TSTP Solution File: ITP020^3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP020^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 : Mon May 20 22:46:13 EDT 2024
% Result : Theorem 0.20s 0.57s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 280
% Syntax : Number of formulae : 898 ( 167 unt; 70 typ; 0 def)
% Number of atoms : 9136 (2183 equ; 0 cnn)
% Maximal formula atoms : 16 ( 11 avg)
% Number of connectives : 2922 ( 936 ~;1259 |; 410 &; 0 @)
% ( 273 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 429 ( 425 >; 4 *; 0 +; 0 <<)
% Number of symbols : 241 ( 238 usr; 142 con; 0-6 aty)
% Number of variables : 1926 ( 0 ^1739 !; 140 ?;1926 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
tyop_2Enum_2Enum: $tType ).
thf(func_def_0,type,
tyop_2Emin_2Ebool: $tType ).
thf(func_def_1,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(func_def_2,type,
tyop_2Enum_2Enum: $tType ).
thf(func_def_3,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
thf(func_def_4,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_6,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_8,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
c_2Epred__set_2EBIJ:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > $o ) > ( X1 > $o ) > $o ) ).
thf(func_def_10,type,
c_2Epred__set_2ECROSS:
!>[X0: $tType,X1: $tType] : ( ( X0 > $o ) > ( X1 > $o ) > tyop_2Epair_2Eprod(X0,X1) > $o ) ).
thf(func_def_11,type,
c_2Ebool_2EF: $o ).
thf(func_def_12,type,
c_2Ebool_2ET: $o ).
thf(func_def_13,type,
c_2Epred__set_2EUNIV:
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_14,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_15,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
sP0: $o > $o > $o ).
thf(func_def_23,type,
sP1: $o > $o > $o ).
thf(func_def_24,type,
sP2: $o > $o > $o ).
thf(func_def_25,type,
sP3: $o > $o > $o > $o ).
thf(func_def_26,type,
sP4: $o > $o > $o > $o ).
thf(func_def_27,type,
sP5: $o > $o > $o > $o ).
thf(func_def_28,type,
sP6: $o > $o > $o > $o ).
thf(func_def_29,type,
sP7: $o > $o > $o > $o ).
thf(func_def_30,type,
sP8: $o > $o > $o > $o ).
thf(func_def_31,type,
sP9: $o > $o > $o > $o ).
thf(func_def_32,type,
sP10: $o > $o > $o > $o ).
thf(func_def_33,type,
sP11: $o > $o > $o > $o ).
thf(func_def_34,type,
sP12: $o > $o > $o > $o ).
thf(func_def_35,type,
sP13: $o > $o > $o > $o ).
thf(func_def_36,type,
sP14: $o > $o > $o > $o ).
thf(func_def_37,type,
sP15: $o > $o > $o > $o ).
thf(func_def_38,type,
sK16:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_39,type,
sK17:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_40,type,
sK18:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_41,type,
sK19:
!>[X0: $tType] : ( $o > ( X0 > $o ) > X0 ) ).
thf(func_def_42,type,
sK20:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_43,type,
sK21:
!>[X0: $tType] : ( ( X0 > $o ) > $o > X0 ) ).
thf(func_def_44,type,
sK22:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_45,type,
sK23:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_46,type,
sK24:
!>[X0: $tType] : ( $o > ( X0 > $o ) > X0 ) ).
thf(func_def_47,type,
sK25:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_48,type,
sK26:
!>[X0: $tType] : ( ( X0 > $o ) > $o > X0 ) ).
thf(func_def_49,type,
sK27:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_50,type,
sK28:
!>[X0: $tType] : ( ( X0 > $o ) > $o > X0 ) ).
thf(func_def_51,type,
sK29:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_52,type,
sK30:
!>[X0: $tType] : ( ( X0 > $o ) > $o > X0 ) ).
thf(func_def_53,type,
sK31:
!>[X0: $tType,X1: $tType] : ( X0 > ( X0 > X1 > $o ) > X1 ) ).
thf(func_def_54,type,
sK32:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > X1 > $o ) > X0 ) ).
thf(func_def_55,type,
sK33:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > $o ) > X0 > X1 ) ).
thf(func_def_56,type,
sK34:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 > $o ) > X0 ) ).
thf(func_def_57,type,
sK35:
!>[X0: $tType] : ( ( X0 > $o ) > $o > X0 ) ).
thf(func_def_58,type,
sK36:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_59,type,
sK37:
!>[X0: $tType] : ( $o > ( X0 > $o ) > X0 ) ).
thf(func_def_60,type,
sK38:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_61,type,
sK39:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X0 > $o ) > X0 > X1 ) ).
thf(func_def_62,type,
sK40:
!>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X0 > $o ) > X1 > X0 ) ).
thf(func_def_63,type,
sK41: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).
thf(func_def_65,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_66,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_67,type,
vAND: $o > $o > $o ).
thf(func_def_68,type,
vIMP: $o > $o > $o ).
thf(func_def_69,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_70,type,
sK43:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f6956,plain,
$false,
inference(avatar_sat_refutation,[],[f776,f781,f785,f818,f822,f826,f830,f834,f842,f862,f866,f870,f874,f878,f882,f886,f890,f894,f941,f945,f949,f953,f1004,f1017,f1021,f1025,f1029,f1033,f1068,f1083,f1272,f1276,f1280,f1284,f1290,f1294,f1298,f1302,f1307,f1311,f1315,f1319,f1323,f1327,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1600,f2198,f2202,f2206,f2317,f2411,f2512,f2613,f2617,f2621,f2625,f2630,f2634,f2639,f2644,f2647,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4079,f4083,f4109,f4113,f4332,f4689,f4693,f4717,f4721,f4725,f4729,f4734,f4738,f4742,f4746,f4750,f4754,f4758,f4762,f4766,f4770,f5250,f5270,f5274,f5536,f5540,f5544,f5548,f5576,f5580,f5584,f5588,f5592,f5596,f5600,f5778,f6116,f6273,f6277,f6281,f6285,f6289,f6293,f6297,f6301,f6305,f6309,f6314,f6318,f6322,f6326,f6330,f6334,f6560,f6564,f6568,f6623,f6639,f6750,f6824,f6900,f6904,f6938,f6942,f6955]) ).
thf(f6955,plain,
( ~ spl42_3
| ~ spl42_23
| ~ spl42_133
| ~ spl42_137 ),
inference(avatar_contradiction_clause,[],[f6954]) ).
thf(f6954,plain,
( $false
| ~ spl42_3
| ~ spl42_23
| ~ spl42_133
| ~ spl42_137 ),
inference(trivial_inequality_removal,[],[f6953]) ).
thf(f6953,plain,
( ( $true = $false )
| ~ spl42_3
| ~ spl42_23
| ~ spl42_133
| ~ spl42_137 ),
inference(forward_demodulation,[],[f6952,f1006]) ).
thf(f1006,plain,
( ! [X0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( $false = vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) )
| ~ spl42_3
| ~ spl42_23 ),
inference(trivial_inequality_removal,[],[f1005]) ).
thf(f1005,plain,
( ! [X0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( ( $true != $true )
| ( $false = vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) ) )
| ~ spl42_3
| ~ spl42_23 ),
inference(superposition,[],[f1003,f784]) ).
thf(f784,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl42_3 ),
inference(avatar_component_clause,[],[f783]) ).
thf(f783,plain,
( spl42_3
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_3])]) ).
thf(f1003,plain,
( ! [X0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( $true != vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) )
| ~ spl42_23 ),
inference(avatar_component_clause,[],[f1002]) ).
thf(f1002,plain,
( spl42_23
<=> ! [X0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( $true != vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_23])]) ).
thf(f6952,plain,
( ( $true = vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),sK40(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) )
| ~ spl42_133
| ~ spl42_137 ),
inference(trivial_inequality_removal,[],[f6943]) ).
thf(f6943,plain,
( ( $true != $true )
| ( $true = vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),sK40(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) )
| ~ spl42_133
| ~ spl42_137 ),
inference(superposition,[],[f6937,f6749]) ).
thf(f6749,plain,
( ( $true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK41),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)) )
| ~ spl42_133 ),
inference(avatar_component_clause,[],[f6747]) ).
thf(f6747,plain,
( spl42_133
<=> ( $true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK41),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_133])]) ).
thf(f6937,plain,
( ! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X7: X0 > X1] :
( ( $true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3) )
| ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),vAPP(sTfun(X0,$o),sTfun(X1,X0),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X1,X0)),sK40(X0,X1),X3),X2)),X3),X2) ) )
| ~ spl42_137 ),
inference(avatar_component_clause,[],[f6936]) ).
thf(f6936,plain,
( spl42_137
<=> ! [X1: $tType,X0: $tType,X7: X0 > X1,X3: X1 > $o,X2: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),vAPP(sTfun(X0,$o),sTfun(X1,X0),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X1,X0)),sK40(X0,X1),X3),X2)),X3),X2) )
| ( $true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_137])]) ).
thf(f6942,plain,
spl42_138,
inference(avatar_split_clause,[],[f499,f6940]) ).
thf(f6940,plain,
( spl42_138
<=> ! [X1: $tType,X0: $tType,X5: X1 > X0,X3: X1 > $o,X2: X0 > $o] :
( ( $true = vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),vAPP(sTfun(X0,$o),sTfun(X0,X1),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X0,X1)),sK39(X0,X1),X3),X2)),X2),X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_138])]) ).
thf(f499,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X5: X1 > X0] :
( ( $true = vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),vAPP(sTfun(X0,$o),sTfun(X0,X1),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X0,X1)),sK39(X0,X1),X3),X2)),X2),X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2) ) ),
inference(cnf_transformation,[],[f294]) ).
thf(f294,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ( ( $true = vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),vAPP(sTfun(X0,$o),sTfun(X0,X1),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X0,X1)),sK39(X0,X1),X3),X2)),X2),X3) )
| ! [X5: X1 > X0] : ( $true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2) ) )
& ( ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),vAPP(sTfun(X0,$o),sTfun(X1,X0),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X1,X0)),sK40(X0,X1),X3),X2)),X3),X2) )
| ! [X7: X0 > X1] : ( $true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f291,f293,f292]) ).
thf(f292,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o] :
( ? [X4: X0 > X1] : ( $true = vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3) )
=> ( $true = vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),vAPP(sTfun(X0,$o),sTfun(X0,X1),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X0,X1)),sK39(X0,X1),X3),X2)),X2),X3) ) ),
introduced(choice_axiom,[]) ).
thf(f293,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o] :
( ? [X6: X1 > X0] : ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X6),X3),X2) )
=> ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),vAPP(sTfun(X0,$o),sTfun(X1,X0),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X1,X0)),sK40(X0,X1),X3),X2)),X3),X2) ) ),
introduced(choice_axiom,[]) ).
thf(f291,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ( ? [X4: X0 > X1] : ( $true = vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3) )
| ! [X5: X1 > X0] : ( $true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2) ) )
& ( ? [X6: X1 > X0] : ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X6),X3),X2) )
| ! [X7: X0 > X1] : ( $true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3) ) ) ),
inference(rectify,[],[f290]) ).
thf(f290,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ( ? [X4: X0 > X1] : ( $true = vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3) )
| ! [X5: X1 > X0] : ( $true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2) ) )
& ( ? [X5: X1 > X0] : ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2) )
| ! [X4: X0 > X1] : ( $true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3) ) ) ),
inference(nnf_transformation,[],[f114]) ).
thf(f114,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ? [X4: X0 > X1] : ( $true = vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3) )
<=> ? [X5: X1 > X0] : ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2) ) ),
inference(fool_elimination,[],[f113]) ).
thf(f113,plain,
! [X0: $tType,X1: $tType,X2: X0 > $o,X3: X1 > $o] :
( ? [X4: X0 > X1] : vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3)
<=> ? [X5: X1 > X0] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2) ),
inference(rectify,[],[f27]) ).
thf(f27,axiom,
! [X0: $tType,X1: $tType,X22: X0 > $o,X23: X1 > $o] :
( ? [X24: X0 > X1] : vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X24),X22),X23)
<=> ? [X25: X1 > X0] : vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),X25),X23),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EBIJ__SYM) ).
thf(f6938,plain,
spl42_137,
inference(avatar_split_clause,[],[f498,f6936]) ).
thf(f498,plain,
! [X1: $tType,X0: $tType,X2: X0 > $o,X3: X1 > $o,X7: X0 > X1] :
( ( $true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(X1,X0),sTfun(sTfun(X1,$o),sTfun(sTfun(X0,$o),$o)),c_2Epred__set_2EBIJ(X1,X0),vAPP(sTfun(X0,$o),sTfun(X1,X0),vAPP(sTfun(X1,$o),sTfun(sTfun(X0,$o),sTfun(X1,X0)),sK40(X0,X1),X3),X2)),X3),X2) )
| ( $true != vAPP(sTfun(X1,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o),vAPP(sTfun(X0,X1),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),$o)),c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3) ) ),
inference(cnf_transformation,[],[f294]) ).
thf(f6904,plain,
spl42_136,
inference(avatar_split_clause,[],[f682,f6902]) ).
thf(f6902,plain,
( spl42_136
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_136])]) ).
thf(f682,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) ),
inference(not_proxy_clausification,[],[f404]) ).
thf(f404,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f222,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X2 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) )
& ( ( ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 ) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ) ),
inference(rectify,[],[f221]) ).
thf(f221,plain,
! [X2: $o,X1: $o,X0: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X0 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) )
& ( ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 ) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ) ),
inference(flattening,[],[f220]) ).
thf(f220,plain,
! [X2: $o,X1: $o,X0: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X0 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) )
& ( ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 ) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ) ),
inference(nnf_transformation,[],[f146]) ).
thf(f146,plain,
! [X2: $o,X1: $o,X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) )
<=> ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 ) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f6900,plain,
spl42_135,
inference(avatar_split_clause,[],[f681,f6898]) ).
thf(f6898,plain,
( spl42_135
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_135])]) ).
thf(f681,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) ),
inference(not_proxy_clausification,[],[f403]) ).
thf(f403,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f6824,plain,
spl42_134,
inference(avatar_split_clause,[],[f580,f6822]) ).
thf(f6822,plain,
( spl42_134
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,$true),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),$true),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_134])]) ).
thf(f580,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,$true),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),$true),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),$true) ) ),
inference(equality_resolution,[],[f402]) ).
thf(f402,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f6750,plain,
spl42_133,
inference(avatar_split_clause,[],[f500,f6747]) ).
thf(f500,plain,
$true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK41),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),
inference(cnf_transformation,[],[f296]) ).
thf(f296,plain,
$true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK41),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f116,f295]) ).
thf(f295,plain,
( ? [X0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum] : ( $true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)) )
=> ( $true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sK41),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)) ) ),
introduced(choice_axiom,[]) ).
thf(f116,plain,
? [X0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum] : ( $true = vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)) ),
inference(fool_elimination,[],[f115]) ).
thf(f115,plain,
? [X0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum] : vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),
inference(rectify,[],[f38]) ).
thf(f38,axiom,
? [X4: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum] : vAPP(sTfun(tyop_2Enum_2Enum,$o),$o,vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o),vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),$o)),c_2Epred__set_2EBIJ(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X4),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ) ).
thf(f6639,plain,
spl42_132,
inference(avatar_split_clause,[],[f486,f6637]) ).
thf(f6637,plain,
( spl42_132
<=> ! [X1: $tType,X0: $tType,X8: X0,X10: X1,X2: X0 > X1 > $o] :
( ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X8),vAPP(X0,X1,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,X1),sK33(X0,X1),X2),X8)) )
| ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK34(X0,X1),X2)),X10) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_132])]) ).
thf(f486,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > $o,X10: X1,X8: X0] :
( ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X8),vAPP(X0,X1,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,X1),sK33(X0,X1),X2),X8)) )
| ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK34(X0,X1),X2)),X10) ) ),
inference(cnf_transformation,[],[f276]) ).
thf(f276,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > $o] :
( ( ! [X3: X0] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),vAPP(sTfun(X0,sTfun(X1,$o)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,$o)),X1),sK31(X0,X1),X3),X2)) )
| ! [X5: X0 > X1] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,vAPP(sTfun(X0,X1),sTfun(sTfun(X0,sTfun(X1,$o)),X0),sK32(X0,X1),X5),X2)),vAPP(X0,X1,X5,vAPP(sTfun(X0,sTfun(X1,$o)),X0,vAPP(sTfun(X0,X1),sTfun(sTfun(X0,sTfun(X1,$o)),X0),sK32(X0,X1),X5),X2))) ) )
& ( ! [X8: X0] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X8),vAPP(X0,X1,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,X1),sK33(X0,X1),X2),X8)) )
| ! [X10: X1] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK34(X0,X1),X2)),X10) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34])],[f271,f275,f274,f273,f272]) ).
thf(f272,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > $o,X3: X0] :
( ? [X4: X1] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4) )
=> ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),vAPP(sTfun(X0,sTfun(X1,$o)),X1,vAPP(X0,sTfun(sTfun(X0,sTfun(X1,$o)),X1),sK31(X0,X1),X3),X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f273,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > $o,X5: X0 > X1] :
( ? [X6: X0] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X6),vAPP(X0,X1,X5,X6)) )
=> ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,vAPP(sTfun(X0,X1),sTfun(sTfun(X0,sTfun(X1,$o)),X0),sK32(X0,X1),X5),X2)),vAPP(X0,X1,X5,vAPP(sTfun(X0,sTfun(X1,$o)),X0,vAPP(sTfun(X0,X1),sTfun(sTfun(X0,sTfun(X1,$o)),X0),sK32(X0,X1),X5),X2))) ) ),
introduced(choice_axiom,[]) ).
thf(f274,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > $o] :
( ? [X7: X0 > X1] :
! [X8: X0] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X8),vAPP(X0,X1,X7,X8)) )
=> ! [X8: X0] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X8),vAPP(X0,X1,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(X0,X1),sK33(X0,X1),X2),X8)) ) ),
introduced(choice_axiom,[]) ).
thf(f275,plain,
! [X1: $tType,X0: $tType,X2: X0 > X1 > $o] :
( ? [X9: X0] :
! [X10: X1] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X9),X10) )
=> ! [X10: X1] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(X0,sTfun(X1,$o)),X0,sK34(X0,X1),X2)),X10) ) ),
introduced(choice_axiom,[]) ).
thf(f271,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > $o] :
( ( ! [X3: X0] :
? [X4: X1] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4) )
| ! [X5: X0 > X1] :
? [X6: X0] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X6),vAPP(X0,X1,X5,X6)) ) )
& ( ? [X7: X0 > X1] :
! [X8: X0] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X8),vAPP(X0,X1,X7,X8)) )
| ? [X9: X0] :
! [X10: X1] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X9),X10) ) ) ),
inference(rectify,[],[f270]) ).
thf(f270,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > $o] :
( ( ! [X3: X0] :
? [X4: X1] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4) )
| ! [X5: X0 > X1] :
? [X6: X0] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X6),vAPP(X0,X1,X5,X6)) ) )
& ( ? [X5: X0 > X1] :
! [X6: X0] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X6),vAPP(X0,X1,X5,X6)) )
| ? [X3: X0] :
! [X4: X1] : ( $true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4) ) ) ),
inference(nnf_transformation,[],[f106]) ).
thf(f106,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > $o] :
( ! [X3: X0] :
? [X4: X1] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4) )
<=> ? [X5: X0 > X1] :
! [X6: X0] : ( $true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X6),vAPP(X0,X1,X5,X6)) ) ),
inference(fool_elimination,[],[f105]) ).
thf(f105,plain,
! [X0: $tType,X1: $tType,X2: X0 > X1 > $o] :
( ! [X3: X0] :
? [X4: X1] : vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)
<=> ? [X5: X0 > X1] :
! [X6: X0] : vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X6),vAPP(X0,X1,X5,X6)) ),
inference(rectify,[],[f26]) ).
thf(f26,axiom,
! [X0: $tType,X1: $tType,X11: X0 > X1 > $o] :
( ! [X5: X0] :
? [X19: X1] : vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X11,X5),X19)
<=> ? [X20: X0 > X1] :
! [X21: X0] : vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X11,X21),vAPP(X0,X1,X20,X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ESKOLEM__THM) ).
thf(f6623,plain,
spl42_131,
inference(avatar_split_clause,[],[f656,f6621]) ).
thf(f6621,plain,
( spl42_131
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true = X1 )
| ( $true = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_131])]) ).
thf(f656,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true = X1 )
| ( $true = X2 ) ),
inference(not_proxy_clausification,[],[f655]) ).
thf(f655,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true = X1 )
| ( vAPP($o,$o,vNOT,X2) != $true ) ),
inference(not_proxy_clausification,[],[f446]) ).
thf(f446,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) )
| ( vAPP($o,$o,vNOT,X2) != $true ) ),
inference(cnf_transformation,[],[f242]) ).
thf(f242,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X0 ) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X0 ) ) )
& ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ) ),
inference(rectify,[],[f241]) ).
thf(f241,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X2 ) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X2 ) ) )
& ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) ) ) ),
inference(flattening,[],[f240]) ).
thf(f240,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X2 ) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X2 ) ) )
& ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f154]) ).
thf(f154,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) )
<=> ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f6568,plain,
spl42_130,
inference(avatar_split_clause,[],[f666,f6566]) ).
thf(f6566,plain,
( spl42_130
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_130])]) ).
thf(f666,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) ) ),
inference(not_proxy_clausification,[],[f665]) ).
thf(f665,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) ) ),
inference(duplicate_literal_removal,[],[f427]) ).
thf(f427,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) ) ),
inference(cnf_transformation,[],[f234]) ).
thf(f234,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X1 ) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X2 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) ) )
& ( ( ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ) ),
inference(rectify,[],[f233]) ).
thf(f233,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X0 ) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X1 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) )
& ( ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X1 ) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) ) ) ),
inference(flattening,[],[f232]) ).
thf(f232,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X0 ) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X1 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) )
& ( ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X1 ) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f150]) ).
thf(f150,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) )
<=> ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X1 ) )
& ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f6564,plain,
spl42_129,
inference(avatar_split_clause,[],[f647,f6562]) ).
thf(f6562,plain,
( spl42_129
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,$true),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,$true),X1),X0) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_129])]) ).
thf(f647,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,$true),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,$true),X1),X0) )
| ( $true = X1 ) ),
inference(not_proxy_clausification,[],[f614]) ).
thf(f614,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,$true),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,$true),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) ) ),
inference(equality_resolution,[],[f465]) ).
thf(f465,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f251]) ).
thf(f251,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X0 ) )
| ( ( $true != X2 )
& ( $true != X0 ) ) )
& ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 ) )
& ( ( $true = X2 )
| ( $true = X0 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) ) ) ),
inference(rectify,[],[f250]) ).
thf(f250,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X2 ) )
| ( ( $true != X1 )
& ( $true != X2 ) ) )
& ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = X1 )
| ( $true = X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) ) ) ),
inference(flattening,[],[f249]) ).
thf(f249,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X2 ) )
| ( ( $true != X1 )
& ( $true != X2 ) ) )
& ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = X1 )
| ( $true = X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f158]) ).
thf(f158,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) )
<=> ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = X1 )
| ( $true = X2 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f6560,plain,
( spl42_128
| spl42_30
| ~ spl42_56 ),
inference(avatar_split_clause,[],[f2281,f2204,f1066,f6557]) ).
thf(f6557,plain,
( spl42_128
<=> ( $false = vAPP(sTfun($o,$o),$o,sK23($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_128])]) ).
thf(f1066,plain,
( spl42_30
<=> ! [X0: $o] : ( $true = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_30])]) ).
thf(f2204,plain,
( spl42_56
<=> ! [X0: $tType,X4: X0,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK23(X0),X1)) )
| ( $true != vAPP(X0,$o,X1,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_56])]) ).
thf(f2281,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP(sTfun($o,$o),$o,sK23($o),vNOT) ) )
| ~ spl42_56 ),
inference(not_proxy_clausification,[],[f2280]) ).
thf(f2280,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK23($o),vNOT)) ) )
| ~ spl42_56 ),
inference(not_proxy_clausification,[],[f2214]) ).
thf(f2214,plain,
( ! [X0: $o] :
( ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK23($o),vNOT)) ) )
| ~ spl42_56 ),
inference(primitive_instantiation,[],[f2205]) ).
thf(f2205,plain,
( ! [X0: $tType,X1: X0 > $o,X4: X0] :
( ( $true != vAPP(X0,$o,X1,X4) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK23(X0),X1)) ) )
| ~ spl42_56 ),
inference(avatar_component_clause,[],[f2204]) ).
thf(f6334,plain,
spl42_127,
inference(avatar_split_clause,[],[f652,f6332]) ).
thf(f6332,plain,
( spl42_127
<=> ! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_127])]) ).
thf(f652,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),$true) ) ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f604,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),$true) )
| ( $true != $true ) ),
inference(equality_resolution,[],[f443]) ).
thf(f443,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true != X0 )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f242]) ).
thf(f6330,plain,
spl42_126,
inference(avatar_split_clause,[],[f645,f6328]) ).
thf(f6328,plain,
( spl42_126
<=> ! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_126])]) ).
thf(f645,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),$true) ) ),
inference(trivial_inequality_removal,[],[f618]) ).
thf(f618,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),$true) )
| ( $true != $true ) ),
inference(equality_resolution,[],[f462]) ).
thf(f462,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true != X0 )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f251]) ).
thf(f6326,plain,
spl42_125,
inference(avatar_split_clause,[],[f593,f6324]) ).
thf(f6324,plain,
( spl42_125
<=> ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,$true),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),$true),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_125])]) ).
thf(f593,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,$true),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),$true),$true) ) ),
inference(equality_resolution,[],[f592]) ).
thf(f592,plain,
! [X2: $o,X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),$true),X0) )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),$true) ) ),
inference(equality_resolution,[],[f424]) ).
thf(f424,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) )
| ( $true != X1 )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) ) ),
inference(cnf_transformation,[],[f234]) ).
thf(f6322,plain,
spl42_124,
inference(avatar_split_clause,[],[f477,f6320]) ).
thf(f6320,plain,
( spl42_124
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_124])]) ).
thf(f477,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) ) ),
inference(cnf_transformation,[],[f257]) ).
thf(f257,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) ) )
& ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f159]) ).
thf(f159,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) ) ),
inference(definition_folding,[],[f137,f158,f157,f156]) ).
thf(f156,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) )
<=> ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f157,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
<=> ( ( $true = X2 )
<=> ( ( $true = X0 )
| ( $true != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f137,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( ( $true = X0 )
| ( $true != X1 ) ) )
<=> ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = X1 )
| ( $true = X2 ) ) ) ),
inference(ennf_transformation,[],[f100]) ).
thf(f100,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( ( $true = X1 )
=> ( $true = X0 ) ) )
<=> ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = X1 )
| ( $true = X2 ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f99,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( X2
<=> ( X1
=> X0 ) )
<=> ( ( vAPP($o,$o,vNOT,X2)
| X0
| vAPP($o,$o,vNOT,X1) )
& ( vAPP($o,$o,vNOT,X0)
| X2 )
& ( X1
| X2 ) ) ),
inference(rectify,[],[f36]) ).
thf(f36,axiom,
! [X28: $o,X29: $o,X30: $o] :
( ( X30
<=> ( X29
=> X28 ) )
<=> ( ( vAPP($o,$o,vNOT,X30)
| X28
| vAPP($o,$o,vNOT,X29) )
& ( vAPP($o,$o,vNOT,X28)
| X30 )
& ( X29
| X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__imp) ).
thf(f6318,plain,
spl42_123,
inference(avatar_split_clause,[],[f476,f6316]) ).
thf(f6316,plain,
( spl42_123
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_123])]) ).
thf(f476,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f257]) ).
thf(f6314,plain,
( spl42_122
| spl42_30
| ~ spl42_51 ),
inference(avatar_split_clause,[],[f2181,f1354,f1066,f6311]) ).
thf(f6311,plain,
( spl42_122
<=> ( $false = vAPP(sTfun($o,$o),$o,sK18($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_122])]) ).
thf(f1354,plain,
( spl42_51
<=> ! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $false = vAPP(X0,$o,X1,X2) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK18(X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_51])]) ).
thf(f2181,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP(sTfun($o,$o),$o,sK18($o),vNOT) ) )
| ~ spl42_51 ),
inference(not_proxy_clausification,[],[f2180]) ).
thf(f2180,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK18($o),vNOT)) ) )
| ~ spl42_51 ),
inference(not_proxy_clausification,[],[f1992]) ).
thf(f1992,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK18($o),vNOT)) ) )
| ~ spl42_51 ),
inference(primitive_instantiation,[],[f1355]) ).
thf(f1355,plain,
( ! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $false = vAPP(X0,$o,X1,X2) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK18(X0),X1)) ) )
| ~ spl42_51 ),
inference(avatar_component_clause,[],[f1354]) ).
thf(f6309,plain,
spl42_121,
inference(avatar_split_clause,[],[f461,f6307]) ).
thf(f6307,plain,
( spl42_121
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_121])]) ).
thf(f461,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f251]) ).
thf(f6305,plain,
spl42_120,
inference(avatar_split_clause,[],[f458,f6303]) ).
thf(f6303,plain,
( spl42_120
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_120])]) ).
thf(f458,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) ) ),
inference(cnf_transformation,[],[f248]) ).
thf(f248,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) ) )
& ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f155]) ).
thf(f155,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) ) ),
inference(definition_folding,[],[f98,f154,f153,f152]) ).
thf(f152,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) )
<=> ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f153,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
<=> ( ( $true = X2 )
<=> ( ( $true = X0 )
| ( $true = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f98,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( ( $true = X0 )
| ( $true = X1 ) ) )
<=> ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = X1 ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 ) ) ) ),
inference(fool_elimination,[],[f97]) ).
thf(f97,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( X2
<=> ( X0
| X1 ) )
<=> ( ( vAPP($o,$o,vNOT,X2)
| X0
| X1 )
& ( vAPP($o,$o,vNOT,X0)
| X2 )
& ( vAPP($o,$o,vNOT,X1)
| X2 ) ) ),
inference(rectify,[],[f35]) ).
thf(f35,axiom,
! [X28: $o,X29: $o,X30: $o] :
( ( X30
<=> ( X28
| X29 ) )
<=> ( ( vAPP($o,$o,vNOT,X30)
| X28
| X29 )
& ( vAPP($o,$o,vNOT,X28)
| X30 )
& ( vAPP($o,$o,vNOT,X29)
| X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__disj) ).
thf(f6301,plain,
spl42_119,
inference(avatar_split_clause,[],[f457,f6299]) ).
thf(f6299,plain,
( spl42_119
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_119])]) ).
thf(f457,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f248]) ).
thf(f6297,plain,
spl42_118,
inference(avatar_split_clause,[],[f442,f6295]) ).
thf(f6295,plain,
( spl42_118
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_118])]) ).
thf(f442,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f242]) ).
thf(f6293,plain,
spl42_117,
inference(avatar_split_clause,[],[f439,f6291]) ).
thf(f6291,plain,
( spl42_117
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_117])]) ).
thf(f439,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) ) ),
inference(cnf_transformation,[],[f239]) ).
thf(f239,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) ) )
& ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f151]) ).
thf(f151,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) ) ),
inference(definition_folding,[],[f96,f150,f149,f148]) ).
thf(f148,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
<=> ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f149,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
<=> ( ( $true = X2 )
<=> ( ( $true = X0 )
& ( $true = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f96,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( ( $true = X0 )
& ( $true = X1 ) ) )
<=> ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X1 ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f95,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( X2
<=> ( X0
& X1 ) )
<=> ( ( vAPP($o,$o,vNOT,X2)
| X0 )
& ( vAPP($o,$o,vNOT,X2)
| X1 )
& ( vAPP($o,$o,vNOT,X0)
| vAPP($o,$o,vNOT,X1)
| X2 ) ) ),
inference(rectify,[],[f34]) ).
thf(f34,axiom,
! [X28: $o,X29: $o,X30: $o] :
( ( X30
<=> ( X28
& X29 ) )
<=> ( ( vAPP($o,$o,vNOT,X30)
| X28 )
& ( vAPP($o,$o,vNOT,X30)
| X29 )
& ( vAPP($o,$o,vNOT,X28)
| vAPP($o,$o,vNOT,X29)
| X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__conj) ).
thf(f6289,plain,
spl42_116,
inference(avatar_split_clause,[],[f438,f6287]) ).
thf(f6287,plain,
( spl42_116
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_116])]) ).
thf(f438,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X0),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f239]) ).
thf(f6285,plain,
spl42_115,
inference(avatar_split_clause,[],[f421,f6283]) ).
thf(f6283,plain,
( spl42_115
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_115])]) ).
thf(f421,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f234]) ).
thf(f6281,plain,
spl42_114,
inference(avatar_split_clause,[],[f400,f6279]) ).
thf(f6279,plain,
( spl42_114
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_114])]) ).
thf(f400,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f6277,plain,
spl42_113,
inference(avatar_split_clause,[],[f399,f6275]) ).
thf(f6275,plain,
( spl42_113
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_113])]) ).
thf(f399,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f6273,plain,
spl42_112,
inference(avatar_split_clause,[],[f398,f6271]) ).
thf(f6271,plain,
( spl42_112
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_112])]) ).
thf(f398,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f6116,plain,
spl42_111,
inference(avatar_split_clause,[],[f390,f6114]) ).
thf(f6114,plain,
( spl42_111
<=> ! [X0: $tType,X6: X0,X2: $o,X1: X0 > $o] :
( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK24(X0),X2),X1)) )
| ( $true != vAPP(X0,$o,X1,X6) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_111])]) ).
thf(f390,plain,
! [X0: $tType,X2: $o,X1: X0 > $o,X6: X0] :
( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK24(X0),X2),X1)) )
| ( $true != vAPP(X0,$o,X1,X6) ) ),
inference(cnf_transformation,[],[f213]) ).
thf(f213,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK23(X0),X1)) )
| ! [X4: X0] :
( ( $true != X2 )
& ( $true != vAPP(X0,$o,X1,X4) ) ) )
& ( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK24(X0),X2),X1)) )
| ( ( $true != X2 )
& ! [X6: X0] : ( $true != vAPP(X0,$o,X1,X6) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f210,f212,f211]) ).
thf(f211,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
=> ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK23(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f212,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ? [X5: X0] :
( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,X5) ) )
=> ( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK24(X0),X2),X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f210,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( $true = X2 )
| ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ! [X4: X0] :
( ( $true != X2 )
& ( $true != vAPP(X0,$o,X1,X4) ) ) )
& ( ? [X5: X0] :
( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,X5) ) )
| ( ( $true != X2 )
& ! [X6: X0] : ( $true != vAPP(X0,$o,X1,X6) ) ) ) ),
inference(rectify,[],[f209]) ).
thf(f209,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( $true = X2 )
| ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ! [X4: X0] :
( ( $true != X2 )
& ( $true != vAPP(X0,$o,X1,X4) ) ) )
& ( ? [X4: X0] :
( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,X4) ) )
| ( ( $true != X2 )
& ! [X3: X0] : ( $true != vAPP(X0,$o,X1,X3) ) ) ) ),
inference(flattening,[],[f208]) ).
thf(f208,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( $true = X2 )
| ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ! [X4: X0] :
( ( $true != X2 )
& ( $true != vAPP(X0,$o,X1,X4) ) ) )
& ( ? [X4: X0] :
( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,X4) ) )
| ( ( $true != X2 )
& ! [X3: X0] : ( $true != vAPP(X0,$o,X1,X3) ) ) ) ),
inference(nnf_transformation,[],[f90]) ).
thf(f90,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( $true = X2 )
| ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) ) )
<=> ? [X4: X0] :
( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,X4) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f89,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( X2
| ? [X3: X0] : vAPP(X0,$o,X1,X3) )
<=> ? [X4: X0] :
( X2
| vAPP(X0,$o,X1,X4) ) ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
! [X0: $tType,X11: X0 > $o,X13: $o] :
( ( X13
| ? [X12: X0] : vAPP(X0,$o,X11,X12) )
<=> ? [X14: X0] :
( X13
| vAPP(X0,$o,X11,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__EXISTS__THM) ).
thf(f5778,plain,
( spl42_110
| spl42_30
| ~ spl42_50 ),
inference(avatar_split_clause,[],[f1971,f1350,f1066,f5775]) ).
thf(f5775,plain,
( spl42_110
<=> ( $false = vAPP(sTfun($o,$o),$o,sK43($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_110])]) ).
thf(f1350,plain,
( spl42_50
<=> ! [X0: $tType,X1: X0 > $o,X3: X0] :
( ( $false = vAPP(X0,$o,X1,X3) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK43(X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_50])]) ).
thf(f1971,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP(sTfun($o,$o),$o,sK43($o),vNOT) ) )
| ~ spl42_50 ),
inference(not_proxy_clausification,[],[f1970]) ).
thf(f1970,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK43($o),vNOT)) ) )
| ~ spl42_50 ),
inference(not_proxy_clausification,[],[f1792]) ).
thf(f1792,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK43($o),vNOT)) ) )
| ~ spl42_50 ),
inference(primitive_instantiation,[],[f1351]) ).
thf(f1351,plain,
( ! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( $false = vAPP(X0,$o,X1,X3) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK43(X0),X1)) ) )
| ~ spl42_50 ),
inference(avatar_component_clause,[],[f1350]) ).
thf(f5600,plain,
spl42_109,
inference(avatar_split_clause,[],[f680,f5598]) ).
thf(f5598,plain,
( spl42_109
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_109])]) ).
thf(f680,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f679]) ).
thf(f679,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f401]) ).
thf(f401,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f5596,plain,
spl42_108,
inference(avatar_split_clause,[],[f676,f5594]) ).
thf(f5594,plain,
( spl42_108
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_108])]) ).
thf(f676,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f675]) ).
thf(f675,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f405]) ).
thf(f405,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f225,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X2 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) ) ) ),
inference(rectify,[],[f224]) ).
thf(f224,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X1 ) ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) ) ) ),
inference(flattening,[],[f223]) ).
thf(f223,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X1 ) ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f145]) ).
thf(f145,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
<=> ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5592,plain,
spl42_107,
inference(avatar_split_clause,[],[f672,f5590]) ).
thf(f5590,plain,
( spl42_107
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_107])]) ).
thf(f672,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f671]) ).
thf(f671,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f409]) ).
thf(f409,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f228]) ).
thf(f228,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X2 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) ) ) ),
inference(rectify,[],[f227]) ).
thf(f227,plain,
! [X1: $o,X0: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X2 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) ) ) ),
inference(flattening,[],[f226]) ).
thf(f226,plain,
! [X1: $o,X0: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X2 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) ) ) ),
inference(nnf_transformation,[],[f144]) ).
thf(f144,plain,
! [X1: $o,X0: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
<=> ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5588,plain,
spl42_106,
inference(avatar_split_clause,[],[f658,f5586]) ).
thf(f5586,plain,
( spl42_106
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_106])]) ).
thf(f658,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f657]) ).
thf(f657,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f434]) ).
thf(f434,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f238]) ).
thf(f238,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X2 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) ) ),
inference(flattening,[],[f237]) ).
thf(f237,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X2 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f148]) ).
thf(f5584,plain,
spl42_105,
inference(avatar_split_clause,[],[f648,f5582]) ).
thf(f5582,plain,
( spl42_105
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_105])]) ).
thf(f648,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f453]) ).
thf(f453,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f247]) ).
thf(f247,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X1 )
& ( $true != X2 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) ) ) ),
inference(rectify,[],[f246]) ).
thf(f246,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X0 )
& ( $true != X1 ) ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) ) ) ),
inference(flattening,[],[f245]) ).
thf(f245,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X0 )
& ( $true != X1 ) ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f152]) ).
thf(f5580,plain,
spl42_104,
inference(avatar_split_clause,[],[f641,f5578]) ).
thf(f5578,plain,
( spl42_104
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X1 )
| ( $false = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_104])]) ).
thf(f641,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X1 )
| ( $false = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f640]) ).
thf(f640,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X1 )
| ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f472]) ).
thf(f472,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f256]) ).
thf(f256,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X1 )
& ( vAPP($o,$o,vNOT,X2) != $true ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) ) ) ),
inference(rectify,[],[f255]) ).
thf(f255,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X0 )
& ( $true != vAPP($o,$o,vNOT,X1) ) ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) ) ) ),
inference(flattening,[],[f254]) ).
thf(f254,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) )
| ( ( vAPP($o,$o,vNOT,X2) != $true )
& ( $true != X0 )
& ( $true != vAPP($o,$o,vNOT,X1) ) ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f156]) ).
thf(f5576,plain,
spl42_103,
inference(avatar_split_clause,[],[f482,f5574]) ).
thf(f5574,plain,
( spl42_103
<=> ! [X0: $tType,X5: X0,X2: X0 > $o,X1: $o] :
( ( $true = X1 )
| ( $true = vAPP(X0,$o,X2,X5) )
| ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK30(X0),X2),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_103])]) ).
thf(f482,plain,
! [X0: $tType,X2: X0 > $o,X1: $o,X5: X0] :
( ( $true = X1 )
| ( $true = vAPP(X0,$o,X2,X5) )
| ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK30(X0),X2),X1)) ) ),
inference(cnf_transformation,[],[f269]) ).
thf(f269,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true = X1 )
| ( $true = vAPP(X0,$o,X2,X3) ) )
| ( ( $true != X1 )
& ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK29(X0),X2)) ) ) )
& ( ( $true = X1 )
| ! [X5: X0] : ( $true = vAPP(X0,$o,X2,X5) )
| ( ( $true != X1 )
& ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK30(X0),X2),X1)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f266,f268,f267]) ).
thf(f267,plain,
! [X0: $tType,X2: X0 > $o] :
( ? [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
=> ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK29(X0),X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f268,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ? [X6: X0] :
( ( $true != X1 )
& ( $true != vAPP(X0,$o,X2,X6) ) )
=> ( ( $true != X1 )
& ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK30(X0),X2),X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f266,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true = X1 )
| ( $true = vAPP(X0,$o,X2,X3) ) )
| ( ( $true != X1 )
& ? [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) ) ) )
& ( ( $true = X1 )
| ! [X5: X0] : ( $true = vAPP(X0,$o,X2,X5) )
| ? [X6: X0] :
( ( $true != X1 )
& ( $true != vAPP(X0,$o,X2,X6) ) ) ) ),
inference(rectify,[],[f265]) ).
thf(f265,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true = X1 )
| ( $true = vAPP(X0,$o,X2,X3) ) )
| ( ( $true != X1 )
& ? [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) ) ) )
& ( ( $true = X1 )
| ! [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) )
| ? [X3: X0] :
( ( $true != X1 )
& ( $true != vAPP(X0,$o,X2,X3) ) ) ) ),
inference(flattening,[],[f264]) ).
thf(f264,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true = X1 )
| ( $true = vAPP(X0,$o,X2,X3) ) )
| ( ( $true != X1 )
& ? [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) ) ) )
& ( ( $true = X1 )
| ! [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) )
| ? [X3: X0] :
( ( $true != X1 )
& ( $true != vAPP(X0,$o,X2,X3) ) ) ) ),
inference(nnf_transformation,[],[f104]) ).
thf(f104,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ! [X3: X0] :
( ( $true = X1 )
| ( $true = vAPP(X0,$o,X2,X3) ) )
<=> ( ( $true = X1 )
| ! [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f103,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ! [X3: X0] :
( X1
| vAPP(X0,$o,X2,X3) )
<=> ( X1
| ! [X4: X0] : vAPP(X0,$o,X2,X4) ) ),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
! [X0: $tType,X15: $o,X16: X0 > $o] :
( ! [X12: X0] :
( X15
| vAPP(X0,$o,X16,X12) )
<=> ( X15
| ! [X14: X0] : vAPP(X0,$o,X16,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__FORALL__OR__THM) ).
thf(f5548,plain,
spl42_102,
inference(avatar_split_clause,[],[f479,f5546]) ).
thf(f5546,plain,
( spl42_102
<=> ! [X0: $tType,X5: X0,X2: X0 > $o,X1: $o] :
( ( $true = vAPP(X0,$o,X2,X5) )
| ( $true = X1 )
| ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK28(X0),X2),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_102])]) ).
thf(f479,plain,
! [X0: $tType,X2: X0 > $o,X1: $o,X5: X0] :
( ( $true = vAPP(X0,$o,X2,X5) )
| ( $true = X1 )
| ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK28(X0),X2),X1)) ) ),
inference(cnf_transformation,[],[f263]) ).
thf(f263,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 ) )
| ( ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK27(X0),X2)) )
& ( $true != X1 ) ) )
& ( ! [X5: X0] : ( $true = vAPP(X0,$o,X2,X5) )
| ( $true = X1 )
| ( ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK28(X0),X2),X1)) )
& ( $true != X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f260,f262,f261]) ).
thf(f261,plain,
! [X0: $tType,X2: X0 > $o] :
( ? [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
=> ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK27(X0),X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f262,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ? [X6: X0] :
( ( $true != vAPP(X0,$o,X2,X6) )
& ( $true != X1 ) )
=> ( ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK28(X0),X2),X1)) )
& ( $true != X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f260,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 ) )
| ( ? [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
& ( $true != X1 ) ) )
& ( ! [X5: X0] : ( $true = vAPP(X0,$o,X2,X5) )
| ( $true = X1 )
| ? [X6: X0] :
( ( $true != vAPP(X0,$o,X2,X6) )
& ( $true != X1 ) ) ) ),
inference(rectify,[],[f259]) ).
thf(f259,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 ) )
| ( ? [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
& ( $true != X1 ) ) )
& ( ! [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) )
| ( $true = X1 )
| ? [X3: X0] :
( ( $true != vAPP(X0,$o,X2,X3) )
& ( $true != X1 ) ) ) ),
inference(flattening,[],[f258]) ).
thf(f258,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 ) )
| ( ? [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
& ( $true != X1 ) ) )
& ( ! [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) )
| ( $true = X1 )
| ? [X3: X0] :
( ( $true != vAPP(X0,$o,X2,X3) )
& ( $true != X1 ) ) ) ),
inference(nnf_transformation,[],[f102]) ).
thf(f102,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ! [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 ) )
<=> ( ! [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) )
| ( $true = X1 ) ) ),
inference(fool_elimination,[],[f101]) ).
thf(f101,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ! [X3: X0] :
( vAPP(X0,$o,X2,X3)
| X1 )
<=> ( ! [X4: X0] : vAPP(X0,$o,X2,X4)
| X1 ) ),
inference(rectify,[],[f24]) ).
thf(f24,axiom,
! [X0: $tType,X11: $o,X13: X0 > $o] :
( ! [X12: X0] :
( vAPP(X0,$o,X13,X12)
| X11 )
<=> ( ! [X14: X0] : vAPP(X0,$o,X13,X14)
| X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__FORALL__OR__THM) ).
thf(f5544,plain,
spl42_101,
inference(avatar_split_clause,[],[f450,f5542]) ).
thf(f5542,plain,
( spl42_101
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_101])]) ).
thf(f450,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 ) ),
inference(cnf_transformation,[],[f244]) ).
thf(f244,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( ( ( ( $true != X0 )
& ( $true != X1 ) )
| ( $true != X2 ) )
& ( ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 ) ) ) )
& ( ( ( ( $true = X2 )
| ( ( $true != X0 )
& ( $true != X1 ) ) )
& ( ( $true = X0 )
| ( $true = X1 )
| ( $true != X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) ) ) ),
inference(flattening,[],[f243]) ).
thf(f243,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( ( ( ( $true != X0 )
& ( $true != X1 ) )
| ( $true != X2 ) )
& ( ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 ) ) ) )
& ( ( ( ( $true = X2 )
| ( ( $true != X0 )
& ( $true != X1 ) ) )
& ( ( $true = X0 )
| ( $true = X1 )
| ( $true != X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f153]) ).
thf(f5540,plain,
spl42_100,
inference(avatar_split_clause,[],[f413,f5538]) ).
thf(f5538,plain,
( spl42_100
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_100])]) ).
thf(f413,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f230]) ).
thf(f230,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) )
| ( ( $true != X0 )
& ( $true != X1 )
& ( $true != X2 ) ) )
& ( ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) ) ),
inference(flattening,[],[f229]) ).
thf(f229,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) )
| ( ( $true != X0 )
& ( $true != X1 )
& ( $true != X2 ) ) )
& ( ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f143]) ).
thf(f143,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) )
<=> ( ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f5536,plain,
spl42_99,
inference(avatar_split_clause,[],[f395,f5534]) ).
thf(f5534,plain,
( spl42_99
<=> ! [X0: $tType,X6: X0,X2: X0 > $o,X1: $o] :
( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK26(X0),X2),X1)) )
| ( $true = X1 )
| ( $true != vAPP(X0,$o,X2,X6) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_99])]) ).
thf(f395,plain,
! [X0: $tType,X2: X0 > $o,X1: $o,X6: X0] :
( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK26(X0),X2),X1)) )
| ( $true = X1 )
| ( $true != vAPP(X0,$o,X2,X6) ) ),
inference(cnf_transformation,[],[f219]) ).
thf(f219,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK25(X0),X2)) )
| ( $true = X1 )
| ! [X4: X0] :
( ( $true != vAPP(X0,$o,X2,X4) )
& ( $true != X1 ) ) )
& ( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK26(X0),X2),X1)) )
| ( $true = X1 )
| ( ! [X6: X0] : ( $true != vAPP(X0,$o,X2,X6) )
& ( $true != X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f216,f218,f217]) ).
thf(f217,plain,
! [X0: $tType,X2: X0 > $o] :
( ? [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
=> ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK25(X0),X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f218,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ? [X5: X0] :
( ( $true = vAPP(X0,$o,X2,X5) )
| ( $true = X1 ) )
=> ( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK26(X0),X2),X1)) )
| ( $true = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f216,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ? [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 )
| ! [X4: X0] :
( ( $true != vAPP(X0,$o,X2,X4) )
& ( $true != X1 ) ) )
& ( ? [X5: X0] :
( ( $true = vAPP(X0,$o,X2,X5) )
| ( $true = X1 ) )
| ( ! [X6: X0] : ( $true != vAPP(X0,$o,X2,X6) )
& ( $true != X1 ) ) ) ),
inference(rectify,[],[f215]) ).
thf(f215,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ? [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 )
| ! [X4: X0] :
( ( $true != vAPP(X0,$o,X2,X4) )
& ( $true != X1 ) ) )
& ( ? [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
| ( $true = X1 ) )
| ( ! [X3: X0] : ( $true != vAPP(X0,$o,X2,X3) )
& ( $true != X1 ) ) ) ),
inference(flattening,[],[f214]) ).
thf(f214,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ? [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 )
| ! [X4: X0] :
( ( $true != vAPP(X0,$o,X2,X4) )
& ( $true != X1 ) ) )
& ( ? [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
| ( $true = X1 ) )
| ( ! [X3: X0] : ( $true != vAPP(X0,$o,X2,X3) )
& ( $true != X1 ) ) ) ),
inference(nnf_transformation,[],[f92]) ).
thf(f92,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ? [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 ) )
<=> ? [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
| ( $true = X1 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f91,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ? [X3: X0] : vAPP(X0,$o,X2,X3)
| X1 )
<=> ? [X4: X0] :
( vAPP(X0,$o,X2,X4)
| X1 ) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X0: $tType,X11: $o,X13: X0 > $o] :
( ( ? [X12: X0] : vAPP(X0,$o,X13,X12)
| X11 )
<=> ? [X14: X0] :
( vAPP(X0,$o,X13,X14)
| X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__OR__EXISTS__THM) ).
thf(f5274,plain,
spl42_98,
inference(avatar_split_clause,[],[f636,f5272]) ).
thf(f5272,plain,
( spl42_98
<=> ! [X0: $tType,X4: X0,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK37(X0),$true),X1)) )
| ( $true != vAPP(X0,$o,X1,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_98])]) ).
thf(f636,plain,
! [X0: $tType,X1: X0 > $o,X4: X0] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK37(X0),$true),X1)) )
| ( $true != vAPP(X0,$o,X1,X4) ) ),
inference(equality_resolution,[],[f494]) ).
thf(f494,plain,
! [X0: $tType,X2: $o,X1: X0 > $o,X4: X0] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK37(X0),X2),X1)) )
| ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X4) ) ),
inference(cnf_transformation,[],[f288]) ).
thf(f288,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK37(X0),X2),X1)) ) )
| ( $true != X2 )
| ! [X4: X0] : ( $true != vAPP(X0,$o,X1,X4) ) )
& ( ( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK38(X0),X1)) ) )
| ! [X6: X0] :
( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X6) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f285,f287,f286]) ).
thf(f286,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ? [X3: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X3) ) )
=> ( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK37(X0),X2),X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f287,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X5: X0] : ( $true = vAPP(X0,$o,X1,X5) )
=> ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK38(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f285,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ? [X3: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X3) ) )
| ( $true != X2 )
| ! [X4: X0] : ( $true != vAPP(X0,$o,X1,X4) ) )
& ( ( ( $true = X2 )
& ? [X5: X0] : ( $true = vAPP(X0,$o,X1,X5) ) )
| ! [X6: X0] :
( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X6) ) ) ) ),
inference(rectify,[],[f284]) ).
thf(f284,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ? [X3: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X3) ) )
| ( $true != X2 )
| ! [X4: X0] : ( $true != vAPP(X0,$o,X1,X4) ) )
& ( ( ( $true = X2 )
& ? [X4: X0] : ( $true = vAPP(X0,$o,X1,X4) ) )
| ! [X3: X0] :
( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X3) ) ) ) ),
inference(flattening,[],[f283]) ).
thf(f283,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ? [X3: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X3) ) )
| ( $true != X2 )
| ! [X4: X0] : ( $true != vAPP(X0,$o,X1,X4) ) )
& ( ( ( $true = X2 )
& ? [X4: X0] : ( $true = vAPP(X0,$o,X1,X4) ) )
| ! [X3: X0] :
( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X3) ) ) ) ),
inference(nnf_transformation,[],[f110]) ).
thf(f110,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ? [X3: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X3) ) )
<=> ( ( $true = X2 )
& ? [X4: X0] : ( $true = vAPP(X0,$o,X1,X4) ) ) ),
inference(fool_elimination,[],[f109]) ).
thf(f109,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ? [X3: X0] :
( X2
& vAPP(X0,$o,X1,X3) )
<=> ( X2
& ? [X4: X0] : vAPP(X0,$o,X1,X4) ) ),
inference(rectify,[],[f21]) ).
thf(f21,axiom,
! [X0: $tType,X11: X0 > $o,X13: $o] :
( ? [X12: X0] :
( X13
& vAPP(X0,$o,X11,X12) )
<=> ( X13
& ? [X14: X0] : vAPP(X0,$o,X11,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__EXISTS__AND__THM) ).
thf(f5270,plain,
spl42_97,
inference(avatar_split_clause,[],[f569,f5268]) ).
thf(f5268,plain,
( spl42_97
<=> ! [X0: $tType,X1: X0 > $o,X3: X0] :
( ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK19(X0),$true),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_97])]) ).
thf(f569,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK19(X0),$true),X1)) ) ),
inference(equality_resolution,[],[f384]) ).
thf(f384,plain,
! [X0: $tType,X2: $o,X3: X0,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK19(X0),X2),X1)) ) ),
inference(cnf_transformation,[],[f201]) ).
thf(f201,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( ( $true = X2 )
& ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) ) )
| ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK19(X0),X2),X1)) ) )
& ( ! [X5: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X5) ) )
| ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK20(X0),X1)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f198,f200,f199]) ).
thf(f199,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ? [X4: X0] :
( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X4) ) )
=> ( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP($o,sTfun(sTfun(X0,$o),X0),sK19(X0),X2),X1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f200,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X6: X0] : ( $true != vAPP(X0,$o,X1,X6) )
=> ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK20(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f198,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( ( $true = X2 )
& ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) ) )
| ? [X4: X0] :
( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X4) ) ) )
& ( ! [X5: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X5) ) )
| ( $true != X2 )
| ? [X6: X0] : ( $true != vAPP(X0,$o,X1,X6) ) ) ),
inference(rectify,[],[f197]) ).
thf(f197,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( ( $true = X2 )
& ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) ) )
| ? [X4: X0] :
( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X4) ) ) )
& ( ! [X4: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X4) ) )
| ( $true != X2 )
| ? [X3: X0] : ( $true != vAPP(X0,$o,X1,X3) ) ) ),
inference(flattening,[],[f196]) ).
thf(f196,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( ( $true = X2 )
& ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) ) )
| ? [X4: X0] :
( ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X4) ) ) )
& ( ! [X4: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X4) ) )
| ( $true != X2 )
| ? [X3: X0] : ( $true != vAPP(X0,$o,X1,X3) ) ) ),
inference(nnf_transformation,[],[f86]) ).
thf(f86,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( ( $true = X2 )
& ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) ) )
<=> ! [X4: X0] :
( ( $true = X2 )
& ( $true = vAPP(X0,$o,X1,X4) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f85,plain,
! [X0: $tType,X1: X0 > $o,X2: $o] :
( ( X2
& ! [X3: X0] : vAPP(X0,$o,X1,X3) )
<=> ! [X4: X0] :
( X2
& vAPP(X0,$o,X1,X4) ) ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X0: $tType,X11: X0 > $o,X13: $o] :
( ( X13
& ! [X12: X0] : vAPP(X0,$o,X11,X12) )
<=> ! [X14: X0] :
( X13
& vAPP(X0,$o,X11,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__FORALL__THM) ).
thf(f5250,plain,
( spl42_96
| spl42_30
| ~ spl42_49 ),
inference(avatar_split_clause,[],[f1771,f1346,f1066,f5247]) ).
thf(f5247,plain,
( spl42_96
<=> ( $false = vAPP(sTfun($o,$o),$o,sK38($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_96])]) ).
thf(f1346,plain,
( spl42_49
<=> ! [X0: $tType,X6: X0,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK38(X0),X1)) )
| ( $true != vAPP(X0,$o,X1,X6) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_49])]) ).
thf(f1771,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP(sTfun($o,$o),$o,sK38($o),vNOT) ) )
| ~ spl42_49 ),
inference(not_proxy_clausification,[],[f1770]) ).
thf(f1770,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK38($o),vNOT)) ) )
| ~ spl42_49 ),
inference(not_proxy_clausification,[],[f1710]) ).
thf(f1710,plain,
( ! [X0: $o] :
( ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK38($o),vNOT)) ) )
| ~ spl42_49 ),
inference(primitive_instantiation,[],[f1347]) ).
thf(f1347,plain,
( ! [X0: $tType,X1: X0 > $o,X6: X0] :
( ( $true != vAPP(X0,$o,X1,X6) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK38(X0),X1)) ) )
| ~ spl42_49 ),
inference(avatar_component_clause,[],[f1346]) ).
thf(f4770,plain,
spl42_95,
inference(avatar_split_clause,[],[f662,f4768]) ).
thf(f4768,plain,
( spl42_95
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_95])]) ).
thf(f662,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f423]) ).
thf(f423,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f234]) ).
thf(f4766,plain,
spl42_94,
inference(avatar_split_clause,[],[f661,f4764]) ).
thf(f4764,plain,
( spl42_94
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_94])]) ).
thf(f661,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f422]) ).
thf(f422,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f234]) ).
thf(f4762,plain,
spl42_93,
inference(avatar_split_clause,[],[f651,f4760]) ).
thf(f4760,plain,
( spl42_93
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_93])]) ).
thf(f651,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f441]) ).
thf(f441,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f242]) ).
thf(f4758,plain,
spl42_92,
inference(avatar_split_clause,[],[f650,f4756]) ).
thf(f4756,plain,
( spl42_92
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X2 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_92])]) ).
thf(f650,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X2 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f440]) ).
thf(f440,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f242]) ).
thf(f4754,plain,
spl42_91,
inference(avatar_split_clause,[],[f644,f4752]) ).
thf(f4752,plain,
( spl42_91
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_91])]) ).
thf(f644,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f460]) ).
thf(f460,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f251]) ).
thf(f4750,plain,
spl42_90,
inference(avatar_split_clause,[],[f631,f4748]) ).
thf(f4748,plain,
( spl42_90
<=> ! [X0: $tType,X2: X0 > $o,X4: X0] :
( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK35(X0),X2),$true)) )
| ( $true != vAPP(X0,$o,X2,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_90])]) ).
thf(f631,plain,
! [X0: $tType,X2: X0 > $o,X4: X0] :
( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK35(X0),X2),$true)) )
| ( $true != vAPP(X0,$o,X2,X4) ) ),
inference(equality_resolution,[],[f491]) ).
thf(f491,plain,
! [X0: $tType,X2: X0 > $o,X1: $o,X4: X0] :
( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK35(X0),X2),X1)) )
| ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f282]) ).
thf(f282,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK35(X0),X2),X1)) )
& ( $true = X1 ) )
| ! [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) )
& ( ( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK36(X0),X2)) )
& ( $true = X1 ) )
| ! [X6: X0] :
( ( $true != vAPP(X0,$o,X2,X6) )
| ( $true != X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f279,f281,f280]) ).
thf(f280,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ? [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
=> ( ( $true = vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK35(X0),X2),X1)) )
& ( $true = X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f281,plain,
! [X0: $tType,X2: X0 > $o] :
( ? [X5: X0] : ( $true = vAPP(X0,$o,X2,X5) )
=> ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK36(X0),X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f279,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ? [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
| ! [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) )
& ( ( ? [X5: X0] : ( $true = vAPP(X0,$o,X2,X5) )
& ( $true = X1 ) )
| ! [X6: X0] :
( ( $true != vAPP(X0,$o,X2,X6) )
| ( $true != X1 ) ) ) ),
inference(rectify,[],[f278]) ).
thf(f278,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ? [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
| ! [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) )
& ( ( ? [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) )
& ( $true = X1 ) )
| ! [X3: X0] :
( ( $true != vAPP(X0,$o,X2,X3) )
| ( $true != X1 ) ) ) ),
inference(flattening,[],[f277]) ).
thf(f277,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ? [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
| ! [X4: X0] : ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) )
& ( ( ? [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) )
& ( $true = X1 ) )
| ! [X3: X0] :
( ( $true != vAPP(X0,$o,X2,X3) )
| ( $true != X1 ) ) ) ),
inference(nnf_transformation,[],[f108]) ).
thf(f108,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ? [X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
<=> ( ? [X4: X0] : ( $true = vAPP(X0,$o,X2,X4) )
& ( $true = X1 ) ) ),
inference(fool_elimination,[],[f107]) ).
thf(f107,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ? [X3: X0] :
( vAPP(X0,$o,X2,X3)
& X1 )
<=> ( ? [X4: X0] : vAPP(X0,$o,X2,X4)
& X1 ) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X0: $tType,X11: $o,X13: X0 > $o] :
( ? [X12: X0] :
( vAPP(X0,$o,X13,X12)
& X11 )
<=> ( ? [X14: X0] : vAPP(X0,$o,X13,X14)
& X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__EXISTS__AND__THM) ).
thf(f4746,plain,
spl42_89,
inference(avatar_split_clause,[],[f622,f4744]) ).
thf(f4744,plain,
( spl42_89
<=> ! [X2: $o,X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),$true),X0) )
| ( $true = X0 )
| ( $true = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_89])]) ).
thf(f622,plain,
! [X2: $o,X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),$true),X0) )
| ( $true = X0 )
| ( $true = X2 ) ),
inference(equality_resolution,[],[f469]) ).
thf(f469,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
| ( $true = X0 )
| ( $true != X1 )
| ( $true = X2 ) ),
inference(cnf_transformation,[],[f253]) ).
thf(f253,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
| ( ( ( ( $true != X0 )
& ( $true = X1 ) )
| ( $true != X2 ) )
& ( ( $true = X0 )
| ( $true != X1 )
| ( $true = X2 ) ) ) )
& ( ( ( ( $true = X2 )
| ( ( $true != X0 )
& ( $true = X1 ) ) )
& ( ( $true = X0 )
| ( $true != X1 )
| ( $true != X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ) ),
inference(flattening,[],[f252]) ).
thf(f252,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
| ( ( ( ( $true != X0 )
& ( $true = X1 ) )
| ( $true != X2 ) )
& ( ( $true = X0 )
| ( $true != X1 )
| ( $true = X2 ) ) ) )
& ( ( ( ( $true = X2 )
| ( ( $true != X0 )
& ( $true = X1 ) ) )
& ( ( $true = X0 )
| ( $true != X1 )
| ( $true != X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f157]) ).
thf(f4742,plain,
spl42_88,
inference(avatar_split_clause,[],[f611,f4740]) ).
thf(f4740,plain,
( spl42_88
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_88])]) ).
thf(f611,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),X1),X0) ) ),
inference(equality_resolution,[],[f447]) ).
thf(f447,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f244]) ).
thf(f4738,plain,
spl42_87,
inference(avatar_split_clause,[],[f572,f4736]) ).
thf(f4736,plain,
( spl42_87
<=> ! [X0: $tType,X2: X0 > $o,X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK21(X0),X2),$true)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_87])]) ).
thf(f572,plain,
! [X0: $tType,X2: X0 > $o,X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK21(X0),X2),$true)) ) ),
inference(equality_resolution,[],[f389]) ).
thf(f389,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: $o] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK21(X0),X2),X1)) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f207]) ).
thf(f207,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ( ! [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
| ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK21(X0),X2),X1)) )
| ( $true != X1 ) )
& ( ! [X5: X0] :
( ( $true = vAPP(X0,$o,X2,X5) )
& ( $true = X1 ) )
| ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK22(X0),X2)) )
| ( $true != X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f204,f206,f205]) ).
thf(f205,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ? [X4: X0] :
( ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) )
=> ( ( $true != vAPP(X0,$o,X2,vAPP($o,X0,vAPP(sTfun(X0,$o),sTfun($o,X0),sK21(X0),X2),X1)) )
| ( $true != X1 ) ) ),
introduced(choice_axiom,[]) ).
thf(f206,plain,
! [X0: $tType,X2: X0 > $o] :
( ? [X6: X0] : ( $true != vAPP(X0,$o,X2,X6) )
=> ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK22(X0),X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f204,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ( ! [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
| ? [X4: X0] :
( ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) ) )
& ( ! [X5: X0] :
( ( $true = vAPP(X0,$o,X2,X5) )
& ( $true = X1 ) )
| ? [X6: X0] : ( $true != vAPP(X0,$o,X2,X6) )
| ( $true != X1 ) ) ),
inference(rectify,[],[f203]) ).
thf(f203,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ( ! [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
| ? [X4: X0] :
( ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) ) )
& ( ! [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
& ( $true = X1 ) )
| ? [X3: X0] : ( $true != vAPP(X0,$o,X2,X3) )
| ( $true != X1 ) ) ),
inference(flattening,[],[f202]) ).
thf(f202,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ( ! [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
| ? [X4: X0] :
( ( $true != vAPP(X0,$o,X2,X4) )
| ( $true != X1 ) ) )
& ( ! [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
& ( $true = X1 ) )
| ? [X3: X0] : ( $true != vAPP(X0,$o,X2,X3) )
| ( $true != X1 ) ) ),
inference(nnf_transformation,[],[f88]) ).
thf(f88,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] : ( $true = vAPP(X0,$o,X2,X3) )
& ( $true = X1 ) )
<=> ! [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
& ( $true = X1 ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f87,plain,
! [X0: $tType,X1: $o,X2: X0 > $o] :
( ( ! [X3: X0] : vAPP(X0,$o,X2,X3)
& X1 )
<=> ! [X4: X0] :
( vAPP(X0,$o,X2,X4)
& X1 ) ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
! [X0: $tType,X11: $o,X13: X0 > $o] :
( ( ! [X12: X0] : vAPP(X0,$o,X13,X12)
& X11 )
<=> ! [X14: X0] :
( vAPP(X0,$o,X13,X14)
& X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__AND__FORALL__THM) ).
thf(f4734,plain,
( spl42_86
| spl42_30
| ~ spl42_48 ),
inference(avatar_split_clause,[],[f1689,f1342,f1066,f4731]) ).
thf(f4731,plain,
( spl42_86
<=> ( $false = vAPP(sTfun($o,$o),$o,sK36($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_86])]) ).
thf(f1342,plain,
( spl42_48
<=> ! [X0: $tType,X6: X0,X2: X0 > $o] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK36(X0),X2)) )
| ( $true != vAPP(X0,$o,X2,X6) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_48])]) ).
thf(f1689,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP(sTfun($o,$o),$o,sK36($o),vNOT) ) )
| ~ spl42_48 ),
inference(not_proxy_clausification,[],[f1688]) ).
thf(f1688,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK36($o),vNOT)) ) )
| ~ spl42_48 ),
inference(not_proxy_clausification,[],[f1628]) ).
thf(f1628,plain,
( ! [X0: $o] :
( ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK36($o),vNOT)) ) )
| ~ spl42_48 ),
inference(primitive_instantiation,[],[f1343]) ).
thf(f1343,plain,
( ! [X0: $tType,X2: X0 > $o,X6: X0] :
( ( $true != vAPP(X0,$o,X2,X6) )
| ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK36(X0),X2)) ) )
| ~ spl42_48 ),
inference(avatar_component_clause,[],[f1342]) ).
thf(f4729,plain,
spl42_85,
inference(avatar_split_clause,[],[f467,f4727]) ).
thf(f4727,plain,
( spl42_85
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_85])]) ).
thf(f467,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f253]) ).
thf(f4725,plain,
spl42_84,
inference(avatar_split_clause,[],[f459,f4723]) ).
thf(f4723,plain,
( spl42_84
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_84])]) ).
thf(f459,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP15,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f251]) ).
thf(f4721,plain,
spl42_83,
inference(avatar_split_clause,[],[f432,f4719]) ).
thf(f4719,plain,
( spl42_83
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( $true = X0 )
| ( $true = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_83])]) ).
thf(f432,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( $true = X0 )
| ( $true = X2 ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f236,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( ( ( $true != X0 )
| ( $true != X1 )
| ( $true != X2 ) )
& ( ( ( $true = X0 )
& ( $true = X1 ) )
| ( $true = X2 ) ) ) )
& ( ( ( ( $true = X2 )
| ( $true != X0 )
| ( $true != X1 ) )
& ( ( ( $true = X0 )
& ( $true = X1 ) )
| ( $true != X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) ) ) ),
inference(flattening,[],[f235]) ).
thf(f235,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( ( ( $true != X0 )
| ( $true != X1 )
| ( $true != X2 ) )
& ( ( ( $true = X0 )
& ( $true = X1 ) )
| ( $true = X2 ) ) ) )
& ( ( ( ( $true = X2 )
| ( $true != X0 )
| ( $true != X1 ) )
& ( ( ( $true = X0 )
& ( $true = X1 ) )
| ( $true != X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) ) ) ),
inference(nnf_transformation,[],[f149]) ).
thf(f4717,plain,
spl42_82,
inference(avatar_split_clause,[],[f431,f4715]) ).
thf(f4715,plain,
( spl42_82
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( $true = X1 )
| ( $true = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_82])]) ).
thf(f431,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( $true = X1 )
| ( $true = X2 ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f4693,plain,
spl42_81,
inference(avatar_split_clause,[],[f351,f4691]) ).
thf(f4691,plain,
( spl42_81
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_81])]) ).
thf(f351,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(cnf_transformation,[],[f170]) ).
thf(f170,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) )
& ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ) ),
inference(nnf_transformation,[],[f140]) ).
thf(f140,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(definition_folding,[],[f133,f139,f138]) ).
thf(f138,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
<=> ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f139,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
<=> ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f133,plain,
! [X0: $o,X1: $o] :
( ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) )
<=> ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = X1 ) ) ) ),
inference(flattening,[],[f132]) ).
thf(f132,plain,
! [X0: $o,X1: $o] :
( ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) )
<=> ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = X1 ) ) ) ),
inference(ennf_transformation,[],[f68]) ).
thf(f68,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) )
=> ( c_2Ebool_2EF = $true ) )
<=> ( ( ( $true = X1 )
=> ( c_2Ebool_2EF = $true ) )
=> ( ( $true = vAPP($o,$o,vNOT,X0) )
=> ( c_2Ebool_2EF = $true ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f67,plain,
! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,
( X0
| X1 ))
=> c_2Ebool_2EF )
<=> ( ( X1
=> c_2Ebool_2EF )
=> ( vAPP($o,$o,vNOT,X0)
=> c_2Ebool_2EF ) ) ),
inference(rectify,[],[f30]) ).
thf(f30,axiom,
! [X26: $o,X27: $o] :
( ( vAPP($o,$o,vNOT,
( X26
| X27 ))
=> c_2Ebool_2EF )
<=> ( ( X27
=> c_2Ebool_2EF )
=> ( vAPP($o,$o,vNOT,X26)
=> c_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).
thf(f4689,plain,
spl42_80,
inference(avatar_split_clause,[],[f350,f4687]) ).
thf(f4687,plain,
( spl42_80
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_80])]) ).
thf(f350,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f170]) ).
thf(f4332,plain,
( spl42_79
| ~ spl42_29
| ~ spl42_55 ),
inference(avatar_split_clause,[],[f4216,f2200,f1062,f4329]) ).
thf(f4329,plain,
( spl42_79
<=> ( $false = vAPP(sTfun($o,$o),$o,sK17($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_79])]) ).
thf(f1062,plain,
( spl42_29
<=> ( $true = vAPP(sTfun($o,$o),$o,c_2Ebool_2E_3F($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_29])]) ).
thf(f2200,plain,
( spl42_55
<=> ! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK17(X0),X1)) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_55])]) ).
thf(f4216,plain,
( ( $false = vAPP(sTfun($o,$o),$o,sK17($o),vNOT) )
| ~ spl42_29
| ~ spl42_55 ),
inference(not_proxy_clausification,[],[f4215]) ).
thf(f4215,plain,
( ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK17($o),vNOT)) )
| ~ spl42_29
| ~ spl42_55 ),
inference(trivial_inequality_removal,[],[f4204]) ).
thf(f4204,plain,
( ( $true != $true )
| ( $true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK17($o),vNOT)) )
| ~ spl42_29
| ~ spl42_55 ),
inference(superposition,[],[f2201,f1064]) ).
thf(f1064,plain,
( ( $true = vAPP(sTfun($o,$o),$o,c_2Ebool_2E_3F($o),vNOT) )
| ~ spl42_29 ),
inference(avatar_component_clause,[],[f1062]) ).
thf(f2201,plain,
( ! [X0: $tType,X1: X0 > $o] :
( ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK17(X0),X1)) ) )
| ~ spl42_55 ),
inference(avatar_component_clause,[],[f2200]) ).
thf(f4113,plain,
spl42_78,
inference(avatar_split_clause,[],[f678,f4111]) ).
thf(f4111,plain,
( spl42_78
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_78])]) ).
thf(f678,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) )
| ( $true = X0 ) ),
inference(not_proxy_clausification,[],[f408]) ).
thf(f408,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f4109,plain,
spl42_77,
inference(avatar_split_clause,[],[f677,f4107]) ).
thf(f4107,plain,
( spl42_77
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_77])]) ).
thf(f677,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) )
| ( $true = X1 ) ),
inference(not_proxy_clausification,[],[f407]) ).
thf(f407,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f4083,plain,
spl42_76,
inference(avatar_split_clause,[],[f674,f4081]) ).
thf(f4081,plain,
( spl42_76
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_76])]) ).
thf(f674,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) )
| ( $true = X0 ) ),
inference(not_proxy_clausification,[],[f412]) ).
thf(f412,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) ) ),
inference(cnf_transformation,[],[f228]) ).
thf(f4079,plain,
spl42_75,
inference(avatar_split_clause,[],[f673,f4077]) ).
thf(f4077,plain,
( spl42_75
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_75])]) ).
thf(f673,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) )
| ( $true = X1 ) ),
inference(not_proxy_clausification,[],[f411]) ).
thf(f411,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) ) ),
inference(cnf_transformation,[],[f228]) ).
thf(f4075,plain,
spl42_74,
inference(avatar_split_clause,[],[f660,f4073]) ).
thf(f4073,plain,
( spl42_74
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_74])]) ).
thf(f660,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true = X0 ) ),
inference(not_proxy_clausification,[],[f437]) ).
thf(f437,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) ) ),
inference(cnf_transformation,[],[f238]) ).
thf(f4071,plain,
spl42_73,
inference(avatar_split_clause,[],[f659,f4069]) ).
thf(f4069,plain,
( spl42_73
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_73])]) ).
thf(f659,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true = X1 ) ),
inference(not_proxy_clausification,[],[f436]) ).
thf(f436,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) ) ),
inference(cnf_transformation,[],[f238]) ).
thf(f4067,plain,
spl42_72,
inference(avatar_split_clause,[],[f649,f4065]) ).
thf(f4065,plain,
( spl42_72
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_72])]) ).
thf(f649,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true = X0 ) ),
inference(not_proxy_clausification,[],[f456]) ).
thf(f456,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) ) ),
inference(cnf_transformation,[],[f247]) ).
thf(f4063,plain,
spl42_71,
inference(avatar_split_clause,[],[f643,f4061]) ).
thf(f4061,plain,
( spl42_71
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_71])]) ).
thf(f643,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true = X0 ) ),
inference(not_proxy_clausification,[],[f475]) ).
thf(f475,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) ) ),
inference(cnf_transformation,[],[f256]) ).
thf(f4059,plain,
spl42_70,
inference(avatar_split_clause,[],[f642,f4057]) ).
thf(f4057,plain,
( spl42_70
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_70])]) ).
thf(f642,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true = X2 ) ),
inference(not_proxy_clausification,[],[f473]) ).
thf(f473,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( vAPP($o,$o,vNOT,X2) != $true ) ),
inference(cnf_transformation,[],[f256]) ).
thf(f4055,plain,
spl42_69,
inference(avatar_split_clause,[],[f625,f4053]) ).
thf(f4053,plain,
( spl42_69
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,$true),$true),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_69])]) ).
thf(f625,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,$true),$true),X0) ) ),
inference(equality_resolution,[],[f624]) ).
thf(f624,plain,
! [X2: $o,X0: $o] :
( ( $true = X0 )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),$true),X0) ) ),
inference(equality_resolution,[],[f466]) ).
thf(f466,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != X1 )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f253]) ).
thf(f4051,plain,
spl42_68,
inference(avatar_split_clause,[],[f623,f4049]) ).
thf(f4049,plain,
( spl42_68
<=> ! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_68])]) ).
thf(f623,plain,
! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),$true) ) ),
inference(equality_resolution,[],[f468]) ).
thf(f468,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f253]) ).
thf(f2647,plain,
( spl42_30
| ~ spl42_52
| ~ spl42_67 ),
inference(avatar_split_clause,[],[f2646,f2642,f1594,f1066]) ).
thf(f1594,plain,
( spl42_52
<=> ! [X0: $o] : ( $false = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_52])]) ).
thf(f2642,plain,
( spl42_67
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,$true),X1),X0) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_67])]) ).
thf(f2646,plain,
( ! [X1: $o] : ( $true = X1 )
| ~ spl42_52
| ~ spl42_67 ),
inference(trivial_inequality_removal,[],[f2645]) ).
thf(f2645,plain,
( ! [X1: $o] :
( ( $true = $false )
| ( $true = X1 ) )
| ~ spl42_52
| ~ spl42_67 ),
inference(forward_demodulation,[],[f2643,f1595]) ).
thf(f1595,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl42_52 ),
inference(avatar_component_clause,[],[f1594]) ).
thf(f2643,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,$true),X1),X0) )
| ( $true = X1 ) )
| ~ spl42_67 ),
inference(avatar_component_clause,[],[f2642]) ).
thf(f2644,plain,
spl42_67,
inference(avatar_split_clause,[],[f621,f2642]) ).
thf(f621,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,$true),X1),X0) )
| ( $true = X1 ) ),
inference(equality_resolution,[],[f470]) ).
thf(f470,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
| ( $true = X1 )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f253]) ).
thf(f2639,plain,
spl42_66,
inference(avatar_split_clause,[],[f610,f2637]) ).
thf(f2637,plain,
( spl42_66
<=> ! [X2: $o,X0: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),$true),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_66])]) ).
thf(f610,plain,
! [X2: $o,X0: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),$true),X0) ) ),
inference(equality_resolution,[],[f448]) ).
thf(f448,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true != X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f244]) ).
thf(f2634,plain,
spl42_65,
inference(avatar_split_clause,[],[f609,f2632]) ).
thf(f2632,plain,
( spl42_65
<=> ! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_65])]) ).
thf(f609,plain,
! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),$true) ) ),
inference(equality_resolution,[],[f449]) ).
thf(f449,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f244]) ).
thf(f2630,plain,
( spl42_52
| spl42_64
| ~ spl42_32 ),
inference(avatar_split_clause,[],[f1453,f1274,f2627,f1594]) ).
thf(f2627,plain,
( spl42_64
<=> ( $true = vAPP(sTfun($o,$o),$o,sK22($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_64])]) ).
thf(f1274,plain,
( spl42_32
<=> ! [X0: $tType,X2: X0 > $o,X5: X0] :
( ( $true = vAPP(X0,$o,X2,X5) )
| ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK22(X0),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_32])]) ).
thf(f1453,plain,
( ! [X0: $o] :
( ( $true = vAPP(sTfun($o,$o),$o,sK22($o),vNOT) )
| ( $false = X0 ) )
| ~ spl42_32 ),
inference(not_proxy_clausification,[],[f1452]) ).
thf(f1452,plain,
( ! [X0: $o] :
( ( $true = vAPP(sTfun($o,$o),$o,sK22($o),vNOT) )
| ( $true = vAPP($o,$o,vNOT,X0) ) )
| ~ spl42_32 ),
inference(not_proxy_clausification,[],[f1419]) ).
thf(f1419,plain,
( ! [X0: $o] :
( ( $true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK22($o),vNOT)) )
| ( $true = vAPP($o,$o,vNOT,X0) ) )
| ~ spl42_32 ),
inference(primitive_instantiation,[],[f1275]) ).
thf(f1275,plain,
( ! [X0: $tType,X2: X0 > $o,X5: X0] :
( ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK22(X0),X2)) )
| ( $true = vAPP(X0,$o,X2,X5) ) )
| ~ spl42_32 ),
inference(avatar_component_clause,[],[f1274]) ).
thf(f2625,plain,
spl42_63,
inference(avatar_split_clause,[],[f600,f2623]) ).
thf(f2623,plain,
( spl42_63
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_63])]) ).
thf(f600,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X1),X0) ) ),
inference(equality_resolution,[],[f428]) ).
thf(f428,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f2621,plain,
spl42_62,
inference(avatar_split_clause,[],[f599,f2619]) ).
thf(f2619,plain,
( spl42_62
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_62])]) ).
thf(f599,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X1),X0) ) ),
inference(equality_resolution,[],[f429]) ).
thf(f429,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f2617,plain,
spl42_61,
inference(avatar_split_clause,[],[f598,f2615]) ).
thf(f2615,plain,
( spl42_61
<=> ! [X2: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),$true),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_61])]) ).
thf(f598,plain,
! [X2: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),$true),$true) ) ),
inference(equality_resolution,[],[f597]) ).
thf(f597,plain,
! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),$true) ) ),
inference(equality_resolution,[],[f430]) ).
thf(f430,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true != X0 )
| ( $true != X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f2613,plain,
spl42_60,
inference(avatar_split_clause,[],[f586,f2611]) ).
thf(f2611,plain,
( spl42_60
<=> ! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X1),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_60])]) ).
thf(f586,plain,
! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X1),X1),X2) ) ),
inference(equality_resolution,[],[f420]) ).
thf(f420,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( X0 != X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f231,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( ( ( $true = X2 )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( $true != X2 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
& ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) )
| ( ( ( X0 != X1 )
| ( $true != X2 ) )
& ( ( X0 = X1 )
| ( $true = X2 ) ) ) ) ),
inference(nnf_transformation,[],[f147]) ).
thf(f147,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( X0 = X1 ) )
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ),
inference(definition_folding,[],[f94,f146,f145,f144,f143]) ).
thf(f94,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( X0 = X1 ) )
<=> ( ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 ) )
& ( ( vAPP($o,$o,vNOT,X2) = $true )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 ) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X2 ) )
& ( ( $true = X0 )
| ( $true = X1 )
| ( $true = X2 ) ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f93,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( X2
<=> ( X0 = X1 ) )
<=> ( ( vAPP($o,$o,vNOT,X2)
| vAPP($o,$o,vNOT,X1)
| X0 )
& ( vAPP($o,$o,vNOT,X2)
| vAPP($o,$o,vNOT,X0)
| X1 )
& ( vAPP($o,$o,vNOT,X1)
| vAPP($o,$o,vNOT,X0)
| X2 )
& ( X0
| X1
| X2 ) ) ),
inference(rectify,[],[f33]) ).
thf(f33,axiom,
! [X28: $o,X29: $o,X30: $o] :
( ( X30
<=> ( X28 = X29 ) )
<=> ( ( vAPP($o,$o,vNOT,X30)
| vAPP($o,$o,vNOT,X29)
| X28 )
& ( vAPP($o,$o,vNOT,X30)
| vAPP($o,$o,vNOT,X28)
| X29 )
& ( vAPP($o,$o,vNOT,X29)
| vAPP($o,$o,vNOT,X28)
| X30 )
& ( X28
| X29
| X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq) ).
thf(f2512,plain,
( spl42_59
| spl42_30 ),
inference(avatar_split_clause,[],[f484,f1066,f2510]) ).
thf(f2510,plain,
( spl42_59
<=> ! [X0: $tType,X2: X0 > $o,X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK29(X0),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_59])]) ).
thf(f484,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: $o] :
( ( $true = X1 )
| ( $true = vAPP(X0,$o,X2,X3) )
| ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK29(X0),X2)) ) ),
inference(cnf_transformation,[],[f269]) ).
thf(f2411,plain,
( spl42_30
| spl42_58 ),
inference(avatar_split_clause,[],[f481,f2409,f1066]) ).
thf(f2409,plain,
( spl42_58
<=> ! [X0: $tType,X2: X0 > $o,X3: X0] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK27(X0),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_58])]) ).
thf(f481,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: $o] :
( ( $true = vAPP(X0,$o,X2,X3) )
| ( $true = X1 )
| ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK27(X0),X2)) ) ),
inference(cnf_transformation,[],[f263]) ).
thf(f2317,plain,
( spl42_30
| spl42_57 ),
inference(avatar_split_clause,[],[f397,f2315,f1066]) ).
thf(f2315,plain,
( spl42_57
<=> ! [X0: $tType,X2: X0 > $o,X4: X0] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK25(X0),X2)) )
| ( $true != vAPP(X0,$o,X2,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_57])]) ).
thf(f397,plain,
! [X0: $tType,X2: X0 > $o,X1: $o,X4: X0] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK25(X0),X2)) )
| ( $true = X1 )
| ( $true != vAPP(X0,$o,X2,X4) ) ),
inference(cnf_transformation,[],[f219]) ).
thf(f2206,plain,
( spl42_56
| spl42_30 ),
inference(avatar_split_clause,[],[f392,f1066,f2204]) ).
thf(f392,plain,
! [X0: $tType,X2: $o,X1: X0 > $o,X4: X0] :
( ( $true = X2 )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK23(X0),X1)) )
| ( $true != vAPP(X0,$o,X1,X4) ) ),
inference(cnf_transformation,[],[f213]) ).
thf(f2202,plain,
spl42_55,
inference(avatar_split_clause,[],[f367,f2200]) ).
thf(f367,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK17(X0),X1)) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ),
inference(cnf_transformation,[],[f184]) ).
thf(f184,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK17(X0),X1)) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f182,f183]) ).
thf(f183,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
=> ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK17(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f182,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
inference(rectify,[],[f181]) ).
thf(f181,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ? [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
inference(nnf_transformation,[],[f76]) ).
thf(f76,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
<=> ? [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f75,plain,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1)
<=> ? [X2: X0] : vAPP(X0,$o,X1,X2) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X0: $tType,X4: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X4)
<=> ? [X5: X0] : vAPP(X0,$o,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(f2198,plain,
spl42_54,
inference(avatar_split_clause,[],[f366,f2196]) ).
thf(f2196,plain,
( spl42_54
<=> ! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK16(X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_54])]) ).
thf(f366,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK16(X0),X1)) ) ),
inference(cnf_transformation,[],[f180]) ).
thf(f180,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK16(X0),X1)) ) )
& ( ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f178,f179]) ).
thf(f179,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) )
=> ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK16(X0),X1)) ) ),
introduced(choice_axiom,[]) ).
thf(f178,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
inference(rectify,[],[f177]) ).
thf(f177,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
| ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
& ( ! [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
inference(nnf_transformation,[],[f74]) ).
thf(f74,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
<=> ! [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f73,plain,
! [X0: $tType,X1: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1)
<=> ! [X2: X0] : vAPP(X0,$o,X1,X2) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X0: $tType,X4: X0 > $o] :
( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X4)
<=> ! [X5: X0] : vAPP(X0,$o,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(f1600,plain,
( spl42_52
| spl42_53
| ~ spl42_31 ),
inference(avatar_split_clause,[],[f1398,f1270,f1597,f1594]) ).
thf(f1597,plain,
( spl42_53
<=> ( $true = vAPP(sTfun($o,$o),$o,sK20($o),vNOT) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_53])]) ).
thf(f1270,plain,
( spl42_31
<=> ! [X0: $tType,X5: X0,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,X5) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK20(X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_31])]) ).
thf(f1398,plain,
( ! [X0: $o] :
( ( $true = vAPP(sTfun($o,$o),$o,sK20($o),vNOT) )
| ( $false = X0 ) )
| ~ spl42_31 ),
inference(not_proxy_clausification,[],[f1397]) ).
thf(f1397,plain,
( ! [X0: $o] :
( ( $true = vAPP(sTfun($o,$o),$o,sK20($o),vNOT) )
| ( $true = vAPP($o,$o,vNOT,X0) ) )
| ~ spl42_31 ),
inference(not_proxy_clausification,[],[f1364]) ).
thf(f1364,plain,
( ! [X0: $o] :
( ( $true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK20($o),vNOT)) )
| ( $true = vAPP($o,$o,vNOT,X0) ) )
| ~ spl42_31 ),
inference(primitive_instantiation,[],[f1271]) ).
thf(f1271,plain,
( ! [X0: $tType,X1: X0 > $o,X5: X0] :
( ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK20(X0),X1)) )
| ( $true = vAPP(X0,$o,X1,X5) ) )
| ~ spl42_31 ),
inference(avatar_component_clause,[],[f1270]) ).
thf(f1356,plain,
spl42_51,
inference(avatar_split_clause,[],[f688,f1354]) ).
thf(f688,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $false = vAPP(X0,$o,X1,X2) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK18(X0),X1)) ) ),
inference(not_proxy_clausification,[],[f687]) ).
thf(f687,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $false = vAPP(X0,$o,X1,X2) )
| ( $true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK18(X0),X1))) ) ),
inference(pi_clausification,[],[f686]) ).
thf(f686,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $false = vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1) )
| ( $true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK18(X0),X1))) ) ),
inference(not_proxy_clausification,[],[f379]) ).
thf(f379,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) )
| ( $true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK18(X0),X1))) ) ),
inference(cnf_transformation,[],[f194]) ).
thf(f194,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) )
| ( $true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK18(X0),X1))) ) )
& ( ! [X3: X0] : ( $true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3)) )
| ( $true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f192,f193]) ).
thf(f193,plain,
! [X0: $tType,X1: X0 > $o] :
( ? [X2: X0] : ( $true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)) )
=> ( $true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK18(X0),X1))) ) ),
introduced(choice_axiom,[]) ).
thf(f192,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) )
| ? [X2: X0] : ( $true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)) ) )
& ( ! [X3: X0] : ( $true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3)) )
| ( $true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) ) ) ),
inference(rectify,[],[f191]) ).
thf(f191,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( $true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) )
| ? [X2: X0] : ( $true != vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)) ) )
& ( ! [X2: X0] : ( $true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)) )
| ( $true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) ) ) ),
inference(nnf_transformation,[],[f119]) ).
thf(f119,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) )
<=> ! [X2: X0] : ( $true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X2)) ) ),
inference(rectify,[],[f84]) ).
thf(f84,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $true = vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) )
<=> ! [X3: X0] : ( $true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3)) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f83,plain,
! [X0: $tType,X1: X0 > $o] :
( vAPP($o,$o,vNOT,
? [X2: X0] : vAPP(X0,$o,X1,X2))
<=> ! [X3: X0] : vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3)) ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X0: $tType,X11: X0 > $o] :
( vAPP($o,$o,vNOT,
? [X5: X0] : vAPP(X0,$o,X11,X5))
<=> ! [X12: X0] : vAPP($o,$o,vNOT,vAPP(X0,$o,X11,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__EXISTS__THM) ).
thf(f1352,plain,
spl42_50,
inference(avatar_split_clause,[],[f685,f1350]) ).
thf(f685,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( $false = vAPP(X0,$o,X1,X3) )
| ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK43(X0),X1)) ) ),
inference(sigma_clausification,[],[f684]) ).
thf(f684,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( $false = vAPP(X0,$o,X1,X3) )
| ( $true = vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1) ) ),
inference(not_proxy_clausification,[],[f683]) ).
thf(f683,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( $false = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) ) ),
inference(not_proxy_clausification,[],[f378]) ).
thf(f378,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( $true = vAPP($o,$o,vNOT,vAPP(X0,$o,X1,X3)) )
| ( $true != vAPP($o,$o,vNOT,vAPP(sTfun(X0,$o),$o,vSIGMA(X0),X1)) ) ),
inference(cnf_transformation,[],[f194]) ).
thf(f1348,plain,
spl42_49,
inference(avatar_split_clause,[],[f638,f1346]) ).
thf(f638,plain,
! [X0: $tType,X1: X0 > $o,X6: X0] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK38(X0),X1)) )
| ( $true != vAPP(X0,$o,X1,X6) ) ),
inference(equality_resolution,[],[f492]) ).
thf(f492,plain,
! [X0: $tType,X2: $o,X1: X0 > $o,X6: X0] :
( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK38(X0),X1)) )
| ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,X6) ) ),
inference(cnf_transformation,[],[f288]) ).
thf(f1344,plain,
spl42_48,
inference(avatar_split_clause,[],[f633,f1342]) ).
thf(f633,plain,
! [X0: $tType,X2: X0 > $o,X6: X0] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK36(X0),X2)) )
| ( $true != vAPP(X0,$o,X2,X6) ) ),
inference(equality_resolution,[],[f489]) ).
thf(f489,plain,
! [X0: $tType,X2: X0 > $o,X1: $o,X6: X0] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK36(X0),X2)) )
| ( $true != vAPP(X0,$o,X2,X6) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f282]) ).
thf(f1340,plain,
spl42_47,
inference(avatar_split_clause,[],[f626,f1338]) ).
thf(f1338,plain,
( spl42_47
<=> ! [X2: $o,X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_47])]) ).
thf(f626,plain,
! [X2: $o,X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),$true),X0) ),
inference(equality_resolution,[],[f474]) ).
thf(f474,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP13,X2),X1),X0) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f256]) ).
thf(f1336,plain,
spl42_46,
inference(avatar_split_clause,[],[f620,f1334]) ).
thf(f1334,plain,
( spl42_46
<=> ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,$true),X1),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_46])]) ).
thf(f620,plain,
! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,$true),X1),$true) ),
inference(equality_resolution,[],[f619]) ).
thf(f619,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),$true) )
| ( $true != X2 ) ),
inference(equality_resolution,[],[f471]) ).
thf(f471,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP14,X2),X1),X0) )
| ( $true != X0 )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f253]) ).
thf(f1332,plain,
( spl42_30
| spl42_45
| ~ spl42_9
| ~ spl42_20 ),
inference(avatar_split_clause,[],[f976,f943,f840,f1329,f1066]) ).
thf(f1329,plain,
( spl42_45
<=> ( $true = vAPP(sTfun($o,$o),$o,c_2Ebool_2E_3F($o),c_2Ebool_2E_7E) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_45])]) ).
thf(f840,plain,
( spl42_9
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_9])]) ).
thf(f943,plain,
( spl42_20
<=> ! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ( $true != vAPP(X0,$o,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_20])]) ).
thf(f976,plain,
( ! [X0: $o] :
( ( $true = vAPP(sTfun($o,$o),$o,c_2Ebool_2E_3F($o),c_2Ebool_2E_7E) )
| ( $true = X0 ) )
| ~ spl42_9
| ~ spl42_20 ),
inference(trivial_inequality_removal,[],[f973]) ).
thf(f973,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = vAPP(sTfun($o,$o),$o,c_2Ebool_2E_3F($o),c_2Ebool_2E_7E) )
| ( $true = X0 ) )
| ~ spl42_9
| ~ spl42_20 ),
inference(superposition,[],[f944,f841]) ).
thf(f841,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) )
| ( $true = X0 ) )
| ~ spl42_9 ),
inference(avatar_component_clause,[],[f840]) ).
thf(f944,plain,
( ! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $true != vAPP(X0,$o,X1,X2) )
| ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) )
| ~ spl42_20 ),
inference(avatar_component_clause,[],[f943]) ).
thf(f1327,plain,
spl42_44,
inference(avatar_split_clause,[],[f613,f1325]) ).
thf(f1325,plain,
( spl42_44
<=> ! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,$true),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_44])]) ).
thf(f613,plain,
! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,$true),X1),X0) ),
inference(equality_resolution,[],[f454]) ).
thf(f454,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f247]) ).
thf(f1323,plain,
spl42_43,
inference(avatar_split_clause,[],[f612,f1321]) ).
thf(f1321,plain,
( spl42_43
<=> ! [X2: $o,X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_43])]) ).
thf(f612,plain,
! [X2: $o,X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),$true),X0) ),
inference(equality_resolution,[],[f455]) ).
thf(f455,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f247]) ).
thf(f1319,plain,
spl42_42,
inference(avatar_split_clause,[],[f608,f1317]) ).
thf(f1317,plain,
( spl42_42
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_42])]) ).
thf(f608,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),$true),X0) ),
inference(equality_resolution,[],[f607]) ).
thf(f607,plain,
! [X2: $o,X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),$true),X0) )
| ( $true != X2 ) ),
inference(equality_resolution,[],[f451]) ).
thf(f451,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( $true != X1 )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f244]) ).
thf(f1315,plain,
spl42_41,
inference(avatar_split_clause,[],[f606,f1313]) ).
thf(f1313,plain,
( spl42_41
<=> ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),X1),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_41])]) ).
thf(f606,plain,
! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),X1),$true) ),
inference(equality_resolution,[],[f605]) ).
thf(f605,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),$true) )
| ( $true != X2 ) ),
inference(equality_resolution,[],[f452]) ).
thf(f452,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X1),X0) )
| ( $true != X0 )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f244]) ).
thf(f1311,plain,
spl42_40,
inference(avatar_split_clause,[],[f601,f1309]) ).
thf(f1309,plain,
( spl42_40
<=> ! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,$true),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_40])]) ).
thf(f601,plain,
! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,$true),X1),X0) ),
inference(equality_resolution,[],[f435]) ).
thf(f435,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f238]) ).
thf(f1307,plain,
spl42_39,
inference(avatar_split_clause,[],[f596,f1304]) ).
thf(f1304,plain,
( spl42_39
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),$true),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_39])]) ).
thf(f596,plain,
$true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),$true),$true),
inference(equality_resolution,[],[f595]) ).
thf(f595,plain,
! [X2: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),$true),$true) )
| ( $true != X2 ) ),
inference(equality_resolution,[],[f594]) ).
thf(f594,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),$true) )
| ( $true != X1 )
| ( $true != X2 ) ),
inference(equality_resolution,[],[f433]) ).
thf(f433,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),X0) )
| ( $true != X0 )
| ( $true != X1 )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f1302,plain,
spl42_38,
inference(avatar_split_clause,[],[f589,f1300]) ).
thf(f1300,plain,
( spl42_38
<=> ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X1),X1),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_38])]) ).
thf(f589,plain,
! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X1),X1),$true) ),
inference(equality_resolution,[],[f588]) ).
thf(f588,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X1),X1),X2) )
| ( $true != X2 ) ),
inference(equality_resolution,[],[f418]) ).
thf(f418,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) )
| ( X0 != X1 )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f1298,plain,
spl42_37,
inference(avatar_split_clause,[],[f585,f1296]) ).
thf(f1296,plain,
( spl42_37
<=> ! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,$true),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_37])]) ).
thf(f585,plain,
! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,$true),X1),X0) ),
inference(equality_resolution,[],[f414]) ).
thf(f414,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f230]) ).
thf(f1294,plain,
spl42_36,
inference(avatar_split_clause,[],[f584,f1292]) ).
thf(f1292,plain,
( spl42_36
<=> ! [X2: $o,X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_36])]) ).
thf(f584,plain,
! [X2: $o,X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),$true),X0) ),
inference(equality_resolution,[],[f415]) ).
thf(f415,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f230]) ).
thf(f1290,plain,
spl42_35,
inference(avatar_split_clause,[],[f583,f1288]) ).
thf(f1288,plain,
( spl42_35
<=> ! [X2: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_35])]) ).
thf(f583,plain,
! [X2: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),$true) ),
inference(equality_resolution,[],[f416]) ).
thf(f416,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f230]) ).
thf(f1284,plain,
spl42_34,
inference(avatar_split_clause,[],[f582,f1282]) ).
thf(f1282,plain,
( spl42_34
<=> ! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,$true),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_34])]) ).
thf(f582,plain,
! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,$true),X1),X0) ),
inference(equality_resolution,[],[f410]) ).
thf(f410,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X1),X0) )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f228]) ).
thf(f1280,plain,
spl42_33,
inference(avatar_split_clause,[],[f581,f1278]) ).
thf(f1278,plain,
( spl42_33
<=> ! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,$true),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_33])]) ).
thf(f581,plain,
! [X0: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,$true),X1),X0) ),
inference(equality_resolution,[],[f406]) ).
thf(f406,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X2),X1),X0) )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f1276,plain,
spl42_32,
inference(avatar_split_clause,[],[f574,f1274]) ).
thf(f574,plain,
! [X0: $tType,X2: X0 > $o,X5: X0] :
( ( $true = vAPP(X0,$o,X2,X5) )
| ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK22(X0),X2)) ) ),
inference(equality_resolution,[],[f387]) ).
thf(f387,plain,
! [X0: $tType,X2: X0 > $o,X1: $o,X5: X0] :
( ( $true = vAPP(X0,$o,X2,X5) )
| ( $true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,sK22(X0),X2)) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f207]) ).
thf(f1272,plain,
spl42_31,
inference(avatar_split_clause,[],[f571,f1270]) ).
thf(f571,plain,
! [X0: $tType,X1: X0 > $o,X5: X0] :
( ( $true = vAPP(X0,$o,X1,X5) )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK20(X0),X1)) ) ),
inference(equality_resolution,[],[f382]) ).
thf(f382,plain,
! [X0: $tType,X2: $o,X1: X0 > $o,X5: X0] :
( ( $true = vAPP(X0,$o,X1,X5) )
| ( $true != X2 )
| ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK20(X0),X1)) ) ),
inference(cnf_transformation,[],[f201]) ).
thf(f1083,plain,
( ~ spl42_23
| ~ spl42_30 ),
inference(avatar_contradiction_clause,[],[f1082]) ).
thf(f1082,plain,
( $false
| ~ spl42_23
| ~ spl42_30 ),
inference(trivial_inequality_removal,[],[f1081]) ).
thf(f1081,plain,
( ( $true != $true )
| ~ spl42_23
| ~ spl42_30 ),
inference(superposition,[],[f1003,f1067]) ).
thf(f1067,plain,
( ! [X0: $o] : ( $true = X0 )
| ~ spl42_30 ),
inference(avatar_component_clause,[],[f1066]) ).
thf(f1068,plain,
( spl42_29
| spl42_30
| ~ spl42_20 ),
inference(avatar_split_clause,[],[f987,f943,f1066,f1062]) ).
thf(f987,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP(sTfun($o,$o),$o,c_2Ebool_2E_3F($o),vNOT) ) )
| ~ spl42_20 ),
inference(not_proxy_clausification,[],[f962]) ).
thf(f962,plain,
( ! [X0: $o] :
( ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP(sTfun($o,$o),$o,c_2Ebool_2E_3F($o),vNOT) ) )
| ~ spl42_20 ),
inference(primitive_instantiation,[],[f944]) ).
thf(f1033,plain,
spl42_28,
inference(avatar_split_clause,[],[f771,f1031]) ).
thf(f1031,plain,
( spl42_28
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_28])]) ).
thf(f771,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true = X1 ) ),
inference(trivial_inequality_removal,[],[f770]) ).
thf(f770,plain,
! [X0: $o,X1: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true = X1 ) ),
inference(forward_demodulation,[],[f712,f756]) ).
thf(f756,plain,
c_2Ebool_2ET = $true,
inference(boolean_simplification,[],[f529]) ).
thf(f529,plain,
$true = vAPP($o,$o,vNOT,vAPP($o,$o,vNOT,c_2Ebool_2ET)),
inference(equality_resolution,[],[f504]) ).
thf(f504,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( vAPP($o,$o,vNOT,c_2Ebool_2ET) != X0 ) ),
inference(definition_unfolding,[],[f307,f299]) ).
thf(f299,plain,
c_2Ebool_2EF = vAPP($o,$o,vNOT,c_2Ebool_2ET),
inference(cnf_transformation,[],[f46]) ).
thf(f46,plain,
( ( c_2Ebool_2ET = vAPP($o,$o,vNOT,c_2Ebool_2EF) )
& ( c_2Ebool_2EF = vAPP($o,$o,vNOT,c_2Ebool_2ET) )
& ! [X0: $o] : ( vAPP($o,$o,vNOT,vAPP($o,$o,vNOT,X0)) = X0 ) ),
inference(fool_elimination,[],[f45]) ).
thf(f45,plain,
( ( vAPP($o,$o,vNOT,c_2Ebool_2EF)
<=> c_2Ebool_2ET )
& ( vAPP($o,$o,vNOT,c_2Ebool_2ET)
<=> c_2Ebool_2EF )
& ! [X0: $o] :
( vAPP($o,$o,vNOT,vAPP($o,$o,vNOT,X0))
<=> X0 ) ),
inference(rectify,[],[f13]) ).
thf(f13,axiom,
( ( vAPP($o,$o,vNOT,c_2Ebool_2EF)
<=> c_2Ebool_2ET )
& ( vAPP($o,$o,vNOT,c_2Ebool_2ET)
<=> c_2Ebool_2EF )
& ! [X8: $o] :
( vAPP($o,$o,vNOT,vAPP($o,$o,vNOT,X8))
<=> X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(f307,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( c_2Ebool_2EF != X0 ) ),
inference(cnf_transformation,[],[f161]) ).
thf(f161,plain,
! [X0: $o] :
( ( ( c_2Ebool_2EF = X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( c_2Ebool_2EF != X0 ) )
& ( ( c_2Ebool_2EF = X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( c_2Ebool_2EF != X0 ) )
& ( ( c_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( c_2Ebool_2ET != X0 ) )
& ( ( c_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( c_2Ebool_2ET != X0 ) ) ),
inference(flattening,[],[f160]) ).
thf(f160,plain,
! [X0: $o] :
( ( ( c_2Ebool_2EF = X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( c_2Ebool_2EF != X0 ) )
& ( ( c_2Ebool_2EF = X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( c_2Ebool_2EF != X0 ) )
& ( ( c_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( c_2Ebool_2ET != X0 ) )
& ( ( c_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( c_2Ebool_2ET != X0 ) ) ),
inference(nnf_transformation,[],[f48]) ).
thf(f48,plain,
! [X0: $o] :
( ( ( c_2Ebool_2EF = X0 )
<=> ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( c_2Ebool_2EF = X0 )
<=> ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( c_2Ebool_2ET = X0 )
<=> ( $true = X0 ) )
& ( ( c_2Ebool_2ET = X0 )
<=> ( $true = X0 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f47,plain,
! [X0: $o] :
( ( ( c_2Ebool_2EF = X0 )
<=> vAPP($o,$o,vNOT,X0) )
& ( ( c_2Ebool_2EF = X0 )
<=> vAPP($o,$o,vNOT,X0) )
& ( ( c_2Ebool_2ET = X0 )
<=> X0 )
& ( ( c_2Ebool_2ET = X0 )
<=> X0 ) ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
! [X8: $o] :
( ( ( c_2Ebool_2EF = X8 )
<=> vAPP($o,$o,vNOT,X8) )
& ( ( c_2Ebool_2EF = X8 )
<=> vAPP($o,$o,vNOT,X8) )
& ( ( c_2Ebool_2ET = X8 )
<=> X8 )
& ( ( c_2Ebool_2ET = X8 )
<=> X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(f712,plain,
! [X0: $o,X1: $o] :
( ( c_2Ebool_2ET = $false )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f711]) ).
thf(f711,plain,
! [X0: $o,X1: $o] :
( ( c_2Ebool_2ET = $false )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ),
inference(not_proxy_clausification,[],[f710]) ).
thf(f710,plain,
! [X0: $o,X1: $o] :
( ( c_2Ebool_2ET = $false )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ),
inference(not_proxy_clausification,[],[f523]) ).
thf(f523,plain,
! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,c_2Ebool_2ET) = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ),
inference(definition_unfolding,[],[f347,f299]) ).
thf(f347,plain,
! [X0: $o,X1: $o] :
( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ),
inference(cnf_transformation,[],[f169]) ).
thf(f169,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) ) )
& ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ) ),
inference(flattening,[],[f168]) ).
thf(f168,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) ) )
& ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) ) ) ),
inference(nnf_transformation,[],[f138]) ).
thf(f1029,plain,
spl42_27,
inference(avatar_split_clause,[],[f769,f1027]) ).
thf(f1027,plain,
( spl42_27
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_27])]) ).
thf(f769,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(trivial_inequality_removal,[],[f768]) ).
thf(f768,plain,
! [X0: $o,X1: $o] :
( ( $true = $false )
| ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(forward_demodulation,[],[f718,f756]) ).
thf(f718,plain,
! [X0: $o,X1: $o] :
( ( c_2Ebool_2ET = $false )
| ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(not_proxy_clausification,[],[f717]) ).
thf(f717,plain,
! [X0: $o,X1: $o] :
( ( c_2Ebool_2ET = $false )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(not_proxy_clausification,[],[f521]) ).
thf(f521,plain,
! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,c_2Ebool_2ET) = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(definition_unfolding,[],[f342,f299]) ).
thf(f342,plain,
! [X0: $o,X1: $o] :
( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(cnf_transformation,[],[f167]) ).
thf(f167,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = vAPP($o,$o,vNOT,X0) )
& ( ( c_2Ebool_2EF = $true )
| ( $true != X1 ) ) ) )
& ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = X1 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ) ),
inference(flattening,[],[f166]) ).
thf(f166,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = vAPP($o,$o,vNOT,X0) )
& ( ( c_2Ebool_2EF = $true )
| ( $true != X1 ) ) ) )
& ( ( c_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( c_2Ebool_2EF != $true )
& ( $true = X1 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ) ),
inference(nnf_transformation,[],[f139]) ).
thf(f1025,plain,
spl42_26,
inference(avatar_split_clause,[],[f694,f1023]) ).
thf(f1023,plain,
( spl42_26
<=> ! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_26])]) ).
thf(f694,plain,
! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) ) ),
inference(not_proxy_clausification,[],[f693]) ).
thf(f693,plain,
! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) ) ),
inference(not_proxy_clausification,[],[f358]) ).
thf(f358,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) ) ),
inference(cnf_transformation,[],[f175]) ).
thf(f175,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != vAPP($o,$o,vNOT,X1) ) )
| ( ( $true != X1 )
& ( $true != X0 ) ) )
& ( ( ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,vNOT,X1) ) )
& ( ( $true = X1 )
| ( $true = X0 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) ) ) ),
inference(rectify,[],[f174]) ).
thf(f174,plain,
! [X1: $o,X0: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != vAPP($o,$o,vNOT,X0) ) )
| ( ( $true != X0 )
& ( $true != X1 ) ) )
& ( ( ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = X0 )
| ( $true = X1 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) ) ),
inference(flattening,[],[f173]) ).
thf(f173,plain,
! [X1: $o,X0: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != vAPP($o,$o,vNOT,X0) ) )
| ( ( $true != X0 )
& ( $true != X1 ) ) )
& ( ( ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = X0 )
| ( $true = X1 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) ) ),
inference(nnf_transformation,[],[f141]) ).
thf(f141,plain,
! [X1: $o,X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
<=> ( ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = X0 )
| ( $true = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1021,plain,
spl42_25,
inference(avatar_split_clause,[],[f372,f1019]) ).
thf(f1019,plain,
( spl42_25
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_25])]) ).
thf(f372,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ),
inference(cnf_transformation,[],[f188]) ).
thf(f188,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
| ( ( $true != X1 )
& ( $true != X0 ) ) )
& ( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
inference(flattening,[],[f187]) ).
thf(f187,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
| ( ( $true != X1 )
& ( $true != X0 ) ) )
& ( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
inference(nnf_transformation,[],[f80]) ).
thf(f80,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
<=> ( ( $true = X1 )
| ( $true = X0 ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f79,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1)
<=> ( X1
| X0 ) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X2: $o,X3: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X2),X3)
<=> ( X3
| X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(f1017,plain,
spl42_24,
inference(avatar_split_clause,[],[f357,f1015]) ).
thf(f1015,plain,
( spl42_24
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_24])]) ).
thf(f357,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) ) ),
inference(cnf_transformation,[],[f175]) ).
thf(f1004,plain,
spl42_23,
inference(avatar_split_clause,[],[f297,f1002]) ).
thf(f297,plain,
! [X0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( $true != vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) ),
inference(cnf_transformation,[],[f121]) ).
thf(f121,plain,
! [X0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( $true != vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) ),
inference(ennf_transformation,[],[f44]) ).
thf(f44,plain,
~ ? [X0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( $true = vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))) ),
inference(fool_elimination,[],[f43]) ).
thf(f43,plain,
~ ? [X0: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),
inference(rectify,[],[f40]) ).
thf(f40,negated_conjecture,
~ ? [X4: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X4),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),
inference(negated_conjecture,[],[f39]) ).
thf(f39,conjecture,
? [X4: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : vAPP(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o,vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o),vAPP(sTfun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),$o)),c_2Epred__set_2EBIJ(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X4),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o),vAPP(sTfun(tyop_2Enum_2Enum,$o),sTfun(sTfun(tyop_2Enum_2Enum,$o),sTfun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),$o)),c_2Epred__set_2ECROSS(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV(tyop_2Enum_2Enum))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
thf(f953,plain,
spl42_22,
inference(avatar_split_clause,[],[f559,f951]) ).
thf(f951,plain,
( spl42_22
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),vAPP($o,$o,vNOT,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_22])]) ).
thf(f559,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),vAPP($o,$o,vNOT,X0)) ),
inference(equality_resolution,[],[f363]) ).
thf(f363,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( vAPP($o,$o,vNOT,X0) != X1 ) ),
inference(cnf_transformation,[],[f176]) ).
thf(f176,plain,
! [X0: $o,X1: $o] :
( ( ( vAPP($o,$o,vNOT,X0) = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) )
& ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( vAPP($o,$o,vNOT,X0) != X1 ) ) ),
inference(nnf_transformation,[],[f142]) ).
thf(f142,plain,
! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,X0) = X1 )
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) ),
inference(definition_folding,[],[f72,f141]) ).
thf(f72,plain,
! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,X0) = X1 )
<=> ( ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = X0 )
| ( $true = X1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f71,plain,
! [X0: $o,X1: $o] :
( ( X1
<=> vAPP($o,$o,vNOT,X0) )
<=> ( ( vAPP($o,$o,vNOT,X1)
| vAPP($o,$o,vNOT,X0) )
& ( X0
| X1 ) ) ),
inference(rectify,[],[f37]) ).
thf(f37,axiom,
! [X31: $o,X32: $o] :
( ( X32
<=> vAPP($o,$o,vNOT,X31) )
<=> ( ( vAPP($o,$o,vNOT,X32)
| vAPP($o,$o,vNOT,X31) )
& ( X31
| X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esat_2Edc__neg) ).
thf(f949,plain,
spl42_21,
inference(avatar_split_clause,[],[f496,f947]) ).
thf(f947,plain,
( spl42_21
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_21])]) ).
thf(f496,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) ) ),
inference(cnf_transformation,[],[f289]) ).
thf(f289,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) ) ) ),
inference(nnf_transformation,[],[f112]) ).
thf(f112,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) )
<=> ( X1 = X2 ) ),
inference(fool_elimination,[],[f111]) ).
thf(f111,plain,
! [X0: $tType,X1: X0,X2: X0] :
( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2)
<=> ( X1 = X2 ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X0: $tType,X2: X0,X3: X0] :
( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X3)
<=> ( X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(f945,plain,
spl42_20,
inference(avatar_split_clause,[],[f368,f943]) ).
thf(f368,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
| ( $true != vAPP(X0,$o,X1,X2) ) ),
inference(cnf_transformation,[],[f184]) ).
thf(f941,plain,
spl42_19,
inference(avatar_split_clause,[],[f365,f939]) ).
thf(f939,plain,
( spl42_19
<=> ! [X0: $tType,X1: X0 > $o,X3: X0] :
( ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_19])]) ).
thf(f365,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( ( $true = vAPP(X0,$o,X1,X3) )
| ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ),
inference(cnf_transformation,[],[f180]) ).
thf(f894,plain,
spl42_18,
inference(avatar_split_clause,[],[f720,f892]) ).
thf(f892,plain,
( spl42_18
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_18])]) ).
thf(f720,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $false = X0 ) ),
inference(not_proxy_clausification,[],[f345]) ).
thf(f345,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $true = vAPP($o,$o,vNOT,X0) ) ),
inference(cnf_transformation,[],[f167]) ).
thf(f890,plain,
spl42_17,
inference(avatar_split_clause,[],[f698,f888]) ).
thf(f888,plain,
( spl42_17
<=> ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,$true),X0) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_17])]) ).
thf(f698,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,$true),X0) )
| ( $true = X0 ) ),
inference(not_proxy_clausification,[],[f555]) ).
thf(f555,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,$true),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) ) ),
inference(equality_resolution,[],[f362]) ).
thf(f362,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f175]) ).
thf(f886,plain,
spl42_16,
inference(avatar_split_clause,[],[f695,f884]) ).
thf(f884,plain,
( spl42_16
<=> ! [X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),$true) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_16])]) ).
thf(f695,plain,
! [X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),$true) )
| ( $true = X1 ) ),
inference(not_proxy_clausification,[],[f558]) ).
thf(f558,plain,
! [X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),$true) )
| ( $true != vAPP($o,$o,vNOT,X1) ) ),
inference(equality_resolution,[],[f359]) ).
thf(f359,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f175]) ).
thf(f882,plain,
spl42_15,
inference(avatar_split_clause,[],[f730,f880]) ).
thf(f880,plain,
( spl42_15
<=> ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_15])]) ).
thf(f730,plain,
! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
inference(not_proxy_clausification,[],[f727]) ).
thf(f727,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
inference(binary_proxy_clausification,[],[f332]) ).
thf(f332,plain,
! [X0: $o] : ( vAPP($o,$o,vNOT,X0) = vAPP($o,$o,c_2Ebool_2E_7E,X0) ),
inference(cnf_transformation,[],[f60]) ).
thf(f60,plain,
! [X0: $o] : ( vAPP($o,$o,vNOT,X0) = vAPP($o,$o,c_2Ebool_2E_7E,X0) ),
inference(fool_elimination,[],[f59]) ).
thf(f59,plain,
! [X0: $o] :
( vAPP($o,$o,c_2Ebool_2E_7E,X0)
<=> vAPP($o,$o,vNOT,X0) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X2: $o] :
( vAPP($o,$o,c_2Ebool_2E_7E,X2)
<=> vAPP($o,$o,vNOT,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(f878,plain,
spl42_14,
inference(avatar_split_clause,[],[f565,f876]) ).
thf(f876,plain,
( spl42_14
<=> ! [X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,$true),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_14])]) ).
thf(f565,plain,
! [X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,$true),X1) ) ),
inference(equality_resolution,[],[f375]) ).
thf(f375,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ),
inference(cnf_transformation,[],[f190]) ).
thf(f190,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( ( $true != X1 )
& ( $true = X0 ) ) )
& ( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ) ),
inference(flattening,[],[f189]) ).
thf(f189,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( ( $true != X1 )
& ( $true = X0 ) ) )
& ( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ) ),
inference(nnf_transformation,[],[f136]) ).
thf(f136,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
<=> ( ( $true = X1 )
| ( $true != X0 ) ) ),
inference(ennf_transformation,[],[f82]) ).
thf(f82,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
<=> ( ( $true = X0 )
=> ( $true = X1 ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f81,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)
<=> ( X0
=> X1 ) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X2: $o,X3: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X2),X3)
<=> ( X2
=> X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(f874,plain,
spl42_13,
inference(avatar_split_clause,[],[f376,f872]) ).
thf(f872,plain,
( spl42_13
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_13])]) ).
thf(f376,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true = X0 ) ),
inference(cnf_transformation,[],[f190]) ).
thf(f870,plain,
spl42_12,
inference(avatar_split_clause,[],[f370,f868]) ).
thf(f868,plain,
( spl42_12
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_12])]) ).
thf(f370,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ),
inference(cnf_transformation,[],[f186]) ).
thf(f186,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) )
& ( ( ( $true = X1 )
& ( $true = X0 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
inference(flattening,[],[f185]) ).
thf(f185,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) )
& ( ( ( $true = X1 )
& ( $true = X0 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
inference(nnf_transformation,[],[f78]) ).
thf(f78,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
<=> ( ( $true = X1 )
& ( $true = X0 ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f77,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1)
<=> ( X1
& X0 ) ),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X2: $o,X3: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X2),X3)
<=> ( X3
& X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(f866,plain,
spl42_11,
inference(avatar_split_clause,[],[f369,f864]) ).
thf(f864,plain,
( spl42_11
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_11])]) ).
thf(f369,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ),
inference(cnf_transformation,[],[f186]) ).
thf(f862,plain,
spl42_10,
inference(avatar_split_clause,[],[f639,f860]) ).
thf(f860,plain,
( spl42_10
<=> ! [X0: $tType,X2: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_10])]) ).
thf(f639,plain,
! [X0: $tType,X2: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X2) ),
inference(equality_resolution,[],[f497]) ).
thf(f497,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) )
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f289]) ).
thf(f842,plain,
spl42_9,
inference(avatar_split_clause,[],[f729,f840]) ).
thf(f729,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
inference(not_proxy_clausification,[],[f728]) ).
thf(f728,plain,
! [X0: $o] :
( ( $false = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
inference(binary_proxy_clausification,[],[f332]) ).
thf(f834,plain,
spl42_8,
inference(avatar_split_clause,[],[f767,f832]) ).
thf(f832,plain,
( spl42_8
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_8])]) ).
thf(f767,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) ),
inference(trivial_inequality_removal,[],[f766]) ).
thf(f766,plain,
! [X0: $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) ) ),
inference(forward_demodulation,[],[f719,f756]) ).
thf(f719,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) )
| ( c_2Ebool_2ET = $false ) ),
inference(not_proxy_clausification,[],[f552]) ).
thf(f552,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) )
| ( vAPP($o,$o,vNOT,c_2Ebool_2ET) = $true ) ),
inference(equality_resolution,[],[f519]) ).
thf(f519,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( vAPP($o,$o,vNOT,c_2Ebool_2ET) = $true )
| ( $true != X1 ) ),
inference(definition_unfolding,[],[f344,f299]) ).
thf(f344,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( c_2Ebool_2EF = $true )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f167]) ).
thf(f830,plain,
spl42_7,
inference(avatar_split_clause,[],[f564,f828]) ).
thf(f828,plain,
( spl42_7
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_7])]) ).
thf(f564,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),$true) ),
inference(equality_resolution,[],[f377]) ).
thf(f377,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f190]) ).
thf(f826,plain,
spl42_6,
inference(avatar_split_clause,[],[f563,f824]) ).
thf(f824,plain,
( spl42_6
<=> ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,$true),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_6])]) ).
thf(f563,plain,
! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,$true),X1) ),
inference(equality_resolution,[],[f373]) ).
thf(f373,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f188]) ).
thf(f822,plain,
spl42_5,
inference(avatar_split_clause,[],[f562,f820]) ).
thf(f820,plain,
( spl42_5
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_5])]) ).
thf(f562,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),$true) ),
inference(equality_resolution,[],[f374]) ).
thf(f374,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f188]) ).
thf(f818,plain,
spl42_4,
inference(avatar_split_clause,[],[f561,f815]) ).
thf(f815,plain,
( spl42_4
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,$true),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_4])]) ).
thf(f561,plain,
$true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,$true),$true),
inference(equality_resolution,[],[f560]) ).
thf(f560,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),$true) )
| ( $true != X0 ) ),
inference(equality_resolution,[],[f371]) ).
thf(f371,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f186]) ).
thf(f785,plain,
spl42_3,
inference(avatar_split_clause,[],[f42,f783]) ).
thf(f42,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f781,plain,
spl42_2,
inference(avatar_split_clause,[],[f756,f778]) ).
thf(f778,plain,
( spl42_2
<=> ( c_2Ebool_2ET = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_2])]) ).
thf(f776,plain,
~ spl42_1,
inference(avatar_split_clause,[],[f41,f773]) ).
thf(f773,plain,
( spl42_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl42_1])]) ).
thf(f41,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP020^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 15:42:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (1340)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (1343)WARNING: value z3 for option sas not known
% 0.13/0.36 % (1344)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (1342)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (1345)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)
% 0.13/0.36 % (1346)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)
% 0.13/0.36 % (1343)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)
% 0.13/0.37 % (1347)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)
% 0.13/0.37 % (1341)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (1347)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38 % Exception at run slice level
% 0.13/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39 % (1348)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.39 % (1349)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)
% 0.13/0.39 % (1350)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)
% 0.13/0.39 % (1348)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.40 % (1349)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.40 % Exception at run slice level
% 0.13/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.41 % (1351)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)
% 0.20/0.56 % (1345)First to succeed.
% 0.20/0.57 % (1345)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1340"
% 0.20/0.57 % (1345)Refutation found. Thanks to Tanya!
% 0.20/0.57 % SZS status Theorem for theBenchmark
% 0.20/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.58 % (1345)------------------------------
% 0.20/0.58 % (1345)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.58 % (1345)Termination reason: Refutation
% 0.20/0.58
% 0.20/0.58 % (1345)Memory used [KB]: 3284
% 0.20/0.58 % (1345)Time elapsed: 0.206 s
% 0.20/0.58 % (1345)Instructions burned: 526 (million)
% 0.20/0.58 % (1340)Success in time 0.217 s
%------------------------------------------------------------------------------