| ( X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f1279,plain,
spl81_88,
inference(avatar_split_clause,[],[f444,f1277]) ).
tff(f1277,plain,
( spl81_88
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X3 )
| ( X2 = X3 )
| ~ sP3(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_88])]) ).
tff(f444,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X3 )
| ( X2 = X3 )
| ~ sP3(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f320]) ).
tff(f1190,plain,
spl81_87,
inference(avatar_split_clause,[],[f426,f1188]) ).
tff(f1188,plain,
( spl81_87
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP1(X0,X1,X2,X3)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_87])]) ).
tff(f426,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP1(X0,X1,X2,X3)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( sP1(X0,X1,X2,X3)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
& ( X1 != X3 ) )
| ( ( X1 = X2 )
& ( X1 = X3 ) )
| ( X2 = X3 ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X3 ) )
& ( ( X1 != X2 )
| ( X1 != X3 ) )
& ( X2 != X3 ) )
| ~ sP1(X0,X1,X2,X3) ) ),
inference(rectify,[],[f308]) ).
tff(f308,plain,
! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( sP1(X1,X2,X3,X0)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
& ( X0 != X2 ) )
| ( ( X2 = X3 )
& ( X0 = X2 ) )
| ( X0 = X3 ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
| ( X0 = X2 ) )
& ( ( X2 != X3 )
| ( X0 != X2 ) )
& ( X0 != X3 ) )
| ~ sP1(X1,X2,X3,X0) ) ),
inference(flattening,[],[f307]) ).
tff(f307,plain,
! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( sP1(X1,X2,X3,X0)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
& ( X0 != X2 ) )
| ( ( X2 = X3 )
& ( X0 = X2 ) )
| ( X0 = X3 ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
| ( X0 = X2 ) )
& ( ( X2 != X3 )
| ( X0 != X2 ) )
& ( X0 != X3 ) )
| ~ sP1(X1,X2,X3,X0) ) ),
inference(nnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( sP1(X1,X2,X3,X0)
<=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
| ( X0 = X2 ) )
& ( ( X2 != X3 )
| ( X0 != X2 ) )
& ( X0 != X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1186,plain,
spl81_86,
inference(avatar_split_clause,[],[f425,f1184]) ).
tff(f1184,plain,
( spl81_86
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP1(X0,X1,X2,X3)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X3 )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_86])]) ).
tff(f425,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP1(X0,X1,X2,X3)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X3 )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f1182,plain,
spl81_85,
inference(avatar_split_clause,[],[f417,f1180]) ).
tff(f1180,plain,
( spl81_85
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_85])]) ).
tff(f417,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ( X1 = X3 ) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( sP0(X0,X1,X2,X3)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
& ( X2 != X3 ) )
| ( ( X1 = X2 )
& ( X2 = X3 ) )
| ( X1 = X3 ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X2 = X3 ) )
& ( ( X1 != X2 )
| ( X2 != X3 ) )
& ( X1 != X3 ) )
| ~ sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f304]) ).
tff(f304,plain,
! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( sP0(X1,X2,X3,X0)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
& ( X0 != X3 ) )
| ( ( X2 = X3 )
& ( X0 = X3 ) )
| ( X0 = X2 ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
| ( X0 = X3 ) )
& ( ( X2 != X3 )
| ( X0 != X3 ) )
& ( X0 != X2 ) )
| ~ sP0(X1,X2,X3,X0) ) ),
inference(flattening,[],[f303]) ).
tff(f303,plain,
! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( sP0(X1,X2,X3,X0)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
& ( X0 != X3 ) )
| ( ( X2 = X3 )
& ( X0 = X3 ) )
| ( X0 = X2 ) )
& ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
| ( X0 = X3 ) )
& ( ( X2 != X3 )
| ( X0 != X3 ) )
& ( X0 != X2 ) )
| ~ sP0(X1,X2,X3,X0) ) ),
inference(nnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( sP0(X1,X2,X3,X0)
<=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
| ( X0 = X3 ) )
& ( ( X2 != X3 )
| ( X0 != X3 ) )
& ( X0 != X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1178,plain,
spl81_84,
inference(avatar_split_clause,[],[f416,f1176]) ).
tff(f1176,plain,
( spl81_84
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X2 = X3 )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_84])]) ).
tff(f416,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X2 = X3 )
| ( X1 = X3 ) ),
inference(cnf_transformation,[],[f305]) ).
tff(f1164,plain,
( spl81_83
| ~ spl81_35
| ~ spl81_70 ),
inference(avatar_split_clause,[],[f1112,f1063,f755,f1162]) ).
tff(f755,plain,
( spl81_35
<=> ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X1,X0),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_35])]) ).
tff(f1063,plain,
( spl81_70
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ sP0(X0,b,a,X1)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X0,X1),arrow_1985332922le_Lin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_70])]) ).
tff(f1112,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ sP0(X0,b,a,X1)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) )
| ~ spl81_35
| ~ spl81_70 ),
inference(resolution,[],[f1064,f756]) ).
tff(f756,plain,
( ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X1,X0),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) )
| ~ spl81_35 ),
inference(avatar_component_clause,[],[f755]) ).
tff(f1064,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X0,X1),arrow_1985332922le_Lin)
| ~ sP0(X0,b,a,X1) )
| ~ spl81_70 ),
inference(avatar_component_clause,[],[f1063]) ).
tff(f1148,plain,
( spl81_82
| ~ spl81_45
| ~ spl81_56
| ~ spl81_78 ),
inference(avatar_split_clause,[],[f1132,f1129,f937,f826,f1146]) ).
tff(f1146,plain,
( spl81_82
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X2,X0),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,sK17(X2,X1,X4)) != aa(X2,X0,X3,sK17(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_82])]) ).
tff(f1129,plain,
( spl81_78
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X2,X0),X5: fun(X2,X0)] :
( ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) )
| ( aa(X2,X0,X5,product_fst(X2,X1,X4)) != aa(X2,X0,X3,product_fst(X2,X1,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_78])]) ).
tff(f1132,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,sK17(X2,X1,X4)) != aa(X2,X0,X3,sK17(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) ) )
| ~ spl81_45
| ~ spl81_56
| ~ spl81_78 ),
inference(forward_demodulation,[],[f1130,f965]) ).
tff(f1130,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) )
| ( aa(X2,X0,X5,product_fst(X2,X1,X4)) != aa(X2,X0,X3,product_fst(X2,X1,X4)) ) )
| ~ spl81_78 ),
inference(avatar_component_clause,[],[f1129]) ).
tff(f1144,plain,
( spl81_81
| ~ spl81_45
| ~ spl81_56
| ~ spl81_77 ),
inference(avatar_split_clause,[],[f1127,f1124,f937,f826,f1142]) ).
tff(f1142,plain,
( spl81_81
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X2,X0),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,sK17(X2,X1,X4)) = aa(X2,X0,X3,sK17(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) != product_apfst(X2,X0,X1,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_81])]) ).
tff(f1124,plain,
( spl81_77
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X2,X0),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,product_fst(X2,X1,X4)) = aa(X2,X0,X3,product_fst(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) != product_apfst(X2,X0,X1,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_77])]) ).
tff(f1127,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,sK17(X2,X1,X4)) = aa(X2,X0,X3,sK17(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) != product_apfst(X2,X0,X1,X3,X4) ) )
| ~ spl81_45
| ~ spl81_56
| ~ spl81_77 ),
inference(forward_demodulation,[],[f1125,f965]) ).
tff(f1125,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,product_fst(X2,X1,X4)) = aa(X2,X0,X3,product_fst(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) != product_apfst(X2,X0,X1,X3,X4) ) )
| ~ spl81_77 ),
inference(avatar_component_clause,[],[f1124]) ).
tff(f1140,plain,
( spl81_80
| ~ spl81_44
| ~ spl81_56
| ~ spl81_76 ),
inference(avatar_split_clause,[],[f1122,f1119,f937,f822,f1138]) ).
tff(f1138,plain,
( spl81_80
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X1,X0),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,sK18(X2,X1,X4)) != aa(X1,X0,X3,sK18(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_80])]) ).
tff(f1119,plain,
( spl81_76
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: product_prod(X2,X1),X3: fun(X1,X0)] :
( ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) )
| ( aa(X1,X0,X5,product_snd(X2,X1,X4)) != aa(X1,X0,X3,product_snd(X2,X1,X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_76])]) ).
tff(f1122,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,sK18(X2,X1,X4)) != aa(X1,X0,X3,sK18(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) ) )
| ~ spl81_44
| ~ spl81_56
| ~ spl81_76 ),
inference(forward_demodulation,[],[f1120,f966]) ).
tff(f1120,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) )
| ( aa(X1,X0,X5,product_snd(X2,X1,X4)) != aa(X1,X0,X3,product_snd(X2,X1,X4)) ) )
| ~ spl81_76 ),
inference(avatar_component_clause,[],[f1119]) ).
tff(f1136,plain,
( spl81_79
| ~ spl81_44
| ~ spl81_56
| ~ spl81_75 ),
inference(avatar_split_clause,[],[f1117,f1114,f937,f822,f1134]) ).
tff(f1134,plain,
( spl81_79
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X1,X0),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,sK18(X2,X1,X4)) = aa(X1,X0,X3,sK18(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) != product_apsnd(X1,X0,X2,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_79])]) ).
tff(f1114,plain,
( spl81_75
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X1,X0),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,product_snd(X2,X1,X4)) = aa(X1,X0,X3,product_snd(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) != product_apsnd(X1,X0,X2,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_75])]) ).
tff(f1117,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,sK18(X2,X1,X4)) = aa(X1,X0,X3,sK18(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) != product_apsnd(X1,X0,X2,X3,X4) ) )
| ~ spl81_44
| ~ spl81_56
| ~ spl81_75 ),
inference(forward_demodulation,[],[f1115,f966]) ).
tff(f1115,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,product_snd(X2,X1,X4)) = aa(X1,X0,X3,product_snd(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) != product_apsnd(X1,X0,X2,X3,X4) ) )
| ~ spl81_75 ),
inference(avatar_component_clause,[],[f1114]) ).
tff(f1131,plain,
spl81_78,
inference(avatar_split_clause,[],[f511,f1129]) ).
tff(f511,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) )
| ( aa(X2,X0,X5,product_fst(X2,X1,X4)) != aa(X2,X0,X3,product_fst(X2,X1,X4)) ) ),
inference(cnf_transformation,[],[f354]) ).
tff(f354,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) )
| ( aa(X2,X0,X5,product_fst(X2,X1,X4)) != aa(X2,X0,X3,product_fst(X2,X1,X4)) ) )
& ( ( aa(X2,X0,X5,product_fst(X2,X1,X4)) = aa(X2,X0,X3,product_fst(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) != product_apfst(X2,X0,X1,X3,X4) ) ) ),
inference(nnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) )
<=> ( aa(X2,X0,X5,product_fst(X2,X1,X4)) = aa(X2,X0,X3,product_fst(X2,X1,X4)) ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X42: fun(X2,X0),X7: product_prod(X2,X1),X37: fun(X2,X0)] :
( ( product_apfst(X2,X0,X1,X37,X7) = product_apfst(X2,X0,X1,X42,X7) )
<=> ( aa(X2,X0,X37,product_fst(X2,X1,X7)) = aa(X2,X0,X42,product_fst(X2,X1,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_apfst__eq__conv) ).
tff(f1126,plain,
spl81_77,
inference(avatar_split_clause,[],[f510,f1124]) ).
tff(f510,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,product_fst(X2,X1,X4)) = aa(X2,X0,X3,product_fst(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) != product_apfst(X2,X0,X1,X3,X4) ) ),
inference(cnf_transformation,[],[f354]) ).
tff(f1121,plain,
spl81_76,
inference(avatar_split_clause,[],[f509,f1119]) ).
tff(f509,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) )
| ( aa(X1,X0,X5,product_snd(X2,X1,X4)) != aa(X1,X0,X3,product_snd(X2,X1,X4)) ) ),
inference(cnf_transformation,[],[f353]) ).
tff(f353,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) )
| ( aa(X1,X0,X5,product_snd(X2,X1,X4)) != aa(X1,X0,X3,product_snd(X2,X1,X4)) ) )
& ( ( aa(X1,X0,X5,product_snd(X2,X1,X4)) = aa(X1,X0,X3,product_snd(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) != product_apsnd(X1,X0,X2,X3,X4) ) ) ),
inference(nnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) )
<=> ( aa(X1,X0,X5,product_snd(X2,X1,X4)) = aa(X1,X0,X3,product_snd(X2,X1,X4)) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X1: $tType,X2: $tType,X0: $tType,X42: fun(X2,X1),X7: product_prod(X0,X2),X37: fun(X2,X1)] :
( ( product_apsnd(X2,X1,X0,X37,X7) = product_apsnd(X2,X1,X0,X42,X7) )
<=> ( aa(X2,X1,X37,product_snd(X0,X2,X7)) = aa(X2,X1,X42,product_snd(X0,X2,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_apsnd__eq__conv) ).
tff(f1116,plain,
spl81_75,
inference(avatar_split_clause,[],[f508,f1114]) ).
tff(f508,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,product_snd(X2,X1,X4)) = aa(X1,X0,X3,product_snd(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) != product_apsnd(X1,X0,X2,X3,X4) ) ),
inference(cnf_transformation,[],[f353]) ).
tff(f1107,plain,
spl81_74,
inference(avatar_split_clause,[],[f565,f1105]) ).
tff(f1105,plain,
( spl81_74
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ~ sP6(X0,X1,X2,X4,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_74])]) ).
tff(f565,plain,
! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ~ sP6(X0,X1,X2,X4,X4) ),
inference(equality_resolution,[],[f465]) ).
tff(f465,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ( X3 != X4 )
| ~ sP6(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f334]) ).
tff(f334,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP6(X0,X1,X2,X3,X4)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
& ( X1 != X2 )
& ( X3 = X4 ) ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ( X3 != X4 )
| ~ sP6(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f333]) ).
tff(f333,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( sP6(X2,X0,X3,X4,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),X3),X0),X2)
& ( X0 != X3 )
& ( X1 = X4 ) ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
| ( X0 = X3 )
| ( X1 != X4 )
| ~ sP6(X2,X0,X3,X4,X1) ) ),
inference(flattening,[],[f332]) ).
tff(f332,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( sP6(X2,X0,X3,X4,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),X3),X0),X2)
& ( X0 != X3 )
& ( X1 = X4 ) ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
| ( X0 = X3 )
| ( X1 != X4 )
| ~ sP6(X2,X0,X3,X4,X1) ) ),
inference(nnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP6(X2,X0,X3,X4,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),X3),X0),X2)
| ( X0 = X3 )
| ( X1 != X4 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
tff(f1103,plain,
spl81_73,
inference(avatar_split_clause,[],[f559,f1101]) ).
tff(f1101,plain,
( spl81_73
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ~ sP2(X0,X1,X2,X4,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_73])]) ).
tff(f559,plain,
! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ~ sP2(X0,X1,X2,X4,X4) ),
inference(equality_resolution,[],[f448]) ).
tff(f448,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ( X3 != X4 )
| ~ sP2(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( sP2(X0,X1,X2,X3,X4)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
& ( X1 != X2 )
& ( X3 = X4 ) ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X2 )
| ( X3 != X4 )
| ~ sP2(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f322]) ).
tff(f322,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( sP2(X2,X4,X1,X3,X0)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
& ( X1 != X4 )
& ( X0 = X3 ) ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
| ( X1 = X4 )
| ( X0 != X3 )
| ~ sP2(X2,X4,X1,X3,X0) ) ),
inference(flattening,[],[f321]) ).
tff(f321,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( sP2(X2,X4,X1,X3,X0)
| ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
& ( X1 != X4 )
& ( X0 = X3 ) ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
| ( X1 = X4 )
| ( X0 != X3 )
| ~ sP2(X2,X4,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( sP2(X2,X4,X1,X3,X0)
<=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
| ( X1 = X4 )
| ( X0 != X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f1097,plain,
spl81_72,
inference(avatar_split_clause,[],[f422,f1095]) ).
tff(f1095,plain,
( spl81_72
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X3 )
| ~ sP1(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_72])]) ).
tff(f422,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X1 = X3 )
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f309]) ).
tff(f1093,plain,
spl81_71,
inference(avatar_split_clause,[],[f413,f1091]) ).
tff(f1091,plain,
( spl81_71
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X2 = X3 )
| ~ sP0(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_71])]) ).
tff(f413,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0)
| ( X2 = X3 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f305]) ).
tff(f1065,plain,
( spl81_70
| ~ spl81_12
| ~ spl81_67 ),
inference(avatar_split_clause,[],[f1049,f1027,f645,f1063]) ).
tff(f645,plain,
( spl81_12
<=> ! [X0: 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),a),b),X0)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_12])]) ).
tff(f1027,plain,
( spl81_67
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
| ~ sP0(X1,X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_67])]) ).
tff(f1049,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ sP0(X0,b,a,X1)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X0,X1),arrow_1985332922le_Lin) )
| ~ spl81_12
| ~ spl81_67 ),
inference(resolution,[],[f1028,f646]) ).
tff(f646,plain,
( ! [X0: 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),a),b),X0)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) )
| ~ spl81_12 ),
inference(avatar_component_clause,[],[f645]) ).
tff(f1028,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
| ~ sP0(X1,X2,X3,X0) )
| ~ spl81_67 ),
inference(avatar_component_clause,[],[f1027]) ).
tff(f1037,plain,
spl81_69,
inference(avatar_split_clause,[],[f428,f1035]) ).
tff(f1035,plain,
( spl81_69
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
| ~ sP1(X1,X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_69])]) ).
tff(f428,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
| ~ sP1(X1,X2,X3,X0) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
| ~ sP1(X1,X2,X3,X0) )
& ( sP1(X1,X2,X3,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0)) ) ),
inference(nnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
<=> sP1(X1,X2,X3,X0) ),
inference(definition_folding,[],[f219,f261]) ).
tff(f219,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
<=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
| ( X0 = X2 ) )
& ( ( X2 != X3 )
| ( X0 != X2 ) )
& ( X0 != X3 ) ) ),
inference(ennf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0))
<=> ( ( ( X0 != X2 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1) )
& ( ( X0 = X2 )
=> ( X2 != X3 ) )
& ( X0 != X3 ) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X18: arrow_411405190le_alt,X8: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X6),arrow_424895264_mktop(X8,X18))
<=> ( ( ( X6 != 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),X7),X6),X8) )
& ( ( X6 = X18 )
=> ( X6 != X7 ) )
& ( X7 != X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_in__mktop) ).
tff(f1033,plain,
spl81_68,
inference(avatar_split_clause,[],[f427,f1031]) ).
tff(f1031,plain,
( spl81_68
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP1(X1,X2,X3,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_68])]) ).
tff(f427,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP1(X1,X2,X3,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_424895264_mktop(X1,X0)) ),
inference(cnf_transformation,[],[f310]) ).
tff(f1029,plain,
spl81_67,
inference(avatar_split_clause,[],[f419,f1027]) ).
tff(f419,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
| ~ sP0(X1,X2,X3,X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
| ~ sP0(X1,X2,X3,X0) )
& ( sP0(X1,X2,X3,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0)) ) ),
inference(nnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
<=> sP0(X1,X2,X3,X0) ),
inference(definition_folding,[],[f218,f259]) ).
tff(f218,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
<=> ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1)
| ( X0 = X3 ) )
& ( ( X2 != X3 )
| ( X0 != X3 ) )
& ( X0 != X2 ) ) ),
inference(ennf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
<=> ( ( ( X0 != X3 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),X1) )
& ( ( X0 = X3 )
=> ( X2 != X3 ) )
& ( X0 != X2 ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X18: arrow_411405190le_alt,X8: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X6),arrow_276188178_mkbot(X8,X18))
<=> ( ( ( X7 != 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),X7),X6),X8) )
& ( ( X7 = X18 )
=> ( X6 != X7 ) )
& ( X6 != X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_in__mkbot) ).
tff(f1025,plain,
spl81_66,
inference(avatar_split_clause,[],[f418,f1023]) ).
tff(f1023,plain,
( spl81_66
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP0(X1,X2,X3,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_66])]) ).
tff(f418,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP0(X1,X2,X3,X0)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0)) ),
inference(cnf_transformation,[],[f306]) ).
tff(f1001,plain,
( spl81_65
| ~ spl81_15
| ~ spl81_32 ),
inference(avatar_split_clause,[],[f746,f737,f659,f999]) ).
tff(f999,plain,
( spl81_65
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(sK80,X0,X1,X2,X3)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_65])]) ).
tff(f737,plain,
( spl81_32
<=> ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(X2,X0,X1,X3,X4)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_32])]) ).
tff(f746,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(sK80,X0,X1,X2,X3)
| ( X2 = X3 ) )
| ~ spl81_15
| ~ spl81_32 ),
inference(resolution,[],[f738,f661]) ).
tff(f738,plain,
( ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| sP5(X2,X0,X1,X3,X4)
| ( X3 = X4 ) )
| ~ spl81_32 ),
inference(avatar_component_clause,[],[f737]) ).
tff(f997,plain,
spl81_64,
inference(avatar_split_clause,[],[f560,f995]) ).
tff(f995,plain,
( spl81_64
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X0),X4)
| ~ sP8(X0,X3,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_64])]) ).
tff(f560,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X0),X4)
| ~ sP8(X0,X3,X2,X3,X4) ),
inference(equality_resolution,[],[f456]) ).
tff(f456,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X0),X4)
| ( X1 != X3 )
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f328]) ).
tff(f993,plain,
spl81_63,
inference(avatar_split_clause,[],[f554,f991]) ).
tff(f991,plain,
( spl81_63
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),X4)
| ~ sP4(X0,X2,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_63])]) ).
tff(f554,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),X4)
| ~ sP4(X0,X2,X2,X3,X4) ),
inference(equality_resolution,[],[f439]) ).
tff(f439,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X3),X4)
| ( X1 != X2 )
| ~ sP4(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f317]) ).
tff(f989,plain,
spl81_62,
inference(avatar_split_clause,[],[f468,f987]) ).
tff(f987,plain,
( spl81_62
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP6(X0,X1,X2,X3,X4)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_62])]) ).
tff(f468,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP6(X0,X1,X2,X3,X4)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0) ),
inference(cnf_transformation,[],[f334]) ).
tff(f985,plain,
spl81_61,
inference(avatar_split_clause,[],[f451,f983]) ).
tff(f983,plain,
( spl81_61
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,X4)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_61])]) ).
tff(f451,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,X4)
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X1),X0) ),
inference(cnf_transformation,[],[f323]) ).
tff(f955,plain,
spl81_60,
inference(avatar_split_clause,[],[f434,f953]) ).
tff(f953,plain,
( spl81_60
<=> ! [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,[spl81_60])]) ).
tff(f434,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,[],[f138]) ).
tff(f138,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,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X37: fun(X2,fun(X0,X1)),X7: X2] : ( product_scomp(X0,X2,X0,X1,aa(X2,fun(X0,product_prod(X2,X0)),product_Pair(X2,X0),X7),X37) = aa(X2,fun(X0,X1),X37,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Pair__scomp) ).
tff(f951,plain,
( spl81_59
| ~ spl81_14
| ~ spl81_32 ),
inference(avatar_split_clause,[],[f745,f737,f654,f949]) ).
tff(f949,plain,
( spl81_59
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(sK10,X0,X1,X2,X3)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_59])]) ).
tff(f745,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(sK10,X0,X1,X2,X3)
| ( X2 = X3 ) )
| ~ spl81_14
| ~ spl81_32 ),
inference(resolution,[],[f738,f656]) ).
tff(f947,plain,
spl81_58,
inference(avatar_split_clause,[],[f395,f945]) ).
tff(f945,plain,
( spl81_58
<=> ! [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),sK21(X0,X1,X2)),sK22(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_58])]) ).
tff(f395,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),sK21(X0,X1,X2)),sK22(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,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),sK21(X0,X1,X2)),sK22(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f119,f291]) ).
tff(f291,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),sK21(X0,X1,X2)),sK22(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f119,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,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType,X1: $tType,X27: product_prod(X0,X1)] :
? [X28: X0,X29: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X28),X29) = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_surj__pair) ).
tff(f943,plain,
spl81_57,
inference(avatar_split_clause,[],[f394,f941]) ).
tff(f941,plain,
( spl81_57
<=> ! [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),sK19(X0,X1,X2)),sK20(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_57])]) ).
tff(f394,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),sK19(X0,X1,X2)),sK20(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,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),sK19(X0,X1,X2)),sK20(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f211,f289]) ).
tff(f289,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),sK19(X0,X1,X2)),sK20(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f211,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,[],[f118]) ).
tff(f118,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,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X1: $tType,X24: product_prod(X0,X1)] :
~ ! [X25: X0,X26: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X25),X26) != X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_prod_Oexhaust) ).
tff(f939,plain,
spl81_56,
inference(avatar_split_clause,[],[f393,f937]) ).
tff(f393,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),sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,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),sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f210,f287]) ).
tff(f287,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),sK17(X0,X1,X2)),sK18(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f210,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,[],[f117]) ).
tff(f117,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,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType,X1: $tType,X27: product_prod(X0,X1)] :
~ ! [X28: X0,X29: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X28),X29) != X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_PairE) ).
tff(f935,plain,
spl81_55,
inference(avatar_split_clause,[],[f380,f933]) ).
tff(f380,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),product_fst(X1,X0,X2)),product_snd(X1,X0,X2)) = X2 ),
inference(cnf_transformation,[],[f108]) ).
tff(f108,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0)] : ( aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),product_fst(X1,X0,X2)),product_snd(X1,X0,X2)) = X2 ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X1: $tType,X0: $tType,X49: product_prod(X0,X1)] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),product_fst(X0,X1,X49)),product_snd(X0,X1,X49)) = X49 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_surjective__pairing) ).
tff(f931,plain,
spl81_54,
inference(avatar_split_clause,[],[f400,f929]) ).
tff(f929,plain,
( spl81_54
<=> ! [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,[spl81_54])]) ).
tff(f400,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,[],[f124]) ).
tff(f124,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,[],[f51]) ).
tff(f51,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X37: 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,X37)) = X37 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_split__curry) ).
tff(f927,plain,
spl81_53,
inference(avatar_split_clause,[],[f399,f925]) ).
tff(f925,plain,
( spl81_53
<=> ! [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,[spl81_53])]) ).
tff(f399,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,[],[f123]) ).
tff(f123,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,[],[f50]) ).
tff(f50,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X37: 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),X37)) = X37 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_curry__split) ).
tff(f897,plain,
( spl81_52
| ~ spl81_13
| ~ spl81_32 ),
inference(avatar_split_clause,[],[f744,f737,f649,f895]) ).
tff(f895,plain,
( spl81_52
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(r,X0,X1,X2,X3)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_52])]) ).
tff(f744,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(r,X0,X1,X2,X3)
| ( X2 = X3 ) )
| ~ spl81_13
| ~ spl81_32 ),
inference(resolution,[],[f738,f651]) ).
tff(f871,plain,
spl81_51,
inference(avatar_split_clause,[],[f519,f869]) ).
tff(f869,plain,
( spl81_51
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: fun(X2,X0),X4: fun(X3,X2),X6: fun(X0,X1)] : ( comp(X0,X1,X3,X6,comp(X2,X0,X3,X5,X4)) = comp(X2,X1,X3,comp(X0,X1,X2,X6,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_51])]) ).
tff(f519,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(X0,X1),X4: fun(X3,X2),X5: fun(X2,X0)] : ( comp(X0,X1,X3,X6,comp(X2,X0,X3,X5,X4)) = comp(X2,X1,X3,comp(X0,X1,X2,X6,X5),X4) ),
inference(cnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: fun(X3,X2),X5: fun(X2,X0),X6: fun(X0,X1)] : ( comp(X0,X1,X3,X6,comp(X2,X0,X3,X5,X4)) = comp(X2,X1,X3,comp(X0,X1,X2,X6,X5),X4) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X2: $tType,X1: $tType,X4: $tType,X0: $tType,X57: fun(X0,X4),X42: fun(X4,X2),X37: fun(X2,X1)] : ( comp(X2,X1,X0,X37,comp(X4,X2,X0,X42,X57)) = comp(X4,X1,X0,comp(X2,X1,X4,X37,X42),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_o__assoc) ).
tff(f867,plain,
spl81_50,
inference(avatar_split_clause,[],[f518,f865]) ).
tff(f865,plain,
( spl81_50
<=> ! [X1: $tType,X3: $tType,X0: $tType,X2: $tType,X5: fun(X3,X0),X4: product_prod(X3,X2),X6: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X6,product_apfst(X3,X0,X2,X5,X4)) = product_apfst(X3,X1,X2,comp(X0,X1,X3,X6,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_50])]) ).
tff(f518,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(X0,X1),X4: product_prod(X3,X2),X5: fun(X3,X0)] : ( product_apfst(X0,X1,X2,X6,product_apfst(X3,X0,X2,X5,X4)) = product_apfst(X3,X1,X2,comp(X0,X1,X3,X6,X5),X4) ),
inference(cnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X3,X2),X5: fun(X3,X0),X6: fun(X0,X1)] : ( product_apfst(X0,X1,X2,X6,product_apfst(X3,X0,X2,X5,X4)) = product_apfst(X3,X1,X2,comp(X0,X1,X3,X6,X5),X4) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X2: $tType,X0: $tType,X1: $tType,X4: $tType,X7: product_prod(X4,X1),X42: fun(X4,X2),X37: fun(X2,X0)] : ( product_apfst(X2,X0,X1,X37,product_apfst(X4,X2,X1,X42,X7)) = product_apfst(X4,X0,X1,comp(X2,X0,X4,X37,X42),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_apfst__compose) ).
tff(f863,plain,
spl81_49,
inference(avatar_split_clause,[],[f517,f861]) ).
tff(f861,plain,
( spl81_49
<=> ! [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,[spl81_49])]) ).
tff(f517,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,[],[f178]) ).
tff(f178,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,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X4: $tType,X41: product_prod(X4,X2),X42: fun(X4,X0),X37: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X37,product_apfst(X4,X0,X2,X42,X41)) = product_apfst(X4,X0,X1,X42,product_apsnd(X2,X1,X4,X37,X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_apsnd__apfst__commute) ).
tff(f859,plain,
spl81_48,
inference(avatar_split_clause,[],[f516,f857]) ).
tff(f857,plain,
( spl81_48
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: $tType,X5: fun(X2,X0),X4: product_prod(X3,X2),X6: fun(X0,X1)] : ( product_apsnd(X0,X1,X3,X6,product_apsnd(X2,X0,X3,X5,X4)) = product_apsnd(X2,X1,X3,comp(X0,X1,X2,X6,X5),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_48])]) ).
tff(f516,plain,
! [X1: $tType,X0: $tType,X3: $tType,X2: $tType,X6: fun(X0,X1),X4: product_prod(X3,X2),X5: fun(X2,X0)] : ( product_apsnd(X0,X1,X3,X6,product_apsnd(X2,X0,X3,X5,X4)) = product_apsnd(X2,X1,X3,comp(X0,X1,X2,X6,X5),X4) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: product_prod(X3,X2),X5: fun(X2,X0),X6: fun(X0,X1)] : ( product_apsnd(X0,X1,X3,X6,product_apsnd(X2,X0,X3,X5,X4)) = product_apsnd(X2,X1,X3,comp(X0,X1,X2,X6,X5),X4) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X2: $tType,X1: $tType,X4: $tType,X0: $tType,X7: product_prod(X0,X4),X42: fun(X4,X2),X37: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X37,product_apsnd(X4,X2,X0,X42,X7)) = product_apsnd(X4,X1,X0,comp(X2,X1,X4,X37,X42),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_apsnd__compose) ).
tff(f852,plain,
spl81_47,
inference(avatar_split_clause,[],[f405,f850]) ).
tff(f850,plain,
( spl81_47
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK27(X0,X1,X2,X3)) != aa(X1,X0,X2,sK27(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_47])]) ).
tff(f405,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK27(X0,X1,X2,X3)) != aa(X1,X0,X2,sK27(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK27(X0,X1,X2,X3)) != aa(X1,X0,X2,sK27(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f216,f297]) ).
tff(f297,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,sK27(X0,X1,X2,X3)) != aa(X1,X0,X2,sK27(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f216,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,[],[f128]) ).
tff(f128,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,[],[f76]) ).
tff(f76,axiom,
! [X1: $tType,X0: $tType,X42: fun(X0,X1),X37: fun(X0,X1)] :
( ! [X28: X0] : ( aa(X0,X1,X37,X28) = aa(X0,X1,X42,X28) )
=> ( X37 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
tff(f841,plain,
spl81_46,
inference(avatar_split_clause,[],[f401,f839]) ).
tff(f839,plain,
( spl81_46
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X1,X0),X2: product_prod(X1,X0)] :
( ( X2 = X3 )
| ( product_snd(X1,X0,X2) != product_snd(X1,X0,X3) )
| ( product_fst(X1,X0,X2) != product_fst(X1,X0,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_46])]) ).
tff(f401,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X1,X0),X3: product_prod(X1,X0)] :
( ( X2 = X3 )
| ( product_snd(X1,X0,X2) != product_snd(X1,X0,X3) )
| ( product_fst(X1,X0,X2) != product_fst(X1,X0,X3) ) ),
inference(cnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0),X3: product_prod(X1,X0)] :
( ( X2 = X3 )
| ( product_snd(X1,X0,X2) != product_snd(X1,X0,X3) )
| ( product_fst(X1,X0,X2) != product_fst(X1,X0,X3) ) ),
inference(flattening,[],[f212]) ).
tff(f212,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0),X3: product_prod(X1,X0)] :
( ( X2 = X3 )
| ( product_snd(X1,X0,X2) != product_snd(X1,X0,X3) )
| ( product_fst(X1,X0,X2) != product_fst(X1,X0,X3) ) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0),X3: product_prod(X1,X0)] :
( ( product_fst(X1,X0,X2) = product_fst(X1,X0,X3) )
=> ( ( product_snd(X1,X0,X2) = product_snd(X1,X0,X3) )
=> ( X2 = X3 ) ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X1: $tType,X0: $tType,X51: product_prod(X0,X1),X27: product_prod(X0,X1)] :
( ( product_fst(X0,X1,X27) = product_fst(X0,X1,X51) )
=> ( ( product_snd(X0,X1,X27) = product_snd(X0,X1,X51) )
=> ( X27 = X51 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_prod__eqI) ).
tff(f828,plain,
spl81_45,
inference(avatar_split_clause,[],[f398,f826]) ).
tff(f398,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( product_fst(X1,X0,aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X3),X2)) = X3 ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( product_fst(X1,X0,aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X3),X2)) = X3 ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X1: $tType,X0: $tType,X21: X1,X22: X0] : ( product_fst(X0,X1,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X22),X21)) = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_fst__conv) ).
tff(f824,plain,
spl81_44,
inference(avatar_split_clause,[],[f397,f822]) ).
tff(f397,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0] : ( product_snd(X0,X1,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)) = X2 ),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0] : ( product_snd(X0,X1,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X2)) = X2 ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X1: $tType,X0: $tType,X21: X0,X22: X1] : ( product_snd(X1,X0,aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X22),X21)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_snd__conv) ).
tff(f820,plain,
spl81_43,
inference(avatar_split_clause,[],[f383,f818]) ).
tff(f818,plain,
( spl81_43
<=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_319942042_below(X0,X2,X1),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_43])]) ).
tff(f383,plain,
! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_319942042_below(X0,X2,X1),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_319942042_below(X0,X2,X1),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ( X1 = X2 ) ),
inference(flattening,[],[f204]) ).
tff(f204,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_319942042_below(X0,X2,X1),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ( X1 = X2 ) ),
inference(ennf_transformation,[],[f111]) ).
tff(f111,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( ( X1 != X2 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_319942042_below(X0,X2,X1),arrow_1985332922le_Lin) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X8: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( ( X6 != X7 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_319942042_below(X8,X7,X6),arrow_1985332922le_Lin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_below__Lin) ).
tff(f816,plain,
spl81_42,
inference(avatar_split_clause,[],[f382,f814]) ).
tff(f814,plain,
( spl81_42
<=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_1158827142_above(X0,X2,X1),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_42])]) ).
tff(f382,plain,
! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_1158827142_above(X0,X2,X1),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_1158827142_above(X0,X2,X1),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ( X1 = X2 ) ),
inference(flattening,[],[f202]) ).
tff(f202,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_1158827142_above(X0,X2,X1),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
| ( X1 = X2 ) ),
inference(ennf_transformation,[],[f110]) ).
tff(f110,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( ( X1 != X2 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_1158827142_above(X0,X2,X1),arrow_1985332922le_Lin) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X8: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X6: arrow_411405190le_alt,X7: arrow_411405190le_alt] :
( ( X6 != X7 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_1158827142_above(X8,X7,X6),arrow_1985332922le_Lin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_above__Lin) ).
tff(f798,plain,
spl81_41,
inference(avatar_split_clause,[],[f481,f796]) ).
tff(f481,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X1,X0,X5,aa(X2,X1,X4,X3)) = aa(X2,X0,comp(X1,X0,X2,X5,X4),X3) ),
inference(cnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X1,X0,X5,aa(X2,X1,X4,X3)) = aa(X2,X0,comp(X1,X0,X2,X5,X4),X3) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X7: X2,X42: fun(X2,X1),X37: fun(X1,X0)] : ( aa(X1,X0,X37,aa(X2,X1,X42,X7)) = aa(X2,X0,comp(X1,X0,X2,X37,X42),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_o__apply) ).
tff(f777,plain,
spl81_40,
inference(avatar_split_clause,[],[f458,f775]) ).
tff(f775,plain,
( spl81_40
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP8(X0,X1,X2,X3,X4)
| ~ sP7(X4,X3,X2,X1,X0)
| ( X1 = X3 )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_40])]) ).
tff(f458,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP8(X0,X1,X2,X3,X4)
| ~ sP7(X4,X3,X2,X1,X0)
| ( X1 = X3 )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f328]) ).
tff(f773,plain,
spl81_39,
inference(avatar_split_clause,[],[f441,f771]) ).
tff(f771,plain,
( spl81_39
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP4(X0,X1,X2,X3,X4)
| ~ sP3(X4,X3,X2,X1,X0)
| ( X1 = X2 )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_39])]) ).
tff(f441,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP4(X0,X1,X2,X3,X4)
| ~ sP3(X4,X3,X2,X1,X0)
| ( X1 = X2 )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f317]) ).
tff(f769,plain,
spl81_38,
inference(avatar_split_clause,[],[f433,f767]) ).
tff(f767,plain,
( spl81_38
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: fun(X1,X0),X3: product_prod(X2,X1)] : ( product_snd(X2,X0,product_apsnd(X1,X0,X2,X4,X3)) = aa(X1,X0,X4,product_snd(X2,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_38])]) ).
tff(f433,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X1,X0)] : ( product_snd(X2,X0,product_apsnd(X1,X0,X2,X4,X3)) = aa(X1,X0,X4,product_snd(X2,X1,X3)) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X1,X0)] : ( product_snd(X2,X0,product_apsnd(X1,X0,X2,X4,X3)) = aa(X1,X0,X4,product_snd(X2,X1,X3)) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X7: product_prod(X1,X2),X37: fun(X2,X0)] : ( product_snd(X1,X0,product_apsnd(X2,X0,X1,X37,X7)) = aa(X2,X0,X37,product_snd(X1,X2,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_snd__apsnd) ).
tff(f765,plain,
spl81_37,
inference(avatar_split_clause,[],[f432,f763]) ).
tff(f763,plain,
( spl81_37
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: fun(X2,X0),X3: product_prod(X2,X1)] : ( aa(X2,X0,X4,product_fst(X2,X1,X3)) = product_fst(X0,X1,product_apfst(X2,X0,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_37])]) ).
tff(f432,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X2,X0)] : ( aa(X2,X0,X4,product_fst(X2,X1,X3)) = product_fst(X0,X1,product_apfst(X2,X0,X1,X4,X3)) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X2,X0)] : ( aa(X2,X0,X4,product_fst(X2,X1,X3)) = product_fst(X0,X1,product_apfst(X2,X0,X1,X4,X3)) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X7: product_prod(X2,X1),X37: fun(X2,X0)] : ( aa(X2,X0,X37,product_fst(X2,X1,X7)) = product_fst(X0,X1,product_apfst(X2,X0,X1,X37,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_fst__apfst) ).
tff(f761,plain,
( spl81_36
| ~ spl81_11
| ~ spl81_25 ),
inference(avatar_split_clause,[],[f708,f703,f641,f759]) ).
tff(f759,plain,
( spl81_36
<=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] : sP7(X0,X1,X2,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_36])]) ).
tff(f641,plain,
( spl81_11
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] : sP6(X0,X2,X2,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_11])]) ).
tff(f703,plain,
( spl81_25
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP7(X0,X1,X3,X3,X4)
| ~ sP6(X0,X1,X4,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_25])]) ).
tff(f708,plain,
( ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] : sP7(X0,X1,X2,X2,X1)
| ~ spl81_11
| ~ spl81_25 ),
inference(resolution,[],[f704,f642]) ).
tff(f642,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] : sP6(X0,X2,X2,X3,X4)
| ~ spl81_11 ),
inference(avatar_component_clause,[],[f641]) ).
tff(f704,plain,
( ! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ~ sP6(X0,X1,X4,X3,X3)
| sP7(X0,X1,X3,X3,X4) )
| ~ spl81_25 ),
inference(avatar_component_clause,[],[f703]) ).
tff(f757,plain,
spl81_35,
inference(avatar_split_clause,[],[f378,f755]) ).
tff(f378,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X1,X0),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X1,X0),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ),
inference(ennf_transformation,[],[f105]) ).
tff(f105,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X1,X0),arrow_1985332922le_Lin) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X7: arrow_411405190le_alt,X8: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X8,X7),arrow_1985332922le_Lin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_mkbot__Lin) ).
tff(f753,plain,
spl81_34,
inference(avatar_split_clause,[],[f377,f751]) ).
tff(f751,plain,
( spl81_34
<=> ! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_424895264_mktop(X1,X0),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_34])]) ).
tff(f377,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_424895264_mktop(X1,X0),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_424895264_mktop(X1,X0),arrow_1985332922le_Lin)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin) ),
inference(ennf_transformation,[],[f104]) ).
tff(f104,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_424895264_mktop(X1,X0),arrow_1985332922le_Lin) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X7: arrow_411405190le_alt,X8: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_424895264_mktop(X8,X7),arrow_1985332922le_Lin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_mktop__Lin) ).
tff(f743,plain,
spl81_33,
inference(avatar_split_clause,[],[f469,f741]) ).
tff(f741,plain,
( spl81_33
<=> ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt,X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP9(X2,X0,X1,X4,X3)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_33])]) ).
tff(f469,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP9(X2,X0,X1,X4,X3)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP9(X2,X0,X1,X4,X3)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ),
inference(definition_folding,[],[f224,f271,f270,f269,f268]) ).
tff(f224,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X1),X0),arrow_319942042_below(X2,X4,X3))
<=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X1 = X4 ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
| ( X0 = X3 )
| ( X1 != X4 ) ) )
| ( X0 = X4 ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
| ( X0 != X4 ) )
& ( X0 != X1 ) ) )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ),
inference(flattening,[],[f223]) ).
tff(f223,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X1),X0),arrow_319942042_below(X2,X4,X3))
<=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X1 = X4 ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
| ( X0 = X3 )
| ( X1 != X4 ) ) )
| ( X0 = X4 ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2)
| ( X0 != X4 ) )
& ( X0 != X1 ) ) )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( X3 != X4 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_319942042_below(X2,X4,X3))
<=> ( ( ( X0 != X4 )
=> ( ( ( X1 != X4 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2) )
& ( ( X1 = X4 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X0),X2)
| ( X0 = X3 ) ) ) ) )
& ( ( X0 = X4 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X3),X2) )
& ( X0 != X1 ) ) ) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X6: arrow_411405190le_alt,X7: arrow_411405190le_alt,X8: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X9: arrow_411405190le_alt,X10: arrow_411405190le_alt] :
( ( X9 != X10 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,arrow_1985332922le_Lin)
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X6),arrow_319942042_below(X8,X10,X9))
<=> ( ( ( X6 != X10 )
=> ( ( ( X7 != X10 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X6),X8) )
& ( ( X7 = X10 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X9),X6),X8)
| ( X6 = X9 ) ) ) ) )
& ( ( X6 = X10 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X9),X8) )
& ( X6 != X7 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_in__below) ).
tff(f739,plain,
spl81_32,
inference(avatar_split_clause,[],[f452,f737]) ).
tff(f452,plain,
! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP5(X2,X0,X1,X3,X4)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP5(X2,X0,X1,X3,X4)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ),
inference(definition_folding,[],[f222,f266,f265,f264,f263]) ).
tff(f222,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X1),X0),arrow_1158827142_above(X2,X4,X3))
<=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X0 = X3 ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
| ( X1 = X4 )
| ( X0 != X3 ) ) )
| ( X1 = X3 ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
| ( X1 != X3 ) )
& ( X0 != X1 ) ) )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ),
inference(flattening,[],[f221]) ).
tff(f221,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),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),X1),X0),arrow_1158827142_above(X2,X4,X3))
<=> ( ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
| ( X0 = X3 ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
| ( X1 = X4 )
| ( X0 != X3 ) ) )
| ( X1 = X3 ) )
& ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2)
| ( X1 != X3 ) )
& ( X0 != X1 ) ) )
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
| ( X3 = X4 ) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( ( X3 != X4 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),arrow_1158827142_above(X2,X4,X3))
<=> ( ( ( X1 != X3 )
=> ( ( ( X0 != X3 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2) )
& ( ( X0 = X3 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X4),X2)
| ( X1 = X4 ) ) ) ) )
& ( ( X1 = X3 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X4),X0),X2) )
& ( X0 != X1 ) ) ) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X6: arrow_411405190le_alt,X7: arrow_411405190le_alt,X8: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X9: arrow_411405190le_alt,X10: arrow_411405190le_alt] :
( ( X9 != X10 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8,arrow_1985332922le_Lin)
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X6),arrow_1158827142_above(X8,X10,X9))
<=> ( ( ( X7 != X9 )
=> ( ( ( X6 != X9 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X6),X8) )
& ( ( X6 = X9 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X7),X10),X8)
| ( X7 = X10 ) ) ) ) )
& ( ( X7 = X9 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X10),X6),X8) )
& ( X6 != X7 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_in__above) ).
tff(f735,plain,
spl81_31,
inference(avatar_split_clause,[],[f396,f733]) ).
tff(f733,plain,
( spl81_31
<=> ! [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,[spl81_31])]) ).
tff(f396,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,[],[f120]) ).
tff(f120,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,[],[f63]) ).
tff(f63,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X7: fun(X0,product_prod(X1,X2))] : ( product_scomp(X0,X1,X2,product_prod(X1,X2),X7,product_Pair(X1,X2)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_scomp__Pair) ).
tff(f729,plain,
( spl81_30
| ~ spl81_8
| ~ spl81_24 ),
inference(avatar_split_clause,[],[f706,f699,f629,f727]) ).
tff(f727,plain,
( spl81_30
<=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] : sP3(X0,X1,X2,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_30])]) ).
tff(f629,plain,
( spl81_8
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] : sP2(X0,X2,X2,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_8])]) ).
tff(f699,plain,
( spl81_24
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( sP3(X0,X3,X2,X3,X4)
| ~ sP2(X0,X4,X2,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_24])]) ).
tff(f706,plain,
( ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] : sP3(X0,X1,X2,X1,X2)
| ~ spl81_8
| ~ spl81_24 ),
inference(resolution,[],[f700,f630]) ).
tff(f630,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] : sP2(X0,X2,X2,X3,X4)
| ~ spl81_8 ),
inference(avatar_component_clause,[],[f629]) ).
tff(f700,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( ~ sP2(X0,X4,X2,X3,X3)
| sP3(X0,X3,X2,X3,X4) )
| ~ spl81_24 ),
inference(avatar_component_clause,[],[f699]) ).
tff(f725,plain,
spl81_29,
inference(avatar_split_clause,[],[f460,f723]) ).
tff(f723,plain,
( spl81_29
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP6(X0,X1,X4,X3,X2)
| ( X1 = X3 )
| ~ sP7(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_29])]) ).
tff(f460,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP6(X0,X1,X4,X3,X2)
| ( X1 = X3 )
| ~ sP7(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f331]) ).
tff(f721,plain,
spl81_28,
inference(avatar_split_clause,[],[f443,f719]) ).
tff(f719,plain,
( spl81_28
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP2(X0,X4,X2,X3,X1)
| ( X2 = X3 )
| ~ sP3(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_28])]) ).
tff(f443,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X4,X2,X3,X1)
| ( X2 = X3 )
| ~ sP3(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f320]) ).
tff(f717,plain,
spl81_27,
inference(avatar_split_clause,[],[f431,f715]) ).
tff(f715,plain,
( spl81_27
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: fun(X2,X0),X3: product_prod(X2,X1)] : ( product_snd(X0,X1,product_apfst(X2,X0,X1,X4,X3)) = product_snd(X2,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_27])]) ).
tff(f431,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X2,X0)] : ( product_snd(X0,X1,product_apfst(X2,X0,X1,X4,X3)) = product_snd(X2,X1,X3) ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X2,X0)] : ( product_snd(X0,X1,product_apfst(X2,X0,X1,X4,X3)) = product_snd(X2,X1,X3) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X7: product_prod(X2,X0),X37: fun(X2,X1)] : ( product_snd(X1,X0,product_apfst(X2,X1,X0,X37,X7)) = product_snd(X2,X0,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_snd__apfst) ).
tff(f713,plain,
spl81_26,
inference(avatar_split_clause,[],[f430,f711]) ).
tff(f711,plain,
( spl81_26
<=> ! [X1: $tType,X2: $tType,X0: $tType,X4: fun(X1,X0),X3: product_prod(X2,X1)] : ( product_fst(X2,X0,product_apsnd(X1,X0,X2,X4,X3)) = product_fst(X2,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_26])]) ).
tff(f430,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X1,X0)] : ( product_fst(X2,X0,product_apsnd(X1,X0,X2,X4,X3)) = product_fst(X2,X1,X3) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,X1),X4: fun(X1,X0)] : ( product_fst(X2,X0,product_apsnd(X1,X0,X2,X4,X3)) = product_fst(X2,X1,X3) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X1: $tType,X2: $tType,X0: $tType,X7: product_prod(X0,X2),X37: fun(X2,X1)] : ( product_fst(X0,X1,product_apsnd(X2,X1,X0,X37,X7)) = product_fst(X0,X2,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fst__apsnd) ).
tff(f705,plain,
spl81_25,
inference(avatar_split_clause,[],[f562,f703]) ).
tff(f562,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP7(X0,X1,X3,X3,X4)
| ~ sP6(X0,X1,X4,X3,X3) ),
inference(equality_resolution,[],[f463]) ).
tff(f463,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP7(X0,X1,X2,X3,X4)
| ( X2 != X3 )
| ~ sP6(X0,X1,X4,X3,X2) ),
inference(cnf_transformation,[],[f331]) ).
tff(f701,plain,
spl81_24,
inference(avatar_split_clause,[],[f556,f699]) ).
tff(f556,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] :
( sP3(X0,X3,X2,X3,X4)
| ~ sP2(X0,X4,X2,X3,X3) ),
inference(equality_resolution,[],[f446]) ).
tff(f446,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP3(X0,X1,X2,X3,X4)
| ( X1 != X3 )
| ~ sP2(X0,X4,X2,X3,X1) ),
inference(cnf_transformation,[],[f320]) ).
tff(f697,plain,
spl81_23,
inference(avatar_split_clause,[],[f457,f695]) ).
tff(f695,plain,
( spl81_23
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP7(X4,X3,X2,X1,X0)
| ~ sP8(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_23])]) ).
tff(f457,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP7(X4,X3,X2,X1,X0)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f328]) ).
tff(f693,plain,
spl81_22,
inference(avatar_split_clause,[],[f440,f691]) ).
tff(f691,plain,
( spl81_22
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP3(X4,X3,X2,X1,X0)
| ~ sP4(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_22])]) ).
tff(f440,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP3(X4,X3,X2,X1,X0)
| ~ sP4(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f317]) ).
tff(f688,plain,
spl81_21,
inference(avatar_split_clause,[],[f388,f686]) ).
tff(f686,plain,
( spl81_21
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_21])]) ).
tff(f388,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f114]) ).
tff(f114,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( member(X0,X2,X1)
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X48: fun(X0,bool),X7: X0] :
( member(X0,X7,X48)
<=> pp(aa(X0,bool,X48,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
tff(f684,plain,
spl81_20,
inference(avatar_split_clause,[],[f387,f682]) ).
tff(f682,plain,
( spl81_20
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_20])]) ).
tff(f387,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f276]) ).
tff(f680,plain,
spl81_19,
inference(avatar_split_clause,[],[f466,f678]) ).
tff(f678,plain,
( spl81_19
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP6(X0,X1,X2,X3,X4)
| ( X3 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_19])]) ).
tff(f466,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP6(X0,X1,X2,X3,X4)
| ( X3 = X4 ) ),
inference(cnf_transformation,[],[f334]) ).
tff(f676,plain,
spl81_18,
inference(avatar_split_clause,[],[f449,f674]) ).
tff(f674,plain,
( spl81_18
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,X4)
| ( X3 = X4 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_18])]) ).
tff(f449,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,X4)
| ( X3 = X4 ) ),
inference(cnf_transformation,[],[f323]) ).
tff(f670,plain,
spl81_17,
inference(avatar_split_clause,[],[f578,f668]) ).
tff(f578,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP0(X0,X1,X3,X3)
| ( X1 = X3 ) ),
inference(duplicate_literal_removal,[],[f544]) ).
tff(f544,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP0(X0,X1,X3,X3)
| ( X1 = X3 )
| ( X1 = X3 ) ),
inference(equality_resolution,[],[f415]) ).
tff(f415,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP0(X0,X1,X2,X3)
| ( X2 != X3 )
| ( X1 = X2 )
| ( X1 = X3 ) ),
inference(cnf_transformation,[],[f305]) ).
tff(f666,plain,
spl81_16,
inference(avatar_split_clause,[],[f577,f664]) ).
tff(f664,plain,
( spl81_16
<=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt] :
( sP1(X0,X3,X2,X3)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_16])]) ).
tff(f577,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP1(X0,X3,X2,X3)
| ( X2 = X3 ) ),
inference(duplicate_literal_removal,[],[f549]) ).
tff(f549,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( sP1(X0,X3,X2,X3)
| ( X2 = X3 )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f424]) ).
tff(f424,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( sP1(X0,X1,X2,X3)
| ( X1 != X3 )
| ( X1 = X2 )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f309]) ).
tff(f662,plain,
spl81_15,
inference(avatar_split_clause,[],[f540,f659]) ).
tff(f540,plain,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK80,arrow_1985332922le_Lin),
inference(cnf_transformation,[],[f370]) ).
tff(f370,plain,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK80,arrow_1985332922le_Lin),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f197,f369]) ).
tff(f369,plain,
( ? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK80,arrow_1985332922le_Lin) ),
introduced(choice_axiom,[]) ).
tff(f197,plain,
? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
? [X17: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X17,arrow_1985332922le_Lin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_linear__alt) ).
tff(f657,plain,
spl81_14,
inference(avatar_split_clause,[],[f376,f654]) ).
tff(f376,plain,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK10,arrow_1985332922le_Lin),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK10,arrow_1985332922le_Lin),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f199,f273]) ).
tff(f273,plain,
( ? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK10,arrow_1985332922le_Lin) ),
introduced(choice_axiom,[]) ).
tff(f199,plain,
? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin),
inference(ennf_transformation,[],[f103]) ).
tff(f103,plain,
~ ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
~ ! [X5: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X5,arrow_1985332922le_Lin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_B_Bthesis_O_A_I_B_BR_O_AR_A_058_ALin_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f652,plain,
spl81_13,
inference(avatar_split_clause,[],[f375,f649]) ).
tff(f375,plain,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),r,arrow_1985332922le_Lin),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),r,arrow_1985332922le_Lin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096R_A_058_ALin_096) ).
tff(f647,plain,
spl81_12,
inference(avatar_split_clause,[],[f371,f645]) ).
tff(f371,plain,
! [X0: 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),a),b),X0)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: 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),a),b),X0)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
inference(ennf_transformation,[],[f102]) ).
tff(f102,plain,
~ ? [X0: 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),a),b),X0)
& member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
inference(rectify,[],[f101]) ).
tff(f101,negated_conjecture,
~ ? [X45: 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),a),b),X45)
& member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X45,arrow_1985332922le_Lin) ),
inference(negated_conjecture,[],[f100]) ).
tff(f100,conjecture,
? [X45: 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),a),b),X45)
& member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X45,arrow_1985332922le_Lin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f643,plain,
spl81_11,
inference(avatar_split_clause,[],[f564,f641]) ).
tff(f564,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] : sP6(X0,X2,X2,X3,X4),
inference(equality_resolution,[],[f467]) ).
tff(f467,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP6(X0,X1,X2,X3,X4)
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f334]) ).
tff(f639,plain,
spl81_10,
inference(avatar_split_clause,[],[f563,f637]) ).
tff(f637,plain,
( spl81_10
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] : sP7(X0,X3,X2,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_10])]) ).
tff(f563,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] : sP7(X0,X3,X2,X3,X4),
inference(equality_resolution,[],[f462]) ).
tff(f462,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP7(X0,X1,X2,X3,X4)
| ( X1 != X3 ) ),
inference(cnf_transformation,[],[f331]) ).
tff(f635,plain,
spl81_9,
inference(avatar_split_clause,[],[f561,f633]) ).
tff(f633,plain,
( spl81_9
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] : ~ sP8(X0,X1,X3,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_9])]) ).
tff(f561,plain,
! [X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ sP8(X0,X1,X3,X3,X4),
inference(equality_resolution,[],[f455]) ).
tff(f455,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( X2 != X3 )
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f328]) ).
tff(f631,plain,
spl81_8,
inference(avatar_split_clause,[],[f558,f629]) ).
tff(f558,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] : sP2(X0,X2,X2,X3,X4),
inference(equality_resolution,[],[f450]) ).
tff(f450,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP2(X0,X1,X2,X3,X4)
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f323]) ).
tff(f627,plain,
spl81_7,
inference(avatar_split_clause,[],[f557,f625]) ).
tff(f625,plain,
( spl81_7
<=> ! [X4: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] : sP3(X0,X1,X3,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_7])]) ).
tff(f557,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] : sP3(X0,X1,X3,X3,X4),
inference(equality_resolution,[],[f445]) ).
tff(f445,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP3(X0,X1,X2,X3,X4)
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f623,plain,
spl81_6,
inference(avatar_split_clause,[],[f555,f621]) ).
tff(f621,plain,
( spl81_6
<=> ! [X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] : ~ sP4(X0,X1,X3,X3,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_6])]) ).
tff(f555,plain,
! [X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ sP4(X0,X1,X3,X3,X4),
inference(equality_resolution,[],[f438]) ).
tff(f438,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X4: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( X2 != X3 )
| ~ sP4(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f317]) ).
tff(f619,plain,
spl81_5,
inference(avatar_split_clause,[],[f553,f617]) ).
tff(f617,plain,
( spl81_5
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] : ~ sP1(X0,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_5])]) ).
tff(f553,plain,
! [X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] : ~ sP1(X0,X1,X3,X3),
inference(equality_resolution,[],[f420]) ).
tff(f420,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ( X2 != X3 )
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f309]) ).
tff(f615,plain,
spl81_4,
inference(avatar_split_clause,[],[f548,f613]) ).
tff(f613,plain,
( spl81_4
<=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt] : ~ sP0(X0,X3,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_4])]) ).
tff(f548,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ sP0(X0,X3,X2,X3),
inference(equality_resolution,[],[f411]) ).
tff(f411,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ( X1 != X3 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f305]) ).
tff(f611,plain,
~ spl81_3,
inference(avatar_split_clause,[],[f374,f608]) ).
tff(f374,plain,
a != b,
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms) ).
tff(f606,plain,
spl81_2,
inference(avatar_split_clause,[],[f373,f603]) ).
tff(f603,plain,
( spl81_2
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_2])]) ).
tff(f373,plain,
pp(fTrue),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f601,plain,
~ spl81_1,
inference(avatar_split_clause,[],[f372,f598]) ).
tff(f598,plain,
( spl81_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl81_1])]) ).
tff(f372,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f98]) ).
tff(f98,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT200_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 22:26:31 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (17780)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (17785)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)
% 0.15/0.39 % (17783)WARNING: value z3 for option sas not known
% 0.15/0.39 % (17781)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (17782)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (17784)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (17786)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)
% 0.15/0.39 % (17783)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)
% 0.15/0.39 % (17787)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)
% 0.15/0.40 % (17787)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.40 % Exception at run slice level
% 0.15/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42 % (17788)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.42 % (17789)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)
% 0.22/0.42 % (17790)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)
% 0.22/0.43 % (17788)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.43 % (17789)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.43 % Exception at run slice level
% 0.22/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.43 % (17785)First to succeed.
% 0.22/0.44 % (17785)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44 % (17785)------------------------------
% 0.22/0.44 % (17785)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.44 % (17785)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (17785)Memory used [KB]: 2171
% 0.22/0.44 % (17785)Time elapsed: 0.053 s
% 0.22/0.44 % (17785)Instructions burned: 174 (million)
% 0.22/0.44 % (17785)------------------------------
% 0.22/0.44 % (17785)------------------------------
% 0.22/0.44 % (17780)Success in time 0.076 s
%------------------------------------------------------------------------------