TSTP Solution File: ITP020_3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP020_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 : Sun May 5 07:00:51 EDT 2024
% Result : Theorem 0.23s 0.49s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 333
% Syntax : Number of formulae : 913 ( 180 unt; 74 typ; 0 def)
% Number of atoms : 2835 ( 153 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 3134 (1138 ~;1267 |; 401 &)
% ( 276 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 108 ( 56 >; 52 *; 0 +; 0 <<)
% Number of predicates : 191 ( 189 usr; 173 prp; 0-3 aty)
% Number of functors : 55 ( 55 usr; 7 con; 0-5 aty)
% Number of variables : 1935 (1748 !; 130 ?;1935 :)
% ( 57 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_7,type,
tyop_2Enum_2Enum: $tType ).
tff(type_def_8,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
app_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
combin_i_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).
tff(func_def_2,type,
combin_k_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).
tff(func_def_3,type,
combin_s_2E0:
!>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).
tff(func_def_4,type,
c_2Ebool_2E_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_5,type,
c_2Ebool_2E_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_6,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_7,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_8,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_9,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_10,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_11,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_12,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_13,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_14,type,
c_2Epred__set_2EBIJ_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(func_def_15,type,
c_2Epred__set_2EBIJ_2E3:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_16,type,
c_2Epred__set_2ECROSS_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool))) ).
tff(func_def_17,type,
c_2Epred__set_2ECROSS_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(X0,X1),tyop_2Emin_2Ebool) ) ).
tff(func_def_18,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_19,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_20,type,
c_2Epred__set_2EUNIV_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ).
tff(func_def_21,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_22,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_23,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_24,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_25,type,
sK16:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_26,type,
sK17:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_27,type,
sK18:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_28,type,
sK19:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_29,type,
sK20:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_30,type,
sK21:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_31,type,
sK22:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).
tff(func_def_32,type,
sK23:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_33,type,
sK24:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_34,type,
sK25:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_35,type,
sK26:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_36,type,
sK27:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).
tff(func_def_37,type,
sK28:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_38,type,
sK29:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_39,type,
sK30:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_40,type,
sK31:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_41,type,
sK32:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * X0 ) > X1 ) ).
tff(func_def_42,type,
sK33:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_43,type,
sK34:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(X0,X1) ) ).
tff(func_def_44,type,
sK35:
!>[X0: $tType,X1: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) > X0 ) ).
tff(func_def_45,type,
sK36:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).
tff(func_def_46,type,
sK37:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_47,type,
sK38:
!>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Ebool ) > X0 ) ).
tff(func_def_48,type,
sK39:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_49,type,
sK40:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_50,type,
sK41:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(X0,X1) ) ).
tff(func_def_51,type,
sK42:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(X1,X0) ) ).
tff(func_def_52,type,
sK43: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(pred_def_2,type,
sP0: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_3,type,
sP1: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_4,type,
sP2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_5,type,
sP3: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_6,type,
sP4: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_7,type,
sP5: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_8,type,
sP6: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_9,type,
sP7: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_10,type,
sP8: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_11,type,
sP9: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_12,type,
sP10: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_13,type,
sP11: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_14,type,
sP12: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_15,type,
sP13: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_16,type,
sP14: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(pred_def_17,type,
sP15: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > $o ).
tff(f2891,plain,
$false,
inference(avatar_sat_refutation,[],[f582,f587,f591,f595,f599,f603,f607,f611,f615,f619,f630,f634,f638,f642,f646,f650,f654,f658,f662,f666,f670,f674,f678,f682,f686,f690,f694,f698,f702,f706,f710,f714,f718,f722,f726,f730,f734,f738,f742,f767,f773,f777,f781,f785,f789,f793,f819,f831,f835,f839,f843,f847,f851,f855,f859,f863,f867,f871,f875,f879,f883,f887,f891,f895,f899,f903,f907,f911,f915,f919,f923,f927,f931,f935,f939,f943,f951,f955,f959,f963,f967,f971,f975,f979,f983,f987,f991,f1052,f1074,f1080,f1097,f1101,f1114,f1118,f1122,f1126,f1130,f1135,f1139,f1143,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1183,f1187,f1263,f1267,f1271,f1275,f1279,f1283,f1308,f1316,f1326,f1334,f1338,f1342,f1346,f1350,f1354,f1358,f1367,f1435,f1440,f1444,f1470,f1474,f1478,f1482,f1486,f1508,f1520,f1521,f1522,f1533,f1534,f1543,f1571,f1842,f1915,f1923,f2146,f2295,f2326,f2347,f2369,f2391,f2416,f2477,f2481,f2485,f2489,f2494,f2499,f2503,f2507,f2511,f2515,f2612,f2677,f2681,f2685,f2702,f2706,f2720,f2742,f2750,f2779,f2841,f2846,f2865,f2869,f2890]) ).
tff(f2890,plain,
( spl44_1
| ~ spl44_4
| ~ spl44_118
| ~ spl44_170
| ~ spl44_171 ),
inference(avatar_split_clause,[],[f2879,f2863,f2843,f1306,f593,f579]) ).
tff(f579,plain,
( spl44_1
<=> p(c_2Ebool_2EF_2E0) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_1])]) ).
tff(f593,plain,
( spl44_4
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_4])]) ).
tff(f1306,plain,
( spl44_118
<=> ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_118])]) ).
tff(f2843,plain,
( spl44_170
<=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK43),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_170])]) ).
tff(f2863,plain,
( spl44_171
<=> ! [X1: $tType,X0: $tType,X5: tyop_2Emin_2Efun(X1,X0),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),sK41(X0,X1,X2,X3)),X2),X3))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),X5),X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_171])]) ).
tff(f2879,plain,
( p(c_2Ebool_2EF_2E0)
| ~ spl44_4
| ~ spl44_118
| ~ spl44_170
| ~ spl44_171 ),
inference(forward_demodulation,[],[f2870,f1321]) ).
tff(f1321,plain,
( ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) )
| ~ spl44_4
| ~ spl44_118 ),
inference(resolution,[],[f1307,f594]) ).
tff(f594,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl44_4 ),
inference(avatar_component_clause,[],[f593]) ).
tff(f1307,plain,
( ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))))
| ~ spl44_118 ),
inference(avatar_component_clause,[],[f1306]) ).
tff(f2870,plain,
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sK41(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))))
| ~ spl44_170
| ~ spl44_171 ),
inference(resolution,[],[f2864,f2845]) ).
tff(f2845,plain,
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK43),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))
| ~ spl44_170 ),
inference(avatar_component_clause,[],[f2843]) ).
tff(f2864,plain,
( ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X5: tyop_2Emin_2Efun(X1,X0)] :
( ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),X5),X3),X2))
| p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),sK41(X0,X1,X2,X3)),X2),X3)) )
| ~ spl44_171 ),
inference(avatar_component_clause,[],[f2863]) ).
tff(f2869,plain,
spl44_172,
inference(avatar_split_clause,[],[f561,f2867]) ).
tff(f2867,plain,
( spl44_172
<=> ! [X1: $tType,X0: $tType,X7: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),sK42(X0,X1,X2,X3)),X3),X2))
| ~ p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X7),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_172])]) ).
tff(f561,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X7: tyop_2Emin_2Efun(X0,X1)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),sK42(X0,X1,X2,X3)),X3),X2))
| ~ p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X7),X2),X3)) ),
inference(definition_unfolding,[],[f549,f551,f551]) ).
tff(f551,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(X0,X1,X2,X3,X4) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X2),X3),X4) ),
inference(cnf_transformation,[],[f113]) ).
tff(f113,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(X0,X1,X2,X3,X4) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X2),X3),X4) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType,X1: $tType,X12: tyop_2Emin_2Efun(X0,X1),X13: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X14: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(X0,X1,X12,X13,X14) = app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),X12),X13),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).
tff(f549,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X7: tyop_2Emin_2Efun(X0,X1)] :
( p(c_2Epred__set_2EBIJ_2E3(X1,X0,sK42(X0,X1,X2,X3),X3,X2))
| ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3)) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EBIJ_2E3(X0,X1,sK41(X0,X1,X2,X3),X2,X3))
| ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
& ( p(c_2Epred__set_2EBIJ_2E3(X1,X0,sK42(X0,X1,X2,X3),X3,X2))
| ! [X7: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f306,f308,f307]) ).
tff(f307,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
=> p(c_2Epred__set_2EBIJ_2E3(X0,X1,sK41(X0,X1,X2,X3),X2,X3)) ),
introduced(choice_axiom,[]) ).
tff(f308,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ? [X6: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X6,X3,X2))
=> p(c_2Epred__set_2EBIJ_2E3(X1,X0,sK42(X0,X1,X2,X3),X3,X2)) ),
introduced(choice_axiom,[]) ).
tff(f306,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
| ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
& ( ? [X6: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X6,X3,X2))
| ! [X7: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X7,X2,X3)) ) ),
inference(rectify,[],[f305]) ).
tff(f305,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
| ! [X5: tyop_2Emin_2Efun(X1,X0)] : ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) )
& ( ? [X5: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2))
| ! [X4: tyop_2Emin_2Efun(X0,X1)] : ~ p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3)) ) ),
inference(nnf_transformation,[],[f112]) ).
tff(f112,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ? [X4: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X4,X2,X3))
<=> ? [X5: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType,X1: $tType,X27: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X28: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)] :
( ? [X29: tyop_2Emin_2Efun(X0,X1)] : p(c_2Epred__set_2EBIJ_2E3(X0,X1,X29,X27,X28))
<=> ? [X30: tyop_2Emin_2Efun(X1,X0)] : p(c_2Epred__set_2EBIJ_2E3(X1,X0,X30,X28,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EBIJ__SYM) ).
tff(f2865,plain,
spl44_171,
inference(avatar_split_clause,[],[f560,f2863]) ).
tff(f560,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X5: tyop_2Emin_2Efun(X1,X0)] :
( p(app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X0,X1),sK41(X0,X1,X2,X3)),X2),X3))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,X0),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(X1,X0),X5),X3),X2)) ),
inference(definition_unfolding,[],[f550,f551,f551]) ).
tff(f550,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X5: tyop_2Emin_2Efun(X1,X0)] :
( p(c_2Epred__set_2EBIJ_2E3(X0,X1,sK41(X0,X1,X2,X3),X2,X3))
| ~ p(c_2Epred__set_2EBIJ_2E3(X1,X0,X5,X3,X2)) ),
inference(cnf_transformation,[],[f309]) ).
tff(f2846,plain,
spl44_170,
inference(avatar_split_clause,[],[f563,f2843]) ).
tff(f563,plain,
p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK43),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
inference(definition_unfolding,[],[f554,f551]) ).
tff(f554,plain,
p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,sK43,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,sK43,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f115,f310]) ).
tff(f310,plain,
( ? [X0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X0,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))
=> p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,sK43,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ),
introduced(choice_axiom,[]) ).
tff(f115,plain,
? [X0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X0,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
? [X3: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X3,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ) ).
tff(f2841,plain,
( spl44_169
| ~ spl44_3
| ~ spl44_15 ),
inference(avatar_split_clause,[],[f755,f644,f589,f2839]) ).
tff(f2839,plain,
( spl44_169
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_5C_2F_2E2(X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_169])]) ).
tff(f589,plain,
( spl44_3
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_3])]) ).
tff(f644,plain,
( spl44_15
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_15])]) ).
tff(f755,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_5C_2F_2E2(X1,X0) ) )
| ~ spl44_3
| ~ spl44_15 ),
inference(resolution,[],[f645,f590]) ).
tff(f590,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = X0 ) )
| ~ spl44_3 ),
inference(avatar_component_clause,[],[f589]) ).
tff(f645,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X1) )
| ~ spl44_15 ),
inference(avatar_component_clause,[],[f644]) ).
tff(f2779,plain,
spl44_168,
inference(avatar_split_clause,[],[f553,f2777]) ).
tff(f2777,plain,
( spl44_168
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_168])]) ).
tff(f553,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Es__thm) ).
tff(f2750,plain,
spl44_167,
inference(avatar_split_clause,[],[f538,f2748]) ).
tff(f2748,plain,
( spl44_167
<=> ! [X1: $tType,X0: $tType,X5: tyop_2Emin_2Efun(X0,X1),X3: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),sK32(X0,X1,X2,X3)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK33(X0,X1,X2,X5)),app_2E2(X0,X1,X5,sK33(X0,X1,X2,X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_167])]) ).
tff(f538,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: X0,X5: tyop_2Emin_2Efun(X0,X1)] :
( p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),sK32(X0,X1,X2,X3)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK33(X0,X1,X2,X5)),app_2E2(X0,X1,X5,sK33(X0,X1,X2,X5)))) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( ( ! [X3: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),sK32(X0,X1,X2,X3)))
| ! [X5: tyop_2Emin_2Efun(X0,X1)] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK33(X0,X1,X2,X5)),app_2E2(X0,X1,X5,sK33(X0,X1,X2,X5)))) )
& ( ! [X8: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,sK34(X0,X1,X2),X8)))
| ! [X10: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK35(X0,X1,X2)),X10)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35])],[f285,f289,f288,f287,f286]) ).
tff(f286,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: X0] :
( ? [X4: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4))
=> p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),sK32(X0,X1,X2,X3))) ),
introduced(choice_axiom,[]) ).
tff(f287,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X5: tyop_2Emin_2Efun(X0,X1)] :
( ? [X6: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6)))
=> ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK33(X0,X1,X2,X5)),app_2E2(X0,X1,X5,sK33(X0,X1,X2,X5)))) ),
introduced(choice_axiom,[]) ).
tff(f288,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( ? [X7: tyop_2Emin_2Efun(X0,X1)] :
! [X8: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,X7,X8)))
=> ! [X8: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,sK34(X0,X1,X2),X8))) ),
introduced(choice_axiom,[]) ).
tff(f289,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( ? [X9: X0] :
! [X10: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X9),X10))
=> ! [X10: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK35(X0,X1,X2)),X10)) ),
introduced(choice_axiom,[]) ).
tff(f285,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( ( ! [X3: X0] :
? [X4: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4))
| ! [X5: tyop_2Emin_2Efun(X0,X1)] :
? [X6: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6))) )
& ( ? [X7: tyop_2Emin_2Efun(X0,X1)] :
! [X8: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,X7,X8)))
| ? [X9: X0] :
! [X10: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X9),X10)) ) ),
inference(rectify,[],[f284]) ).
tff(f284,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( ( ! [X3: X0] :
? [X4: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4))
| ! [X5: tyop_2Emin_2Efun(X0,X1)] :
? [X6: X0] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6))) )
& ( ? [X5: tyop_2Emin_2Efun(X0,X1)] :
! [X6: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6)))
| ? [X3: X0] :
! [X4: X1] : ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4)) ) ),
inference(nnf_transformation,[],[f107]) ).
tff(f107,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( ! [X3: X0] :
? [X4: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X3),X4))
<=> ? [X5: tyop_2Emin_2Efun(X0,X1)] :
! [X6: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X6),app_2E2(X0,X1,X5,X6))) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType,X1: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( ! [X11: X0] :
? [X24: X1] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17,X11),X24))
<=> ? [X25: tyop_2Emin_2Efun(X0,X1)] :
! [X26: X0] : p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X17,X26),app_2E2(X0,X1,X25,X26))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ESKOLEM__THM) ).
tff(f2742,plain,
spl44_166,
inference(avatar_split_clause,[],[f363,f2740]) ).
tff(f2740,plain,
( spl44_166
<=> ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0,X1) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_166])]) ).
tff(f363,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0,X1) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0),X1) ),
inference(cnf_transformation,[],[f76]) ).
tff(f76,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0,X1) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0),X1) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X12: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X13: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X12,X13) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X12),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) ).
tff(f2720,plain,
spl44_165,
inference(avatar_split_clause,[],[f537,f2718]) ).
tff(f2718,plain,
( spl44_165
<=> ! [X1: $tType,X0: $tType,X8: X0,X10: X1,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] :
( p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,sK34(X0,X1,X2),X8)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK35(X0,X1,X2)),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_165])]) ).
tff(f537,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X10: X1,X8: X0] :
( p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X8),app_2E2(X0,X1,sK34(X0,X1,X2),X8)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK35(X0,X1,X2)),X10)) ),
inference(cnf_transformation,[],[f290]) ).
tff(f2706,plain,
spl44_164,
inference(avatar_split_clause,[],[f548,f2704]) ).
tff(f2704,plain,
( spl44_164
<=> ! [X1: $tType,X0: $tType,X3: tyop_2Emin_2Efun(X0,X1),X2: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK40(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK40(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_164])]) ).
tff(f548,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK40(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK40(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK40(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK40(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f136,f303]) ).
tff(f303,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ? [X4: X0] : ( app_2E2(X0,X1,X2,X4) != app_2E2(X0,X1,X3,X4) )
=> ( app_2E2(X0,X1,X2,sK40(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK40(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f136,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ? [X4: X0] : ( app_2E2(X0,X1,X2,X4) != app_2E2(X0,X1,X3,X4) ) ),
inference(ennf_transformation,[],[f111]) ).
tff(f111,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ! [X4: X0] : ( app_2E2(X0,X1,X2,X4) = app_2E2(X0,X1,X3,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X0: $tType,X1: $tType,X3: tyop_2Emin_2Efun(X0,X1),X4: tyop_2Emin_2Efun(X0,X1)] :
( ! [X5: X0] : ( app_2E2(X0,X1,X3,X5) = app_2E2(X0,X1,X4,X5) )
=> ( X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).
tff(f2702,plain,
( spl44_163
| ~ spl44_3
| ~ spl44_14 ),
inference(avatar_split_clause,[],[f753,f640,f589,f2700]) ).
tff(f2700,plain,
( spl44_163
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_5C_2F_2E2(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_163])]) ).
tff(f640,plain,
( spl44_14
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_14])]) ).
tff(f753,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_5C_2F_2E2(X0,X1) ) )
| ~ spl44_3
| ~ spl44_14 ),
inference(resolution,[],[f641,f590]) ).
tff(f641,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X0) )
| ~ spl44_14 ),
inference(avatar_component_clause,[],[f640]) ).
tff(f2685,plain,
spl44_162,
inference(avatar_split_clause,[],[f455,f2683]) ).
tff(f2683,plain,
( spl44_162
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X0,X1,X2)
| p(X0)
| ~ sP5(X0,X2,X1)
| ~ sP4(X1,X2,X0)
| ~ sP3(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_162])]) ).
tff(f455,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X0,X1,X2)
| p(X0)
| ~ sP5(X0,X2,X1)
| ~ sP4(X1,X2,X0)
| ~ sP3(X2,X1,X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP6(X0,X1,X2)
| ( p(X0)
& p(X1)
& ~ p(X2) )
| ~ sP5(X0,X2,X1)
| ~ sP4(X1,X2,X0)
| ~ sP3(X2,X1,X0) )
& ( ( ( ~ p(X0)
| ~ p(X1)
| p(X2) )
& sP5(X0,X2,X1)
& sP4(X1,X2,X0)
& sP3(X2,X1,X0) )
| ~ sP6(X0,X1,X2) ) ),
inference(rectify,[],[f235]) ).
tff(f235,plain,
! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
( ( sP6(X2,X1,X0)
| ( p(X2)
& p(X1)
& ~ p(X0) )
| ~ sP5(X2,X0,X1)
| ~ sP4(X1,X0,X2)
| ~ sP3(X0,X1,X2) )
& ( ( ( ~ p(X2)
| ~ p(X1)
| p(X0) )
& sP5(X2,X0,X1)
& sP4(X1,X0,X2)
& sP3(X0,X1,X2) )
| ~ sP6(X2,X1,X0) ) ),
inference(flattening,[],[f234]) ).
tff(f234,plain,
! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
( ( sP6(X2,X1,X0)
| ( p(X2)
& p(X1)
& ~ p(X0) )
| ~ sP5(X2,X0,X1)
| ~ sP4(X1,X0,X2)
| ~ sP3(X0,X1,X2) )
& ( ( ( ~ p(X2)
| ~ p(X1)
| p(X0) )
& sP5(X2,X0,X1)
& sP4(X1,X0,X2)
& sP3(X0,X1,X2) )
| ~ sP6(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
( sP6(X2,X1,X0)
<=> ( ( ~ p(X2)
| ~ p(X1)
| p(X0) )
& sP5(X2,X0,X1)
& sP4(X1,X0,X2)
& sP3(X0,X1,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
tff(f2681,plain,
spl44_161,
inference(avatar_split_clause,[],[f454,f2679]) ).
tff(f2679,plain,
( spl44_161
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X0,X1,X2)
| p(X1)
| ~ sP5(X0,X2,X1)
| ~ sP4(X1,X2,X0)
| ~ sP3(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_161])]) ).
tff(f454,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X0,X1,X2)
| p(X1)
| ~ sP5(X0,X2,X1)
| ~ sP4(X1,X2,X0)
| ~ sP3(X2,X1,X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f2677,plain,
spl44_160,
inference(avatar_split_clause,[],[f453,f2675]) ).
tff(f2675,plain,
( spl44_160
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X0,X1,X2)
| ~ p(X2)
| ~ sP5(X0,X2,X1)
| ~ sP4(X1,X2,X0)
| ~ sP3(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_160])]) ).
tff(f453,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X0,X1,X2)
| ~ p(X2)
| ~ sP5(X0,X2,X1)
| ~ sP4(X1,X2,X0)
| ~ sP3(X2,X1,X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f2612,plain,
( spl44_159
| ~ spl44_4
| ~ spl44_13 ),
inference(avatar_split_clause,[],[f751,f636,f593,f2610]) ).
tff(f2610,plain,
( spl44_159
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_2F_5C_2E2(X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_159])]) ).
tff(f636,plain,
( spl44_13
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_13])]) ).
tff(f751,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_2F_5C_2E2(X1,X0) ) )
| ~ spl44_4
| ~ spl44_13 ),
inference(resolution,[],[f637,f594]) ).
tff(f637,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| p(X1) )
| ~ spl44_13 ),
inference(avatar_component_clause,[],[f636]) ).
tff(f2515,plain,
spl44_158,
inference(avatar_split_clause,[],[f557,f2513]) ).
tff(f2513,plain,
( spl44_158
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1)))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_158])]) ).
tff(f557,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1)))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) ),
inference(definition_unfolding,[],[f381,f362]) ).
tff(f362,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) ),
inference(cnf_transformation,[],[f75]) ).
tff(f75,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X12: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X12) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
tff(f381,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1)))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1)))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f180,f181]) ).
tff(f181,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK17(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f180,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(rectify,[],[f179]) ).
tff(f179,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(nnf_transformation,[],[f83]) ).
tff(f83,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X1))
<=> ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X3))
<=> ? [X11: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).
tff(f2511,plain,
spl44_157,
inference(avatar_split_clause,[],[f545,f2509]) ).
tff(f2509,plain,
( spl44_157
<=> ! [X0: $tType,X4: X0,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK38(X0,X1,X2)))
| ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_157])]) ).
tff(f545,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK38(X0,X1,X2)))
| ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( ( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK38(X0,X1,X2))) )
| ~ p(X2)
| ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
& ( ( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK39(X0,X1))) )
| ! [X6: X0] :
( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f299,f301,f300]) ).
tff(f300,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ? [X3: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
=> ( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK38(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
tff(f301,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK39(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f299,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( ? [X3: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
| ~ p(X2)
| ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
& ( ( p(X2)
& ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
| ! [X6: X0] :
( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ) ),
inference(rectify,[],[f298]) ).
tff(f298,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( ? [X3: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
| ~ p(X2)
| ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
& ( ( p(X2)
& ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
| ! [X3: X0] :
( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ) ),
inference(flattening,[],[f297]) ).
tff(f297,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( ? [X3: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
| ~ p(X2)
| ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
& ( ( p(X2)
& ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
| ! [X3: X0] :
( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ) ),
inference(nnf_transformation,[],[f109]) ).
tff(f109,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ? [X3: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
<=> ( p(X2)
& ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X18: tyop_2Emin_2Ebool] :
( ? [X5: X0] :
( p(X18)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X5)) )
<=> ( p(X18)
& ? [X19: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__EXISTS__AND__THM) ).
tff(f2507,plain,
spl44_156,
inference(avatar_split_clause,[],[f542,f2505]) ).
tff(f2505,plain,
( spl44_156
<=> ! [X0: $tType,X4: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK36(X0,X1,X2)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_156])]) ).
tff(f542,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK36(X0,X1,X2)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK36(X0,X1,X2)))
& p(X1) )
| ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) )
& ( ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK37(X0,X2)))
& p(X1) )
| ! [X6: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
| ~ p(X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f293,f295,f294]) ).
tff(f294,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
=> ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK36(X0,X1,X2)))
& p(X1) ) ),
introduced(choice_axiom,[]) ).
tff(f295,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK37(X0,X2))) ),
introduced(choice_axiom,[]) ).
tff(f293,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ? [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
| ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) )
& ( ( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
& p(X1) )
| ! [X6: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
| ~ p(X1) ) ) ),
inference(rectify,[],[f292]) ).
tff(f292,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ? [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
| ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) )
& ( ( ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& p(X1) )
| ! [X3: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(X1) ) ) ),
inference(flattening,[],[f291]) ).
tff(f291,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ? [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
| ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) )
& ( ( ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& p(X1) )
| ! [X3: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(X1) ) ) ),
inference(nnf_transformation,[],[f108]) ).
tff(f108,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
<=> ( ? [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& p(X1) ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType,X17: tyop_2Emin_2Ebool,X18: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X5))
& p(X17) )
<=> ( ? [X19: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X19))
& p(X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__EXISTS__AND__THM) ).
tff(f2503,plain,
spl44_155,
inference(avatar_split_clause,[],[f533,f2501]) ).
tff(f2501,plain,
( spl44_155
<=> ! [X0: $tType,X5: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK31(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_155])]) ).
tff(f533,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X5: X0] :
( p(X1)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK31(X0,X1,X2))) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] :
( p(X1)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
| ( ~ p(X1)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK30(X0,X2))) ) )
& ( p(X1)
| ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| ( ~ p(X1)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK31(X0,X1,X2))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f280,f282,f281]) ).
tff(f281,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
=> ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK30(X0,X2))) ),
introduced(choice_axiom,[]) ).
tff(f282,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X6: X0] :
( ~ p(X1)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) )
=> ( ~ p(X1)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK31(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
tff(f280,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] :
( p(X1)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
| ( ~ p(X1)
& ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) )
& ( p(X1)
| ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| ? [X6: X0] :
( ~ p(X1)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) ) ) ),
inference(rectify,[],[f279]) ).
tff(f279,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] :
( p(X1)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
| ( ~ p(X1)
& ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) )
& ( p(X1)
| ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ? [X3: X0] :
( ~ p(X1)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) ) ) ),
inference(flattening,[],[f278]) ).
tff(f278,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] :
( p(X1)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
| ( ~ p(X1)
& ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) )
& ( p(X1)
| ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ? [X3: X0] :
( ~ p(X1)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) ) ) ),
inference(nnf_transformation,[],[f106]) ).
tff(f106,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ! [X3: X0] :
( p(X1)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3)) )
<=> ( p(X1)
| ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType,X20: tyop_2Emin_2Ebool,X21: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ! [X5: X0] :
( p(X20)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X21,X5)) )
<=> ( p(X20)
| ! [X19: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X21,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__FORALL__OR__THM) ).
tff(f2499,plain,
spl44_154,
inference(avatar_split_clause,[],[f530,f2497]) ).
tff(f2497,plain,
( spl44_154
<=> ! [X0: $tType,X5: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| p(X1)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK29(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_154])]) ).
tff(f530,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| p(X1)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK29(X0,X1,X2))) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1) )
| ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK28(X0,X2)))
& ~ p(X1) ) )
& ( ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| p(X1)
| ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK29(X0,X1,X2)))
& ~ p(X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f274,f276,f275]) ).
tff(f275,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
=> ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK28(X0,X2))) ),
introduced(choice_axiom,[]) ).
tff(f276,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X6: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
& ~ p(X1) )
=> ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK29(X0,X1,X2)))
& ~ p(X1) ) ),
introduced(choice_axiom,[]) ).
tff(f274,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1) )
| ( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& ~ p(X1) ) )
& ( ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| p(X1)
| ? [X6: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
& ~ p(X1) ) ) ),
inference(rectify,[],[f273]) ).
tff(f273,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1) )
| ( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& ~ p(X1) ) )
& ( ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| p(X1)
| ? [X3: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& ~ p(X1) ) ) ),
inference(flattening,[],[f272]) ).
tff(f272,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1) )
| ( ? [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& ~ p(X1) ) )
& ( ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| p(X1)
| ? [X3: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& ~ p(X1) ) ) ),
inference(nnf_transformation,[],[f105]) ).
tff(f105,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ! [X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1) )
<=> ( ! [X4: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| p(X1) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType,X17: tyop_2Emin_2Ebool,X18: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ! [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X5))
| p(X17) )
<=> ( ! [X19: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X19))
| p(X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__FORALL__OR__THM) ).
tff(f2494,plain,
( spl44_153
| ~ spl44_47
| ~ spl44_142 ),
inference(avatar_split_clause,[],[f2186,f2143,f817,f2491]) ).
tff(f2491,plain,
( spl44_153
<=> ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_153])]) ).
tff(f817,plain,
( spl44_47
<=> ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_47])]) ).
tff(f2143,plain,
( spl44_142
<=> p(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_142])]) ).
tff(f2186,plain,
( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) )
| ~ spl44_47
| ~ spl44_142 ),
inference(resolution,[],[f2145,f818]) ).
tff(f818,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
| ~ spl44_47 ),
inference(avatar_component_clause,[],[f817]) ).
tff(f2145,plain,
( p(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
| ~ spl44_142 ),
inference(avatar_component_clause,[],[f2143]) ).
tff(f2489,plain,
spl44_152,
inference(avatar_split_clause,[],[f445,f2487]) ).
tff(f2487,plain,
( spl44_152
<=> ! [X0: $tType,X6: X0,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK27(X0,X1,X2)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_152])]) ).
tff(f445,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X6: X0] :
( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK27(X0,X1,X2)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK26(X0,X1)))
| ! [X4: X0] :
( ~ p(X2)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
& ( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK27(X0,X1,X2)))
| ( ~ p(X2)
& ! [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f230,f232,f231]) ).
tff(f231,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK26(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f232,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ? [X5: X0] :
( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
=> ( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK27(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
tff(f230,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( p(X2)
| ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ! [X4: X0] :
( ~ p(X2)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
& ( ? [X5: X0] :
( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
| ( ~ p(X2)
& ! [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ) ),
inference(rectify,[],[f229]) ).
tff(f229,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( p(X2)
| ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ! [X4: X0] :
( ~ p(X2)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
& ( ? [X4: X0] :
( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
| ( ~ p(X2)
& ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ) ),
inference(flattening,[],[f228]) ).
tff(f228,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( p(X2)
| ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ! [X4: X0] :
( ~ p(X2)
& ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
& ( ? [X4: X0] :
( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
| ( ~ p(X2)
& ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ) ),
inference(nnf_transformation,[],[f100]) ).
tff(f100,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( p(X2)
| ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
<=> ? [X4: X0] :
( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X18: tyop_2Emin_2Ebool] :
( ( p(X18)
| ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X5)) )
<=> ? [X19: X0] :
( p(X18)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__EXISTS__THM) ).
tff(f2485,plain,
spl44_151,
inference(avatar_split_clause,[],[f442,f2483]) ).
tff(f2483,plain,
( spl44_151
<=> ! [X0: $tType,X6: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK25(X0,X1,X2)))
| p(X1)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_151])]) ).
tff(f442,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X6: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK25(X0,X1,X2)))
| p(X1)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK24(X0,X2)))
| p(X1)
| ! [X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& ~ p(X1) ) )
& ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK25(X0,X1,X2)))
| p(X1)
| ( ! [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
& ~ p(X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f224,f226,f225]) ).
tff(f225,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK24(X0,X2))) ),
introduced(choice_axiom,[]) ).
tff(f226,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| p(X1) )
=> ( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK25(X0,X1,X2)))
| p(X1) ) ),
introduced(choice_axiom,[]) ).
tff(f224,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1)
| ! [X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& ~ p(X1) ) )
& ( ? [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| p(X1) )
| ( ! [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
& ~ p(X1) ) ) ),
inference(rectify,[],[f223]) ).
tff(f223,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1)
| ! [X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& ~ p(X1) ) )
& ( ? [X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| p(X1) )
| ( ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& ~ p(X1) ) ) ),
inference(flattening,[],[f222]) ).
tff(f222,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1)
| ! [X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& ~ p(X1) ) )
& ( ? [X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| p(X1) )
| ( ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& ~ p(X1) ) ) ),
inference(nnf_transformation,[],[f99]) ).
tff(f99,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1) )
<=> ? [X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| p(X1) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType,X17: tyop_2Emin_2Ebool,X18: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X5))
| p(X17) )
<=> ? [X19: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X19))
| p(X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__OR__EXISTS__THM) ).
tff(f2481,plain,
spl44_150,
inference(avatar_split_clause,[],[f439,f2479]) ).
tff(f2479,plain,
( spl44_150
<=> ! [X0: $tType,X3: X0,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK22(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_150])]) ).
tff(f439,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK22(X0,X1,X2))) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( ( p(X2)
& ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
| ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK22(X0,X1,X2))) )
& ( ! [X5: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
| ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK23(X0,X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f218,f220,f219]) ).
tff(f219,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ? [X4: X0] :
( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
=> ( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK22(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
tff(f220,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6))
=> ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK23(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f218,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( ( p(X2)
& ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
| ? [X4: X0] :
( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
& ( ! [X5: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) )
| ~ p(X2)
| ? [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ),
inference(rectify,[],[f217]) ).
tff(f217,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( ( p(X2)
& ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
| ? [X4: X0] :
( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
& ( ! [X4: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
| ~ p(X2)
| ? [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ),
inference(flattening,[],[f216]) ).
tff(f216,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( ( p(X2)
& ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
| ? [X4: X0] :
( ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) )
& ( ! [X4: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) )
| ~ p(X2)
| ? [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ) ),
inference(nnf_transformation,[],[f98]) ).
tff(f98,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Ebool] :
( ( p(X2)
& ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
<=> ! [X4: X0] :
( p(X2)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X18: tyop_2Emin_2Ebool] :
( ( p(X18)
& ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X5)) )
<=> ! [X19: X0] :
( p(X18)
& p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__FORALL__THM) ).
tff(f2477,plain,
spl44_149,
inference(avatar_split_clause,[],[f436,f2475]) ).
tff(f2475,plain,
( spl44_149
<=> ! [X0: $tType,X3: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK20(X0,X1,X2)))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_149])]) ).
tff(f436,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK20(X0,X1,X2)))
| ~ p(X1) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK20(X0,X1,X2)))
| ~ p(X1) )
& ( ! [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
& p(X1) )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK21(X0,X2)))
| ~ p(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f212,f214,f213]) ).
tff(f213,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) )
=> ( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK20(X0,X1,X2)))
| ~ p(X1) ) ),
introduced(choice_axiom,[]) ).
tff(f214,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
=> ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK21(X0,X2))) ),
introduced(choice_axiom,[]) ).
tff(f212,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
| ? [X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) ) )
& ( ! [X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
& p(X1) )
| ? [X6: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
| ~ p(X1) ) ),
inference(rectify,[],[f211]) ).
tff(f211,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
| ? [X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) ) )
& ( ! [X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& p(X1) )
| ? [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(X1) ) ),
inference(flattening,[],[f210]) ).
tff(f210,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
| ? [X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
| ~ p(X1) ) )
& ( ! [X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& p(X1) )
| ? [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(X1) ) ),
inference(nnf_transformation,[],[f97]) ).
tff(f97,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
& p(X1) )
<=> ! [X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4))
& p(X1) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType,X17: tyop_2Emin_2Ebool,X18: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X5))
& p(X17) )
<=> ! [X19: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X18,X19))
& p(X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__AND__FORALL__THM) ).
tff(f2416,plain,
( spl44_119
| spl44_148 ),
inference(avatar_split_clause,[],[f543,f2414,f1310]) ).
tff(f1310,plain,
( spl44_119
<=> ! [X0: tyop_2Emin_2Ebool] : ~ p(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_119])]) ).
tff(f2414,plain,
( spl44_148
<=> ! [X0: $tType,X6: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK39(X0,X1)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_148])]) ).
tff(f543,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X6: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK39(X0,X1)))
| ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X6)) ),
inference(cnf_transformation,[],[f302]) ).
tff(f2391,plain,
( spl44_119
| spl44_147 ),
inference(avatar_split_clause,[],[f540,f2389,f1310]) ).
tff(f2389,plain,
( spl44_147
<=> ! [X0: $tType,X6: X0,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK37(X0,X2)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_147])]) ).
tff(f540,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X6: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK37(X0,X2)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X6))
| ~ p(X1) ),
inference(cnf_transformation,[],[f296]) ).
tff(f2369,plain,
( spl44_146
| spl44_140 ),
inference(avatar_split_clause,[],[f535,f1910,f2367]) ).
tff(f2367,plain,
( spl44_146
<=> ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK30(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_146])]) ).
tff(f1910,plain,
( spl44_140
<=> ! [X1: tyop_2Emin_2Ebool] : p(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_140])]) ).
tff(f535,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK30(X0,X2))) ),
inference(cnf_transformation,[],[f283]) ).
tff(f2347,plain,
( spl44_140
| spl44_145 ),
inference(avatar_split_clause,[],[f532,f2345,f1910]) ).
tff(f2345,plain,
( spl44_145
<=> ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK28(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_145])]) ).
tff(f532,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X3))
| p(X1)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK28(X0,X2))) ),
inference(cnf_transformation,[],[f277]) ).
tff(f2326,plain,
( spl44_144
| spl44_140 ),
inference(avatar_split_clause,[],[f447,f1910,f2324]) ).
tff(f2324,plain,
( spl44_144
<=> ! [X0: $tType,X4: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK26(X0,X1)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_144])]) ).
tff(f447,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: X0] :
( p(X2)
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK26(X0,X1)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4)) ),
inference(cnf_transformation,[],[f233]) ).
tff(f2295,plain,
( spl44_143
| ~ spl44_3
| ~ spl44_142 ),
inference(avatar_split_clause,[],[f2188,f2143,f589,f2292]) ).
tff(f2292,plain,
( spl44_143
<=> ( c_2Ebool_2ET_2E0 = sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_143])]) ).
tff(f2188,plain,
( ( c_2Ebool_2ET_2E0 = sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) )
| ~ spl44_3
| ~ spl44_142 ),
inference(resolution,[],[f2145,f590]) ).
tff(f2146,plain,
( spl44_142
| spl44_1
| ~ spl44_48
| ~ spl44_114
| ~ spl44_131 ),
inference(avatar_split_clause,[],[f1924,f1437,f1269,f829,f579,f2143]) ).
tff(f829,plain,
( spl44_48
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_48])]) ).
tff(f1269,plain,
( spl44_114
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_114])]) ).
tff(f1437,plain,
( spl44_131
<=> ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_131])]) ).
tff(f1924,plain,
( p(c_2Ebool_2EF_2E0)
| p(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
| ~ spl44_48
| ~ spl44_114
| ~ spl44_131 ),
inference(forward_demodulation,[],[f1286,f1439]) ).
tff(f1439,plain,
( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) )
| ~ spl44_131 ),
inference(avatar_component_clause,[],[f1437]) ).
tff(f1286,plain,
( p(c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
| p(sK16(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
| ~ spl44_48
| ~ spl44_114 ),
inference(resolution,[],[f1270,f830]) ).
tff(f830,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) )
| ~ spl44_48 ),
inference(avatar_component_clause,[],[f829]) ).
tff(f1270,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1)))
| p(c_2Ebool_2E_21_2E1(X0,X1)) )
| ~ spl44_114 ),
inference(avatar_component_clause,[],[f1269]) ).
tff(f1923,plain,
( spl44_1
| ~ spl44_140 ),
inference(avatar_contradiction_clause,[],[f1921]) ).
tff(f1921,plain,
( $false
| spl44_1
| ~ spl44_140 ),
inference(resolution,[],[f1911,f581]) ).
tff(f581,plain,
( ~ p(c_2Ebool_2EF_2E0)
| spl44_1 ),
inference(avatar_component_clause,[],[f579]) ).
tff(f1911,plain,
( ! [X1: tyop_2Emin_2Ebool] : p(X1)
| ~ spl44_140 ),
inference(avatar_component_clause,[],[f1910]) ).
tff(f1915,plain,
( spl44_140
| spl44_141 ),
inference(avatar_split_clause,[],[f444,f1913,f1910]) ).
tff(f1913,plain,
( spl44_141
<=> ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK24(X0,X2)))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_141])]) ).
tff(f444,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X4: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK24(X0,X2)))
| p(X1)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X4)) ),
inference(cnf_transformation,[],[f227]) ).
tff(f1842,plain,
( spl44_139
| ~ spl44_4
| ~ spl44_12 ),
inference(avatar_split_clause,[],[f749,f632,f593,f1840]) ).
tff(f1840,plain,
( spl44_139
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_2F_5C_2E2(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_139])]) ).
tff(f632,plain,
( spl44_12
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_12])]) ).
tff(f749,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_2F_5C_2E2(X0,X1) ) )
| ~ spl44_4
| ~ spl44_12 ),
inference(resolution,[],[f633,f594]) ).
tff(f633,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| p(X0) )
| ~ spl44_12 ),
inference(avatar_component_clause,[],[f632]) ).
tff(f1571,plain,
( spl44_89
| ~ spl44_3
| ~ spl44_47
| ~ spl44_121 ),
inference(avatar_split_clause,[],[f1525,f1324,f817,f589,f1049]) ).
tff(f1049,plain,
( spl44_89
<=> ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2ET_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_89])]) ).
tff(f1324,plain,
( spl44_121
<=> ! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_121])]) ).
tff(f1525,plain,
( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2ET_2E0) )
| ~ spl44_3
| ~ spl44_47
| ~ spl44_121 ),
inference(forward_demodulation,[],[f1327,f1329]) ).
tff(f1329,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X1) )
| ~ spl44_3
| ~ spl44_121 ),
inference(resolution,[],[f1325,f590]) ).
tff(f1325,plain,
( ! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2))
| ~ spl44_121 ),
inference(avatar_component_clause,[],[f1324]) ).
tff(f1327,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X1)) )
| ~ spl44_47
| ~ spl44_121 ),
inference(resolution,[],[f1325,f818]) ).
tff(f1543,plain,
( spl44_99
| ~ spl44_4
| ~ spl44_55
| ~ spl44_118 ),
inference(avatar_split_clause,[],[f1528,f1306,f857,f593,f1132]) ).
tff(f1132,plain,
( spl44_99
<=> ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2EF_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_99])]) ).
tff(f857,plain,
( spl44_55
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_55])]) ).
tff(f1528,plain,
( ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2EF_2E0) )
| ~ spl44_4
| ~ spl44_55
| ~ spl44_118 ),
inference(forward_demodulation,[],[f1318,f1321]) ).
tff(f1318,plain,
( ! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))) )
| ~ spl44_55
| ~ spl44_118 ),
inference(resolution,[],[f1307,f858]) ).
tff(f858,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
| ~ spl44_55 ),
inference(avatar_component_clause,[],[f857]) ).
tff(f1534,plain,
( spl44_2
| ~ spl44_3
| ~ spl44_121 ),
inference(avatar_split_clause,[],[f1523,f1324,f589,f584]) ).
tff(f584,plain,
( spl44_2
<=> p(c_2Ebool_2ET_2E0) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_2])]) ).
tff(f1523,plain,
( p(c_2Ebool_2ET_2E0)
| ~ spl44_3
| ~ spl44_121 ),
inference(forward_demodulation,[],[f1325,f1329]) ).
tff(f1533,plain,
( ~ spl44_1
| ~ spl44_4
| ~ spl44_118 ),
inference(avatar_split_clause,[],[f1531,f1306,f593,f579]) ).
tff(f1531,plain,
( ~ p(c_2Ebool_2EF_2E0)
| ~ spl44_4
| ~ spl44_118 ),
inference(forward_demodulation,[],[f1307,f1321]) ).
tff(f1522,plain,
( ~ spl44_119
| ~ spl44_121 ),
inference(avatar_contradiction_clause,[],[f1515]) ).
tff(f1515,plain,
( $false
| ~ spl44_119
| ~ spl44_121 ),
inference(resolution,[],[f1311,f1325]) ).
tff(f1311,plain,
( ! [X0: tyop_2Emin_2Ebool] : ~ p(X0)
| ~ spl44_119 ),
inference(avatar_component_clause,[],[f1310]) ).
tff(f1521,plain,
( ~ spl44_10
| ~ spl44_119 ),
inference(avatar_contradiction_clause,[],[f1516]) ).
tff(f1516,plain,
( $false
| ~ spl44_10
| ~ spl44_119 ),
inference(resolution,[],[f1311,f618]) ).
tff(f618,plain,
( ! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2))
| ~ spl44_10 ),
inference(avatar_component_clause,[],[f617]) ).
tff(f617,plain,
( spl44_10
<=> ! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_10])]) ).
tff(f1520,plain,
( ~ spl44_2
| ~ spl44_119 ),
inference(avatar_contradiction_clause,[],[f1518]) ).
tff(f1518,plain,
( $false
| ~ spl44_2
| ~ spl44_119 ),
inference(resolution,[],[f1311,f586]) ).
tff(f586,plain,
( p(c_2Ebool_2ET_2E0)
| ~ spl44_2 ),
inference(avatar_component_clause,[],[f584]) ).
tff(f1508,plain,
( spl44_119
| spl44_138 ),
inference(avatar_split_clause,[],[f437,f1506,f1310]) ).
tff(f1506,plain,
( spl44_138
<=> ! [X0: $tType,X5: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK23(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_138])]) ).
tff(f437,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5))
| ~ p(X2)
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK23(X0,X1))) ),
inference(cnf_transformation,[],[f221]) ).
tff(f1486,plain,
( spl44_119
| spl44_137 ),
inference(avatar_split_clause,[],[f434,f1484,f1310]) ).
tff(f1484,plain,
( spl44_137
<=> ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK21(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_137])]) ).
tff(f434,plain,
! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Ebool,X5: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X2,X5))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X2,sK21(X0,X2)))
| ~ p(X1) ),
inference(cnf_transformation,[],[f215]) ).
tff(f1482,plain,
spl44_136,
inference(avatar_split_clause,[],[f430,f1480]) ).
tff(f1480,plain,
( spl44_136
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_136])]) ).
tff(f430,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) )
& ( p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
| ( X1 != X2 ) ) ),
inference(nnf_transformation,[],[f95]) ).
tff(f95,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
<=> p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType,X12: X0,X13: X0] :
( ( X12 = X13 )
<=> p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X12),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
tff(f1478,plain,
spl44_135,
inference(avatar_split_clause,[],[f395,f1476]) ).
tff(f1476,plain,
( spl44_135
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_135])]) ).
tff(f395,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ( ~ p(X1)
& p(X0) ) ) ),
inference(flattening,[],[f189]) ).
tff(f189,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ( ~ p(X1)
& p(X0) ) ) ),
inference(nnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(ennf_transformation,[],[f87]) ).
tff(f87,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X0)
=> p(X1) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
( ( p(X12)
=> p(X13) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X12),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
tff(f1474,plain,
spl44_134,
inference(avatar_split_clause,[],[f388,f1472]) ).
tff(f1472,plain,
( spl44_134
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_134])]) ).
tff(f388,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ( ~ p(X1)
& ~ p(X0) ) ) ),
inference(flattening,[],[f185]) ).
tff(f185,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ( ~ p(X1)
& ~ p(X0) ) ) ),
inference(nnf_transformation,[],[f85]) ).
tff(f85,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
( ( p(X13)
| p(X12) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X12),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
tff(f1470,plain,
spl44_133,
inference(avatar_split_clause,[],[f383,f1468]) ).
tff(f1468,plain,
( spl44_133
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_133])]) ).
tff(f383,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( ( p(X1)
& p(X0) )
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
inference(flattening,[],[f183]) ).
tff(f183,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( ( p(X1)
& p(X0) )
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
inference(nnf_transformation,[],[f84]) ).
tff(f84,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
& p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
( ( p(X13)
& p(X12) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X12),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
tff(f1444,plain,
spl44_132,
inference(avatar_split_clause,[],[f556,f1442]) ).
tff(f1442,plain,
( spl44_132
<=> ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_132])]) ).
tff(f556,plain,
! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(definition_unfolding,[],[f382,f362]) ).
tff(f382,plain,
! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(cnf_transformation,[],[f182]) ).
tff(f1440,plain,
( spl44_131
| ~ spl44_4
| spl44_120 ),
inference(avatar_split_clause,[],[f1362,f1313,f593,f1437]) ).
tff(f1313,plain,
( spl44_120
<=> p(c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_120])]) ).
tff(f1362,plain,
( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) )
| ~ spl44_4
| spl44_120 ),
inference(resolution,[],[f1315,f594]) ).
tff(f1315,plain,
( ~ p(c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
| spl44_120 ),
inference(avatar_component_clause,[],[f1313]) ).
tff(f1435,plain,
spl44_130,
inference(avatar_split_clause,[],[f547,f1433]) ).
tff(f1433,plain,
( spl44_130
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_130])]) ).
tff(f547,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ),
inference(cnf_transformation,[],[f110]) ).
tff(f110,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X1: $tType,X9: X0,X10: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X9),X10) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).
tff(f1367,plain,
spl44_129,
inference(avatar_split_clause,[],[f424,f1365]) ).
tff(f1365,plain,
( spl44_129
<=> ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK18(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_129])]) ).
tff(f424,plain,
! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK18(X0,X1))) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK18(X0,X1))) )
& ( ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4))
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK19(X0,X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f203,f205,f204]) ).
tff(f204,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK18(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f205,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK19(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f203,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
& ( ! [X4: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4))
| ? [X5: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X5)) ) ),
inference(rectify,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
& ( ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ) ),
inference(nnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
<=> ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ),
inference(ennf_transformation,[],[f91]) ).
tff(f91,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
<=> ! [X3: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType,X17: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ ? [X11: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X11))
<=> ! [X5: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X17,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__EXISTS__THM) ).
tff(f1358,plain,
spl44_128,
inference(avatar_split_clause,[],[f423,f1356]) ).
tff(f1356,plain,
( spl44_128
<=> ! [X0: $tType,X4: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4))
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK19(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_128])]) ).
tff(f423,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X4: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X4))
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK19(X0,X1))) ),
inference(cnf_transformation,[],[f206]) ).
tff(f1354,plain,
spl44_127,
inference(avatar_split_clause,[],[f394,f1352]) ).
tff(f1352,plain,
( spl44_127
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_127])]) ).
tff(f394,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f190]) ).
tff(f1350,plain,
spl44_126,
inference(avatar_split_clause,[],[f393,f1348]) ).
tff(f1348,plain,
( spl44_126
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_126])]) ).
tff(f393,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| p(X0) ),
inference(cnf_transformation,[],[f190]) ).
tff(f1346,plain,
spl44_125,
inference(avatar_split_clause,[],[f387,f1344]) ).
tff(f1344,plain,
( spl44_125
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_125])]) ).
tff(f387,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f186]) ).
tff(f1342,plain,
spl44_124,
inference(avatar_split_clause,[],[f386,f1340]) ).
tff(f1340,plain,
( spl44_124
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_124])]) ).
tff(f386,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X0) ),
inference(cnf_transformation,[],[f186]) ).
tff(f1338,plain,
spl44_123,
inference(avatar_split_clause,[],[f385,f1336]) ).
tff(f1336,plain,
( spl44_123
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_123])]) ).
tff(f385,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f184]) ).
tff(f1334,plain,
spl44_122,
inference(avatar_split_clause,[],[f384,f1332]) ).
tff(f1332,plain,
( spl44_122
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_122])]) ).
tff(f384,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f184]) ).
tff(f1326,plain,
spl44_121,
inference(avatar_split_clause,[],[f570,f1324]) ).
tff(f570,plain,
! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2)),
inference(equality_resolution,[],[f429]) ).
tff(f429,plain,
! [X0: $tType,X2: X0,X1: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f208]) ).
tff(f1316,plain,
( spl44_119
| ~ spl44_120
| ~ spl44_49
| ~ spl44_94 ),
inference(avatar_split_clause,[],[f1188,f1112,f833,f1313,f1310]) ).
tff(f833,plain,
( spl44_49
<=> ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_49])]) ).
tff(f1112,plain,
( spl44_94
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_94])]) ).
tff(f1188,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2E_21_2E1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
| ~ p(X0) )
| ~ spl44_49
| ~ spl44_94 ),
inference(resolution,[],[f1113,f834]) ).
tff(f834,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| ~ p(X0) )
| ~ spl44_49 ),
inference(avatar_component_clause,[],[f833]) ).
tff(f1113,plain,
( ! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) )
| ~ spl44_94 ),
inference(avatar_component_clause,[],[f1112]) ).
tff(f1308,plain,
spl44_118,
inference(avatar_split_clause,[],[f555,f1306]) ).
tff(f555,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(definition_unfolding,[],[f312,f551]) ).
tff(f312,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(cnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ~ p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(ennf_transformation,[],[f61]) ).
tff(f61,plain,
~ ? [X0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(rectify,[],[f60]) ).
tff(f60,negated_conjecture,
~ ? [X3: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
inference(negated_conjecture,[],[f59]) ).
tff(f59,conjecture,
? [X3: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
tff(f1283,plain,
spl44_117,
inference(avatar_split_clause,[],[f516,f1281]) ).
tff(f1281,plain,
( spl44_117
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP15(X0,X1,X2)
| ~ sP13(X2,X1,X0)
| p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_117])]) ).
tff(f516,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP15(X0,X1,X2)
| ~ sP13(X2,X1,X0)
| p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP15(X0,X1,X2)
| ~ sP13(X2,X1,X0)
| ( p(X1)
& ~ p(X2) )
| ( ~ p(X0)
& ~ p(X2) ) )
& ( ( sP13(X2,X1,X0)
& ( ~ p(X1)
| p(X2) )
& ( p(X0)
| p(X2) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(rectify,[],[f264]) ).
tff(f264,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP15(X1,X0,X2)
| ~ sP13(X2,X0,X1)
| ( p(X0)
& ~ p(X2) )
| ( ~ p(X1)
& ~ p(X2) ) )
& ( ( sP13(X2,X0,X1)
& ( ~ p(X0)
| p(X2) )
& ( p(X1)
| p(X2) ) )
| ~ sP15(X1,X0,X2) ) ),
inference(flattening,[],[f263]) ).
tff(f263,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP15(X1,X0,X2)
| ~ sP13(X2,X0,X1)
| ( p(X0)
& ~ p(X2) )
| ( ~ p(X1)
& ~ p(X2) ) )
& ( ( sP13(X2,X0,X1)
& ( ~ p(X0)
| p(X2) )
& ( p(X1)
| p(X2) ) )
| ~ sP15(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP15(X1,X0,X2)
<=> ( sP13(X2,X0,X1)
& ( ~ p(X0)
| p(X2) )
& ( p(X1)
| p(X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
tff(f1279,plain,
spl44_116,
inference(avatar_split_clause,[],[f497,f1277]) ).
tff(f1277,plain,
( spl44_116
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP12(X0,X1,X2)
| ~ sP10(X2,X1,X0)
| p(X1)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_116])]) ).
tff(f497,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP12(X0,X1,X2)
| ~ sP10(X2,X1,X0)
| p(X1)
| p(X0) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP12(X0,X1,X2)
| ~ sP10(X2,X1,X0)
| ( p(X1)
& ~ p(X2) )
| ( p(X0)
& ~ p(X2) ) )
& ( ( sP10(X2,X1,X0)
& ( ~ p(X1)
| p(X2) )
& ( ~ p(X0)
| p(X2) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(rectify,[],[f255]) ).
tff(f255,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP12(X1,X0,X2)
| ~ sP10(X2,X0,X1)
| ( p(X0)
& ~ p(X2) )
| ( p(X1)
& ~ p(X2) ) )
& ( ( sP10(X2,X0,X1)
& ( ~ p(X0)
| p(X2) )
& ( ~ p(X1)
| p(X2) ) )
| ~ sP12(X1,X0,X2) ) ),
inference(flattening,[],[f254]) ).
tff(f254,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP12(X1,X0,X2)
| ~ sP10(X2,X0,X1)
| ( p(X0)
& ~ p(X2) )
| ( p(X1)
& ~ p(X2) ) )
& ( ( sP10(X2,X0,X1)
& ( ~ p(X0)
| p(X2) )
& ( ~ p(X1)
| p(X2) ) )
| ~ sP12(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP12(X1,X0,X2)
<=> ( sP10(X2,X0,X1)
& ( ~ p(X0)
| p(X2) )
& ( ~ p(X1)
| p(X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
tff(f1275,plain,
spl44_115,
inference(avatar_split_clause,[],[f475,f1273]) ).
tff(f1273,plain,
( spl44_115
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP9(X0,X1,X2)
| ~ p(X1)
| ~ p(X2)
| ~ sP7(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_115])]) ).
tff(f475,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP9(X0,X1,X2)
| ~ p(X1)
| ~ p(X2)
| ~ sP7(X1,X2,X0) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP9(X0,X1,X2)
| ( p(X0)
& ~ p(X1) )
| ( p(X0)
& ~ p(X2) )
| ~ sP7(X1,X2,X0) )
& ( ( ( ~ p(X0)
| p(X1) )
& ( ~ p(X0)
| p(X2) )
& sP7(X1,X2,X0) )
| ~ sP9(X0,X1,X2) ) ),
inference(rectify,[],[f247]) ).
tff(f247,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP9(X2,X0,X1)
| ( p(X2)
& ~ p(X0) )
| ( p(X2)
& ~ p(X1) )
| ~ sP7(X0,X1,X2) )
& ( ( ( ~ p(X2)
| p(X0) )
& ( ~ p(X2)
| p(X1) )
& sP7(X0,X1,X2) )
| ~ sP9(X2,X0,X1) ) ),
inference(flattening,[],[f246]) ).
tff(f246,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP9(X2,X0,X1)
| ( p(X2)
& ~ p(X0) )
| ( p(X2)
& ~ p(X1) )
| ~ sP7(X0,X1,X2) )
& ( ( ( ~ p(X2)
| p(X0) )
& ( ~ p(X2)
| p(X1) )
& sP7(X0,X1,X2) )
| ~ sP9(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP9(X2,X0,X1)
<=> ( ( ~ p(X2)
| p(X0) )
& ( ~ p(X2)
| p(X1) )
& sP7(X0,X1,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
tff(f1271,plain,
spl44_114,
inference(avatar_split_clause,[],[f380,f1269]) ).
tff(f380,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1))) ),
inference(cnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1))) )
& ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f176,f177]) ).
tff(f177,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
=> ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK16(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f176,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(rectify,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ! [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(nnf_transformation,[],[f82]) ).
tff(f82,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X1))
<=> ! [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X3))
<=> ! [X11: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).
tff(f1267,plain,
( spl44_113
| ~ spl44_39
| ~ spl44_58 ),
inference(avatar_split_clause,[],[f1026,f869,f740,f1265]) ).
tff(f1265,plain,
( spl44_113
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X1,X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_113])]) ).
tff(f740,plain,
( spl44_39
<=> ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X2,X1,X1)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_39])]) ).
tff(f869,plain,
( spl44_58
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X2,X1)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_58])]) ).
tff(f1026,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X1,X1)
| ~ p(X0) )
| ~ spl44_39
| ~ spl44_58 ),
inference(resolution,[],[f870,f741]) ).
tff(f741,plain,
( ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X2,X1,X1)
| ~ p(X2) )
| ~ spl44_39 ),
inference(avatar_component_clause,[],[f740]) ).
tff(f870,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ sP6(X0,X1,X2)
| sP5(X0,X2,X1) )
| ~ spl44_58 ),
inference(avatar_component_clause,[],[f869]) ).
tff(f1263,plain,
spl44_112,
inference(avatar_split_clause,[],[f361,f1261]) ).
tff(f1261,plain,
( spl44_112
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_112])]) ).
tff(f361,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ),
inference(cnf_transformation,[],[f74]) ).
tff(f74,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType,X12: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X12) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
tff(f1187,plain,
spl44_111,
inference(avatar_split_clause,[],[f576,f1185]) ).
tff(f1185,plain,
( spl44_111
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP9(X0,X1,X2)
| p(X0)
| ~ sP7(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_111])]) ).
tff(f576,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP9(X0,X1,X2)
| p(X0)
| ~ sP7(X1,X2,X0) ),
inference(duplicate_literal_removal,[],[f478]) ).
tff(f478,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP9(X0,X1,X2)
| p(X0)
| p(X0)
| ~ sP7(X1,X2,X0) ),
inference(cnf_transformation,[],[f248]) ).
tff(f1183,plain,
spl44_110,
inference(avatar_split_clause,[],[f575,f1181]) ).
tff(f1181,plain,
( spl44_110
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP12(X0,X1,X2)
| ~ sP10(X2,X1,X0)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_110])]) ).
tff(f575,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP12(X0,X1,X2)
| ~ sP10(X2,X1,X0)
| ~ p(X2) ),
inference(duplicate_literal_removal,[],[f494]) ).
tff(f494,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP12(X0,X1,X2)
| ~ sP10(X2,X1,X0)
| ~ p(X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f256]) ).
tff(f1175,plain,
spl44_109,
inference(avatar_split_clause,[],[f574,f1173]) ).
tff(f1173,plain,
( spl44_109
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP15(X0,X1,X2)
| ~ sP13(X2,X1,X0)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_109])]) ).
tff(f574,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP15(X0,X1,X2)
| ~ sP13(X2,X1,X0)
| ~ p(X2) ),
inference(duplicate_literal_removal,[],[f513]) ).
tff(f513,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP15(X0,X1,X2)
| ~ sP13(X2,X1,X0)
| ~ p(X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f265]) ).
tff(f1171,plain,
spl44_108,
inference(avatar_split_clause,[],[f523,f1169]) ).
tff(f1169,plain,
( spl44_108
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| ~ p(X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_108])]) ).
tff(f523,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| ~ p(X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP13(X0,X1,X2)
| ( p(X0)
& ~ p(X1)
& p(X2) ) )
& ( ~ p(X0)
| p(X1)
| ~ p(X2)
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f269]) ).
tff(f269,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP13(X2,X0,X1)
| ( p(X2)
& ~ p(X0)
& p(X1) ) )
& ( ~ p(X2)
| p(X0)
| ~ p(X1)
| ~ sP13(X2,X0,X1) ) ),
inference(flattening,[],[f268]) ).
tff(f268,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP13(X2,X0,X1)
| ( p(X2)
& ~ p(X0)
& p(X1) ) )
& ( ~ p(X2)
| p(X0)
| ~ p(X1)
| ~ sP13(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X2,X0,X1)
<=> ( ~ p(X2)
| p(X0)
| ~ p(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
tff(f1167,plain,
spl44_107,
inference(avatar_split_clause,[],[f520,f1165]) ).
tff(f1165,plain,
( spl44_107
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
| p(X0)
| ~ p(X1)
| p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_107])]) ).
tff(f520,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
| p(X0)
| ~ p(X1)
| p(X2) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP14(X0,X1,X2)
| ( ( ( ~ p(X0)
& p(X1) )
| ~ p(X2) )
& ( p(X0)
| ~ p(X1)
| p(X2) ) ) )
& ( ( ( p(X2)
| ( ~ p(X0)
& p(X1) ) )
& ( p(X0)
| ~ p(X1)
| ~ p(X2) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(flattening,[],[f266]) ).
tff(f266,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP14(X0,X1,X2)
| ( ( ( ~ p(X0)
& p(X1) )
| ~ p(X2) )
& ( p(X0)
| ~ p(X1)
| p(X2) ) ) )
& ( ( ( p(X2)
| ( ~ p(X0)
& p(X1) ) )
& ( p(X0)
| ~ p(X1)
| ~ p(X2) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
<=> ( p(X2)
<=> ( p(X0)
| ~ p(X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
tff(f1163,plain,
spl44_106,
inference(avatar_split_clause,[],[f517,f1161]) ).
tff(f1161,plain,
( spl44_106
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(X1)
| ~ p(X2)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_106])]) ).
tff(f517,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(X1)
| ~ p(X2)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f267]) ).
tff(f1159,plain,
spl44_105,
inference(avatar_split_clause,[],[f504,f1157]) ).
tff(f1157,plain,
( spl44_105
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| p(X2)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_105])]) ).
tff(f504,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| p(X2)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP10(X0,X1,X2)
| ( p(X0)
& ~ p(X1)
& ~ p(X2) ) )
& ( ~ p(X0)
| p(X1)
| p(X2)
| ~ sP10(X0,X1,X2) ) ),
inference(rectify,[],[f260]) ).
tff(f260,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP10(X2,X0,X1)
| ( p(X2)
& ~ p(X0)
& ~ p(X1) ) )
& ( ~ p(X2)
| p(X0)
| p(X1)
| ~ sP10(X2,X0,X1) ) ),
inference(flattening,[],[f259]) ).
tff(f259,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP10(X2,X0,X1)
| ( p(X2)
& ~ p(X0)
& ~ p(X1) ) )
& ( ~ p(X2)
| p(X0)
| p(X1)
| ~ sP10(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X2,X0,X1)
<=> ( ~ p(X2)
| p(X0)
| p(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
tff(f1155,plain,
spl44_104,
inference(avatar_split_clause,[],[f501,f1153]) ).
tff(f1153,plain,
( spl44_104
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
| p(X0)
| p(X1)
| p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_104])]) ).
tff(f501,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
| p(X0)
| p(X1)
| p(X2) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP11(X0,X1,X2)
| ( ( ( ~ p(X0)
& ~ p(X1) )
| ~ p(X2) )
& ( p(X0)
| p(X1)
| p(X2) ) ) )
& ( ( ( p(X2)
| ( ~ p(X0)
& ~ p(X1) ) )
& ( p(X0)
| p(X1)
| ~ p(X2) ) )
| ~ sP11(X0,X1,X2) ) ),
inference(flattening,[],[f257]) ).
tff(f257,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP11(X0,X1,X2)
| ( ( ( ~ p(X0)
& ~ p(X1) )
| ~ p(X2) )
& ( p(X0)
| p(X1)
| p(X2) ) ) )
& ( ( ( p(X2)
| ( ~ p(X0)
& ~ p(X1) ) )
& ( p(X0)
| p(X1)
| ~ p(X2) ) )
| ~ sP11(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
<=> ( p(X2)
<=> ( p(X0)
| p(X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
tff(f1151,plain,
spl44_103,
inference(avatar_split_clause,[],[f498,f1149]) ).
tff(f1149,plain,
( spl44_103
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| ~ p(X2)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_103])]) ).
tff(f498,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| ~ p(X2)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f258]) ).
tff(f1147,plain,
spl44_102,
inference(avatar_split_clause,[],[f485,f1145]) ).
tff(f1145,plain,
( spl44_102
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_102])]) ).
tff(f485,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP7(X0,X1,X2)
| ( p(X0)
& p(X1)
& ~ p(X2) ) )
& ( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP7(X0,X1,X2) ) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP7(X0,X1,X2)
| ( p(X0)
& p(X1)
& ~ p(X2) ) )
& ( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP7(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP7(X0,X1,X2)
<=> ( ~ p(X0)
| ~ p(X1)
| p(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
tff(f1143,plain,
spl44_101,
inference(avatar_split_clause,[],[f484,f1141]) ).
tff(f1141,plain,
( spl44_101
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
| ~ p(X0)
| ~ p(X1)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_101])]) ).
tff(f484,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
| ~ p(X0)
| ~ p(X1)
| ~ p(X2) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP8(X0,X1,X2)
| ( ( ~ p(X0)
| ~ p(X1)
| ~ p(X2) )
& ( ( p(X0)
& p(X1) )
| p(X2) ) ) )
& ( ( ( p(X2)
| ~ p(X0)
| ~ p(X1) )
& ( ( p(X0)
& p(X1) )
| ~ p(X2) ) )
| ~ sP8(X0,X1,X2) ) ),
inference(flattening,[],[f249]) ).
tff(f249,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP8(X0,X1,X2)
| ( ( ~ p(X0)
| ~ p(X1)
| ~ p(X2) )
& ( ( p(X0)
& p(X1) )
| p(X2) ) ) )
& ( ( ( p(X2)
| ~ p(X0)
| ~ p(X1) )
& ( ( p(X0)
& p(X1) )
| ~ p(X2) ) )
| ~ sP8(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
<=> ( p(X2)
<=> ( p(X0)
& p(X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
tff(f1139,plain,
spl44_100,
inference(avatar_split_clause,[],[f481,f1137]) ).
tff(f1137,plain,
( spl44_100
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ p(X0)
| ~ p(X1)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_100])]) ).
tff(f481,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ p(X0)
| ~ p(X1)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f250]) ).
tff(f1135,plain,
( spl44_99
| spl44_1
| ~ spl44_55 ),
inference(avatar_split_clause,[],[f1089,f857,f579,f1132]) ).
tff(f1089,plain,
( ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2EF_2E0) )
| spl44_1
| ~ spl44_55 ),
inference(resolution,[],[f858,f581]) ).
tff(f1130,plain,
spl44_98,
inference(avatar_split_clause,[],[f464,f1128]) ).
tff(f1128,plain,
( spl44_98
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| p(X2)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_98])]) ).
tff(f464,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| p(X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP3(X0,X1,X2)
| ( ~ p(X0)
& ~ p(X1)
& ~ p(X2) ) )
& ( p(X0)
| p(X1)
| p(X2)
| ~ sP3(X0,X1,X2) ) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP3(X0,X1,X2)
| ( ~ p(X0)
& ~ p(X1)
& ~ p(X2) ) )
& ( p(X0)
| p(X1)
| p(X2)
| ~ sP3(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP3(X0,X1,X2)
<=> ( p(X0)
| p(X1)
| p(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f1126,plain,
spl44_97,
inference(avatar_split_clause,[],[f460,f1124]) ).
tff(f1124,plain,
( spl44_97
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_97])]) ).
tff(f460,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP4(X0,X1,X2)
| ( p(X0)
& p(X1)
& ~ p(X2) ) )
& ( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP4(X0,X1,X2) ) ),
inference(rectify,[],[f241]) ).
tff(f241,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP4(X1,X0,X2)
| ( p(X1)
& p(X0)
& ~ p(X2) ) )
& ( ~ p(X1)
| ~ p(X0)
| p(X2)
| ~ sP4(X1,X0,X2) ) ),
inference(flattening,[],[f240]) ).
tff(f240,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP4(X1,X0,X2)
| ( p(X1)
& p(X0)
& ~ p(X2) ) )
& ( ~ p(X1)
| ~ p(X0)
| p(X2)
| ~ sP4(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP4(X1,X0,X2)
<=> ( ~ p(X1)
| ~ p(X0)
| p(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
tff(f1122,plain,
spl44_96,
inference(avatar_split_clause,[],[f456,f1120]) ).
tff(f1120,plain,
( spl44_96
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_96])]) ).
tff(f456,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP5(X0,X1,X2)
| ( p(X0)
& p(X1)
& ~ p(X2) ) )
& ( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP5(X0,X1,X2) ) ),
inference(rectify,[],[f238]) ).
tff(f238,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP5(X2,X0,X1)
| ( p(X2)
& p(X0)
& ~ p(X1) ) )
& ( ~ p(X2)
| ~ p(X0)
| p(X1)
| ~ sP5(X2,X0,X1) ) ),
inference(flattening,[],[f237]) ).
tff(f237,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP5(X2,X0,X1)
| ( p(X2)
& p(X0)
& ~ p(X1) ) )
& ( ~ p(X2)
| ~ p(X0)
| p(X1)
| ~ sP5(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X2,X0,X1)
<=> ( ~ p(X2)
| ~ p(X0)
| p(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
tff(f1118,plain,
spl44_95,
inference(avatar_split_clause,[],[f452,f1116]) ).
tff(f1116,plain,
( spl44_95
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_95])]) ).
tff(f452,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f236]) ).
tff(f1114,plain,
spl44_94,
inference(avatar_split_clause,[],[f379,f1112]) ).
tff(f379,plain,
! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ),
inference(cnf_transformation,[],[f178]) ).
tff(f1101,plain,
spl44_93,
inference(avatar_split_clause,[],[f470,f1099]) ).
tff(f1099,plain,
( spl44_93
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ~ p(X2)
| ~ sP6(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_93])]) ).
tff(f470,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ~ p(X2)
| ~ sP6(X2,X1,X0) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( ( ( p(X2)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ p(X2) ) )
| ~ sP6(X2,X1,X0) )
& ( sP6(X2,X1,X0)
| ( ( ( X0 != X1 )
| ~ p(X2) )
& ( ( X0 = X1 )
| p(X2) ) ) ) ),
inference(nnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( p(X2)
<=> ( X0 = X1 ) )
<=> sP6(X2,X1,X0) ),
inference(definition_folding,[],[f101,f145,f144,f143,f142]) ).
tff(f101,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( p(X2)
<=> ( X0 = X1 ) )
<=> ( ( ~ p(X2)
| ~ p(X1)
| p(X0) )
& ( ~ p(X2)
| ~ p(X0)
| p(X1) )
& ( ~ p(X1)
| ~ p(X0)
| p(X2) )
& ( p(X0)
| p(X1)
| p(X2) ) ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X33: tyop_2Emin_2Ebool,X34: tyop_2Emin_2Ebool,X35: tyop_2Emin_2Ebool] :
( ( p(X35)
<=> ( X33 = X34 ) )
<=> ( ( ~ p(X35)
| ~ p(X34)
| p(X33) )
& ( ~ p(X35)
| ~ p(X33)
| p(X34) )
& ( ~ p(X34)
| ~ p(X33)
| p(X35) )
& ( p(X33)
| p(X34)
| p(X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq) ).
tff(f1097,plain,
spl44_92,
inference(avatar_split_clause,[],[f468,f1095]) ).
tff(f1095,plain,
( spl44_92
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X2,X1,X0)
| ( X0 = X1 )
| p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_92])]) ).
tff(f468,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X2,X1,X0)
| ( X0 = X1 )
| p(X2) ),
inference(cnf_transformation,[],[f245]) ).
tff(f1080,plain,
( spl44_91
| spl44_1 ),
inference(avatar_split_clause,[],[f407,f579,f1078]) ).
tff(f1078,plain,
( spl44_91
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ sP0(X0,X1)
| p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_91])]) ).
tff(f407,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2EF_2E0)
| p(X0)
| p(X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP0(X0,X1)
| ( ~ p(c_2Ebool_2EF_2E0)
& ~ p(X0)
& ~ p(X1) ) )
& ( p(c_2Ebool_2EF_2E0)
| p(X0)
| p(X1)
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f195]) ).
tff(f195,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP0(X0,X1)
| ( ~ p(c_2Ebool_2EF_2E0)
& ~ p(X0)
& ~ p(X1) ) )
& ( p(c_2Ebool_2EF_2E0)
| p(X0)
| p(X1)
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
<=> ( p(c_2Ebool_2EF_2E0)
| p(X0)
| p(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1074,plain,
( spl44_90
| spl44_1 ),
inference(avatar_split_clause,[],[f402,f579,f1072]) ).
tff(f1072,plain,
( spl44_90
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ sP1(X0,X1)
| p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_90])]) ).
tff(f402,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2EF_2E0)
| p(X0)
| p(X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP1(X0,X1)
| ( ~ p(c_2Ebool_2EF_2E0)
& ~ p(X0)
& ( p(c_2Ebool_2EF_2E0)
| ~ p(X1) ) ) )
& ( p(c_2Ebool_2EF_2E0)
| p(X0)
| ( ~ p(c_2Ebool_2EF_2E0)
& p(X1) )
| ~ sP1(X0,X1) ) ),
inference(flattening,[],[f193]) ).
tff(f193,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP1(X0,X1)
| ( ~ p(c_2Ebool_2EF_2E0)
& ~ p(X0)
& ( p(c_2Ebool_2EF_2E0)
| ~ p(X1) ) ) )
& ( p(c_2Ebool_2EF_2E0)
| p(X0)
| ( ~ p(c_2Ebool_2EF_2E0)
& p(X1) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP1(X0,X1)
<=> ( p(c_2Ebool_2EF_2E0)
| p(X0)
| ( ~ p(c_2Ebool_2EF_2E0)
& p(X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1052,plain,
( spl44_89
| ~ spl44_10
| ~ spl44_47
| ~ spl44_66 ),
inference(avatar_split_clause,[],[f1039,f901,f817,f617,f1049]) ).
tff(f901,plain,
( spl44_66
<=> ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = c_2Emin_2E_3D_2E2(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_66])]) ).
tff(f1039,plain,
( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2ET_2E0) )
| ~ spl44_10
| ~ spl44_47
| ~ spl44_66 ),
inference(forward_demodulation,[],[f1032,f902]) ).
tff(f902,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = c_2Emin_2E_3D_2E2(X0,X1,X1) )
| ~ spl44_66 ),
inference(avatar_component_clause,[],[f901]) ).
tff(f1032,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Emin_2E_3D_2E2(X0,X1,X1)) )
| ~ spl44_10
| ~ spl44_47 ),
inference(resolution,[],[f818,f618]) ).
tff(f991,plain,
spl44_88,
inference(avatar_split_clause,[],[f528,f989]) ).
tff(f989,plain,
( spl44_88
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
| ~ sP15(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_88])]) ).
tff(f528,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
| ~ sP15(X1,X0,X2) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP14(X0,X1,X2)
| ~ sP15(X1,X0,X2) )
& ( sP15(X1,X0,X2)
| ~ sP14(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
<=> sP15(X1,X0,X2) ),
inference(definition_folding,[],[f135,f157,f156,f155]) ).
tff(f135,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( p(X2)
<=> ( p(X0)
| ~ p(X1) ) )
<=> ( ( ~ p(X2)
| p(X0)
| ~ p(X1) )
& ( ~ p(X0)
| p(X2) )
& ( p(X1)
| p(X2) ) ) ),
inference(ennf_transformation,[],[f104]) ).
tff(f104,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( p(X2)
<=> ( p(X1)
=> p(X0) ) )
<=> ( ( ~ p(X2)
| p(X0)
| ~ p(X1) )
& ( ~ p(X0)
| p(X2) )
& ( p(X1)
| p(X2) ) ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X33: tyop_2Emin_2Ebool,X34: tyop_2Emin_2Ebool,X35: tyop_2Emin_2Ebool] :
( ( p(X35)
<=> ( p(X34)
=> p(X33) ) )
<=> ( ( ~ p(X35)
| p(X33)
| ~ p(X34) )
& ( ~ p(X33)
| p(X35) )
& ( p(X34)
| p(X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__imp) ).
tff(f987,plain,
spl44_87,
inference(avatar_split_clause,[],[f527,f985]) ).
tff(f985,plain,
( spl44_87
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP15(X1,X0,X2)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_87])]) ).
tff(f527,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP15(X1,X0,X2)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f271]) ).
tff(f983,plain,
spl44_86,
inference(avatar_split_clause,[],[f522,f981]) ).
tff(f981,plain,
( spl44_86
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
| ~ p(X0)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_86])]) ).
tff(f522,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
| ~ p(X0)
| ~ p(X2) ),
inference(cnf_transformation,[],[f267]) ).
tff(f979,plain,
spl44_85,
inference(avatar_split_clause,[],[f521,f977]) ).
tff(f977,plain,
( spl44_85
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
| p(X1)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_85])]) ).
tff(f521,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP14(X0,X1,X2)
| p(X1)
| ~ p(X2) ),
inference(cnf_transformation,[],[f267]) ).
tff(f975,plain,
spl44_84,
inference(avatar_split_clause,[],[f519,f973]) ).
tff(f973,plain,
( spl44_84
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ p(X0)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_84])]) ).
tff(f519,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ p(X0)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f267]) ).
tff(f971,plain,
spl44_83,
inference(avatar_split_clause,[],[f518,f969]) ).
tff(f969,plain,
( spl44_83
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| p(X1)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_83])]) ).
tff(f518,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| p(X1)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f267]) ).
tff(f967,plain,
spl44_82,
inference(avatar_split_clause,[],[f512,f965]) ).
tff(f965,plain,
( spl44_82
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X2,X1,X0)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_82])]) ).
tff(f512,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X2,X1,X0)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f265]) ).
tff(f963,plain,
spl44_81,
inference(avatar_split_clause,[],[f511,f961]) ).
tff(f961,plain,
( spl44_81
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(X2)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_81])]) ).
tff(f511,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f265]) ).
tff(f959,plain,
spl44_80,
inference(avatar_split_clause,[],[f510,f957]) ).
tff(f957,plain,
( spl44_80
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X2)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_80])]) ).
tff(f510,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f265]) ).
tff(f955,plain,
spl44_79,
inference(avatar_split_clause,[],[f509,f953]) ).
tff(f953,plain,
( spl44_79
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
| ~ sP12(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_79])]) ).
tff(f509,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
| ~ sP12(X1,X0,X2) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP11(X0,X1,X2)
| ~ sP12(X1,X0,X2) )
& ( sP12(X1,X0,X2)
| ~ sP11(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
<=> sP12(X1,X0,X2) ),
inference(definition_folding,[],[f103,f153,f152,f151]) ).
tff(f103,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( p(X2)
<=> ( p(X0)
| p(X1) ) )
<=> ( ( ~ p(X2)
| p(X0)
| p(X1) )
& ( ~ p(X0)
| p(X2) )
& ( ~ p(X1)
| p(X2) ) ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X33: tyop_2Emin_2Ebool,X34: tyop_2Emin_2Ebool,X35: tyop_2Emin_2Ebool] :
( ( p(X35)
<=> ( p(X33)
| p(X34) ) )
<=> ( ( ~ p(X35)
| p(X33)
| p(X34) )
& ( ~ p(X33)
| p(X35) )
& ( ~ p(X34)
| p(X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__disj) ).
tff(f951,plain,
( spl44_77
| ~ spl44_78
| ~ spl44_11 ),
inference(avatar_split_clause,[],[f748,f628,f948,f945]) ).
tff(f945,plain,
( spl44_77
<=> ! [X0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ET_2E0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_77])]) ).
tff(f948,plain,
( spl44_78
<=> ( c_2Ebool_2ET_2E0 = c_2Ebool_2EF_2E0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_78])]) ).
tff(f628,plain,
( spl44_11
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_11])]) ).
tff(f748,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
| ( c_2Ebool_2ET_2E0 = X0 ) )
| ~ spl44_11 ),
inference(equality_factoring,[],[f629]) ).
tff(f629,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) )
| ~ spl44_11 ),
inference(avatar_component_clause,[],[f628]) ).
tff(f943,plain,
spl44_76,
inference(avatar_split_clause,[],[f508,f941]) ).
tff(f941,plain,
( spl44_76
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP12(X1,X0,X2)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_76])]) ).
tff(f508,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP12(X1,X0,X2)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f262]) ).
tff(f939,plain,
spl44_75,
inference(avatar_split_clause,[],[f503,f937]) ).
tff(f937,plain,
( spl44_75
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
| ~ p(X0)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_75])]) ).
tff(f503,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
| ~ p(X0)
| ~ p(X2) ),
inference(cnf_transformation,[],[f258]) ).
tff(f935,plain,
spl44_74,
inference(avatar_split_clause,[],[f502,f933]) ).
tff(f933,plain,
( spl44_74
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
| ~ p(X1)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_74])]) ).
tff(f502,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP11(X0,X1,X2)
| ~ p(X1)
| ~ p(X2) ),
inference(cnf_transformation,[],[f258]) ).
tff(f931,plain,
spl44_73,
inference(avatar_split_clause,[],[f500,f929]) ).
tff(f929,plain,
( spl44_73
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ p(X0)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_73])]) ).
tff(f500,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ p(X0)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f258]) ).
tff(f927,plain,
spl44_72,
inference(avatar_split_clause,[],[f499,f925]) ).
tff(f925,plain,
( spl44_72
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ p(X1)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_72])]) ).
tff(f499,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ p(X1)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f258]) ).
tff(f923,plain,
spl44_71,
inference(avatar_split_clause,[],[f493,f921]) ).
tff(f921,plain,
( spl44_71
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X2,X1,X0)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_71])]) ).
tff(f493,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X2,X1,X0)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
tff(f919,plain,
spl44_70,
inference(avatar_split_clause,[],[f492,f917]) ).
tff(f917,plain,
( spl44_70
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_70])]) ).
tff(f492,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
tff(f915,plain,
spl44_69,
inference(avatar_split_clause,[],[f491,f913]) ).
tff(f913,plain,
( spl44_69
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_69])]) ).
tff(f491,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
tff(f911,plain,
spl44_68,
inference(avatar_split_clause,[],[f490,f909]) ).
tff(f909,plain,
( spl44_68
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
| ~ sP9(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_68])]) ).
tff(f490,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
| ~ sP9(X2,X0,X1) ),
inference(cnf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( sP8(X0,X1,X2)
| ~ sP9(X2,X0,X1) )
& ( sP9(X2,X0,X1)
| ~ sP8(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
<=> sP9(X2,X0,X1) ),
inference(definition_folding,[],[f102,f149,f148,f147]) ).
tff(f102,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool] :
( ( p(X2)
<=> ( p(X0)
& p(X1) ) )
<=> ( ( ~ p(X2)
| p(X0) )
& ( ~ p(X2)
| p(X1) )
& ( ~ p(X0)
| ~ p(X1)
| p(X2) ) ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X33: tyop_2Emin_2Ebool,X34: tyop_2Emin_2Ebool,X35: tyop_2Emin_2Ebool] :
( ( p(X35)
<=> ( p(X33)
& p(X34) ) )
<=> ( ( ~ p(X35)
| p(X33) )
& ( ~ p(X35)
| p(X34) )
& ( ~ p(X33)
| ~ p(X34)
| p(X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__conj) ).
tff(f907,plain,
spl44_67,
inference(avatar_split_clause,[],[f489,f905]) ).
tff(f905,plain,
( spl44_67
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP9(X2,X0,X1)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_67])]) ).
tff(f489,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP9(X2,X0,X1)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f253]) ).
tff(f903,plain,
( spl44_66
| ~ spl44_3
| ~ spl44_10 ),
inference(avatar_split_clause,[],[f626,f617,f589,f901]) ).
tff(f626,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = c_2Emin_2E_3D_2E2(X0,X1,X1) )
| ~ spl44_3
| ~ spl44_10 ),
inference(resolution,[],[f618,f590]) ).
tff(f899,plain,
spl44_65,
inference(avatar_split_clause,[],[f483,f897]) ).
tff(f897,plain,
( spl44_65
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
| p(X0)
| p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_65])]) ).
tff(f483,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
| p(X0)
| p(X2) ),
inference(cnf_transformation,[],[f250]) ).
tff(f895,plain,
spl44_64,
inference(avatar_split_clause,[],[f482,f893]) ).
tff(f893,plain,
( spl44_64
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
| p(X1)
| p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_64])]) ).
tff(f482,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP8(X0,X1,X2)
| p(X1)
| p(X2) ),
inference(cnf_transformation,[],[f250]) ).
tff(f891,plain,
spl44_63,
inference(avatar_split_clause,[],[f480,f889]) ).
tff(f889,plain,
( spl44_63
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_63])]) ).
tff(f480,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f250]) ).
tff(f887,plain,
spl44_62,
inference(avatar_split_clause,[],[f479,f885]) ).
tff(f885,plain,
( spl44_62
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_62])]) ).
tff(f479,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f250]) ).
tff(f883,plain,
spl44_61,
inference(avatar_split_clause,[],[f474,f881]) ).
tff(f881,plain,
( spl44_61
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_61])]) ).
tff(f474,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
tff(f879,plain,
spl44_60,
inference(avatar_split_clause,[],[f473,f877]) ).
tff(f877,plain,
( spl44_60
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_60])]) ).
tff(f473,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
tff(f875,plain,
spl44_59,
inference(avatar_split_clause,[],[f472,f873]) ).
tff(f873,plain,
( spl44_59
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP7(X1,X2,X0)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_59])]) ).
tff(f472,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP7(X1,X2,X0)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
tff(f871,plain,
spl44_58,
inference(avatar_split_clause,[],[f451,f869]) ).
tff(f451,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X2,X1)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f236]) ).
tff(f867,plain,
spl44_57,
inference(avatar_split_clause,[],[f450,f865]) ).
tff(f865,plain,
( spl44_57
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP4(X1,X2,X0)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_57])]) ).
tff(f450,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP4(X1,X2,X0)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f236]) ).
tff(f863,plain,
spl44_56,
inference(avatar_split_clause,[],[f449,f861]) ).
tff(f861,plain,
( spl44_56
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP3(X2,X1,X0)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_56])]) ).
tff(f449,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP3(X2,X1,X0)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f236]) ).
tff(f859,plain,
( spl44_55
| ~ spl44_3
| ~ spl44_6 ),
inference(avatar_split_clause,[],[f625,f601,f589,f857]) ).
tff(f601,plain,
( spl44_6
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_6])]) ).
tff(f625,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
| ~ spl44_3
| ~ spl44_6 ),
inference(resolution,[],[f602,f590]) ).
tff(f602,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) )
| ~ spl44_6 ),
inference(avatar_component_clause,[],[f601]) ).
tff(f855,plain,
spl44_54,
inference(avatar_split_clause,[],[f431,f853]) ).
tff(f853,plain,
( spl44_54
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_54])]) ).
tff(f431,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f96]) ).
tff(f96,plain,
! [X0: $tType,X1: X0,X2: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
<=> ( X1 = X2 ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType,X6: X0,X7: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X6,X7))
<=> ( X6 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).
tff(f851,plain,
spl44_53,
inference(avatar_split_clause,[],[f376,f849]) ).
tff(f849,plain,
( spl44_53
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_53])]) ).
tff(f376,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ( ~ p(X1)
& p(X0) ) )
& ( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
inference(flattening,[],[f173]) ).
tff(f173,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ( ~ p(X1)
& p(X0) ) )
& ( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
<=> ( p(X1)
| ~ p(X0) ) ),
inference(ennf_transformation,[],[f81]) ).
tff(f81,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
<=> ( p(X0)
=> p(X1) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X6,X7))
<=> ( p(X6)
=> p(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
tff(f847,plain,
spl44_52,
inference(avatar_split_clause,[],[f373,f845]) ).
tff(f845,plain,
( spl44_52
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_52])]) ).
tff(f373,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ( ~ p(X1)
& ~ p(X0) ) )
& ( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
inference(flattening,[],[f171]) ).
tff(f171,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ( ~ p(X1)
& ~ p(X0) ) )
& ( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f80]) ).
tff(f80,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
<=> ( p(X1)
| p(X0) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X6,X7))
<=> ( p(X7)
| p(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
tff(f843,plain,
spl44_51,
inference(avatar_split_clause,[],[f372,f841]) ).
tff(f841,plain,
( spl44_51
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_51])]) ).
tff(f372,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) )
& ( ( p(X1)
& p(X0) )
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
inference(flattening,[],[f169]) ).
tff(f169,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) )
& ( ( p(X1)
& p(X0) )
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f79]) ).
tff(f79,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
<=> ( p(X1)
& p(X0) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X6,X7))
<=> ( p(X7)
& p(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
tff(f839,plain,
spl44_50,
inference(avatar_split_clause,[],[f360,f837]) ).
tff(f837,plain,
( spl44_50
<=> ! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_50])]) ).
tff(f360,plain,
! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ),
inference(cnf_transformation,[],[f73]) ).
tff(f73,plain,
! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType,X9: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).
tff(f835,plain,
spl44_49,
inference(avatar_split_clause,[],[f355,f833]) ).
tff(f355,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ),
inference(cnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ) ),
inference(nnf_transformation,[],[f70]) ).
tff(f70,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X12: tyop_2Emin_2Ebool] :
( ~ p(X12)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
tff(f831,plain,
spl44_48,
inference(avatar_split_clause,[],[f354,f829]) ).
tff(f354,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ),
inference(cnf_transformation,[],[f165]) ).
tff(f819,plain,
( spl44_47
| ~ spl44_4
| ~ spl44_5 ),
inference(avatar_split_clause,[],[f623,f597,f593,f817]) ).
tff(f597,plain,
( spl44_5
<=> ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_5])]) ).
tff(f623,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
| ~ spl44_4
| ~ spl44_5 ),
inference(resolution,[],[f598,f594]) ).
tff(f598,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2E_7E_2E1(X0))
| ~ p(X0) )
| ~ spl44_5 ),
inference(avatar_component_clause,[],[f597]) ).
tff(f793,plain,
spl44_46,
inference(avatar_split_clause,[],[f418,f791]) ).
tff(f791,plain,
( spl44_46
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP2(X0,X1)
| p(X0)
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_46])]) ).
tff(f418,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP2(X0,X1)
| p(X0)
| ~ p(X1) ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP2(X0,X1)
| ( p(X0)
& p(X1) )
| ( ~ p(X1)
& ~ p(X0) ) )
& ( ( ( ~ p(X0)
| ~ p(X1) )
& ( p(X1)
| p(X0) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f199]) ).
tff(f199,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
( ( sP2(X1,X0)
| ( p(X1)
& p(X0) )
| ( ~ p(X0)
& ~ p(X1) ) )
& ( ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X0)
| p(X1) ) )
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f198]) ).
tff(f198,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
( ( sP2(X1,X0)
| ( p(X1)
& p(X0) )
| ( ~ p(X0)
& ~ p(X1) ) )
& ( ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X0)
| p(X1) ) )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X1: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool] :
( sP2(X1,X0)
<=> ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X0)
| p(X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f789,plain,
spl44_45,
inference(avatar_split_clause,[],[f415,f787]) ).
tff(f787,plain,
( spl44_45
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP2(X0,X1)
| p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_45])]) ).
tff(f415,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP2(X0,X1)
| p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f200]) ).
tff(f785,plain,
spl44_44,
inference(avatar_split_clause,[],[f414,f783]) ).
tff(f783,plain,
( spl44_44
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_44])]) ).
tff(f414,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
tff(f781,plain,
spl44_43,
inference(avatar_split_clause,[],[f413,f779]) ).
tff(f779,plain,
( spl44_43
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_43])]) ).
tff(f413,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
tff(f777,plain,
spl44_42,
inference(avatar_split_clause,[],[f367,f775]) ).
tff(f775,plain,
( spl44_42
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ~ p(X0)
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_42])]) ).
tff(f367,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ~ p(X0)
| ~ p(X1) ),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( ~ p(X0)
& p(X1) )
| ( ~ p(X1)
& p(X0) ) ),
inference(flattening,[],[f125]) ).
tff(f125,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( ~ p(X0)
& p(X1) )
| ( ~ p(X1)
& p(X0) ) ),
inference(ennf_transformation,[],[f77]) ).
tff(f77,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X0)
=> p(X1) )
=> ( ( p(X1)
=> p(X0) )
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X15: tyop_2Emin_2Ebool,X16: tyop_2Emin_2Ebool] :
( ( p(X15)
=> p(X16) )
=> ( ( p(X16)
=> p(X15) )
=> ( X15 = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
tff(f773,plain,
spl44_41,
inference(avatar_split_clause,[],[f364,f771]) ).
tff(f771,plain,
( spl44_41
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| p(X1)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_41])]) ).
tff(f364,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| p(X1)
| p(X0) ),
inference(cnf_transformation,[],[f126]) ).
tff(f767,plain,
( spl44_40
| ~ spl44_8
| ~ spl44_18 ),
inference(avatar_split_clause,[],[f762,f656,f609,f765]) ).
tff(f765,plain,
( spl44_40
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP1(X0,X1)
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_40])]) ).
tff(f609,plain,
( spl44_8
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_8])]) ).
tff(f656,plain,
( spl44_18
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP1(X0,X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_18])]) ).
tff(f762,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP1(X0,X1)
| ~ p(X1) )
| ~ spl44_8
| ~ spl44_18 ),
inference(resolution,[],[f657,f610]) ).
tff(f610,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
| ~ p(X1) )
| ~ spl44_8 ),
inference(avatar_component_clause,[],[f609]) ).
tff(f657,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ sP0(X0,X1)
| sP1(X0,X1) )
| ~ spl44_18 ),
inference(avatar_component_clause,[],[f656]) ).
tff(f742,plain,
spl44_39,
inference(avatar_split_clause,[],[f573,f740]) ).
tff(f573,plain,
! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X2,X1,X1)
| ~ p(X2) ),
inference(equality_resolution,[],[f469]) ).
tff(f469,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP6(X2,X1,X0)
| ( X0 != X1 )
| ~ p(X2) ),
inference(cnf_transformation,[],[f245]) ).
tff(f738,plain,
spl44_38,
inference(avatar_split_clause,[],[f572,f736]) ).
tff(f736,plain,
( spl44_38
<=> ! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ sP6(X2,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_38])]) ).
tff(f572,plain,
! [X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ~ sP6(X2,X1,X1) ),
inference(equality_resolution,[],[f471]) ).
tff(f471,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ( X0 != X1 )
| ~ sP6(X2,X1,X0) ),
inference(cnf_transformation,[],[f245]) ).
tff(f734,plain,
spl44_37,
inference(avatar_split_clause,[],[f526,f732]) ).
tff(f732,plain,
( spl44_37
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X0,X1,X2)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_37])]) ).
tff(f526,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X0,X1,X2)
| p(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f730,plain,
spl44_36,
inference(avatar_split_clause,[],[f525,f728]) ).
tff(f728,plain,
( spl44_36
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X0,X1,X2)
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_36])]) ).
tff(f525,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X0,X1,X2)
| ~ p(X1) ),
inference(cnf_transformation,[],[f270]) ).
tff(f726,plain,
spl44_35,
inference(avatar_split_clause,[],[f524,f724]) ).
tff(f724,plain,
( spl44_35
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X0,X1,X2)
| p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_35])]) ).
tff(f524,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP13(X0,X1,X2)
| p(X2) ),
inference(cnf_transformation,[],[f270]) ).
tff(f722,plain,
spl44_34,
inference(avatar_split_clause,[],[f507,f720]) ).
tff(f720,plain,
( spl44_34
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X0,X1,X2)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_34])]) ).
tff(f507,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X0,X1,X2)
| p(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f718,plain,
spl44_33,
inference(avatar_split_clause,[],[f506,f716]) ).
tff(f716,plain,
( spl44_33
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X0,X1,X2)
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_33])]) ).
tff(f506,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X0,X1,X2)
| ~ p(X1) ),
inference(cnf_transformation,[],[f261]) ).
tff(f714,plain,
spl44_32,
inference(avatar_split_clause,[],[f505,f712]) ).
tff(f712,plain,
( spl44_32
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X0,X1,X2)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_32])]) ).
tff(f505,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP10(X0,X1,X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f261]) ).
tff(f710,plain,
spl44_31,
inference(avatar_split_clause,[],[f488,f708]) ).
tff(f708,plain,
( spl44_31
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP7(X0,X1,X2)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_31])]) ).
tff(f488,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP7(X0,X1,X2)
| p(X0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f706,plain,
spl44_30,
inference(avatar_split_clause,[],[f487,f704]) ).
tff(f704,plain,
( spl44_30
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP7(X0,X1,X2)
| p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_30])]) ).
tff(f487,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP7(X0,X1,X2)
| p(X1) ),
inference(cnf_transformation,[],[f252]) ).
tff(f702,plain,
spl44_29,
inference(avatar_split_clause,[],[f486,f700]) ).
tff(f700,plain,
( spl44_29
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP7(X0,X1,X2)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_29])]) ).
tff(f486,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP7(X0,X1,X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f252]) ).
tff(f698,plain,
spl44_28,
inference(avatar_split_clause,[],[f467,f696]) ).
tff(f696,plain,
( spl44_28
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP3(X0,X1,X2)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_28])]) ).
tff(f467,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP3(X0,X1,X2)
| ~ p(X0) ),
inference(cnf_transformation,[],[f244]) ).
tff(f694,plain,
spl44_27,
inference(avatar_split_clause,[],[f466,f692]) ).
tff(f692,plain,
( spl44_27
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP3(X0,X1,X2)
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_27])]) ).
tff(f466,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP3(X0,X1,X2)
| ~ p(X1) ),
inference(cnf_transformation,[],[f244]) ).
tff(f690,plain,
spl44_26,
inference(avatar_split_clause,[],[f465,f688]) ).
tff(f688,plain,
( spl44_26
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP3(X0,X1,X2)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_26])]) ).
tff(f465,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP3(X0,X1,X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f244]) ).
tff(f686,plain,
spl44_25,
inference(avatar_split_clause,[],[f463,f684]) ).
tff(f684,plain,
( spl44_25
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP4(X0,X1,X2)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_25])]) ).
tff(f463,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP4(X0,X1,X2)
| p(X0) ),
inference(cnf_transformation,[],[f242]) ).
tff(f682,plain,
spl44_24,
inference(avatar_split_clause,[],[f462,f680]) ).
tff(f680,plain,
( spl44_24
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP4(X0,X1,X2)
| p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_24])]) ).
tff(f462,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP4(X0,X1,X2)
| p(X1) ),
inference(cnf_transformation,[],[f242]) ).
tff(f678,plain,
spl44_23,
inference(avatar_split_clause,[],[f461,f676]) ).
tff(f676,plain,
( spl44_23
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP4(X0,X1,X2)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_23])]) ).
tff(f461,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP4(X0,X1,X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f242]) ).
tff(f674,plain,
spl44_22,
inference(avatar_split_clause,[],[f459,f672]) ).
tff(f672,plain,
( spl44_22
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X1,X2)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_22])]) ).
tff(f459,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X1,X2)
| p(X0) ),
inference(cnf_transformation,[],[f239]) ).
tff(f670,plain,
spl44_21,
inference(avatar_split_clause,[],[f458,f668]) ).
tff(f668,plain,
( spl44_21
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X1,X2)
| p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_21])]) ).
tff(f458,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X1,X2)
| p(X1) ),
inference(cnf_transformation,[],[f239]) ).
tff(f666,plain,
spl44_20,
inference(avatar_split_clause,[],[f457,f664]) ).
tff(f664,plain,
( spl44_20
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X1,X2)
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_20])]) ).
tff(f457,plain,
! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP5(X0,X1,X2)
| ~ p(X2) ),
inference(cnf_transformation,[],[f239]) ).
tff(f662,plain,
spl44_19,
inference(avatar_split_clause,[],[f412,f660]) ).
tff(f660,plain,
( spl44_19
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_19])]) ).
tff(f412,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( sP0(X0,X1)
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f133,f138,f137]) ).
tff(f133,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2EF_2E0)
| p(X0)
| p(X1) )
<=> ( p(c_2Ebool_2EF_2E0)
| p(X0)
| ( ~ p(c_2Ebool_2EF_2E0)
& p(X1) ) ) ),
inference(flattening,[],[f132]) ).
tff(f132,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2EF_2E0)
| p(X0)
| p(X1) )
<=> ( p(c_2Ebool_2EF_2E0)
| p(X0)
| ( ~ p(c_2Ebool_2EF_2E0)
& p(X1) ) ) ),
inference(ennf_transformation,[],[f89]) ).
tff(f89,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( ~ ( p(X0)
| p(X1) )
=> p(c_2Ebool_2EF_2E0) )
<=> ( ( p(X1)
=> p(c_2Ebool_2EF_2E0) )
=> ( ~ p(X0)
=> p(c_2Ebool_2EF_2E0) ) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X31: tyop_2Emin_2Ebool,X32: tyop_2Emin_2Ebool] :
( ( ~ ( p(X31)
| p(X32) )
=> p(c_2Ebool_2EF_2E0) )
<=> ( ( p(X32)
=> p(c_2Ebool_2EF_2E0) )
=> ( ~ p(X31)
=> p(c_2Ebool_2EF_2E0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).
tff(f658,plain,
spl44_18,
inference(avatar_split_clause,[],[f411,f656]) ).
tff(f411,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP1(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
tff(f654,plain,
spl44_17,
inference(avatar_split_clause,[],[f378,f652]) ).
tff(f652,plain,
( spl44_17
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_17])]) ).
tff(f378,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f174]) ).
tff(f650,plain,
spl44_16,
inference(avatar_split_clause,[],[f377,f648]) ).
tff(f648,plain,
( spl44_16
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_16])]) ).
tff(f377,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| p(X0) ),
inference(cnf_transformation,[],[f174]) ).
tff(f646,plain,
spl44_15,
inference(avatar_split_clause,[],[f375,f644]) ).
tff(f375,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f172]) ).
tff(f642,plain,
spl44_14,
inference(avatar_split_clause,[],[f374,f640]) ).
tff(f374,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X0) ),
inference(cnf_transformation,[],[f172]) ).
tff(f638,plain,
spl44_13,
inference(avatar_split_clause,[],[f371,f636]) ).
tff(f371,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f170]) ).
tff(f634,plain,
spl44_12,
inference(avatar_split_clause,[],[f370,f632]) ).
tff(f370,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f170]) ).
tff(f630,plain,
spl44_11,
inference(avatar_split_clause,[],[f345,f628]) ).
tff(f345,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(cnf_transformation,[],[f65]) ).
tff(f65,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X8 )
| ( c_2Ebool_2ET_2E0 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
tff(f619,plain,
spl44_10,
inference(avatar_split_clause,[],[f571,f617]) ).
tff(f571,plain,
! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2)),
inference(equality_resolution,[],[f432]) ).
tff(f432,plain,
! [X0: $tType,X2: X0,X1: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f209]) ).
tff(f615,plain,
spl44_9,
inference(avatar_split_clause,[],[f409,f613]) ).
tff(f613,plain,
( spl44_9
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_9])]) ).
tff(f409,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f196]) ).
tff(f611,plain,
spl44_8,
inference(avatar_split_clause,[],[f408,f609]) ).
tff(f408,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP0(X0,X1)
| ~ p(X1) ),
inference(cnf_transformation,[],[f196]) ).
tff(f607,plain,
spl44_7,
inference(avatar_split_clause,[],[f405,f605]) ).
tff(f605,plain,
( spl44_7
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP1(X0,X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl44_7])]) ).
tff(f405,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( sP1(X0,X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f194]) ).
tff(f603,plain,
spl44_6,
inference(avatar_split_clause,[],[f359,f601]) ).
tff(f359,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) )
& ( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ) ),
inference(nnf_transformation,[],[f72]) ).
tff(f72,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
<=> ~ p(X0) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X6: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X6))
<=> ~ p(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).
tff(f599,plain,
spl44_5,
inference(avatar_split_clause,[],[f358,f597]) ).
tff(f358,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ),
inference(cnf_transformation,[],[f167]) ).
tff(f595,plain,
spl44_4,
inference(avatar_split_clause,[],[f329,f593]) ).
tff(f329,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) ) ),
inference(flattening,[],[f161]) ).
tff(f161,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) ) ),
inference(nnf_transformation,[],[f63]) ).
tff(f63,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2EF_2E0 = X0 )
<=> ~ p(X0) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
<=> ~ p(X0) )
& ( ( c_2Ebool_2ET_2E0 = X0 )
<=> p(X0) )
& ( ( c_2Ebool_2ET_2E0 = X0 )
<=> p(X0) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X8: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2EF_2E0 = X8 )
<=> ~ p(X8) )
& ( ( c_2Ebool_2EF_2E0 = X8 )
<=> ~ p(X8) )
& ( ( c_2Ebool_2ET_2E0 = X8 )
<=> p(X8) )
& ( ( c_2Ebool_2ET_2E0 = X8 )
<=> p(X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(f591,plain,
spl44_3,
inference(avatar_split_clause,[],[f325,f589]) ).
tff(f325,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) ),
inference(cnf_transformation,[],[f162]) ).
tff(f587,plain,
spl44_2,
inference(avatar_split_clause,[],[f314,f584]) ).
tff(f314,plain,
p(c_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
p(c_2Ebool_2ET_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).
tff(f582,plain,
~ spl44_1,
inference(avatar_split_clause,[],[f313,f579]) ).
tff(f313,plain,
~ p(c_2Ebool_2EF_2E0),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
~ p(c_2Ebool_2EF_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ITP020_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 18:56:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (26339)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (26342)WARNING: value z3 for option sas not known
% 0.15/0.38 % (26340)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (26341)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (26343)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (26342)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (26344)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (26345)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (26346)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 % (26346)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41 % (26347)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.41 % (26349)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)
% 0.15/0.41 % (26348)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)
% 0.23/0.41 % (26347)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.41 % Exception at run slice level
% 0.23/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.41 % (26348)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.43 % (26350)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)
% 0.23/0.48 % (26344)First to succeed.
% 0.23/0.49 % (26344)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26339"
% 0.23/0.49 % (26344)Refutation found. Thanks to Tanya!
% 0.23/0.49 % SZS status Theorem for theBenchmark
% 0.23/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.50 % (26344)------------------------------
% 0.23/0.50 % (26344)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.23/0.50 % (26344)Termination reason: Refutation
% 0.23/0.50
% 0.23/0.50 % (26344)Memory used [KB]: 2080
% 0.23/0.50 % (26344)Time elapsed: 0.109 s
% 0.23/0.50 % (26344)Instructions burned: 179 (million)
% 0.23/0.50 % (26339)Success in time 0.13 s
%------------------------------------------------------------------------------