TSTP Solution File: SCT198_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT198_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 : n019.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 14:57:15 EDT 2024
% Result : Theorem 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 284
% Syntax : Number of formulae : 677 ( 183 unt; 109 typ; 0 def)
% Number of atoms : 1596 ( 544 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1667 ( 639 ~; 657 |; 160 &)
% ( 147 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 186 ( 98 >; 88 *; 0 +; 0 <<)
% Number of predicates : 127 ( 125 usr; 112 prp; 0-5 aty)
% Number of functors : 93 ( 93 usr; 6 con; 0-7 aty)
% Number of variables : 2274 (1935 !; 50 ?;2274 :)
% ( 289 !>; 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,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_17,type,
fFalse: bool ).
tff(func_def_18,type,
fTrue: bool ).
tff(func_def_19,type,
a: arrow_411405190le_alt ).
tff(func_def_20,type,
b: arrow_411405190le_alt ).
tff(func_def_21,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_22,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_23,type,
sK12:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_24,type,
sK13:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_25,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_26,type,
sK15:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_27,type,
sK16:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_28,type,
sK17:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_29,type,
sK18:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_30,type,
sK19:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_31,type,
sK20:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_32,type,
sK21:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_33,type,
sK22:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,bool)) > X1 ) ).
tff(func_def_34,type,
sK23:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,bool)) > X0 ) ).
tff(func_def_35,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X0 ) ).
tff(func_def_36,type,
sK25:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X1 ) ).
tff(func_def_37,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_38,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X1 ) ).
tff(func_def_39,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X0 ) ).
tff(func_def_40,type,
sK29:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_41,type,
sK30:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_42,type,
sK31:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_43,type,
sK32:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_44,type,
sK33:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_45,type,
sK34:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_46,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_47,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_48,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_49,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_50,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X0 ) ).
tff(func_def_51,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X2 ) ).
tff(func_def_52,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X0 ) ).
tff(func_def_53,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X2 ) ).
tff(func_def_54,type,
sK43:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).
tff(func_def_55,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).
tff(func_def_56,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X1 ) ).
tff(func_def_57,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X0 ) ).
tff(func_def_58,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_59,type,
sK48:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_60,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X0 ) ).
tff(func_def_61,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X1 ) ).
tff(func_def_62,type,
sK51:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_63,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_64,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_65,type,
sK54:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_66,type,
sK55:
!>[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_67,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)))) > X1 ) ).
tff(func_def_68,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)))) > X2 ) ).
tff(func_def_69,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)))) > X3 ) ).
tff(func_def_70,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)))) > X4 ) ).
tff(func_def_71,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_72,type,
sK61:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_73,type,
sK62:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X4 ) ).
tff(func_def_74,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) > X3 ) ).
tff(func_def_75,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) > X2 ) ).
tff(func_def_76,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) > X1 ) ).
tff(func_def_77,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) > X0 ) ).
tff(func_def_78,type,
sK67:
!>[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_79,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))))) > X1 ) ).
tff(func_def_80,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))))) > X2 ) ).
tff(func_def_81,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))))) > X3 ) ).
tff(func_def_82,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))))) > X4 ) ).
tff(func_def_83,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))))) > X5 ) ).
tff(func_def_84,type,
sK73:
!>[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_85,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) > X4 ) ).
tff(func_def_86,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) > X3 ) ).
tff(func_def_87,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) > X2 ) ).
tff(func_def_88,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) > X1 ) ).
tff(func_def_89,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) > X0 ) ).
tff(func_def_90,type,
sK79: 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(f1661,plain,
$false,
inference(avatar_sat_refutation,[],[f584,f589,f594,f598,f602,f606,f610,f614,f618,f622,f626,f630,f635,f639,f643,f649,f653,f657,f661,f666,f670,f674,f678,f684,f690,f694,f698,f702,f708,f713,f717,f723,f727,f731,f735,f739,f743,f747,f767,f785,f792,f796,f800,f810,f821,f825,f832,f836,f840,f844,f896,f900,f904,f908,f912,f916,f920,f924,f954,f958,f962,f966,f990,f994,f998,f1002,f1054,f1058,f1062,f1068,f1072,f1080,f1085,f1090,f1095,f1099,f1104,f1108,f1112,f1116,f1142,f1147,f1151,f1155,f1237,f1241,f1245,f1249,f1253,f1257,f1261,f1350,f1360,f1366,f1371,f1382,f1388,f1395,f1399,f1403,f1407,f1411,f1415,f1419,f1556,f1561,f1567,f1572,f1583,f1652,f1659,f1660]) ).
tff(f1660,plain,
( spl80_3
| ~ spl80_15
| ~ spl80_100 ),
inference(avatar_split_clause,[],[f1552,f1401,f641,f591]) ).
tff(f591,plain,
( spl80_3
<=> ( a = b ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_3])]) ).
tff(f641,plain,
( spl80_15
<=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt] :
( sP0(X0,X3,X2,X3)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_15])]) ).
tff(f1401,plain,
( spl80_100
<=> ! [X0: arrow_411405190le_alt] : ~ sP0(sK79,b,a,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_100])]) ).
tff(f1552,plain,
( ( a = b )
| ~ spl80_15
| ~ spl80_100 ),
inference(resolution,[],[f1402,f642]) ).
tff(f642,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)
| ( X2 = X3 ) )
| ~ spl80_15 ),
inference(avatar_component_clause,[],[f641]) ).
tff(f1402,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP0(sK79,b,a,X0)
| ~ spl80_100 ),
inference(avatar_component_clause,[],[f1401]) ).
tff(f1659,plain,
( spl80_111
| ~ spl80_42
| ~ spl80_43
| ~ spl80_54
| ~ spl80_55
| ~ spl80_90
| ~ spl80_110 ),
inference(avatar_split_clause,[],[f1655,f1650,f1255,f910,f906,f798,f794,f1657]) ).
tff(f1657,plain,
( spl80_111
<=> ! [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,[spl80_111])]) ).
tff(f794,plain,
( spl80_42
<=> ! [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,[spl80_42])]) ).
tff(f798,plain,
( spl80_43
<=> ! [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,[spl80_43])]) ).
tff(f906,plain,
( spl80_54
<=> ! [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,[spl80_54])]) ).
tff(f910,plain,
( spl80_55
<=> ! [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),sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_55])]) ).
tff(f1255,plain,
( spl80_90
<=> ! [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,[spl80_90])]) ).
tff(f1650,plain,
( spl80_110
<=> ! [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,[spl80_110])]) ).
tff(f1655,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) )
| ~ spl80_42
| ~ spl80_43
| ~ spl80_54
| ~ spl80_55
| ~ spl80_90
| ~ spl80_110 ),
inference(forward_demodulation,[],[f1654,f1329]) ).
tff(f1329,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,sK16(X1,X0,X2)),sK17(X1,X0,X2)) )
| ~ spl80_42
| ~ spl80_43
| ~ spl80_54
| ~ spl80_55
| ~ spl80_90 ),
inference(forward_demodulation,[],[f1328,f934]) ).
tff(f934,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( product_fst(X1,X0,X2) = sK16(X1,X0,X2) )
| ~ spl80_43
| ~ spl80_55 ),
inference(superposition,[],[f799,f911]) ).
tff(f911,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),sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X2 )
| ~ spl80_55 ),
inference(avatar_component_clause,[],[f910]) ).
tff(f799,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 )
| ~ spl80_43 ),
inference(avatar_component_clause,[],[f798]) ).
tff(f1328,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)),sK17(X1,X0,X2)) )
| ~ spl80_42
| ~ spl80_54
| ~ spl80_55
| ~ spl80_90 ),
inference(forward_demodulation,[],[f1302,f935]) ).
tff(f935,plain,
( ! [X1: $tType,X0: $tType,X2: product_prod(X1,X0)] : ( product_snd(X1,X0,X2) = sK17(X1,X0,X2) )
| ~ spl80_42
| ~ spl80_55 ),
inference(superposition,[],[f795,f911]) ).
tff(f795,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 )
| ~ spl80_42 ),
inference(avatar_component_clause,[],[f794]) ).
tff(f1302,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) )
| ~ spl80_54
| ~ spl80_90 ),
inference(superposition,[],[f1256,f907]) ).
tff(f907,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 )
| ~ spl80_54 ),
inference(avatar_component_clause,[],[f906]) ).
tff(f1256,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) )
| ~ spl80_90 ),
inference(avatar_component_clause,[],[f1255]) ).
tff(f1654,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,sK16(X2,X1,X3)),sK17(X2,X1,X3)) )
| ~ spl80_42
| ~ spl80_43
| ~ spl80_55
| ~ spl80_110 ),
inference(forward_demodulation,[],[f1653,f934]) ).
tff(f1653,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)),sK17(X2,X1,X3)) )
| ~ spl80_42
| ~ spl80_55
| ~ spl80_110 ),
inference(forward_demodulation,[],[f1651,f935]) ).
tff(f1651,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)) )
| ~ spl80_110 ),
inference(avatar_component_clause,[],[f1650]) ).
tff(f1652,plain,
spl80_110,
inference(avatar_split_clause,[],[f423,f1650]) ).
tff(f423,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,[],[f135]) ).
tff(f135,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,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X40: product_prod(X1,X2),X36: 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),X36),X40) = aa(X2,X0,aa(X1,fun(X2,X0),X36,product_fst(X1,X2,X40)),product_snd(X1,X2,X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_prod__case__beta) ).
tff(f1583,plain,
spl80_109,
inference(avatar_split_clause,[],[f472,f1581]) ).
tff(f1581,plain,
( spl80_109
<=> ! [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,[spl80_109])]) ).
tff(f472,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,[],[f153]) ).
tff(f153,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,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X8: X2,X9: X1,X36: fun(product_prod(X1,X2),X0)] : ( aa(X2,X0,aa(X1,fun(X2,X0),product_curry(X1,X2,X0,X36),X9),X8) = aa(product_prod(X1,X2),X0,X36,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X9),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_curry__conv) ).
tff(f1572,plain,
( spl80_108
| ~ spl80_39
| ~ spl80_107 ),
inference(avatar_split_clause,[],[f1568,f1565,f765,f1570]) ).
tff(f1570,plain,
( spl80_108
<=> ! [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),sK14(X0,X1,X2))),sK15(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_108])]) ).
tff(f765,plain,
( spl80_39
<=> ! [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,[spl80_39])]) ).
tff(f1565,plain,
( spl80_107
<=> ! [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),sK14(X0,X1,X2)),sK15(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_107])]) ).
tff(f1568,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),sK14(X0,X1,X2))),sK15(X0,X1,X2)))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) )
| ~ spl80_39
| ~ spl80_107 ),
inference(forward_demodulation,[],[f1566,f766]) ).
tff(f766,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) )
| ~ spl80_39 ),
inference(avatar_component_clause,[],[f765]) ).
tff(f1566,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),sK14(X0,X1,X2)),sK15(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) )
| ~ spl80_107 ),
inference(avatar_component_clause,[],[f1565]) ).
tff(f1567,plain,
spl80_107,
inference(avatar_split_clause,[],[f379,f1565]) ).
tff(f379,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),sK14(X0,X1,X2)),sK15(X0,X1,X2))))
| ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X0,X1),bool)] :
( ( pp(aa(product_prod(X0,X1),bool,X2,sK13(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),sK14(X0,X1,X2)),sK15(X0,X1,X2))))
| ! [X8: product_prod(X0,X1)] : ~ pp(aa(product_prod(X0,X1),bool,X2,X8)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f275,f277,f276]) ).
tff(f276,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,sK13(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f277,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),sK14(X0,X1,X2)),sK15(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f275,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,[],[f274]) ).
tff(f274,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,[],[f112]) ).
tff(f112,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,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType,X1: $tType,X10: fun(product_prod(X0,X1),bool)] :
( ? [X11: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X10,X11))
<=> ? [X12: X0,X13: X1] : pp(aa(product_prod(X0,X1),bool,X10,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X12),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_split__paired__Ex) ).
tff(f1561,plain,
( spl80_106
| ~ spl80_39
| ~ spl80_105 ),
inference(avatar_split_clause,[],[f1557,f1554,f765,f1559]) ).
tff(f1559,plain,
( spl80_106
<=> ! [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),sK10(X0,X1,X2))),sK11(X0,X1,X2)))
| pp(aa(product_prod(X0,X1),bool,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_106])]) ).
tff(f1554,plain,
( spl80_105
<=> ! [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),sK10(X0,X1,X2)),sK11(X0,X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_105])]) ).
tff(f1557,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),sK10(X0,X1,X2))),sK11(X0,X1,X2)))
| pp(aa(product_prod(X0,X1),bool,X2,X3)) )
| ~ spl80_39
| ~ spl80_105 ),
inference(forward_demodulation,[],[f1555,f766]) ).
tff(f1555,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),sK10(X0,X1,X2)),sK11(X0,X1,X2)))) )
| ~ spl80_105 ),
inference(avatar_component_clause,[],[f1554]) ).
tff(f1556,plain,
spl80_105,
inference(avatar_split_clause,[],[f378,f1554]) ).
tff(f378,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),sK10(X0,X1,X2)),sK11(X0,X1,X2)))) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,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),sK10(X0,X1,X2)),sK11(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,sK12(X0,X1,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f270,f272,f271]) ).
tff(f271,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),sK10(X0,X1,X2)),sK11(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
tff(f272,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,sK12(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
tff(f270,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,[],[f269]) ).
tff(f269,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,[],[f111]) ).
tff(f111,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,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType,X1: $tType,X10: fun(product_prod(X0,X1),bool)] :
( ! [X11: product_prod(X0,X1)] : pp(aa(product_prod(X0,X1),bool,X10,X11))
<=> ! [X12: X0,X13: X1] : pp(aa(product_prod(X0,X1),bool,X10,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X12),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_split__paired__All) ).
tff(f1419,plain,
spl80_104,
inference(avatar_split_clause,[],[f447,f1417]) ).
tff(f1417,plain,
( spl80_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] :
( 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,[spl80_104])]) ).
tff(f447,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,[],[f320]) ).
tff(f320,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,[],[f319]) ).
tff(f319,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,[],[f318]) ).
tff(f318,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,[],[f264]) ).
tff(f264,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(f1415,plain,
spl80_103,
inference(avatar_split_clause,[],[f442,f1413]) ).
tff(f1413,plain,
( spl80_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_319942042_below(X0,X3,X4))
| ~ sP8(X4,X3,X2,X1,X0)
| ~ sP9(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_103])]) ).
tff(f442,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,[],[f317]) ).
tff(f317,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,[],[f316]) ).
tff(f316,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,[],[f265]) ).
tff(f265,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(f1411,plain,
spl80_102,
inference(avatar_split_clause,[],[f441,f1409]) ).
tff(f1409,plain,
( spl80_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] :
( 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,[spl80_102])]) ).
tff(f441,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( 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,[],[f317]) ).
tff(f1407,plain,
spl80_101,
inference(avatar_split_clause,[],[f430,f1405]) ).
tff(f1405,plain,
( spl80_101
<=> ! [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,[spl80_101])]) ).
tff(f430,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,[],[f309]) ).
tff(f309,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,[],[f308]) ).
tff(f308,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,[],[f307]) ).
tff(f307,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,[],[f259]) ).
tff(f259,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(f1403,plain,
( spl80_100
| ~ spl80_13
| ~ spl80_88 ),
inference(avatar_split_clause,[],[f1356,f1247,f632,f1401]) ).
tff(f632,plain,
( spl80_13
<=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK79,arrow_1985332922le_Lin) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_13])]) ).
tff(f1247,plain,
( spl80_88
<=> ! [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,[spl80_88])]) ).
tff(f1356,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP0(sK79,b,a,X0)
| ~ spl80_13
| ~ spl80_88 ),
inference(resolution,[],[f1248,f634]) ).
tff(f634,plain,
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK79,arrow_1985332922le_Lin)
| ~ spl80_13 ),
inference(avatar_component_clause,[],[f632]) ).
tff(f1248,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) )
| ~ spl80_88 ),
inference(avatar_component_clause,[],[f1247]) ).
tff(f1399,plain,
spl80_99,
inference(avatar_split_clause,[],[f425,f1397]) ).
tff(f1397,plain,
( spl80_99
<=> ! [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,[spl80_99])]) ).
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,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,[],[f306]) ).
tff(f306,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,[],[f305]) ).
tff(f305,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,[],[f260]) ).
tff(f260,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(f1395,plain,
spl80_98,
inference(avatar_split_clause,[],[f424,f1393]) ).
tff(f1393,plain,
( spl80_98
<=> ! [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,[spl80_98])]) ).
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,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,[],[f306]) ).
tff(f1388,plain,
( spl80_97
| ~ spl80_42
| ~ spl80_43
| ~ spl80_55
| ~ spl80_96 ),
inference(avatar_split_clause,[],[f1384,f1380,f910,f798,f794,f1386]) ).
tff(f1386,plain,
( spl80_97
<=> ! [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,sK17(X1,X0,X2)),sK16(X1,X0,X2)))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK23(X0,X1,X3)),sK22(X0,X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_97])]) ).
tff(f1380,plain,
( spl80_96
<=> ! [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,sK23(X0,X1,X3)),sK22(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,[spl80_96])]) ).
tff(f1384,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,sK17(X1,X0,X2)),sK16(X1,X0,X2)))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK23(X0,X1,X3)),sK22(X0,X1,X3))) )
| ~ spl80_42
| ~ spl80_43
| ~ spl80_55
| ~ spl80_96 ),
inference(forward_demodulation,[],[f1383,f935]) ).
tff(f1383,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)),sK16(X1,X0,X2)))
| pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,sK23(X0,X1,X3)),sK22(X0,X1,X3))) )
| ~ spl80_43
| ~ spl80_55
| ~ spl80_96 ),
inference(forward_demodulation,[],[f1381,f934]) ).
tff(f1381,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,sK23(X0,X1,X3)),sK22(X0,X1,X3)))
| ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X3,product_snd(X1,X0,X2)),product_fst(X1,X0,X2))) )
| ~ spl80_96 ),
inference(avatar_component_clause,[],[f1380]) ).
tff(f1382,plain,
spl80_96,
inference(avatar_split_clause,[],[f390,f1380]) ).
tff(f390,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,sK23(X0,X1,X3)),sK22(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,[],[f286]) ).
tff(f286,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,sK23(X0,X1,X3)),sK22(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,[sK22,sK23])],[f208,f285]) ).
tff(f285,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,sK23(X0,X1,X3)),sK22(X0,X1,X3))) ),
introduced(choice_axiom,[]) ).
tff(f208,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,[],[f122]) ).
tff(f122,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,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X1: $tType,X40: product_prod(X1,X0),X10: fun(X0,fun(X1,bool))] :
( pp(aa(X1,bool,aa(X0,fun(X1,bool),X10,product_snd(X1,X0,X40)),product_fst(X1,X0,X40)))
=> ~ ! [X27: X1,X28: X0] : ~ pp(aa(X1,bool,aa(X0,fun(X1,bool),X10,X28),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_exE__realizer_H) ).
tff(f1371,plain,
( spl80_95
| ~ spl80_39
| ~ spl80_94 ),
inference(avatar_split_clause,[],[f1367,f1364,f765,f1369]) ).
tff(f1369,plain,
( spl80_95
<=> ! [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,sK13(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_95])]) ).
tff(f1364,plain,
( spl80_94
<=> ! [X1: $tType,X0: $tType,X4: X0,X5: X1,X2: fun(product_prod(X0,X1),bool)] :
( pp(aa(product_prod(X0,X1),bool,X2,sK13(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,[spl80_94])]) ).
tff(f1367,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,sK13(X0,X1,X2))) )
| ~ spl80_39
| ~ spl80_94 ),
inference(forward_demodulation,[],[f1365,f766]) ).
tff(f1365,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,sK13(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))) )
| ~ spl80_94 ),
inference(avatar_component_clause,[],[f1364]) ).
tff(f1366,plain,
spl80_94,
inference(avatar_split_clause,[],[f380,f1364]) ).
tff(f380,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X0,X1),bool),X4: X0,X5: X1] :
( pp(aa(product_prod(X0,X1),bool,X2,sK13(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,[],[f278]) ).
tff(f1360,plain,
( spl80_93
| ~ spl80_39
| ~ spl80_92 ),
inference(avatar_split_clause,[],[f1351,f1348,f765,f1358]) ).
tff(f1358,plain,
( spl80_93
<=> ! [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,sK12(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_93])]) ).
tff(f1348,plain,
( spl80_92
<=> ! [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,sK12(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_92])]) ).
tff(f1351,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,sK12(X0,X1,X2))) )
| ~ spl80_39
| ~ spl80_92 ),
inference(forward_demodulation,[],[f1349,f766]) ).
tff(f1349,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,sK12(X0,X1,X2))) )
| ~ spl80_92 ),
inference(avatar_component_clause,[],[f1348]) ).
tff(f1350,plain,
spl80_92,
inference(avatar_split_clause,[],[f377,f1348]) ).
tff(f377,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,sK12(X0,X1,X2))) ),
inference(cnf_transformation,[],[f273]) ).
tff(f1261,plain,
spl80_91,
inference(avatar_split_clause,[],[f520,f1259]) ).
tff(f1259,plain,
( spl80_91
<=> ! [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,[spl80_91])]) ).
tff(f520,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,[],[f249]) ).
tff(f249,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,[],[f188]) ).
tff(f188,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,[],[f91]) ).
tff(f91,axiom,
! [X2: $tType,X1: $tType,X4: $tType,X0: $tType,X54: fun(X0,X4),X35: fun(X4,X1),X8: fun(X0,X2),X9: fun(X2,X1)] :
( ( comp(X2,X1,X0,X9,X8) = comp(X4,X1,X0,X35,X54) )
=> ! [X55: X0] : ( aa(X2,X1,X9,aa(X0,X2,X8,X55)) = aa(X4,X1,X35,aa(X0,X4,X54,X55)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_o__eq__elim) ).
tff(f1257,plain,
spl80_90,
inference(avatar_split_clause,[],[f471,f1255]) ).
tff(f471,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,[],[f152]) ).
tff(f152,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,[],[f17]) ).
tff(f17,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X8: X2,X9: X1,X22: fun(X1,fun(X2,X0))] : ( product_prod_rec(X1,X2,X0,X22,aa(X2,product_prod(X1,X2),aa(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X9),X8)) = aa(X2,X0,aa(X1,fun(X2,X0),X22,X9),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_prod_Orecs) ).
tff(f1253,plain,
spl80_89,
inference(avatar_split_clause,[],[f452,f1251]) ).
tff(f1251,plain,
( spl80_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] :
( 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,[spl80_89])]) ).
tff(f452,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( 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,[],[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] :
( ( 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,[],[f322]) ).
tff(f322,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,[],[f321]) ).
tff(f321,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,[],[f263]) ).
tff(f263,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(f1249,plain,
( spl80_88
| ~ spl80_33
| ~ spl80_68 ),
inference(avatar_split_clause,[],[f1143,f1056,f725,f1247]) ).
tff(f725,plain,
( spl80_33
<=> ! [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,[spl80_33])]) ).
tff(f1056,plain,
( spl80_68
<=> ! [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_424895264_mktop(X0,X1),arrow_1985332922le_Lin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_68])]) ).
tff(f1143,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) )
| ~ spl80_33
| ~ spl80_68 ),
inference(resolution,[],[f1057,f726]) ).
tff(f726,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) )
| ~ spl80_33 ),
inference(avatar_component_clause,[],[f725]) ).
tff(f1057,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_424895264_mktop(X0,X1),arrow_1985332922le_Lin)
| ~ sP0(X0,b,a,X1) )
| ~ spl80_68 ),
inference(avatar_component_clause,[],[f1056]) ).
tff(f1245,plain,
spl80_87,
inference(avatar_split_clause,[],[f449,f1243]) ).
tff(f1243,plain,
( spl80_87
<=> ! [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,[spl80_87])]) ).
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] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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,[],[f323]) ).
tff(f1241,plain,
spl80_86,
inference(avatar_split_clause,[],[f435,f1239]) ).
tff(f1239,plain,
( spl80_86
<=> ! [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,[spl80_86])]) ).
tff(f435,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,[],[f312]) ).
tff(f312,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,[],[f311]) ).
tff(f311,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,[],[f310]) ).
tff(f310,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,[],[f258]) ).
tff(f258,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(f1237,plain,
spl80_85,
inference(avatar_split_clause,[],[f432,f1235]) ).
tff(f1235,plain,
( spl80_85
<=> ! [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,[spl80_85])]) ).
tff(f432,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,[],[f312]) ).
tff(f1155,plain,
spl80_84,
inference(avatar_split_clause,[],[f414,f1153]) ).
tff(f1153,plain,
( spl80_84
<=> ! [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 )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_84])]) ).
tff(f414,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 )
| ( X1 = X3 ) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,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)
& ( 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 ) )
| ~ sP1(X0,X1,X2,X3) ) ),
inference(rectify,[],[f300]) ).
tff(f300,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 != 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 ) )
| ~ sP1(X1,X2,X3,X0) ) ),
inference(flattening,[],[f299]) ).
tff(f299,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 != 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 ) )
| ~ sP1(X1,X2,X3,X0) ) ),
inference(nnf_transformation,[],[f255]) ).
tff(f255,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 = X3 ) )
& ( ( X2 != X3 )
| ( X0 != X3 ) )
& ( X0 != X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1151,plain,
spl80_83,
inference(avatar_split_clause,[],[f413,f1149]) ).
tff(f1149,plain,
( spl80_83
<=> ! [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)
| ( X2 = X3 )
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_83])]) ).
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] :
( 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)
| ( X2 = X3 )
| ( X1 = X3 ) ),
inference(cnf_transformation,[],[f301]) ).
tff(f1147,plain,
spl80_82,
inference(avatar_split_clause,[],[f405,f1145]) ).
tff(f1145,plain,
( spl80_82
<=> ! [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 )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_82])]) ).
tff(f405,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 )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,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)
& ( 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 ) )
| ~ sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f296]) ).
tff(f296,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 != 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 ) )
| ~ sP0(X1,X2,X3,X0) ) ),
inference(flattening,[],[f295]) ).
tff(f295,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 != 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 ) )
| ~ sP0(X1,X2,X3,X0) ) ),
inference(nnf_transformation,[],[f253]) ).
tff(f253,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 = X2 ) )
& ( ( X2 != X3 )
| ( X0 != X2 ) )
& ( X0 != X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1142,plain,
spl80_81,
inference(avatar_split_clause,[],[f404,f1140]) ).
tff(f1140,plain,
( spl80_81
<=> ! [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 = X3 )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_81])]) ).
tff(f404,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 = X3 )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f297]) ).
tff(f1116,plain,
( spl80_80
| ~ spl80_43
| ~ spl80_55
| ~ spl80_76 ),
inference(avatar_split_clause,[],[f1100,f1097,f910,f798,f1114]) ).
tff(f1114,plain,
( spl80_80
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X2,X0),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,sK16(X2,X1,X4)) != aa(X2,X0,X3,sK16(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_80])]) ).
tff(f1097,plain,
( spl80_76
<=> ! [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,[spl80_76])]) ).
tff(f1100,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,sK16(X2,X1,X4)) != aa(X2,X0,X3,sK16(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) = product_apfst(X2,X0,X1,X3,X4) ) )
| ~ spl80_43
| ~ spl80_55
| ~ spl80_76 ),
inference(forward_demodulation,[],[f1098,f934]) ).
tff(f1098,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)) ) )
| ~ spl80_76 ),
inference(avatar_component_clause,[],[f1097]) ).
tff(f1112,plain,
( spl80_79
| ~ spl80_43
| ~ spl80_55
| ~ spl80_74 ),
inference(avatar_split_clause,[],[f1091,f1088,f910,f798,f1110]) ).
tff(f1110,plain,
( spl80_79
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X2,X0),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,sK16(X2,X1,X4)) = aa(X2,X0,X3,sK16(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) != product_apfst(X2,X0,X1,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_79])]) ).
tff(f1088,plain,
( spl80_74
<=> ! [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,[spl80_74])]) ).
tff(f1091,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X0),X4: product_prod(X2,X1),X5: fun(X2,X0)] :
( ( aa(X2,X0,X5,sK16(X2,X1,X4)) = aa(X2,X0,X3,sK16(X2,X1,X4)) )
| ( product_apfst(X2,X0,X1,X5,X4) != product_apfst(X2,X0,X1,X3,X4) ) )
| ~ spl80_43
| ~ spl80_55
| ~ spl80_74 ),
inference(forward_demodulation,[],[f1089,f934]) ).
tff(f1089,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) ) )
| ~ spl80_74 ),
inference(avatar_component_clause,[],[f1088]) ).
tff(f1108,plain,
( spl80_78
| ~ spl80_42
| ~ spl80_55
| ~ spl80_73 ),
inference(avatar_split_clause,[],[f1086,f1083,f910,f794,f1106]) ).
tff(f1106,plain,
( spl80_78
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X1,X0),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,sK17(X2,X1,X4)) != aa(X1,X0,X3,sK17(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_78])]) ).
tff(f1083,plain,
( spl80_73
<=> ! [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,[spl80_73])]) ).
tff(f1086,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,sK17(X2,X1,X4)) != aa(X1,X0,X3,sK17(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) = product_apsnd(X1,X0,X2,X3,X4) ) )
| ~ spl80_42
| ~ spl80_55
| ~ spl80_73 ),
inference(forward_demodulation,[],[f1084,f935]) ).
tff(f1084,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)) ) )
| ~ spl80_73 ),
inference(avatar_component_clause,[],[f1083]) ).
tff(f1104,plain,
( spl80_77
| ~ spl80_42
| ~ spl80_55
| ~ spl80_72 ),
inference(avatar_split_clause,[],[f1081,f1078,f910,f794,f1102]) ).
tff(f1102,plain,
( spl80_77
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,X1),X3: fun(X1,X0),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,sK17(X2,X1,X4)) = aa(X1,X0,X3,sK17(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) != product_apsnd(X1,X0,X2,X3,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_77])]) ).
tff(f1078,plain,
( spl80_72
<=> ! [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,[spl80_72])]) ).
tff(f1081,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,X0),X4: product_prod(X2,X1),X5: fun(X1,X0)] :
( ( aa(X1,X0,X5,sK17(X2,X1,X4)) = aa(X1,X0,X3,sK17(X2,X1,X4)) )
| ( product_apsnd(X1,X0,X2,X5,X4) != product_apsnd(X1,X0,X2,X3,X4) ) )
| ~ spl80_42
| ~ spl80_55
| ~ spl80_72 ),
inference(forward_demodulation,[],[f1079,f935]) ).
tff(f1079,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) ) )
| ~ spl80_72 ),
inference(avatar_component_clause,[],[f1078]) ).
tff(f1099,plain,
spl80_76,
inference(avatar_split_clause,[],[f499,f1097]) ).
tff(f499,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,[],[f346]) ).
tff(f346,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,[],[f170]) ).
tff(f170,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,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X41: fun(X2,X0),X6: product_prod(X2,X1),X36: fun(X2,X0)] :
( ( product_apfst(X2,X0,X1,X36,X6) = product_apfst(X2,X0,X1,X41,X6) )
<=> ( aa(X2,X0,X36,product_fst(X2,X1,X6)) = aa(X2,X0,X41,product_fst(X2,X1,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_apfst__eq__conv) ).
tff(f1095,plain,
( spl80_75
| ~ spl80_12
| ~ spl80_66 ),
inference(avatar_split_clause,[],[f1038,f1000,f628,f1093]) ).
tff(f1093,plain,
( spl80_75
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ sP1(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,[spl80_75])]) ).
tff(f628,plain,
( spl80_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,[spl80_12])]) ).
tff(f1000,plain,
( spl80_66
<=> ! [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))
| ~ sP1(X1,X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_66])]) ).
tff(f1038,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt] :
( ~ sP1(X0,b,a,X1)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X0,X1),arrow_1985332922le_Lin) )
| ~ spl80_12
| ~ spl80_66 ),
inference(resolution,[],[f1001,f629]) ).
tff(f629,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) )
| ~ spl80_12 ),
inference(avatar_component_clause,[],[f628]) ).
tff(f1001,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))
| ~ sP1(X1,X2,X3,X0) )
| ~ spl80_66 ),
inference(avatar_component_clause,[],[f1000]) ).
tff(f1090,plain,
spl80_74,
inference(avatar_split_clause,[],[f498,f1088]) ).
tff(f498,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,[],[f346]) ).
tff(f1085,plain,
spl80_73,
inference(avatar_split_clause,[],[f497,f1083]) ).
tff(f497,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,[],[f345]) ).
tff(f345,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,[],[f169]) ).
tff(f169,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,[],[f65]) ).
tff(f65,axiom,
! [X1: $tType,X2: $tType,X0: $tType,X41: fun(X2,X1),X6: product_prod(X0,X2),X36: fun(X2,X1)] :
( ( product_apsnd(X2,X1,X0,X36,X6) = product_apsnd(X2,X1,X0,X41,X6) )
<=> ( aa(X2,X1,X36,product_snd(X0,X2,X6)) = aa(X2,X1,X41,product_snd(X0,X2,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_apsnd__eq__conv) ).
tff(f1080,plain,
spl80_72,
inference(avatar_split_clause,[],[f496,f1078]) ).
tff(f496,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,[],[f345]) ).
tff(f1072,plain,
spl80_71,
inference(avatar_split_clause,[],[f549,f1070]) ).
tff(f1070,plain,
( spl80_71
<=> ! [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,[spl80_71])]) ).
tff(f549,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,[],[f453]) ).
tff(f453,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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,[],[f326]) ).
tff(f326,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,[],[f325]) ).
tff(f325,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,[],[f324]) ).
tff(f324,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,[],[f262]) ).
tff(f262,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(f1068,plain,
spl80_70,
inference(avatar_split_clause,[],[f543,f1066]) ).
tff(f1066,plain,
( spl80_70
<=> ! [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,[spl80_70])]) ).
tff(f543,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,[],[f436]) ).
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] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),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,[],[f315]) ).
tff(f315,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,[],[f314]) ).
tff(f314,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,[],[f313]) ).
tff(f313,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,[],[f257]) ).
tff(f257,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(f1062,plain,
spl80_69,
inference(avatar_split_clause,[],[f410,f1060]) ).
tff(f1060,plain,
( spl80_69
<=> ! [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 )
| ~ sP1(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_69])]) ).
tff(f410,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 )
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f301]) ).
tff(f1058,plain,
( spl80_68
| ~ spl80_12
| ~ spl80_64 ),
inference(avatar_split_clause,[],[f1014,f992,f628,f1056]) ).
tff(f992,plain,
( spl80_64
<=> ! [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))
| ~ sP0(X1,X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_64])]) ).
tff(f1014,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_424895264_mktop(X0,X1),arrow_1985332922le_Lin) )
| ~ spl80_12
| ~ spl80_64 ),
inference(resolution,[],[f993,f629]) ).
tff(f993,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))
| ~ sP0(X1,X2,X3,X0) )
| ~ spl80_64 ),
inference(avatar_component_clause,[],[f992]) ).
tff(f1054,plain,
spl80_67,
inference(avatar_split_clause,[],[f401,f1052]) ).
tff(f1052,plain,
( spl80_67
<=> ! [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 )
| ~ sP0(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_67])]) ).
tff(f401,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 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f297]) ).
tff(f1002,plain,
spl80_66,
inference(avatar_split_clause,[],[f416,f1000]) ).
tff(f416,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))
| ~ sP1(X1,X2,X3,X0) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_276188178_mkbot(X1,X0))
| ~ 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_276188178_mkbot(X1,X0)) ) ),
inference(nnf_transformation,[],[f256]) ).
tff(f256,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))
<=> sP1(X1,X2,X3,X0) ),
inference(definition_folding,[],[f213,f255]) ).
tff(f213,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,[],[f128]) ).
tff(f128,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,[],[f13]) ).
tff(f13,axiom,
! [X17: arrow_411405190le_alt,X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),arrow_276188178_mkbot(X7,X17))
<=> ( ( ( X6 != X17 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),X7) )
& ( ( X6 = X17 )
=> ( X5 != X6 ) )
& ( X5 != X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_in__mkbot) ).
tff(f998,plain,
spl80_65,
inference(avatar_split_clause,[],[f415,f996]) ).
tff(f996,plain,
( spl80_65
<=> ! [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_276188178_mkbot(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_65])]) ).
tff(f415,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_276188178_mkbot(X1,X0)) ),
inference(cnf_transformation,[],[f302]) ).
tff(f994,plain,
spl80_64,
inference(avatar_split_clause,[],[f407,f992]) ).
tff(f407,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))
| ~ sP0(X1,X2,X3,X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,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))
| ~ 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_424895264_mktop(X1,X0)) ) ),
inference(nnf_transformation,[],[f254]) ).
tff(f254,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))
<=> sP0(X1,X2,X3,X0) ),
inference(definition_folding,[],[f212,f253]) ).
tff(f212,plain,
! [X0: arrow_411405190le_alt,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X3),X2),arrow_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,[],[f127]) ).
tff(f127,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,[],[f14]) ).
tff(f14,axiom,
! [X17: arrow_411405190le_alt,X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),arrow_424895264_mktop(X7,X17))
<=> ( ( ( X5 != X17 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),X7) )
& ( ( X5 = X17 )
=> ( X5 != X6 ) )
& ( X6 != X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_in__mktop) ).
tff(f990,plain,
spl80_63,
inference(avatar_split_clause,[],[f406,f988]) ).
tff(f988,plain,
( spl80_63
<=> ! [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_424895264_mktop(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_63])]) ).
tff(f406,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_424895264_mktop(X1,X0)) ),
inference(cnf_transformation,[],[f298]) ).
tff(f966,plain,
spl80_62,
inference(avatar_split_clause,[],[f544,f964]) ).
tff(f964,plain,
( spl80_62
<=> ! [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,[spl80_62])]) ).
tff(f544,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,[],[f444]) ).
tff(f444,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,[],[f320]) ).
tff(f962,plain,
spl80_61,
inference(avatar_split_clause,[],[f538,f960]) ).
tff(f960,plain,
( spl80_61
<=> ! [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,[spl80_61])]) ).
tff(f538,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,[],[f427]) ).
tff(f427,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,[],[f309]) ).
tff(f958,plain,
spl80_60,
inference(avatar_split_clause,[],[f456,f956]) ).
tff(f956,plain,
( spl80_60
<=> ! [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,[spl80_60])]) ).
tff(f456,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,[],[f326]) ).
tff(f954,plain,
spl80_59,
inference(avatar_split_clause,[],[f439,f952]) ).
tff(f952,plain,
( spl80_59
<=> ! [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,[spl80_59])]) ).
tff(f439,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( 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,[],[f315]) ).
tff(f924,plain,
spl80_58,
inference(avatar_split_clause,[],[f422,f922]) ).
tff(f922,plain,
( spl80_58
<=> ! [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,[spl80_58])]) ).
tff(f422,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,[],[f134]) ).
tff(f134,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,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X36: fun(X2,fun(X0,X1)),X6: X2] : ( product_scomp(X0,X2,X0,X1,aa(X2,fun(X0,product_prod(X2,X0)),product_Pair(X2,X0),X6),X36) = aa(X2,fun(X0,X1),X36,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Pair__scomp) ).
tff(f920,plain,
spl80_57,
inference(avatar_split_clause,[],[f383,f918]) ).
tff(f918,plain,
( spl80_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),sK20(X0,X1,X2)),sK21(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_57])]) ).
tff(f383,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),sK20(X0,X1,X2)),sK21(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,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),sK20(X0,X1,X2)),sK21(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f115,f283]) ).
tff(f283,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),sK20(X0,X1,X2)),sK21(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f115,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,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType,X1: $tType,X26: product_prod(X0,X1)] :
? [X27: X0,X28: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X27),X28) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_surj__pair) ).
tff(f916,plain,
spl80_56,
inference(avatar_split_clause,[],[f382,f914]) ).
tff(f914,plain,
( spl80_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),sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_56])]) ).
tff(f382,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),sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,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),sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f205,f281]) ).
tff(f281,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),sK18(X0,X1,X2)),sK19(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f205,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,[],[f114]) ).
tff(f114,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,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType,X1: $tType,X23: product_prod(X0,X1)] :
~ ! [X24: X0,X25: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X24),X25) != X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_prod_Oexhaust) ).
tff(f912,plain,
spl80_55,
inference(avatar_split_clause,[],[f381,f910]) ).
tff(f381,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),sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,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),sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f204,f279]) ).
tff(f279,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),sK16(X0,X1,X2)),sK17(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f204,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,[],[f113]) ).
tff(f113,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,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType,X1: $tType,X26: product_prod(X0,X1)] :
~ ! [X27: X0,X28: X1] : ( aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X27),X28) != X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_PairE) ).
tff(f908,plain,
spl80_54,
inference(avatar_split_clause,[],[f368,f906]) ).
tff(f368,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,[],[f104]) ).
tff(f104,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,[],[f71]) ).
tff(f71,axiom,
! [X1: $tType,X0: $tType,X26: 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,X26)),product_snd(X0,X1,X26)) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_pair__collapse) ).
tff(f904,plain,
spl80_53,
inference(avatar_split_clause,[],[f388,f902]) ).
tff(f902,plain,
( spl80_53
<=> ! [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,[spl80_53])]) ).
tff(f388,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,[],[f120]) ).
tff(f120,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,[],[f49]) ).
tff(f49,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X36: 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,X36)) = X36 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_split__curry) ).
tff(f900,plain,
( spl80_52
| ~ spl80_13
| ~ spl80_31 ),
inference(avatar_split_clause,[],[f719,f715,f632,f898]) ).
tff(f898,plain,
( spl80_52
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP9(sK79,X0,X1,X2,X3)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_52])]) ).
tff(f715,plain,
( spl80_31
<=> ! [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,[spl80_31])]) ).
tff(f719,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP9(sK79,X0,X1,X2,X3)
| ( X2 = X3 ) )
| ~ spl80_13
| ~ spl80_31 ),
inference(resolution,[],[f716,f634]) ).
tff(f716,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)
| sP9(X2,X0,X1,X4,X3)
| ( X3 = X4 ) )
| ~ spl80_31 ),
inference(avatar_component_clause,[],[f715]) ).
tff(f896,plain,
spl80_51,
inference(avatar_split_clause,[],[f387,f894]) ).
tff(f894,plain,
( spl80_51
<=> ! [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,[spl80_51])]) ).
tff(f387,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,[],[f119]) ).
tff(f119,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,[],[f48]) ).
tff(f48,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X36: 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),X36)) = X36 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_curry__split) ).
tff(f844,plain,
spl80_50,
inference(avatar_split_clause,[],[f507,f842]) ).
tff(f842,plain,
( spl80_50
<=> ! [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,[spl80_50])]) ).
tff(f507,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,[],[f176]) ).
tff(f176,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,[],[f93]) ).
tff(f93,axiom,
! [X2: $tType,X1: $tType,X4: $tType,X0: $tType,X57: fun(X0,X4),X41: fun(X4,X2),X36: fun(X2,X1)] : ( comp(X2,X1,X0,X36,comp(X4,X2,X0,X41,X57)) = comp(X4,X1,X0,comp(X2,X1,X4,X36,X41),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_o__assoc) ).
tff(f840,plain,
spl80_49,
inference(avatar_split_clause,[],[f506,f838]) ).
tff(f838,plain,
( spl80_49
<=> ! [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,[spl80_49])]) ).
tff(f506,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,[],[f175]) ).
tff(f175,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,[],[f87]) ).
tff(f87,axiom,
! [X2: $tType,X0: $tType,X1: $tType,X4: $tType,X6: product_prod(X4,X1),X41: fun(X4,X2),X36: fun(X2,X0)] : ( product_apfst(X2,X0,X1,X36,product_apfst(X4,X2,X1,X41,X6)) = product_apfst(X4,X0,X1,comp(X2,X0,X4,X36,X41),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_apfst__compose) ).
tff(f836,plain,
spl80_48,
inference(avatar_split_clause,[],[f505,f834]) ).
tff(f834,plain,
( spl80_48
<=> ! [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,[spl80_48])]) ).
tff(f505,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,[],[f174]) ).
tff(f174,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,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X4: $tType,X40: product_prod(X4,X2),X41: fun(X4,X0),X36: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X36,product_apfst(X4,X0,X2,X41,X40)) = product_apfst(X4,X0,X1,X41,product_apsnd(X2,X1,X4,X36,X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_apsnd__apfst__commute) ).
tff(f832,plain,
spl80_47,
inference(avatar_split_clause,[],[f504,f830]) ).
tff(f830,plain,
( spl80_47
<=> ! [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,[spl80_47])]) ).
tff(f504,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,[],[f173]) ).
tff(f173,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,[],[f88]) ).
tff(f88,axiom,
! [X2: $tType,X1: $tType,X4: $tType,X0: $tType,X6: product_prod(X0,X4),X41: fun(X4,X2),X36: fun(X2,X1)] : ( product_apsnd(X2,X1,X0,X36,product_apsnd(X4,X2,X0,X41,X6)) = product_apsnd(X4,X1,X0,comp(X2,X1,X4,X36,X41),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_apsnd__compose) ).
tff(f825,plain,
( spl80_46
| ~ spl80_13
| ~ spl80_30 ),
inference(avatar_split_clause,[],[f718,f711,f632,f823]) ).
tff(f823,plain,
( spl80_46
<=> ! [X0: arrow_411405190le_alt,X3: arrow_411405190le_alt,X2: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(sK79,X0,X1,X2,X3)
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_46])]) ).
tff(f711,plain,
( spl80_30
<=> ! [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,[spl80_30])]) ).
tff(f718,plain,
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( sP5(sK79,X0,X1,X2,X3)
| ( X2 = X3 ) )
| ~ spl80_13
| ~ spl80_30 ),
inference(resolution,[],[f712,f634]) ).
tff(f712,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 ) )
| ~ spl80_30 ),
inference(avatar_component_clause,[],[f711]) ).
tff(f821,plain,
spl80_45,
inference(avatar_split_clause,[],[f393,f819]) ).
tff(f819,plain,
( spl80_45
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK26(X0,X1,X2,X3)) != aa(X1,X0,X2,sK26(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_45])]) ).
tff(f393,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK26(X0,X1,X2,X3)) != aa(X1,X0,X2,sK26(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK26(X0,X1,X2,X3)) != aa(X1,X0,X2,sK26(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f210,f289]) ).
tff(f289,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,sK26(X0,X1,X2,X3)) != aa(X1,X0,X2,sK26(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f210,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,[],[f124]) ).
tff(f124,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,X41: fun(X0,X1),X36: fun(X0,X1)] :
( ! [X27: X0] : ( aa(X0,X1,X36,X27) = aa(X0,X1,X41,X27) )
=> ( X36 = X41 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
tff(f810,plain,
spl80_44,
inference(avatar_split_clause,[],[f389,f808]) ).
tff(f808,plain,
( spl80_44
<=> ! [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,[spl80_44])]) ).
tff(f389,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,[],[f207]) ).
tff(f207,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,[],[f206]) ).
tff(f206,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,[],[f121]) ).
tff(f121,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,[],[f69]) ).
tff(f69,axiom,
! [X1: $tType,X0: $tType,X45: product_prod(X0,X1),X26: product_prod(X0,X1)] :
( ( product_fst(X0,X1,X26) = product_fst(X0,X1,X45) )
=> ( ( product_snd(X0,X1,X26) = product_snd(X0,X1,X45) )
=> ( X26 = X45 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_prod__eqI) ).
tff(f800,plain,
spl80_43,
inference(avatar_split_clause,[],[f386,f798]) ).
tff(f386,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,[],[f118]) ).
tff(f118,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,[],[f75]) ).
tff(f75,axiom,
! [X1: $tType,X0: $tType,X20: X1,X21: X0] : ( product_fst(X0,X1,aa(X1,product_prod(X0,X1),aa(X0,fun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X21),X20)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_fst__conv) ).
tff(f796,plain,
spl80_42,
inference(avatar_split_clause,[],[f385,f794]) ).
tff(f385,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,[],[f117]) ).
tff(f117,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,[],[f73]) ).
tff(f73,axiom,
! [X1: $tType,X0: $tType,X20: X0,X21: X1] : ( product_snd(X1,X0,aa(X0,product_prod(X1,X0),aa(X1,fun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X21),X20)) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_snd__conv) ).
tff(f792,plain,
spl80_41,
inference(avatar_split_clause,[],[f371,f790]) ).
tff(f790,plain,
( spl80_41
<=> ! [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,[spl80_41])]) ).
tff(f371,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,[],[f199]) ).
tff(f199,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,[],[f198]) ).
tff(f198,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,[],[f107]) ).
tff(f107,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,[],[f10]) ).
tff(f10,axiom,
! [X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_319942042_below(X7,X6,X5),arrow_1985332922le_Lin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_below__Lin) ).
tff(f785,plain,
spl80_40,
inference(avatar_split_clause,[],[f370,f783]) ).
tff(f783,plain,
( spl80_40
<=> ! [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,[spl80_40])]) ).
tff(f370,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,[],[f197]) ).
tff(f197,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,[],[f196]) ).
tff(f196,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,[],[f106]) ).
tff(f106,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,[],[f9]) ).
tff(f9,axiom,
! [X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_1158827142_above(X7,X6,X5),arrow_1985332922le_Lin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_above__Lin) ).
tff(f767,plain,
spl80_39,
inference(avatar_split_clause,[],[f469,f765]) ).
tff(f469,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,[],[f150]) ).
tff(f150,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,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X6: X2,X41: fun(X2,X1),X36: fun(X1,X0)] : ( aa(X1,X0,X36,aa(X2,X1,X41,X6)) = aa(X2,X0,comp(X1,X0,X2,X36,X41),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_o__apply) ).
tff(f747,plain,
spl80_38,
inference(avatar_split_clause,[],[f446,f745]) ).
tff(f745,plain,
( spl80_38
<=> ! [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,[spl80_38])]) ).
tff(f446,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,[],[f320]) ).
tff(f743,plain,
( spl80_37
| ~ spl80_11
| ~ spl80_23 ),
inference(avatar_split_clause,[],[f685,f676,f624,f741]) ).
tff(f741,plain,
( spl80_37
<=> ! [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,[spl80_37])]) ).
tff(f624,plain,
( spl80_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,[spl80_11])]) ).
tff(f676,plain,
( spl80_23
<=> ! [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,[spl80_23])]) ).
tff(f685,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)
| ~ spl80_11
| ~ spl80_23 ),
inference(resolution,[],[f677,f625]) ).
tff(f625,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)
| ~ spl80_11 ),
inference(avatar_component_clause,[],[f624]) ).
tff(f677,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) )
| ~ spl80_23 ),
inference(avatar_component_clause,[],[f676]) ).
tff(f739,plain,
spl80_36,
inference(avatar_split_clause,[],[f429,f737]) ).
tff(f737,plain,
( spl80_36
<=> ! [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,[spl80_36])]) ).
tff(f429,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,[],[f309]) ).
tff(f735,plain,
spl80_35,
inference(avatar_split_clause,[],[f421,f733]) ).
tff(f733,plain,
( spl80_35
<=> ! [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,[spl80_35])]) ).
tff(f421,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,[],[f133]) ).
tff(f133,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,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X6: product_prod(X1,X2),X36: fun(X2,X0)] : ( product_snd(X1,X0,product_apsnd(X2,X0,X1,X36,X6)) = aa(X2,X0,X36,product_snd(X1,X2,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_snd__apsnd) ).
tff(f731,plain,
spl80_34,
inference(avatar_split_clause,[],[f420,f729]) ).
tff(f729,plain,
( spl80_34
<=> ! [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,[spl80_34])]) ).
tff(f420,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,[],[f132]) ).
tff(f132,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,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X6: product_prod(X2,X1),X36: fun(X2,X0)] : ( aa(X2,X0,X36,product_fst(X2,X1,X6)) = product_fst(X0,X1,product_apfst(X2,X0,X1,X36,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_fst__apfst) ).
tff(f727,plain,
spl80_33,
inference(avatar_split_clause,[],[f366,f725]) ).
tff(f366,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,[],[f195]) ).
tff(f195,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,[],[f101]) ).
tff(f101,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,[],[f12]) ).
tff(f12,axiom,
! [X6: arrow_411405190le_alt,X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_424895264_mktop(X7,X6),arrow_1985332922le_Lin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_mktop__Lin) ).
tff(f723,plain,
spl80_32,
inference(avatar_split_clause,[],[f365,f721]) ).
tff(f721,plain,
( spl80_32
<=> ! [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,[spl80_32])]) ).
tff(f365,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,[],[f194]) ).
tff(f194,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,[],[f100]) ).
tff(f100,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,[],[f11]) ).
tff(f11,axiom,
! [X6: arrow_411405190le_alt,X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7,arrow_1985332922le_Lin)
=> member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_276188178_mkbot(X7,X6),arrow_1985332922le_Lin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_mkbot__Lin) ).
tff(f717,plain,
spl80_31,
inference(avatar_split_clause,[],[f457,f715]) ).
tff(f457,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,[],[f266]) ).
tff(f266,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,[],[f218,f265,f264,f263,f262]) ).
tff(f218,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,[],[f217]) ).
tff(f217,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,[],[f137]) ).
tff(f137,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,[],[f7]) ).
tff(f7,axiom,
! [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt,X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8: arrow_411405190le_alt,X9: arrow_411405190le_alt] :
( ( X8 != X9 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7,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),X6),X5),arrow_319942042_below(X7,X9,X8))
<=> ( ( ( X5 != 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),X6),X5),X7) )
& ( ( 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),X8),X5),X7)
| ( X5 = X8 ) ) ) ) )
& ( ( X5 = 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),X6),X8),X7) )
& ( X5 != X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_in__below) ).
tff(f713,plain,
spl80_30,
inference(avatar_split_clause,[],[f440,f711]) ).
tff(f440,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,[],[f261]) ).
tff(f261,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,[],[f216,f260,f259,f258,f257]) ).
tff(f216,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,[],[f215]) ).
tff(f215,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,[],[f136]) ).
tff(f136,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,[],[f6]) ).
tff(f6,axiom,
! [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt,X7: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X8: arrow_411405190le_alt,X9: arrow_411405190le_alt] :
( ( X8 != X9 )
=> ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X7,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),X6),X5),arrow_1158827142_above(X7,X9,X8))
<=> ( ( ( X6 != X8 )
=> ( ( ( X5 != X8 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X5),X7) )
& ( ( X5 = X8 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X6),X9),X7)
| ( X6 = X9 ) ) ) ) )
& ( ( X6 = X8 )
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X9),X5),X7) )
& ( X5 != X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_in__above) ).
tff(f708,plain,
spl80_29,
inference(avatar_split_clause,[],[f384,f706]) ).
tff(f706,plain,
( spl80_29
<=> ! [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,[spl80_29])]) ).
tff(f384,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,[],[f116]) ).
tff(f116,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,[],[f80]) ).
tff(f80,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X6: fun(X0,product_prod(X1,X2))] : ( product_scomp(X0,X1,X2,product_prod(X1,X2),X6,product_Pair(X1,X2)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_scomp__Pair) ).
tff(f702,plain,
spl80_28,
inference(avatar_split_clause,[],[f448,f700]) ).
tff(f700,plain,
( spl80_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] :
( sP6(X0,X1,X4,X3,X2)
| ( X1 = X3 )
| ~ sP7(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_28])]) ).
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] :
( sP6(X0,X1,X4,X3,X2)
| ( X1 = X3 )
| ~ sP7(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f323]) ).
tff(f698,plain,
spl80_27,
inference(avatar_split_clause,[],[f431,f696]) ).
tff(f696,plain,
( spl80_27
<=> ! [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,[spl80_27])]) ).
tff(f431,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,[],[f312]) ).
tff(f694,plain,
spl80_26,
inference(avatar_split_clause,[],[f419,f692]) ).
tff(f692,plain,
( spl80_26
<=> ! [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,[spl80_26])]) ).
tff(f419,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,[],[f131]) ).
tff(f131,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,[],[f67]) ).
tff(f67,axiom,
! [X1: $tType,X0: $tType,X2: $tType,X6: product_prod(X2,X0),X36: fun(X2,X1)] : ( product_snd(X1,X0,product_apfst(X2,X1,X0,X36,X6)) = product_snd(X2,X0,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_snd__apfst) ).
tff(f690,plain,
spl80_25,
inference(avatar_split_clause,[],[f418,f688]) ).
tff(f688,plain,
( spl80_25
<=> ! [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,[spl80_25])]) ).
tff(f418,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,[],[f130]) ).
tff(f130,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,[],[f64]) ).
tff(f64,axiom,
! [X1: $tType,X2: $tType,X0: $tType,X6: product_prod(X0,X2),X36: fun(X2,X1)] : ( product_fst(X0,X1,product_apsnd(X2,X1,X0,X36,X6)) = product_fst(X0,X2,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_fst__apsnd) ).
tff(f684,plain,
( spl80_24
| ~ spl80_8
| ~ spl80_22 ),
inference(avatar_split_clause,[],[f679,f672,f612,f682]) ).
tff(f682,plain,
( spl80_24
<=> ! [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,[spl80_24])]) ).
tff(f612,plain,
( spl80_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,[spl80_8])]) ).
tff(f672,plain,
( spl80_22
<=> ! [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,[spl80_22])]) ).
tff(f679,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)
| ~ spl80_8
| ~ spl80_22 ),
inference(resolution,[],[f673,f613]) ).
tff(f613,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)
| ~ spl80_8 ),
inference(avatar_component_clause,[],[f612]) ).
tff(f673,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) )
| ~ spl80_22 ),
inference(avatar_component_clause,[],[f672]) ).
tff(f678,plain,
spl80_23,
inference(avatar_split_clause,[],[f546,f676]) ).
tff(f546,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,[],[f451]) ).
tff(f451,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP7(X0,X1,X2,X3,X4)
| ( X2 != X3 )
| ~ sP6(X0,X1,X4,X3,X2) ),
inference(cnf_transformation,[],[f323]) ).
tff(f674,plain,
spl80_22,
inference(avatar_split_clause,[],[f540,f672]) ).
tff(f540,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,[],[f434]) ).
tff(f434,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,[],[f312]) ).
tff(f670,plain,
spl80_21,
inference(avatar_split_clause,[],[f445,f668]) ).
tff(f668,plain,
( spl80_21
<=> ! [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,[spl80_21])]) ).
tff(f445,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,[],[f320]) ).
tff(f666,plain,
spl80_20,
inference(avatar_split_clause,[],[f428,f664]) ).
tff(f664,plain,
( spl80_20
<=> ! [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,[spl80_20])]) ).
tff(f428,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,[],[f309]) ).
tff(f661,plain,
spl80_19,
inference(avatar_split_clause,[],[f376,f659]) ).
tff(f659,plain,
( spl80_19
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_19])]) ).
tff(f376,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,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,[],[f110]) ).
tff(f110,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,X50: fun(X0,bool),X6: X0] :
( member(X0,X6,X50)
<=> pp(aa(X0,bool,X50,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
tff(f657,plain,
spl80_18,
inference(avatar_split_clause,[],[f375,f655]) ).
tff(f655,plain,
( spl80_18
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_18])]) ).
tff(f375,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f268]) ).
tff(f653,plain,
spl80_17,
inference(avatar_split_clause,[],[f454,f651]) ).
tff(f651,plain,
( spl80_17
<=> ! [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,[spl80_17])]) ).
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] :
( sP6(X0,X1,X2,X3,X4)
| ( X3 = X4 ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f649,plain,
spl80_16,
inference(avatar_split_clause,[],[f437,f647]) ).
tff(f647,plain,
( spl80_16
<=> ! [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,[spl80_16])]) ).
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] :
( sP2(X0,X1,X2,X3,X4)
| ( X3 = X4 ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f643,plain,
spl80_15,
inference(avatar_split_clause,[],[f561,f641]) ).
tff(f561,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)
| ( X2 = X3 ) ),
inference(duplicate_literal_removal,[],[f528]) ).
tff(f528,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)
| ( X2 = X3 )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f403]) ).
tff(f403,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)
| ( X1 != X3 )
| ( X1 = X2 )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f297]) ).
tff(f639,plain,
spl80_14,
inference(avatar_split_clause,[],[f560,f637]) ).
tff(f637,plain,
( spl80_14
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( sP1(X0,X1,X3,X3)
| ( X1 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_14])]) ).
tff(f560,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)
| ( X1 = X3 ) ),
inference(duplicate_literal_removal,[],[f533]) ).
tff(f533,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)
| ( X1 = X3 )
| ( X1 = X3 ) ),
inference(equality_resolution,[],[f412]) ).
tff(f412,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)
| ( X2 != X3 )
| ( X1 = X2 )
| ( X1 = X3 ) ),
inference(cnf_transformation,[],[f301]) ).
tff(f635,plain,
spl80_13,
inference(avatar_split_clause,[],[f524,f632]) ).
tff(f524,plain,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK79,arrow_1985332922le_Lin),
inference(cnf_transformation,[],[f360]) ).
tff(f360,plain,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),sK79,arrow_1985332922le_Lin),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79])],[f192,f359]) ).
tff(f359,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),sK79,arrow_1985332922le_Lin) ),
introduced(choice_axiom,[]) ).
tff(f192,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,[],[f8]) ).
tff(f8,axiom,
? [X16: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X16,arrow_1985332922le_Lin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_linear__alt) ).
tff(f630,plain,
spl80_12,
inference(avatar_split_clause,[],[f361,f628]) ).
tff(f361,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,[],[f193]) ).
tff(f193,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,[],[f99]) ).
tff(f99,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,[],[f98]) ).
tff(f98,negated_conjecture,
~ ? [X44: 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),X44)
& member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X44,arrow_1985332922le_Lin) ),
inference(negated_conjecture,[],[f97]) ).
tff(f97,conjecture,
? [X44: 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),X44)
& member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X44,arrow_1985332922le_Lin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f626,plain,
spl80_11,
inference(avatar_split_clause,[],[f548,f624]) ).
tff(f548,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,[],[f455]) ).
tff(f455,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X4: arrow_411405190le_alt] :
( sP6(X0,X1,X2,X3,X4)
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f622,plain,
spl80_10,
inference(avatar_split_clause,[],[f547,f620]) ).
tff(f620,plain,
( spl80_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,[spl80_10])]) ).
tff(f547,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,[],[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] :
( sP7(X0,X1,X2,X3,X4)
| ( X1 != X3 ) ),
inference(cnf_transformation,[],[f323]) ).
tff(f618,plain,
spl80_9,
inference(avatar_split_clause,[],[f545,f616]) ).
tff(f616,plain,
( spl80_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,[spl80_9])]) ).
tff(f545,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,[],[f443]) ).
tff(f443,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,[],[f320]) ).
tff(f614,plain,
spl80_8,
inference(avatar_split_clause,[],[f542,f612]) ).
tff(f542,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X4: arrow_411405190le_alt] : sP2(X0,X2,X2,X3,X4),
inference(equality_resolution,[],[f438]) ).
tff(f438,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,[],[f315]) ).
tff(f610,plain,
spl80_7,
inference(avatar_split_clause,[],[f541,f608]) ).
tff(f608,plain,
( spl80_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,[spl80_7])]) ).
tff(f541,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,[],[f433]) ).
tff(f433,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,[],[f312]) ).
tff(f606,plain,
spl80_6,
inference(avatar_split_clause,[],[f539,f604]) ).
tff(f604,plain,
( spl80_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,[spl80_6])]) ).
tff(f539,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,[],[f426]) ).
tff(f426,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,[],[f309]) ).
tff(f602,plain,
spl80_5,
inference(avatar_split_clause,[],[f537,f600]) ).
tff(f600,plain,
( spl80_5
<=> ! [X2: arrow_411405190le_alt,X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X3: arrow_411405190le_alt] : ~ sP1(X0,X3,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_5])]) ).
tff(f537,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),
inference(equality_resolution,[],[f408]) ).
tff(f408,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 )
| ~ sP1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f301]) ).
tff(f598,plain,
spl80_4,
inference(avatar_split_clause,[],[f532,f596]) ).
tff(f596,plain,
( spl80_4
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1: arrow_411405190le_alt,X3: arrow_411405190le_alt] : ~ sP0(X0,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_4])]) ).
tff(f532,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),
inference(equality_resolution,[],[f399]) ).
tff(f399,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 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f297]) ).
tff(f594,plain,
~ spl80_3,
inference(avatar_split_clause,[],[f364,f591]) ).
tff(f364,plain,
a != b,
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
tff(f589,plain,
spl80_2,
inference(avatar_split_clause,[],[f363,f586]) ).
tff(f586,plain,
( spl80_2
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_2])]) ).
tff(f363,plain,
pp(fTrue),
inference(cnf_transformation,[],[f96]) ).
tff(f96,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f584,plain,
~ spl80_1,
inference(avatar_split_clause,[],[f362,f581]) ).
tff(f581,plain,
( spl80_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl80_1])]) ).
tff(f362,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f95]) ).
tff(f95,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SCT198_5 : TPTP v8.1.2. Released v6.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n019.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Apr 29 22:26:59 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (20049)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39 % (20055)WARNING: value z3 for option sas not known
% 0.16/0.39 % (20056)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.39 % (20054)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.39 % (20058)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)
% 0.16/0.39 % (20057)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)
% 0.16/0.39 % (20059)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)
% 0.16/0.39 % (20055)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)
% 0.16/0.39 % (20053)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39 % (20059)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40 % Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41 % Exception at run slice level
% 0.22/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41 % (20068)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.41 % (20069)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 % (20068)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % (20069)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % Exception at run slice level
% 0.22/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42 % (20073)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)
% 0.22/0.44 % (20077)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.22/0.46 % (20057)First to succeed.
% 0.22/0.48 % (20057)Refutation found. Thanks to Tanya!
% 0.22/0.48 % SZS status Theorem for theBenchmark
% 0.22/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.48 % (20057)------------------------------
% 0.22/0.48 % (20057)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.48 % (20057)Termination reason: Refutation
% 0.22/0.48
% 0.22/0.48 % (20057)Memory used [KB]: 2121
% 0.22/0.48 % (20057)Time elapsed: 0.091 s
% 0.22/0.48 % (20057)Instructions burned: 161 (million)
% 0.22/0.48 % (20057)------------------------------
% 0.22/0.48 % (20057)------------------------------
% 0.22/0.48 % (20049)Success in time 0.113 s
%------------------------------------------------------------------------------