TSTP Solution File: ITP006^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP006^1 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:42:15 EDT 2024
% Result : Theorem 1.71s 0.61s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 361
% Syntax : Number of formulae : 1191 ( 199 unt; 95 typ; 0 def)
% Number of atoms : 19061 (2661 equ; 0 cnn)
% Maximal formula atoms : 32 ( 17 avg)
% Number of connectives : 4150 (1394 ~;2015 |; 343 &; 0 @)
% ( 329 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 186 ( 185 >; 1 *; 0 +; 0 <<)
% Number of symbols : 299 ( 296 usr; 234 con; 0-6 aty)
% Number of variables : 2324 ( 0 ^2236 !; 82 ?;2324 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
u: $tType ).
thf(type_def_8,type,
du: $tType ).
thf(func_def_0,type,
u: $tType ).
thf(func_def_1,type,
d: $tType ).
thf(func_def_2,type,
du: $tType ).
thf(func_def_3,type,
tyop_2Emin_2Ebool: d ).
thf(func_def_4,type,
tyop_2Emin_2Efun: d > d > d ).
thf(func_def_5,type,
s: d > u > du ).
thf(func_def_6,type,
app_2E2: du > du > u ).
thf(func_def_7,type,
combin_i_2E0: u ).
thf(func_def_8,type,
combin_k_2E0: u ).
thf(func_def_9,type,
combin_s_2E0: u ).
thf(func_def_10,type,
c_2Ebool_2E_21_2E0: u ).
thf(func_def_11,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(func_def_12,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(func_def_13,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(func_def_14,type,
c_2Emin_2E_3D_2E0: u ).
thf(func_def_15,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(func_def_16,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(func_def_17,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(func_def_18,type,
c_2Ebool_2E_3F_2E0: u ).
thf(func_def_19,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(func_def_20,type,
c_2Ebool_2EF_2E0: u ).
thf(func_def_21,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E0: u ).
thf(func_def_22,type,
c_2EquantHeuristics_2EGUESS__EXISTS_2E2: du > du > u ).
thf(func_def_23,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0: u ).
thf(func_def_24,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2: du > du > u ).
thf(func_def_25,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0: u ).
thf(func_def_26,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2: du > du > u ).
thf(func_def_27,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E0: u ).
thf(func_def_28,type,
c_2EquantHeuristics_2EGUESS__FORALL_2E2: du > du > u ).
thf(func_def_29,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E0: u ).
thf(func_def_30,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2: du > du > u ).
thf(func_def_31,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0: u ).
thf(func_def_32,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2: du > du > u ).
thf(func_def_33,type,
c_2Ebool_2ET_2E0: u ).
thf(func_def_34,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(func_def_35,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(func_def_36,type,
c_2Ebool_2E_7E_2E0: u ).
thf(func_def_37,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(func_def_38,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(func_def_39,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(func_def_40,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_41,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_42,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(func_def_43,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(func_def_44,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_45,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(func_def_46,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(func_def_47,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(func_def_48,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(func_def_49,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(func_def_50,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(func_def_51,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_56,type,
vIMP: $o > $o > $o ).
thf(func_def_57,type,
vOR: $o > $o > $o ).
thf(func_def_58,type,
sP0: $o > $o > $o ).
thf(func_def_59,type,
sP1: $o > $o > $o ).
thf(func_def_60,type,
sP2: $o > $o > $o ).
thf(func_def_61,type,
sP3: $o > $o > $o > $o ).
thf(func_def_62,type,
sP4: $o > $o > $o > $o ).
thf(func_def_63,type,
sP5: $o > $o > $o > $o ).
thf(func_def_64,type,
sP6: $o > $o > $o > $o ).
thf(func_def_65,type,
sP7: $o > $o > $o > $o ).
thf(func_def_66,type,
sP8: $o > $o > $o > $o ).
thf(func_def_67,type,
sP9: $o > $o > $o > $o ).
thf(func_def_68,type,
sP10: $o > $o > $o > $o ).
thf(func_def_69,type,
sP11: $o > $o > $o > $o ).
thf(func_def_70,type,
sP12: $o > $o > $o > $o ).
thf(func_def_71,type,
sP13: $o > $o > $o > $o > $o ).
thf(func_def_72,type,
sK14: d ).
thf(func_def_73,type,
sK15: d ).
thf(func_def_74,type,
sK16: u ).
thf(func_def_75,type,
sK17: u ).
thf(func_def_76,type,
sK18: u ).
thf(func_def_77,type,
sK19: u > d > u ).
thf(func_def_78,type,
sK20: u > d > u ).
thf(func_def_79,type,
sK21: u > u > d > d > u ).
thf(func_def_80,type,
sK22: u > u > d > d > u ).
thf(func_def_81,type,
sK23: u > u > d > d > u ).
thf(func_def_82,type,
sK24: u > u > d > d > u ).
thf(func_def_83,type,
sK25: u > u > d > d > u ).
thf(func_def_84,type,
sK26: u > u > d > d > u ).
thf(func_def_85,type,
sK27: u > u > d > d > u ).
thf(func_def_86,type,
sK28: u > u > d > d > u ).
thf(func_def_87,type,
sK29: u > u > d > d > u ).
thf(func_def_88,type,
sK30: u > u > d > d > u ).
thf(func_def_89,type,
sK31: u > u > d > d > u ).
thf(func_def_91,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_92,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_93,type,
vAND: $o > $o > $o ).
thf(func_def_94,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f4186,plain,
$false,
inference(avatar_sat_refutation,[],[f706,f711,f715,f748,f752,f756,f760,f764,f772,f792,f796,f800,f804,f808,f812,f816,f820,f868,f873,f879,f885,f889,f893,f897,f901,f938,f942,f946,f950,f954,f958,f962,f966,f970,f974,f978,f982,f986,f1006,f1042,f1046,f1050,f1054,f1058,f1062,f1066,f1070,f1074,f1078,f1082,f1086,f1090,f1094,f1098,f1176,f1180,f1184,f1196,f1200,f1204,f1208,f1212,f1216,f1220,f1224,f1306,f1312,f1316,f1320,f1324,f1328,f1332,f1340,f1383,f1391,f1395,f1399,f1433,f1437,f1441,f1512,f1522,f1526,f1530,f1534,f1538,f1542,f1553,f1557,f1561,f1565,f1569,f1657,f1693,f1703,f1707,f1711,f1719,f1723,f1738,f1750,f1754,f1766,f1836,f1840,f1862,f1866,f1870,f1888,f1892,f1905,f1918,f1950,f1954,f1975,f1979,f2014,f2018,f2022,f2026,f2030,f2088,f2092,f2128,f2132,f2148,f2152,f2237,f2241,f2292,f2311,f2315,f2341,f2345,f2381,f2543,f2552,f2556,f2560,f2564,f2568,f2659,f2683,f2687,f2691,f2695,f2700,f2744,f2748,f2752,f2756,f2760,f2764,f2773,f2777,f2899,f2921,f2925,f2958,f2962,f2966,f2970,f2975,f2979,f2983,f2987,f2991,f2995,f3162,f3195,f3199,f3203,f3207,f3211,f3215,f3219,f3223,f3227,f3231,f3316,f3406,f3410,f3446,f3450,f3454,f3504,f3508,f3518,f3551,f3555,f3560,f3564,f3568,f3572,f3576,f3580,f3584,f3588,f3592,f3596,f3600,f3970,f4046,f4050,f4122,f4160,f4182,f4185]) ).
thf(f4185,plain,
( ~ spl32_136
| ~ spl32_156
| ~ spl32_206 ),
inference(avatar_contradiction_clause,[],[f4184]) ).
thf(f4184,plain,
( $false
| ~ spl32_136
| ~ spl32_156
| ~ spl32_206 ),
inference(trivial_inequality_removal,[],[f4183]) ).
thf(f4183,plain,
( ( $true = $false )
| ~ spl32_136
| ~ spl32_156
| ~ spl32_206 ),
inference(forward_demodulation,[],[f4177,f2542]) ).
thf(f2542,plain,
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_136 ),
inference(avatar_component_clause,[],[f2540]) ).
thf(f2540,plain,
( spl32_136
<=> ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_136])]) ).
thf(f4177,plain,
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_156
| ~ spl32_206 ),
inference(trivial_inequality_removal,[],[f4169]) ).
thf(f4169,plain,
( ( $true = $false )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_156
| ~ spl32_206 ),
inference(superposition,[],[f2898,f4159]) ).
thf(f4159,plain,
( ! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,sK18),X1),sK14),X0))))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_206 ),
inference(avatar_component_clause,[],[f4158]) ).
thf(f4158,plain,
( spl32_206
<=> ! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,sK18),X1),sK14),X0))))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_206])]) ).
thf(f2898,plain,
( ! [X0: u] : ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK15),X0)))))) )
| ~ spl32_156 ),
inference(avatar_component_clause,[],[f2897]) ).
thf(f2897,plain,
( spl32_156
<=> ! [X0: u] : ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK15),X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_156])]) ).
thf(f4182,plain,
( ~ spl32_136
| ~ spl32_156
| ~ spl32_206 ),
inference(avatar_contradiction_clause,[],[f4181]) ).
thf(f4181,plain,
( $false
| ~ spl32_136
| ~ spl32_156
| ~ spl32_206 ),
inference(trivial_inequality_removal,[],[f4180]) ).
thf(f4180,plain,
( ( $true = $false )
| ~ spl32_136
| ~ spl32_156
| ~ spl32_206 ),
inference(forward_demodulation,[],[f4179,f2542]) ).
thf(f4179,plain,
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_156
| ~ spl32_206 ),
inference(trivial_inequality_removal,[],[f4167]) ).
thf(f4167,plain,
( ( $true = $false )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_156
| ~ spl32_206 ),
inference(superposition,[],[f4159,f2898]) ).
thf(f4160,plain,
( spl32_206
| ~ spl32_66
| ~ spl32_129 ),
inference(avatar_split_clause,[],[f2282,f2239,f1304,f4158]) ).
thf(f1304,plain,
( spl32_66
<=> ! [X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_66])]) ).
thf(f2239,plain,
( spl32_129
<=> ! [X17: u,X0: d,X16: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,X17),X16),X1),X0))))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_129])]) ).
thf(f2282,plain,
( ! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,sK18),X1),sK14),X0))))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_66
| ~ spl32_129 ),
inference(trivial_inequality_removal,[],[f2276]) ).
thf(f2276,plain,
( ! [X0: d,X1: u] :
( ( $true != $true )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,sK18),X1),sK14),X0))))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_66
| ~ spl32_129 ),
inference(superposition,[],[f1305,f2240]) ).
thf(f2240,plain,
( ! [X0: d,X1: d,X16: u,X17: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,X17),X16),X1),X0))))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) ) )
| ~ spl32_129 ),
inference(avatar_component_clause,[],[f2239]) ).
thf(f1305,plain,
( ! [X5: u] :
( ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) ) )
| ~ spl32_66 ),
inference(avatar_component_clause,[],[f1304]) ).
thf(f4122,plain,
( spl32_205
| ~ spl32_99 ),
inference(avatar_split_clause,[],[f1734,f1721,f4120]) ).
thf(f4120,plain,
( spl32_205
<=> ! [X0: d,X1: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_205])]) ).
thf(f1721,plain,
( spl32_99
<=> ! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_99])]) ).
thf(f1734,plain,
( ! [X0: d,X1: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))) )
| ~ spl32_99 ),
inference(equality_resolution,[],[f1722]) ).
thf(f1722,plain,
( ! [X2: u,X0: d,X1: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) )
| ~ spl32_99 ),
inference(avatar_component_clause,[],[f1721]) ).
thf(f4050,plain,
( spl32_204
| ~ spl32_26
| ~ spl32_29
| ~ spl32_105 ),
inference(avatar_split_clause,[],[f1858,f1838,f948,f936,f4048]) ).
thf(f4048,plain,
( spl32_204
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),$true),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X1),X0),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_204])]) ).
thf(f936,plain,
( spl32_26
<=> ! [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,[spl32_26])]) ).
thf(f948,plain,
( spl32_29
<=> ! [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,[spl32_29])]) ).
thf(f1838,plain,
( spl32_105
<=> ! [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,[spl32_105])]) ).
thf(f1858,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),$true),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X1),X0),$true) ) )
| ~ spl32_26
| ~ spl32_29
| ~ spl32_105 ),
inference(trivial_inequality_removal,[],[f1857]) ).
thf(f1857,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),$true),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X1),X0),$true) ) )
| ~ spl32_26
| ~ spl32_29
| ~ spl32_105 ),
inference(forward_demodulation,[],[f1856,f949]) ).
thf(f949,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) )
| ~ spl32_29 ),
inference(avatar_component_clause,[],[f948]) ).
thf(f1856,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),$true),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X1),X0),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X1),$true),X0) ) )
| ~ spl32_26
| ~ spl32_105 ),
inference(trivial_inequality_removal,[],[f1848]) ).
thf(f1848,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),$true),X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X1),X0),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X1),$true),X0) ) )
| ~ spl32_26
| ~ spl32_105 ),
inference(superposition,[],[f1839,f937]) ).
thf(f937,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) )
| ~ spl32_26 ),
inference(avatar_component_clause,[],[f936]) ).
thf(f1839,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 = X0 )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X2),X1),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) ) )
| ~ spl32_105 ),
inference(avatar_component_clause,[],[f1838]) ).
thf(f4046,plain,
( spl32_203
| ~ spl32_3
| ~ spl32_93 ),
inference(avatar_split_clause,[],[f1663,f1655,f713,f4044]) ).
thf(f4044,plain,
( spl32_203
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X0),X1) )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,$true),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_203])]) ).
thf(f713,plain,
( spl32_3
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_3])]) ).
thf(f1655,plain,
( spl32_93
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,$true),X1),X0) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_93])]) ).
thf(f1663,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X0),X1) )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,$true),X0),X1) ) )
| ~ spl32_3
| ~ spl32_93 ),
inference(trivial_inequality_removal,[],[f1662]) ).
thf(f1662,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X0),X1) )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,$true),X0),X1) ) )
| ~ spl32_3
| ~ spl32_93 ),
inference(superposition,[],[f1656,f714]) ).
thf(f714,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl32_3 ),
inference(avatar_component_clause,[],[f713]) ).
thf(f1656,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) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X1),X0) )
| ( $true = X1 ) )
| ~ spl32_93 ),
inference(avatar_component_clause,[],[f1655]) ).
thf(f3970,plain,
( spl32_202
| ~ spl32_3
| ~ spl32_81 ),
inference(avatar_split_clause,[],[f1515,f1510,f713,f3968]) ).
thf(f3968,plain,
( spl32_202
<=> ! [X0: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,$true)) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_202])]) ).
thf(f1510,plain,
( spl32_81
<=> ! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_81])]) ).
thf(f1515,plain,
( ! [X0: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,$true)) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0)) ) )
| ~ spl32_3
| ~ spl32_81 ),
inference(superposition,[],[f1511,f714]) ).
thf(f1511,plain,
( ! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0)))) )
| ~ spl32_81 ),
inference(avatar_component_clause,[],[f1510]) ).
thf(f3600,plain,
( spl32_201
| ~ spl32_26
| ~ spl32_28
| ~ spl32_103 ),
inference(avatar_split_clause,[],[f1832,f1764,f944,f936,f3598]) ).
thf(f3598,plain,
( spl32_201
<=> ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,$true),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),$true),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_201])]) ).
thf(f944,plain,
( spl32_28
<=> ! [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,[spl32_28])]) ).
thf(f1764,plain,
( spl32_103
<=> ! [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,[spl32_103])]) ).
thf(f1832,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,$true),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),$true),$true) ) )
| ~ spl32_26
| ~ spl32_28
| ~ spl32_103 ),
inference(trivial_inequality_removal,[],[f1831]) ).
thf(f1831,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,$true),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),$true),$true) ) )
| ~ spl32_26
| ~ spl32_28
| ~ spl32_103 ),
inference(forward_demodulation,[],[f1774,f945]) ).
thf(f945,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) )
| ~ spl32_28 ),
inference(avatar_component_clause,[],[f944]) ).
thf(f1774,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,$true),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),$true),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),$true),$true) ) )
| ~ spl32_26
| ~ spl32_103 ),
inference(trivial_inequality_removal,[],[f1768]) ).
thf(f1768,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,$true),$true),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),$true),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),$true),$true) ) )
| ~ spl32_26
| ~ spl32_103 ),
inference(superposition,[],[f1765,f937]) ).
thf(f1765,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($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)),sP6,$true),X1),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) ) )
| ~ spl32_103 ),
inference(avatar_component_clause,[],[f1764]) ).
thf(f3596,plain,
( spl32_200
| ~ spl32_3
| ~ spl32_92 ),
inference(avatar_split_clause,[],[f1641,f1567,f713,f3594]) ).
thf(f3594,plain,
( spl32_200
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),$true) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_200])]) ).
thf(f1567,plain,
( spl32_92
<=> ! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_92])]) ).
thf(f1641,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),$true) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_92 ),
inference(trivial_inequality_removal,[],[f1640]) ).
thf(f1640,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),$true) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_92 ),
inference(superposition,[],[f1568,f714]) ).
thf(f1568,plain,
( ! [X2: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),$true) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),$true) ) )
| ~ spl32_92 ),
inference(avatar_component_clause,[],[f1567]) ).
thf(f3592,plain,
( spl32_199
| ~ spl32_3
| ~ spl32_91 ),
inference(avatar_split_clause,[],[f1623,f1563,f713,f3590]) ).
thf(f3590,plain,
( spl32_199
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),$true) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_199])]) ).
thf(f1563,plain,
( spl32_91
<=> ! [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,[spl32_91])]) ).
thf(f1623,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),$true) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_91 ),
inference(trivial_inequality_removal,[],[f1622]) ).
thf(f1622,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),$true) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_91 ),
inference(superposition,[],[f1564,f714]) ).
thf(f1564,plain,
( ! [X2: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),$true) )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),$true) ) )
| ~ spl32_91 ),
inference(avatar_component_clause,[],[f1563]) ).
thf(f3588,plain,
( spl32_198
| ~ spl32_3
| ~ spl32_90 ),
inference(avatar_split_clause,[],[f1617,f1559,f713,f3586]) ).
thf(f3586,plain,
( spl32_198
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_198])]) ).
thf(f1559,plain,
( spl32_90
<=> ! [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,[spl32_90])]) ).
thf(f1617,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),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_90 ),
inference(trivial_inequality_removal,[],[f1616]) ).
thf(f1616,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X2),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_90 ),
inference(superposition,[],[f1560,f714]) ).
thf(f1560,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) ) )
| ~ spl32_90 ),
inference(avatar_component_clause,[],[f1559]) ).
thf(f3584,plain,
( spl32_197
| ~ spl32_3
| ~ spl32_89 ),
inference(avatar_split_clause,[],[f1612,f1555,f713,f3582]) ).
thf(f3582,plain,
( spl32_197
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X2),X0) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_197])]) ).
thf(f1555,plain,
( spl32_89
<=> ! [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,[spl32_89])]) ).
thf(f1612,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),X2),X0) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_89 ),
inference(trivial_inequality_removal,[],[f1611]) ).
thf(f1611,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X1),X2),X0) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_89 ),
inference(superposition,[],[f1556,f714]) ).
thf(f1556,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) ) )
| ~ spl32_89 ),
inference(avatar_component_clause,[],[f1555]) ).
thf(f3580,plain,
( spl32_196
| ~ spl32_3
| ~ spl32_88 ),
inference(avatar_split_clause,[],[f1607,f1551,f713,f3578]) ).
thf(f3578,plain,
( spl32_196
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),X2) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_196])]) ).
thf(f1551,plain,
( spl32_88
<=> ! [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,[spl32_88])]) ).
thf(f1607,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),X2) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_88 ),
inference(trivial_inequality_removal,[],[f1606]) ).
thf(f1606,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),X2) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_88 ),
inference(superposition,[],[f1552,f714]) ).
thf(f1552,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) ) )
| ~ spl32_88 ),
inference(avatar_component_clause,[],[f1551]) ).
thf(f3576,plain,
( spl32_195
| ~ spl32_3
| ~ spl32_87 ),
inference(avatar_split_clause,[],[f1605,f1540,f713,f3574]) ).
thf(f3574,plain,
( spl32_195
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_195])]) ).
thf(f1540,plain,
( spl32_87
<=> ! [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,[spl32_87])]) ).
thf(f1605,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),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_87 ),
inference(trivial_inequality_removal,[],[f1604]) ).
thf(f1604,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_87 ),
inference(superposition,[],[f1541,f714]) ).
thf(f1541,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) ) )
| ~ spl32_87 ),
inference(avatar_component_clause,[],[f1540]) ).
thf(f3572,plain,
( spl32_194
| ~ spl32_3
| ~ spl32_86 ),
inference(avatar_split_clause,[],[f1588,f1536,f713,f3570]) ).
thf(f3570,plain,
( spl32_194
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X2),X0) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_194])]) ).
thf(f1536,plain,
( spl32_86
<=> ! [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,[spl32_86])]) ).
thf(f1588,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),X2),X0) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_86 ),
inference(trivial_inequality_removal,[],[f1587]) ).
thf(f1587,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X2),X0) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_86 ),
inference(superposition,[],[f1537,f714]) ).
thf(f1537,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) ) )
| ~ spl32_86 ),
inference(avatar_component_clause,[],[f1536]) ).
thf(f3568,plain,
( spl32_193
| ~ spl32_3
| ~ spl32_85 ),
inference(avatar_split_clause,[],[f1583,f1532,f713,f3566]) ).
thf(f3566,plain,
( spl32_193
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X1),X2) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_193])]) ).
thf(f1532,plain,
( spl32_85
<=> ! [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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_85])]) ).
thf(f1583,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),X1),X2) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_85 ),
inference(trivial_inequality_removal,[],[f1582]) ).
thf(f1582,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X1),X2) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_85 ),
inference(superposition,[],[f1533,f714]) ).
thf(f1533,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) ) )
| ~ spl32_85 ),
inference(avatar_component_clause,[],[f1532]) ).
thf(f3564,plain,
( spl32_192
| ~ spl32_3
| ~ spl32_84 ),
inference(avatar_split_clause,[],[f1580,f1528,f713,f3562]) ).
thf(f3562,plain,
( spl32_192
<=> ! [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) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_192])]) ).
thf(f1528,plain,
( spl32_84
<=> ! [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,[spl32_84])]) ).
thf(f1580,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) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_84 ),
inference(trivial_inequality_removal,[],[f1579]) ).
thf(f1579,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X0),X2) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_84 ),
inference(superposition,[],[f1529,f714]) ).
thf(f1529,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X1),X2),X0) ) )
| ~ spl32_84 ),
inference(avatar_component_clause,[],[f1528]) ).
thf(f3560,plain,
( spl32_191
| ~ spl32_156
| ~ spl32_188 ),
inference(avatar_split_clause,[],[f3547,f3516,f2897,f3557]) ).
thf(f3557,plain,
( spl32_191
<=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_191])]) ).
thf(f3516,plain,
( spl32_188
<=> ! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_188])]) ).
thf(f3547,plain,
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_156
| ~ spl32_188 ),
inference(trivial_inequality_removal,[],[f3537]) ).
thf(f3537,plain,
( ( $true = $false )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_156
| ~ spl32_188 ),
inference(superposition,[],[f3517,f2898]) ).
thf(f3517,plain,
( ! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_188 ),
inference(avatar_component_clause,[],[f3516]) ).
thf(f3555,plain,
( spl32_190
| ~ spl32_3
| ~ spl32_83 ),
inference(avatar_split_clause,[],[f1576,f1524,f713,f3553]) ).
thf(f3553,plain,
( spl32_190
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_190])]) ).
thf(f1524,plain,
( spl32_83
<=> ! [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,[spl32_83])]) ).
thf(f1576,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),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_83 ),
inference(trivial_inequality_removal,[],[f1575]) ).
thf(f1575,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X2),X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_83 ),
inference(superposition,[],[f1525,f714]) ).
thf(f1525,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X2),X1) ) )
| ~ spl32_83 ),
inference(avatar_component_clause,[],[f1524]) ).
thf(f3551,plain,
( spl32_189
| ~ spl32_3
| ~ spl32_82 ),
inference(avatar_split_clause,[],[f1572,f1520,f713,f3549]) ).
thf(f3549,plain,
( spl32_189
<=> ! [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) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_189])]) ).
thf(f1520,plain,
( spl32_82
<=> ! [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,[spl32_82])]) ).
thf(f1572,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) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_82 ),
inference(trivial_inequality_removal,[],[f1571]) ).
thf(f1571,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X2),X1),X0) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_82 ),
inference(superposition,[],[f1521,f714]) ).
thf(f1521,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) )
| ~ spl32_82 ),
inference(avatar_component_clause,[],[f1520]) ).
thf(f3518,plain,
( spl32_188
| ~ spl32_66
| ~ spl32_126 ),
inference(avatar_split_clause,[],[f2218,f2146,f1304,f3516]) ).
thf(f2146,plain,
( spl32_126
<=> ! [X0: d,X3: u,X25: u,X2: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X25)))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_126])]) ).
thf(f2218,plain,
( ! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_66
| ~ spl32_126 ),
inference(trivial_inequality_removal,[],[f2212]) ).
thf(f2212,plain,
( ! [X2: u,X0: d,X1: u] :
( ( $true != $true )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),sK14)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_66
| ~ spl32_126 ),
inference(superposition,[],[f1305,f2147]) ).
thf(f2147,plain,
( ! [X2: u,X3: u,X0: d,X1: d,X25: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X25)))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) )
| ~ spl32_126 ),
inference(avatar_component_clause,[],[f2146]) ).
thf(f3508,plain,
( spl32_187
| ~ spl32_66
| ~ spl32_118 ),
inference(avatar_split_clause,[],[f2057,f2016,f1304,f3506]) ).
thf(f3506,plain,
( spl32_187
<=> ! [X0: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,sK18),X0),sK14),X1))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),sK14)),X0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_187])]) ).
thf(f2016,plain,
( spl32_118
<=> ! [X11: u,X0: d,X10: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_118])]) ).
thf(f2057,plain,
( ! [X0: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,sK18),X0),sK14),X1))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),sK14)),X0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_66
| ~ spl32_118 ),
inference(trivial_inequality_removal,[],[f2051]) ).
thf(f2051,plain,
( ! [X0: u,X1: d] :
( ( $true != $true )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,sK18),X0),sK14),X1))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),sK14)),X0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_66
| ~ spl32_118 ),
inference(superposition,[],[f1305,f2017]) ).
thf(f2017,plain,
( ! [X10: u,X0: d,X11: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) ) )
| ~ spl32_118 ),
inference(avatar_component_clause,[],[f2016]) ).
thf(f3504,plain,
( spl32_186
| ~ spl32_66
| ~ spl32_117 ),
inference(avatar_split_clause,[],[f2043,f2012,f1304,f3502]) ).
thf(f3502,plain,
( spl32_186
<=> ! [X0: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK29,sK18),X0),sK14),X1))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),sK14)),X0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_186])]) ).
thf(f2012,plain,
( spl32_117
<=> ! [X0: d,X3: u,X2: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK29,X3),X2),X1),X0))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_117])]) ).
thf(f2043,plain,
( ! [X0: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK29,sK18),X0),sK14),X1))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),sK14)),X0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_66
| ~ spl32_117 ),
inference(trivial_inequality_removal,[],[f2037]) ).
thf(f2037,plain,
( ! [X0: u,X1: d] :
( ( $true != $true )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK29,sK18),X0),sK14),X1))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),sK14)),X0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) )
| ~ spl32_66
| ~ spl32_117 ),
inference(superposition,[],[f1305,f2013]) ).
thf(f2013,plain,
( ! [X2: u,X3: u,X0: d,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK29,X3),X2),X1),X0))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) )
| ~ spl32_117 ),
inference(avatar_component_clause,[],[f2012]) ).
thf(f3454,plain,
( spl32_185
| ~ spl32_3
| ~ spl32_15 ),
inference(avatar_split_clause,[],[f863,f810,f713,f3452]) ).
thf(f3452,plain,
( spl32_185
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( $false = X0 )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_185])]) ).
thf(f810,plain,
( spl32_15
<=> ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,$true),X0) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_15])]) ).
thf(f863,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( $false = X0 )
| ( $true = X1 ) )
| ~ spl32_3
| ~ spl32_15 ),
inference(duplicate_literal_removal,[],[f862]) ).
thf(f862,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( $false = X0 )
| ( $false = X0 )
| ( $true = X1 ) )
| ~ spl32_3
| ~ spl32_15 ),
inference(binary_proxy_clausification,[],[f860]) ).
thf(f860,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( X0 = X1 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_15 ),
inference(duplicate_literal_removal,[],[f854]) ).
thf(f854,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) )
| ( X0 = X1 )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_15 ),
inference(binary_proxy_clausification,[],[f853]) ).
thf(f853,plain,
( ! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) = X0 )
| ( X0 = X1 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_15 ),
inference(superposition,[],[f811,f714]) ).
thf(f811,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,$true),X0) )
| ( $true = X0 ) )
| ~ spl32_15 ),
inference(avatar_component_clause,[],[f810]) ).
thf(f3450,plain,
( spl32_184
| ~ spl32_3
| ~ spl32_80 ),
inference(avatar_split_clause,[],[f1483,f1439,f713,f3448]) ).
thf(f3448,plain,
( spl32_184
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X1),$true),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_184])]) ).
thf(f1439,plain,
( spl32_80
<=> ! [X2: $o,X0: $o,X3: $o] :
( ( $true = X0 )
| ( $true = X3 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),$true),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_80])]) ).
thf(f1483,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X1),$true),X2) ) )
| ~ spl32_3
| ~ spl32_80 ),
inference(trivial_inequality_removal,[],[f1482]) ).
thf(f1482,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X1),$true),X2) ) )
| ~ spl32_3
| ~ spl32_80 ),
inference(superposition,[],[f1440,f714]) ).
thf(f1440,plain,
( ! [X2: $o,X3: $o,X0: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),$true),X0) )
| ( $true = X3 )
| ( $true = X0 ) )
| ~ spl32_80 ),
inference(avatar_component_clause,[],[f1439]) ).
thf(f3446,plain,
( spl32_183
| ~ spl32_3
| ~ spl32_79 ),
inference(avatar_split_clause,[],[f1453,f1435,f713,f3444]) ).
thf(f3444,plain,
( spl32_183
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_183])]) ).
thf(f1435,plain,
( spl32_79
<=> ! [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)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_79])]) ).
thf(f1453,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_79 ),
inference(trivial_inequality_removal,[],[f1452]) ).
thf(f1452,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_79 ),
inference(superposition,[],[f1436,f714]) ).
thf(f1436,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X2),X1),X0) )
| ( $true = X1 )
| ( $true = X2 ) )
| ~ spl32_79 ),
inference(avatar_component_clause,[],[f1435]) ).
thf(f3410,plain,
( spl32_182
| ~ spl32_3
| ~ spl32_76 ),
inference(avatar_split_clause,[],[f1417,f1393,f713,f3408]) ).
thf(f3408,plain,
( spl32_182
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),$true),$true),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_182])]) ).
thf(f1393,plain,
( spl32_76
<=> ! [X0: $o,X3: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),$true),$true),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_76])]) ).
thf(f1417,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),$true),$true),X1) ) )
| ~ spl32_3
| ~ spl32_76 ),
inference(trivial_inequality_removal,[],[f1416]) ).
thf(f1416,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),$true),$true),X1) ) )
| ~ spl32_3
| ~ spl32_76 ),
inference(superposition,[],[f1394,f714]) ).
thf(f1394,plain,
( ! [X3: $o,X0: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),$true),$true),X0) )
| ( $true = X0 ) )
| ~ spl32_76 ),
inference(avatar_component_clause,[],[f1393]) ).
thf(f3406,plain,
( spl32_181
| ~ spl32_3
| ~ spl32_75 ),
inference(avatar_split_clause,[],[f1403,f1389,f713,f3404]) ).
thf(f3404,plain,
( spl32_181
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X0),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_181])]) ).
thf(f1389,plain,
( spl32_75
<=> ! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X2),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_75])]) ).
thf(f1403,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_75 ),
inference(trivial_inequality_removal,[],[f1402]) ).
thf(f1402,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_75 ),
inference(superposition,[],[f1390,f714]) ).
thf(f1390,plain,
( ! [X2: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X2),X1),$true) )
| ( $true = X2 ) )
| ~ spl32_75 ),
inference(avatar_component_clause,[],[f1389]) ).
thf(f3316,plain,
( spl32_180
| ~ spl32_3
| ~ spl32_14 ),
inference(avatar_split_clause,[],[f852,f806,f713,f3314]) ).
thf(f3314,plain,
( spl32_180
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( $false = X0 )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_180])]) ).
thf(f806,plain,
( spl32_14
<=> ! [X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),$true) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_14])]) ).
thf(f852,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( $false = X0 )
| ( $true = X1 ) )
| ~ spl32_3
| ~ spl32_14 ),
inference(duplicate_literal_removal,[],[f851]) ).
thf(f851,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( $false = X0 )
| ( $false = X0 )
| ( $true = X1 ) )
| ~ spl32_3
| ~ spl32_14 ),
inference(binary_proxy_clausification,[],[f849]) ).
thf(f849,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( X0 = X1 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_14 ),
inference(duplicate_literal_removal,[],[f843]) ).
thf(f843,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( X0 = X1 )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_14 ),
inference(binary_proxy_clausification,[],[f842]) ).
thf(f842,plain,
( ! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) = X0 )
| ( X0 = X1 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_14 ),
inference(superposition,[],[f807,f714]) ).
thf(f807,plain,
( ! [X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),$true) )
| ( $true = X1 ) )
| ~ spl32_14 ),
inference(avatar_component_clause,[],[f806]) ).
thf(f3231,plain,
( spl32_179
| ~ spl32_68
| ~ spl32_86 ),
inference(avatar_split_clause,[],[f1590,f1536,f1314,f3229]) ).
thf(f3229,plain,
( spl32_179
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X2),X0) )
| ( $true = X2 )
| ( $true = X1 )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_179])]) ).
thf(f1314,plain,
( spl32_68
<=> ! [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 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_68])]) ).
thf(f1590,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),X2),X0) )
| ( $true = X2 )
| ( $true = X1 )
| ( $true = X0 ) )
| ~ spl32_68
| ~ spl32_86 ),
inference(trivial_inequality_removal,[],[f1585]) ).
thf(f1585,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X1),X2),X0) )
| ( $true = X2 )
| ( $true = X1 )
| ( $true = X0 ) )
| ~ spl32_68
| ~ spl32_86 ),
inference(superposition,[],[f1537,f1315]) ).
thf(f1315,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 ) )
| ~ spl32_68 ),
inference(avatar_component_clause,[],[f1314]) ).
thf(f3227,plain,
( spl32_178
| ~ spl32_3
| ~ spl32_73 ),
inference(avatar_split_clause,[],[f1378,f1338,f713,f3225]) ).
thf(f3225,plain,
( spl32_178
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_178])]) ).
thf(f1338,plain,
( spl32_73
<=> ! [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,[spl32_73])]) ).
thf(f1378,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_73 ),
inference(trivial_inequality_removal,[],[f1377]) ).
thf(f1377,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_73 ),
inference(superposition,[],[f1339,f714]) ).
thf(f1339,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) )
| ( $false = X1 )
| ( $true = X2 )
| ( $false = X0 ) )
| ~ spl32_73 ),
inference(avatar_component_clause,[],[f1338]) ).
thf(f3223,plain,
( spl32_177
| ~ spl32_3
| ~ spl32_72 ),
inference(avatar_split_clause,[],[f1373,f1330,f713,f3221]) ).
thf(f3221,plain,
( spl32_177
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_177])]) ).
thf(f1330,plain,
( spl32_72
<=> ! [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,[spl32_72])]) ).
thf(f1373,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_72 ),
inference(trivial_inequality_removal,[],[f1372]) ).
thf(f1372,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_72 ),
inference(superposition,[],[f1331,f714]) ).
thf(f1331,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) )
| ( $false = X1 )
| ( $true = X2 )
| ( $false = X0 ) )
| ~ spl32_72 ),
inference(avatar_component_clause,[],[f1330]) ).
thf(f3219,plain,
( spl32_176
| ~ spl32_3
| ~ spl32_71 ),
inference(avatar_split_clause,[],[f1366,f1326,f713,f3217]) ).
thf(f3217,plain,
( spl32_176
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_176])]) ).
thf(f1326,plain,
( spl32_71
<=> ! [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,[spl32_71])]) ).
thf(f1366,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_71 ),
inference(trivial_inequality_removal,[],[f1365]) ).
thf(f1365,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $false = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP4,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_71 ),
inference(superposition,[],[f1327,f714]) ).
thf(f1327,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) )
| ( $false = X1 )
| ( $true = X2 )
| ( $false = X0 ) )
| ~ spl32_71 ),
inference(avatar_component_clause,[],[f1326]) ).
thf(f3215,plain,
( spl32_175
| ~ spl32_3
| ~ spl32_70 ),
inference(avatar_split_clause,[],[f1360,f1322,f713,f3213]) ).
thf(f3213,plain,
( spl32_175
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_175])]) ).
thf(f1322,plain,
( spl32_70
<=> ! [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)),sP7,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_70])]) ).
thf(f1360,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_70 ),
inference(trivial_inequality_removal,[],[f1359]) ).
thf(f1359,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_70 ),
inference(superposition,[],[f1323,f714]) ).
thf(f1323,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 )
| ( $true = X2 )
| ( $false = X0 ) )
| ~ spl32_70 ),
inference(avatar_component_clause,[],[f1322]) ).
thf(f3211,plain,
( spl32_174
| ~ spl32_3
| ~ spl32_13 ),
inference(avatar_split_clause,[],[f837,f802,f713,f3209]) ).
thf(f3209,plain,
( spl32_174
<=> ! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $false = X0 )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_174])]) ).
thf(f802,plain,
( spl32_13
<=> ! [X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,$true),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_13])]) ).
thf(f837,plain,
( ! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $false = X0 )
| ( $true = X1 ) )
| ~ spl32_3
| ~ spl32_13 ),
inference(duplicate_literal_removal,[],[f836]) ).
thf(f836,plain,
( ! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $false = X0 )
| ( $false = X0 )
| ( $true = X1 ) )
| ~ spl32_3
| ~ spl32_13 ),
inference(binary_proxy_clausification,[],[f834]) ).
thf(f834,plain,
( ! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( X0 = X1 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_13 ),
inference(duplicate_literal_removal,[],[f833]) ).
thf(f833,plain,
( ! [X0: $o,X1: $o] :
( ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( X0 = X1 )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_13 ),
inference(binary_proxy_clausification,[],[f827]) ).
thf(f827,plain,
( ! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) != X0 )
| ( X0 = X1 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_13 ),
inference(superposition,[],[f803,f714]) ).
thf(f803,plain,
( ! [X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,$true),X1) )
| ( $true = X1 ) )
| ~ spl32_13 ),
inference(avatar_component_clause,[],[f802]) ).
thf(f3207,plain,
( spl32_173
| ~ spl32_3
| ~ spl32_69 ),
inference(avatar_split_clause,[],[f1353,f1318,f713,f3205]) ).
thf(f3205,plain,
( spl32_173
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_173])]) ).
thf(f1318,plain,
( spl32_69
<=> ! [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)),sP10,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_69])]) ).
thf(f1353,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_69 ),
inference(trivial_inequality_removal,[],[f1352]) ).
thf(f1352,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $false = X0 )
| ( $false = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_69 ),
inference(superposition,[],[f1319,f714]) ).
thf(f1319,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 )
| ( $false = X2 )
| ( $false = X0 ) )
| ~ spl32_69 ),
inference(avatar_component_clause,[],[f1318]) ).
thf(f3203,plain,
( spl32_172
| ~ spl32_3
| ~ spl32_67 ),
inference(avatar_split_clause,[],[f1345,f1310,f713,f3201]) ).
thf(f3201,plain,
( spl32_172
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_172])]) ).
thf(f1310,plain,
( spl32_67
<=> ! [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,[spl32_67])]) ).
thf(f1345,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_67 ),
inference(trivial_inequality_removal,[],[f1344]) ).
thf(f1344,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true = X0 )
| ( $true = X2 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP3,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_67 ),
inference(superposition,[],[f1311,f714]) ).
thf(f1311,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 )
| ( $true = X2 )
| ( $true = X0 ) )
| ~ spl32_67 ),
inference(avatar_component_clause,[],[f1310]) ).
thf(f3199,plain,
spl32_171,
inference(avatar_split_clause,[],[f602,f3197]) ).
thf(f3197,plain,
( spl32_171
<=> ! [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) )
| ( $false = X0 )
| ( $true = X2 )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_171])]) ).
thf(f602,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) )
| ( $false = X0 )
| ( $true = X2 )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f374]) ).
thf(f374,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,[],[f219]) ).
thf(f219,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,[],[f162]) ).
thf(f162,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,[],[f96,f161,f160,f159,f158]) ).
thf(f158,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(f159,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(f160,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) )
<=> ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f161,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) )
<=> ( ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = vAPP($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(f96,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( X0 = X1 ) )
<=> ( ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 ) )
& ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = vAPP($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,[],[f95]) ).
thf(f95,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,[],[f45]) ).
thf(f45,axiom,
! [X46: $o,X47: $o,X48: $o] :
( ( X48
<=> ( X46 = X47 ) )
<=> ( ( vAPP($o,$o,vNOT,X48)
| vAPP($o,$o,vNOT,X47)
| X46 )
& ( vAPP($o,$o,vNOT,X48)
| vAPP($o,$o,vNOT,X46)
| X47 )
& ( vAPP($o,$o,vNOT,X47)
| vAPP($o,$o,vNOT,X46)
| X48 )
& ( X46
| X47
| X48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__eq) ).
thf(f3195,plain,
spl32_170,
inference(avatar_split_clause,[],[f601,f3193]) ).
thf(f3193,plain,
( spl32_170
<=> ! [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) )
| ( $true = X0 )
| ( $true = X2 )
| ( $false = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_170])]) ).
thf(f601,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) )
| ( $true = X0 )
| ( $true = X2 )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[],[f374]) ).
thf(f3162,plain,
( spl32_169
| ~ spl32_3
| ~ spl32_66 ),
inference(avatar_split_clause,[],[f1308,f1304,f713,f3160]) ).
thf(f3160,plain,
( spl32_169
<=> ! [X0: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X0)))) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_169])]) ).
thf(f1308,plain,
( ! [X0: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X0)))) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X0)))) ) )
| ~ spl32_3
| ~ spl32_66 ),
inference(trivial_inequality_removal,[],[f1307]) ).
thf(f1307,plain,
( ! [X0: u] :
( ( $true != $true )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X0)))) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X0)))) ) )
| ~ spl32_3
| ~ spl32_66 ),
inference(superposition,[],[f1305,f714]) ).
thf(f2995,plain,
( spl32_168
| ~ spl32_62
| ~ spl32_89 ),
inference(avatar_split_clause,[],[f1614,f1555,f1210,f2993]) ).
thf(f2993,plain,
( spl32_168
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X1),X0) )
| ( $true = X1 )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_168])]) ).
thf(f1210,plain,
( spl32_62
<=> ! [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 = X0 )
| ( $true = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_62])]) ).
thf(f1614,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X1),X0) )
| ( $true = X1 )
| ( $true = X0 ) )
| ~ spl32_62
| ~ spl32_89 ),
inference(trivial_inequality_removal,[],[f1609]) ).
thf(f1609,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X1),X0) )
| ( $true = X1 )
| ( $true = X0 ) )
| ~ spl32_62
| ~ spl32_89 ),
inference(superposition,[],[f1556,f1211]) ).
thf(f1211,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 = X0 )
| ( $true = X2 ) )
| ~ spl32_62 ),
inference(avatar_component_clause,[],[f1210]) ).
thf(f2991,plain,
( spl32_167
| ~ spl32_3
| ~ spl32_65 ),
inference(avatar_split_clause,[],[f1302,f1222,f713,f2989]) ).
thf(f2989,plain,
( spl32_167
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_167])]) ).
thf(f1222,plain,
( spl32_65
<=> ! [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)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_65])]) ).
thf(f1302,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_65 ),
inference(trivial_inequality_removal,[],[f1301]) ).
thf(f1301,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X2 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_65 ),
inference(superposition,[],[f1223,f714]) ).
thf(f1223,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 )
| ( $false = X1 ) )
| ~ spl32_65 ),
inference(avatar_component_clause,[],[f1222]) ).
thf(f2987,plain,
( spl32_166
| ~ spl32_3
| ~ spl32_64 ),
inference(avatar_split_clause,[],[f1300,f1218,f713,f2985]) ).
thf(f2985,plain,
( spl32_166
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_166])]) ).
thf(f1218,plain,
( spl32_64
<=> ! [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)),sP9,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_64])]) ).
thf(f1300,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_64 ),
inference(trivial_inequality_removal,[],[f1299]) ).
thf(f1299,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X2 )
| ( $false = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_64 ),
inference(superposition,[],[f1219,f714]) ).
thf(f1219,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 )
| ( $false = X2 ) )
| ~ spl32_64 ),
inference(avatar_component_clause,[],[f1218]) ).
thf(f2983,plain,
( spl32_165
| ~ spl32_3
| ~ spl32_63 ),
inference(avatar_split_clause,[],[f1291,f1214,f713,f2981]) ).
thf(f2981,plain,
( spl32_165
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_165])]) ).
thf(f1214,plain,
( spl32_63
<=> ! [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,[spl32_63])]) ).
thf(f1291,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_63 ),
inference(trivial_inequality_removal,[],[f1290]) ).
thf(f1290,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X2 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_63 ),
inference(superposition,[],[f1215,f714]) ).
thf(f1215,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 = X0 )
| ( $false = X1 ) )
| ~ spl32_63 ),
inference(avatar_component_clause,[],[f1214]) ).
thf(f2979,plain,
( spl32_164
| ~ spl32_3
| ~ spl32_61 ),
inference(avatar_split_clause,[],[f1235,f1206,f713,f2977]) ).
thf(f2977,plain,
( spl32_164
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_164])]) ).
thf(f1206,plain,
( spl32_61
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $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,[spl32_61])]) ).
thf(f1235,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X0),X1) ) )
| ~ spl32_3
| ~ spl32_61 ),
inference(trivial_inequality_removal,[],[f1234]) ).
thf(f1234,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X0),X1) ) )
| ~ spl32_3
| ~ spl32_61 ),
inference(superposition,[],[f1207,f714]) ).
thf(f1207,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X1),X0) )
| ( $true = X1 )
| ( $true = X0 ) )
| ~ spl32_61 ),
inference(avatar_component_clause,[],[f1206]) ).
thf(f2975,plain,
( spl32_163
| ~ spl32_126
| ~ spl32_156 ),
inference(avatar_split_clause,[],[f2917,f2897,f2146,f2972]) ).
thf(f2972,plain,
( spl32_163
<=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_163])]) ).
thf(f2917,plain,
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)))) )
| ~ spl32_126
| ~ spl32_156 ),
inference(trivial_inequality_removal,[],[f2904]) ).
thf(f2904,plain,
( ( $true = $false )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)))) )
| ~ spl32_126
| ~ spl32_156 ),
inference(superposition,[],[f2898,f2147]) ).
thf(f2970,plain,
( spl32_162
| ~ spl32_3
| ~ spl32_59 ),
inference(avatar_split_clause,[],[f1230,f1198,f713,f2968]) ).
thf(f2968,plain,
( spl32_162
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_162])]) ).
thf(f1198,plain,
( spl32_59
<=> ! [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) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_59])]) ).
thf(f1230,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_59 ),
inference(trivial_inequality_removal,[],[f1229]) ).
thf(f1229,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_59 ),
inference(superposition,[],[f1199,f714]) ).
thf(f1199,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 ) )
| ~ spl32_59 ),
inference(avatar_component_clause,[],[f1198]) ).
thf(f2966,plain,
( spl32_161
| ~ spl32_3
| ~ spl32_58 ),
inference(avatar_split_clause,[],[f1226,f1194,f713,f2964]) ).
thf(f2964,plain,
( spl32_161
<=> ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_161])]) ).
thf(f1194,plain,
( spl32_58
<=> ! [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)),sP12,X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_58])]) ).
thf(f1226,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_58 ),
inference(trivial_inequality_removal,[],[f1225]) ).
thf(f1225,plain,
( ! [X2: $o,X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X2 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),X2) ) )
| ~ spl32_3
| ~ spl32_58 ),
inference(superposition,[],[f1195,f714]) ).
thf(f1195,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 = X0 )
| ( $true = X2 ) )
| ~ spl32_58 ),
inference(avatar_component_clause,[],[f1194]) ).
thf(f2962,plain,
spl32_160,
inference(avatar_split_clause,[],[f604,f2960]) ).
thf(f2960,plain,
( spl32_160
<=> ! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),$true) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_160])]) ).
thf(f604,plain,
! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),$true) )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f525]) ).
thf(f525,plain,
! [X0: $o,X1: $o] :
( ( X0 = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),$true) ) ),
inference(equality_resolution,[],[f376]) ).
thf(f376,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( X0 = X1 )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),X2) ) ),
inference(cnf_transformation,[],[f219]) ).
thf(f2958,plain,
spl32_159,
inference(avatar_split_clause,[],[f603,f2956]) ).
thf(f2956,plain,
( spl32_159
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),$true) )
| ( $false = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_159])]) ).
thf(f603,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X1),$true) )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[],[f525]) ).
thf(f2925,plain,
( spl32_158
| ~ spl32_3
| ~ spl32_57 ),
inference(avatar_split_clause,[],[f1190,f1182,f713,f2923]) ).
thf(f2923,plain,
( spl32_158
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_158])]) ).
thf(f1182,plain,
( spl32_57
<=> ! [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,[spl32_57])]) ).
thf(f1190,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) ) )
| ~ spl32_3
| ~ spl32_57 ),
inference(trivial_inequality_removal,[],[f1189]) ).
thf(f1189,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) ) )
| ~ spl32_3
| ~ spl32_57 ),
inference(superposition,[],[f1183,f714]) ).
thf(f1183,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) ) )
| ~ spl32_57 ),
inference(avatar_component_clause,[],[f1182]) ).
thf(f2921,plain,
( spl32_157
| ~ spl32_3
| ~ spl32_56 ),
inference(avatar_split_clause,[],[f1186,f1178,f713,f2919]) ).
thf(f2919,plain,
( spl32_157
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_157])]) ).
thf(f1178,plain,
( spl32_56
<=> ! [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,[spl32_56])]) ).
thf(f1186,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) ) )
| ~ spl32_3
| ~ spl32_56 ),
inference(trivial_inequality_removal,[],[f1185]) ).
thf(f1185,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) ) )
| ~ spl32_3
| ~ spl32_56 ),
inference(superposition,[],[f1179,f714]) ).
thf(f1179,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) ) )
| ~ spl32_56 ),
inference(avatar_component_clause,[],[f1178]) ).
thf(f2899,plain,
( spl32_156
| ~ spl32_18
| ~ spl32_127 ),
inference(avatar_split_clause,[],[f2233,f2150,f865,f2897]) ).
thf(f865,plain,
( spl32_18
<=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_18])]) ).
thf(f2150,plain,
( spl32_127
<=> ! [X17: u,X19: u,X0: d,X16: u,X1: d] :
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_127])]) ).
thf(f2233,plain,
( ! [X0: u] : ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK15),X0)))))) )
| ~ spl32_18
| ~ spl32_127 ),
inference(trivial_inequality_removal,[],[f2230]) ).
thf(f2230,plain,
( ! [X0: u] :
( ( $true != $true )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK15),X0)))))) ) )
| ~ spl32_18
| ~ spl32_127 ),
inference(superposition,[],[f2151,f867]) ).
thf(f867,plain,
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)))) )
| ~ spl32_18 ),
inference(avatar_component_clause,[],[f865]) ).
thf(f2151,plain,
( ! [X0: d,X1: d,X19: u,X16: u,X17: u] :
( ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19)))))) ) )
| ~ spl32_127 ),
inference(avatar_component_clause,[],[f2150]) ).
thf(f2777,plain,
( spl32_155
| ~ spl32_44
| ~ spl32_89 ),
inference(avatar_split_clause,[],[f1615,f1555,f1056,f2775]) ).
thf(f2775,plain,
( spl32_155
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),$true) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_155])]) ).
thf(f1056,plain,
( spl32_44
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),X1),X0) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_44])]) ).
thf(f1615,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),$true) )
| ( $true = X0 ) )
| ~ spl32_44
| ~ spl32_89 ),
inference(trivial_inequality_removal,[],[f1608]) ).
thf(f1608,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),X1),$true) )
| ( $true = X0 ) )
| ~ spl32_44
| ~ spl32_89 ),
inference(superposition,[],[f1556,f1057]) ).
thf(f1057,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),X1),X0) )
| ( $true = X1 ) )
| ~ spl32_44 ),
inference(avatar_component_clause,[],[f1056]) ).
thf(f2773,plain,
( spl32_154
| ~ spl32_3
| ~ spl32_46 ),
inference(avatar_split_clause,[],[f1162,f1064,f713,f2771]) ).
thf(f2771,plain,
( spl32_154
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),$true),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_154])]) ).
thf(f1064,plain,
( spl32_46
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),$true),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_46])]) ).
thf(f1162,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),$true),X0) ) )
| ~ spl32_3
| ~ spl32_46 ),
inference(trivial_inequality_removal,[],[f1161]) ).
thf(f1161,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),$true),X0) ) )
| ~ spl32_3
| ~ spl32_46 ),
inference(superposition,[],[f1065,f714]) ).
thf(f1065,plain,
( ! [X0: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),$true),X0) )
| ( $true = X0 ) )
| ~ spl32_46 ),
inference(avatar_component_clause,[],[f1064]) ).
thf(f2764,plain,
( spl32_153
| ~ spl32_3
| ~ spl32_45 ),
inference(avatar_split_clause,[],[f1147,f1060,f713,f2762]) ).
thf(f2762,plain,
( spl32_153
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_153])]) ).
thf(f1060,plain,
( spl32_45
<=> ! [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,[spl32_45])]) ).
thf(f1147,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_45 ),
inference(trivial_inequality_removal,[],[f1146]) ).
thf(f1146,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_45 ),
inference(superposition,[],[f1061,f714]) ).
thf(f1061,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 ) )
| ~ spl32_45 ),
inference(avatar_component_clause,[],[f1060]) ).
thf(f2760,plain,
( spl32_152
| ~ spl32_3
| ~ spl32_43 ),
inference(avatar_split_clause,[],[f1121,f1052,f713,f2758]) ).
thf(f2758,plain,
( spl32_152
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),$true),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_152])]) ).
thf(f1052,plain,
( spl32_43
<=> ! [X2: $o,X0: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),$true),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_43])]) ).
thf(f1121,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),$true),X1) ) )
| ~ spl32_3
| ~ spl32_43 ),
inference(trivial_inequality_removal,[],[f1120]) ).
thf(f1120,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),$true),X1) ) )
| ~ spl32_3
| ~ spl32_43 ),
inference(superposition,[],[f1053,f714]) ).
thf(f1053,plain,
( ! [X2: $o,X0: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),$true),X0) )
| ( $true = X2 ) )
| ~ spl32_43 ),
inference(avatar_component_clause,[],[f1052]) ).
thf(f2756,plain,
( spl32_151
| ~ spl32_3
| ~ spl32_41 ),
inference(avatar_split_clause,[],[f1106,f1044,f713,f2754]) ).
thf(f2754,plain,
( spl32_151
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_151])]) ).
thf(f1044,plain,
( spl32_41
<=> ! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),$true) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_41])]) ).
thf(f1106,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_41 ),
inference(trivial_inequality_removal,[],[f1105]) ).
thf(f1105,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X0),X1),$true) ) )
| ~ spl32_3
| ~ spl32_41 ),
inference(superposition,[],[f1045,f714]) ).
thf(f1045,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 = X2 ) )
| ~ spl32_41 ),
inference(avatar_component_clause,[],[f1044]) ).
thf(f2752,plain,
( spl32_150
| ~ spl32_3
| ~ spl32_40 ),
inference(avatar_split_clause,[],[f1101,f1040,f713,f2750]) ).
thf(f2750,plain,
( spl32_150
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_150])]) ).
thf(f1040,plain,
( spl32_40
<=> ! [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,[spl32_40])]) ).
thf(f1101,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X0),X1) ) )
| ~ spl32_3
| ~ spl32_40 ),
inference(trivial_inequality_removal,[],[f1100]) ).
thf(f1100,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X0),X0),X1) ) )
| ~ spl32_3
| ~ spl32_40 ),
inference(superposition,[],[f1041,f714]) ).
thf(f1041,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 ) )
| ~ spl32_40 ),
inference(avatar_component_clause,[],[f1040]) ).
thf(f2748,plain,
spl32_149,
inference(avatar_split_clause,[],[f693,f2746]) ).
thf(f2746,plain,
( spl32_149
<=> ! [X0: $o] :
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X0))) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_149])]) ).
thf(f693,plain,
! [X0: $o] :
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X0))) )
| ( $true = X0 ) ),
inference(binary_proxy_clausification,[],[f264]) ).
thf(f264,plain,
! [X0: $o] : ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X0))) = X0 ),
inference(cnf_transformation,[],[f109]) ).
thf(f109,plain,
! [X0: $o] : ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X0))) = X0 ),
inference(rectify,[],[f15]) ).
thf(f15,axiom,
! [X8: $o] : ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X8))) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).
thf(f2744,plain,
spl32_148,
inference(avatar_split_clause,[],[f692,f2742]) ).
thf(f2742,plain,
( spl32_148
<=> ! [X0: $o] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X0))) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_148])]) ).
thf(f692,plain,
! [X0: $o] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X0))) )
| ( $false = X0 ) ),
inference(binary_proxy_clausification,[],[f264]) ).
thf(f2700,plain,
( spl32_147
| ~ spl32_18
| ~ spl32_142 ),
inference(avatar_split_clause,[],[f2660,f2656,f865,f2697]) ).
thf(f2697,plain,
( spl32_147
<=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_147])]) ).
thf(f2656,plain,
( spl32_142
<=> ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_142])]) ).
thf(f2660,plain,
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,$true))) )
| ~ spl32_18
| ~ spl32_142 ),
inference(superposition,[],[f867,f2658]) ).
thf(f2658,plain,
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,$true)) )
| ~ spl32_142 ),
inference(avatar_component_clause,[],[f2656]) ).
thf(f2695,plain,
( spl32_146
| ~ spl32_37
| ~ spl32_89 ),
inference(avatar_split_clause,[],[f1613,f1555,f980,f2693]) ).
thf(f2693,plain,
( spl32_146
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),$true),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_146])]) ).
thf(f980,plain,
( spl32_37
<=> ! [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,[spl32_37])]) ).
thf(f1613,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),$true),$true) )
| ~ spl32_37
| ~ spl32_89 ),
inference(trivial_inequality_removal,[],[f1610]) ).
thf(f1610,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X0),$true),$true) ) )
| ~ spl32_37
| ~ spl32_89 ),
inference(superposition,[],[f1556,f981]) ).
thf(f981,plain,
( ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),X1),$true) )
| ~ spl32_37 ),
inference(avatar_component_clause,[],[f980]) ).
thf(f2691,plain,
( spl32_145
| ~ spl32_34
| ~ spl32_86 ),
inference(avatar_split_clause,[],[f1591,f1536,f968,f2689]) ).
thf(f2689,plain,
( spl32_145
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,$true),X0),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_145])]) ).
thf(f968,plain,
( spl32_34
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_34])]) ).
thf(f1591,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,$true),X0),$true) )
| ~ spl32_34
| ~ spl32_86 ),
inference(trivial_inequality_removal,[],[f1584]) ).
thf(f1584,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,$true),X0),$true) ) )
| ~ spl32_34
| ~ spl32_86 ),
inference(superposition,[],[f1537,f969]) ).
thf(f969,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),$true),X0) )
| ~ spl32_34 ),
inference(avatar_component_clause,[],[f968]) ).
thf(f2687,plain,
( spl32_144
| ~ spl32_33
| ~ spl32_86 ),
inference(avatar_split_clause,[],[f1589,f1536,f964,f2685]) ).
thf(f2685,plain,
( spl32_144
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),$true),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_144])]) ).
thf(f964,plain,
( spl32_33
<=> ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X1),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_33])]) ).
thf(f1589,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),$true),$true) )
| ~ spl32_33
| ~ spl32_86 ),
inference(trivial_inequality_removal,[],[f1586]) ).
thf(f1586,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X0),$true),$true) ) )
| ~ spl32_33
| ~ spl32_86 ),
inference(superposition,[],[f1537,f965]) ).
thf(f965,plain,
( ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X1),$true) )
| ~ spl32_33 ),
inference(avatar_component_clause,[],[f964]) ).
thf(f2683,plain,
( spl32_143
| ~ spl32_31
| ~ spl32_84 ),
inference(avatar_split_clause,[],[f1581,f1528,f956,f2681]) ).
thf(f2681,plain,
( spl32_143
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X0),X0),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_143])]) ).
thf(f956,plain,
( spl32_31
<=> ! [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,[spl32_31])]) ).
thf(f1581,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X0),X0),$true) )
| ~ spl32_31
| ~ spl32_84 ),
inference(trivial_inequality_removal,[],[f1578]) ).
thf(f1578,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP5,X0),X0),$true) ) )
| ~ spl32_31
| ~ spl32_84 ),
inference(superposition,[],[f1529,f957]) ).
thf(f957,plain,
( ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP6,X1),X1),$true) )
| ~ spl32_31 ),
inference(avatar_component_clause,[],[f956]) ).
thf(f2659,plain,
( spl32_142
| ~ spl32_18
| ~ spl32_81 ),
inference(avatar_split_clause,[],[f1514,f1510,f865,f2656]) ).
thf(f1514,plain,
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,$true)) )
| ~ spl32_18
| ~ spl32_81 ),
inference(superposition,[],[f1511,f867]) ).
thf(f2568,plain,
( spl32_141
| ~ spl32_3
| ~ spl32_25 ),
inference(avatar_split_clause,[],[f934,f899,f713,f2566]) ).
thf(f2566,plain,
( spl32_141
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_141])]) ).
thf(f899,plain,
( spl32_25
<=> ! [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,[spl32_25])]) ).
thf(f934,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) ) )
| ~ spl32_3
| ~ spl32_25 ),
inference(trivial_inequality_removal,[],[f933]) ).
thf(f933,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X0),X1) ) )
| ~ spl32_3
| ~ spl32_25 ),
inference(superposition,[],[f900,f714]) ).
thf(f900,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true = X0 )
| ( $true = X1 ) )
| ~ spl32_25 ),
inference(avatar_component_clause,[],[f899]) ).
thf(f2564,plain,
( spl32_140
| ~ spl32_3
| ~ spl32_24 ),
inference(avatar_split_clause,[],[f931,f895,f713,f2562]) ).
thf(f2562,plain,
( spl32_140
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_140])]) ).
thf(f895,plain,
( spl32_24
<=> ! [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,[spl32_24])]) ).
thf(f931,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) ) )
| ~ spl32_3
| ~ spl32_24 ),
inference(trivial_inequality_removal,[],[f930]) ).
thf(f930,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) ) )
| ~ spl32_3
| ~ spl32_24 ),
inference(superposition,[],[f896,f714]) ).
thf(f896,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $true = X1 )
| ( $true = X0 ) )
| ~ spl32_24 ),
inference(avatar_component_clause,[],[f895]) ).
thf(f2560,plain,
( spl32_139
| ~ spl32_3
| ~ spl32_23 ),
inference(avatar_split_clause,[],[f923,f891,f713,f2558]) ).
thf(f2558,plain,
( spl32_139
<=> ! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_139])]) ).
thf(f891,plain,
( spl32_23
<=> ! [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,[spl32_23])]) ).
thf(f923,plain,
( ! [X0: $o,X1: $o] :
( ( $false = X0 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) )
| ~ spl32_3
| ~ spl32_23 ),
inference(trivial_inequality_removal,[],[f922]) ).
thf(f922,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $false = X0 )
| ( $false = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) )
| ~ spl32_3
| ~ spl32_23 ),
inference(superposition,[],[f892,f714]) ).
thf(f892,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( $false = X1 )
| ( $false = X0 ) )
| ~ spl32_23 ),
inference(avatar_component_clause,[],[f891]) ).
thf(f2556,plain,
( spl32_138
| ~ spl32_3
| ~ spl32_22 ),
inference(avatar_split_clause,[],[f918,f887,f713,f2554]) ).
thf(f2554,plain,
( spl32_138
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_138])]) ).
thf(f887,plain,
( spl32_22
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_22])]) ).
thf(f918,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) ) )
| ~ spl32_3
| ~ spl32_22 ),
inference(trivial_inequality_removal,[],[f917]) ).
thf(f917,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) ) )
| ~ spl32_3
| ~ spl32_22 ),
inference(superposition,[],[f888,f714]) ).
thf(f888,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
| ( $true = X0 )
| ( $true = X1 ) )
| ~ spl32_22 ),
inference(avatar_component_clause,[],[f887]) ).
thf(f2552,plain,
( spl32_137
| ~ spl32_3
| ~ spl32_21 ),
inference(avatar_split_clause,[],[f906,f883,f713,f2550]) ).
thf(f2550,plain,
( spl32_137
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_137])]) ).
thf(f883,plain,
( spl32_21
<=> ! [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,[spl32_21])]) ).
thf(f906,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) )
| ~ spl32_3
| ~ spl32_21 ),
inference(trivial_inequality_removal,[],[f905]) ).
thf(f905,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),X1) ) )
| ~ spl32_3
| ~ spl32_21 ),
inference(superposition,[],[f884,f714]) ).
thf(f884,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) )
| ( $true = X0 )
| ( $true = X1 ) )
| ~ spl32_21 ),
inference(avatar_component_clause,[],[f883]) ).
thf(f2543,plain,
( spl32_136
| ~ spl32_3
| spl32_19 ),
inference(avatar_split_clause,[],[f875,f870,f713,f2540]) ).
thf(f870,plain,
( spl32_19
<=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_19])]) ).
thf(f875,plain,
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_3
| spl32_19 ),
inference(trivial_inequality_removal,[],[f874]) ).
thf(f874,plain,
( ( $true != $true )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| ~ spl32_3
| spl32_19 ),
inference(superposition,[],[f872,f714]) ).
thf(f872,plain,
( ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
| spl32_19 ),
inference(avatar_component_clause,[],[f870]) ).
thf(f2381,plain,
spl32_135,
inference(avatar_split_clause,[],[f449,f2379]) ).
thf(f2379,plain,
( spl32_135
<=> ! [X2: d,X3: u,X4: u,X0: d,X5: u,X1: d] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X2),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2))),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2)))),combin_s_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),X3)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X2),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_135])]) ).
thf(f449,plain,
! [X2: d,X3: u,X0: d,X1: d,X4: u,X5: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X2),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2))),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2)))),combin_s_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),X3)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X2),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5))))) ),
inference(cnf_transformation,[],[f131]) ).
thf(f131,plain,
! [X0: d,X1: d,X2: d,X3: u,X4: u,X5: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X2),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2))),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X2)))),combin_s_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),X3)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X2),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X2))),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5))))) ),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
! [X0: d,X1: d,X7: d,X2: u,X3: u,X4: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X7),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X7)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X7))),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X7))),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X7)))),combin_s_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X7))),X2)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X7),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X7)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X7))),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).
thf(f2345,plain,
spl32_134,
inference(avatar_split_clause,[],[f563,f2343]) ).
thf(f2343,plain,
( spl32_134
<=> ! [X26: u,X0: d,X3: u,X2: u,X1: d] :
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK28,X3),X2),X1),X0))))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X26)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_134])]) ).
thf(f563,plain,
! [X2: u,X3: u,X0: d,X1: d,X26: u] :
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK28,X3),X2),X1),X0))))))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X26)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ),
inference(not_proxy_clausification,[],[f562]) ).
thf(f562,plain,
! [X2: u,X3: u,X0: d,X1: d,X26: u] :
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK28,X3),X2),X1),X0))))))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X26))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ),
inference(not_proxy_clausification,[],[f429]) ).
thf(f429,plain,
! [X2: u,X3: u,X0: d,X1: d,X26: u] :
( ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK28,X3),X2),X1),X0)))))))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X26))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f252,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ( ! [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0)) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0)))))) ) ) )
& ( ! [X8: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK22,X8),X4),X1),X0)))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8))))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) ) ) )
& ! [X10: u,X11: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) )
| ( ! [X13: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X13))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0)) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0))))) ) ) )
& ( ! [X14: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK24,X14),X10),X1),X0)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14)))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) ) ) )
& ! [X16: u,X17: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,X17),X16),X1),X0)))))))) ) )
& ( ! [X19: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) ) ) )
& ! [X20: u,X21: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK26,X21),X20),X1),X0))))))) ) )
& ( ! [X23: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X23)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)))) ) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( ! [X25: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X25))))))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK27,X3),X2),X1),X0)))))) ) ) )
& ( ! [X26: u] :
( ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK28,X3),X2),X1),X0)))))))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X26))))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( ! [X29: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X29)))))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK29,X3),X2),X1),X0))))) ) ) )
& ( ! [X30: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK30,X3),X2),X1),X0))))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X30)))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30])],[f241,f251,f250,f249,f248,f247,f246,f245,f244,f243,f242]) ).
thf(f242,plain,
! [X0: d,X1: d,X4: u,X5: u] :
( ? [X6: u] :
( ! [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))))) ) )
=> ( ! [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0)) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0)))))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f243,plain,
! [X0: d,X1: d,X4: u,X8: u] :
( ? [X9: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X9))) )
=> ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK22,X8),X4),X1),X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f244,plain,
! [X0: d,X1: d,X10: u,X11: u] :
( ? [X12: u] :
( ! [X13: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X12) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X13))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X12)))) ) )
=> ( ! [X13: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X13))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0)) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0))))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f245,plain,
! [X0: d,X1: d,X10: u,X14: u] :
( ? [X15: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X15))) )
=> ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK24,X14),X10),X1),X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f246,plain,
! [X0: d,X1: d,X16: u,X17: u] :
( ? [X18: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X18))))))) )
=> ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,X17),X16),X1),X0)))))))) ) ),
introduced(choice_axiom,[]) ).
thf(f247,plain,
! [X0: d,X1: d,X20: u,X21: u] :
( ? [X22: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X22)))))) )
=> ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK26,X21),X20),X1),X0))))))) ) ),
introduced(choice_axiom,[]) ).
thf(f248,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X24: u] :
( ! [X25: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X25))))))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X24))))) ) )
=> ( ! [X25: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X25))))))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK27,X3),X2),X1),X0)))))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f249,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X27: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X27))))))) )
=> ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK28,X3),X2),X1),X0)))))))) ) ),
introduced(choice_axiom,[]) ).
thf(f250,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X28: u] :
( ! [X29: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X29)))))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X28)))) ) )
=> ( ! [X29: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X29)))))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK29,X3),X2),X1),X0))))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f251,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X31: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X31)))))) )
=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK30,X3),X2),X1),X0))))))) ) ),
introduced(choice_axiom,[]) ).
thf(f241,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ? [X6: u] :
( ! [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))))) ) ) )
& ( ! [X8: u] :
( ? [X9: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X9))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8))))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) ) ) )
& ! [X10: u,X11: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) )
| ? [X12: u] :
( ! [X13: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X12) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X13))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X12)))) ) ) )
& ( ! [X14: u] :
( ? [X15: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X15))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14)))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) ) ) )
& ! [X16: u,X17: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) )
| ? [X18: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X18))))))) ) )
& ( ! [X19: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) ) ) )
& ! [X20: u,X21: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)))) )
| ? [X22: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X22)))))) ) )
& ( ! [X23: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X23)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)))) ) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ? [X24: u] :
( ! [X25: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X25))))))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X24))))) ) ) )
& ( ! [X26: u] :
( ? [X27: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X27))))))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X26))))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ? [X28: u] :
( ! [X29: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X29)))))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X28)))) ) ) )
& ( ! [X30: u] :
( ? [X31: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X31)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X30)))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ) ),
inference(rectify,[],[f240]) ).
thf(f240,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ? [X6: u] :
( ! [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))))) ) ) )
& ( ! [X6: u] :
( ? [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) ) ) )
& ! [X8: u,X9: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)))) )
| ? [X10: u] :
( ! [X11: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10)))) ) ) )
& ( ! [X10: u] :
( ? [X11: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10)))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)))) ) ) )
& ! [X12: u,X13: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)))) )
| ? [X14: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14))))))) ) )
& ( ! [X14: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14))))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)))) ) ) )
& ! [X15: u,X16: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)))) )
| ? [X17: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X17)))))) ) )
& ( ! [X17: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X17)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)))) ) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ? [X18: u] :
( ! [X19: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X18))))) ) ) )
& ( ! [X18: u] :
( ? [X19: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X18))))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ? [X20: u] :
( ! [X21: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X21)))))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X20)))) ) ) )
& ( ! [X20: u] :
( ? [X21: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X21)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X20)))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ) ),
inference(flattening,[],[f239]) ).
thf(f239,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ? [X6: u] :
( ! [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))))) ) ) )
& ( ! [X6: u] :
( ? [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) ) ) )
& ! [X8: u,X9: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)))) )
| ? [X10: u] :
( ! [X11: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10)))) ) ) )
& ( ! [X10: u] :
( ? [X11: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10)))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)))) ) ) )
& ! [X12: u,X13: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)))) )
| ? [X14: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14))))))) ) )
& ( ! [X14: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14))))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)))) ) ) )
& ! [X15: u,X16: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)))) )
| ? [X17: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X17)))))) ) )
& ( ! [X17: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X17)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)))) ) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ? [X18: u] :
( ! [X19: u] : ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) )
& ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X18))))) ) ) )
& ( ! [X18: u] :
( ? [X19: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X18))))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ? [X20: u] :
( ! [X21: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X21)))))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X20)))) ) ) )
& ( ! [X20: u] :
( ? [X21: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X21)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X20)))) ) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ) ),
inference(nnf_transformation,[],[f149]) ).
thf(f149,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
<=> ! [X6: u] :
( ? [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))))) ) ) )
& ! [X8: u,X9: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)))) )
<=> ! [X10: u] :
( ? [X11: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10)))) ) ) )
& ! [X12: u,X13: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)))) )
<=> ! [X14: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14))))))) ) )
& ! [X15: u,X16: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)))) )
<=> ! [X17: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X17)))))) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
<=> ! [X18: u] :
( ? [X19: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X18))))) ) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
<=> ! [X20: u] :
( ? [X21: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X21)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X20)))) ) ) ) ),
inference(ennf_transformation,[],[f104]) ).
thf(f104,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
<=> ! [X6: u] :
( ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))))) )
=> ? [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) ) ) )
& ! [X8: u,X9: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)))) )
<=> ! [X10: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10)))) )
=> ? [X11: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11))) ) ) )
& ! [X12: u,X13: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)))) )
<=> ! [X14: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14))))))) ) )
& ! [X15: u,X16: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)))) )
<=> ! [X17: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X17)))))) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
<=> ! [X18: u] :
( ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X18))))) )
=> ? [X19: u] : ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) ) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
<=> ! [X20: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X20)))) )
=> ? [X21: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X21)))))) ) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f103,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u,X5: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5))))
<=> ! [X6: u] :
( vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6)))))
=> ? [X7: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) ) ) )
& ! [X8: u,X9: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9))))
<=> ! [X10: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X9)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10))))
=> ? [X11: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X8)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11))) ) ) )
& ! [X12: u,X13: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13))))
<=> ! [X14: u] : vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X13)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X12)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14))))))) )
& ! [X15: u,X16: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16))))
<=> ! [X17: u] : vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X15)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X17)))))) )
& ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3))))
<=> ! [X18: u] :
( vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X18)))))
=> ? [X19: u] : vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) ) )
& ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3))))
<=> ! [X20: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X20))))
=> ? [X21: u] : vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X21)))))) ) ) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [X0: d,X1: d,X23: u,X24: u] :
( ! [X39: u,X40: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X39)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X40))))
<=> ! [X41: u] :
( vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X40)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X41)))))
=> ? [X42: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X41) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X39)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X42))) ) ) )
& ! [X35: u,X36: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X35)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X36))))
<=> ! [X37: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X36)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X37))))
=> ? [X38: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X37) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X35)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X38))) ) ) )
& ! [X32: u,X33: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X32)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X33))))
<=> ! [X34: u] : vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X33)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X32)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X34))))))) )
& ! [X29: u,X30: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X29)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X30))))
<=> ! [X31: u] : vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X30)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X29)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X31)))))) )
& ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X23)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X24))))
<=> ! [X27: u] :
( vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X24)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X27)))))
=> ? [X28: u] : vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X24)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X23)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X28))))))) ) )
& ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X23)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X24))))
<=> ! [X25: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X24)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X25))))
=> ? [X26: u] : vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X24)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X23)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X26)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
thf(f2341,plain,
spl32_133,
inference(avatar_split_clause,[],[f426,f2339]) ).
thf(f2339,plain,
( spl32_133
<=> ! [X30: u,X0: d,X3: u,X2: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK30,X3),X2),X1),X0))))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X30)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_133])]) ).
thf(f426,plain,
! [X2: u,X3: u,X0: d,X1: d,X30: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK30,X3),X2),X1),X0))))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X30)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2315,plain,
spl32_132,
inference(avatar_split_clause,[],[f568,f2313]) ).
thf(f2313,plain,
( spl32_132
<=> ! [X4: u,X0: d,X8: u,X5: u,X1: d] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK22,X8),X4),X1),X0)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_132])]) ).
thf(f568,plain,
! [X0: d,X1: d,X8: u,X4: u,X5: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK22,X8),X4),X1),X0)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) ) ),
inference(not_proxy_clausification,[],[f439]) ).
thf(f439,plain,
! [X0: d,X1: d,X8: u,X4: u,X5: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK22,X8),X4),X1),X0)))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X8))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2311,plain,
spl32_131,
inference(avatar_split_clause,[],[f436,f2309]) ).
thf(f2309,plain,
( spl32_131
<=> ! [X11: u,X0: d,X14: u,X10: u,X1: d] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK24,X14),X10),X1),X0)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_131])]) ).
thf(f436,plain,
! [X10: u,X0: d,X11: u,X1: d,X14: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK24,X14),X10),X1),X0)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X14)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2292,plain,
spl32_130,
inference(avatar_split_clause,[],[f448,f2290]) ).
thf(f2290,plain,
( spl32_130
<=> ! [X0: d,X3: u,X2: u,X1: d] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK31,X3),X2),X1),X0)))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK31,X3),X2),X1),X0)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_130])]) ).
thf(f448,plain,
! [X2: u,X3: u,X0: d,X1: d] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK31,X3),X2),X1),X0)))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK31,X3),X2),X1),X0)))) ) ),
inference(cnf_transformation,[],[f257]) ).
thf(f257,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK31,X3),X2),X1),X0)))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK31,X3),X2),X1),X0)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f152,f256]) ).
thf(f256,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ? [X4: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4))) )
=> ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK31,X3),X2),X1),X0)))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK31,X3),X2),X1),X0)))) ) ),
introduced(choice_axiom,[]) ).
thf(f152,plain,
! [X0: d,X1: d,X2: u,X3: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3) )
| ? [X4: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4))) ) ),
inference(ennf_transformation,[],[f1]) ).
thf(f1,axiom,
! [X0: d,X1: d,X2: u,X3: u] :
( ! [X4: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X4))) )
=> ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
thf(f2241,plain,
spl32_129,
inference(avatar_split_clause,[],[f567,f2239]) ).
thf(f567,plain,
! [X0: d,X1: d,X16: u,X17: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,X17),X16),X1),X0))))))) ) ),
inference(not_proxy_clausification,[],[f435]) ).
thf(f435,plain,
! [X0: d,X1: d,X16: u,X17: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK25,X17),X16),X1),X0)))))))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2237,plain,
spl32_128,
inference(avatar_split_clause,[],[f433,f2235]) ).
thf(f2235,plain,
( spl32_128
<=> ! [X20: u,X0: d,X21: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK26,X21),X20),X1),X0))))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_128])]) ).
thf(f433,plain,
! [X21: u,X0: d,X1: d,X20: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK26,X21),X20),X1),X0))))))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2152,plain,
spl32_127,
inference(avatar_split_clause,[],[f566,f2150]) ).
thf(f566,plain,
! [X0: d,X1: d,X19: u,X16: u,X17: u] :
( ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) ) ),
inference(not_proxy_clausification,[],[f434]) ).
thf(f434,plain,
! [X0: d,X1: d,X19: u,X16: u,X17: u] :
( ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X19))))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X17)))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2148,plain,
spl32_126,
inference(avatar_split_clause,[],[f565,f2146]) ).
thf(f565,plain,
! [X2: u,X3: u,X0: d,X1: d,X25: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X25)))))) ) ),
inference(not_proxy_clausification,[],[f431]) ).
thf(f431,plain,
! [X2: u,X3: u,X0: d,X1: d,X25: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $true != vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X25))))))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2132,plain,
spl32_125,
inference(avatar_split_clause,[],[f432,f2130]) ).
thf(f2130,plain,
( spl32_125
<=> ! [X21: u,X20: u,X0: d,X23: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X23)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_125])]) ).
thf(f432,plain,
! [X21: u,X0: d,X1: d,X23: u,X20: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X23)))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X20)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X21)))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2128,plain,
spl32_124,
inference(avatar_split_clause,[],[f428,f2126]) ).
thf(f2126,plain,
( spl32_124
<=> ! [X29: u,X0: d,X3: u,X2: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X29)))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_124])]) ).
thf(f428,plain,
! [X2: u,X3: u,X0: d,X29: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X29)))))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2092,plain,
spl32_123,
inference(avatar_split_clause,[],[f441,f2090]) ).
thf(f2090,plain,
( spl32_123
<=> ! [X4: u,X0: d,X5: u,X1: d,X7: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_123])]) ).
thf(f441,plain,
! [X0: d,X1: d,X7: u,X4: u,X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X7))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0)) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2088,plain,
spl32_122,
inference(avatar_split_clause,[],[f438,f2086]) ).
thf(f2086,plain,
( spl32_122
<=> ! [X11: u,X0: d,X13: u,X10: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X13))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_122])]) ).
thf(f438,plain,
! [X10: u,X0: d,X11: u,X1: d,X13: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X13))) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0)) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2030,plain,
( spl32_121
| ~ spl32_3
| ~ spl32_8 ),
inference(avatar_split_clause,[],[f788,f762,f713,f2028]) ).
thf(f2028,plain,
( spl32_121
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_121])]) ).
thf(f762,plain,
( spl32_8
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_8])]) ).
thf(f788,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_8 ),
inference(duplicate_literal_removal,[],[f786]) ).
thf(f786,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_8 ),
inference(binary_proxy_clausification,[],[f785]) ).
thf(f785,plain,
( ! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X0),X1) = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_8 ),
inference(superposition,[],[f763,f714]) ).
thf(f763,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) )
| ~ spl32_8 ),
inference(avatar_component_clause,[],[f762]) ).
thf(f2026,plain,
spl32_120,
inference(avatar_split_clause,[],[f569,f2024]) ).
thf(f2024,plain,
( spl32_120
<=> ! [X4: u,X0: d,X5: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_120])]) ).
thf(f569,plain,
! [X0: d,X1: d,X4: u,X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0))))) ) ),
inference(not_proxy_clausification,[],[f440]) ).
thf(f440,plain,
! [X0: d,X1: d,X4: u,X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)))) )
| ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X5)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK21,X5),X4),X1),X0)))))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2022,plain,
spl32_119,
inference(avatar_split_clause,[],[f564,f2020]) ).
thf(f2020,plain,
( spl32_119
<=> ! [X0: d,X3: u,X2: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK27,X3),X2),X1),X0))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_119])]) ).
thf(f564,plain,
! [X2: u,X3: u,X0: d,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $false = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK27,X3),X2),X1),X0))))) ) ),
inference(not_proxy_clausification,[],[f430]) ).
thf(f430,plain,
! [X2: u,X3: u,X0: d,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $true = vAPP($o,$o,vNOT,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK27,X3),X2),X1),X0)))))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2018,plain,
spl32_118,
inference(avatar_split_clause,[],[f437,f2016]) ).
thf(f437,plain,
! [X10: u,X0: d,X11: u,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X11)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK23,X11),X10),X1),X0))))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f2014,plain,
spl32_117,
inference(avatar_split_clause,[],[f427,f2012]) ).
thf(f427,plain,
! [X2: u,X3: u,X0: d,X1: d] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__EXISTS_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X1)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)))) )
| ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),vAPP(d,u,vAPP(d,sTfun(d,u),vAPP(u,sTfun(d,sTfun(d,u)),vAPP(u,sTfun(u,sTfun(d,sTfun(d,u))),sK29,X3),X2),X1),X0))))) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f1979,plain,
spl32_116,
inference(avatar_split_clause,[],[f348,f1977]) ).
thf(f1977,plain,
( spl32_116
<=> ! [X2: u,X0: d,X1: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_116])]) ).
thf(f348,plain,
! [X2: u,X0: d,X1: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ),
inference(cnf_transformation,[],[f205]) ).
thf(f205,plain,
! [X0: d,X1: u,X2: u] :
( ( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) ) ) ),
inference(nnf_transformation,[],[f92]) ).
thf(f92,plain,
! [X0: d,X1: u,X2: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
<=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f91,plain,
! [X0: d,X1: u,X2: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
<=> vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
! [X0: d,X13: u,X14: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X13) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14) )
<=> vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X13)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X14)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(f1975,plain,
spl32_115,
inference(avatar_split_clause,[],[f347,f1973]) ).
thf(f1973,plain,
( spl32_115
<=> ! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_115])]) ).
thf(f347,plain,
! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool))),c_2Emin_2E_3D_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) ) ),
inference(cnf_transformation,[],[f205]) ).
thf(f1954,plain,
spl32_114,
inference(avatar_split_clause,[],[f306,f1952]) ).
thf(f1952,plain,
( spl32_114
<=> ! [X0: $o > $o > $o,X1: $o] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP($o,sTfun($o,$o),X0,X1))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X0))),vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_114])]) ).
thf(f306,plain,
! [X0: $o > $o > $o,X1: $o] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP($o,sTfun($o,$o),X0,X1))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X0))),vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X1)))) ),
inference(cnf_transformation,[],[f121]) ).
thf(f121,plain,
! [X0: $o > $o > $o,X1: $o] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP($o,sTfun($o,$o),X0,X1))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X0))),vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X1)))) ),
inference(rectify,[],[f29]) ).
thf(f29,axiom,
! [X8: $o > $o > $o,X9: $o] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP($o,sTfun($o,$o),X8,X9))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X8))),vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X9)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(f1950,plain,
( spl32_113
| ~ spl32_3
| ~ spl32_7 ),
inference(avatar_split_clause,[],[f784,f758,f713,f1948]) ).
thf(f1948,plain,
( spl32_113
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X1),X0) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_113])]) ).
thf(f758,plain,
( spl32_7
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_7])]) ).
thf(f784,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X1),X0) )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_7 ),
inference(duplicate_literal_removal,[],[f782]) ).
thf(f782,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X1),X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_7 ),
inference(binary_proxy_clausification,[],[f781]) ).
thf(f781,plain,
( ! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X1),X0) = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_7 ),
inference(superposition,[],[f759,f714]) ).
thf(f759,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),$true) )
| ~ spl32_7 ),
inference(avatar_component_clause,[],[f758]) ).
thf(f1918,plain,
spl32_112,
inference(avatar_split_clause,[],[f418,f1916]) ).
thf(f1916,plain,
( spl32_112
<=> ! [X0: d,X3: u,X2: u,X1: d] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0))),combin_k_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_112])]) ).
thf(f418,plain,
! [X2: u,X3: u,X0: d,X1: d] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0))),combin_k_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X3))) ),
inference(cnf_transformation,[],[f123]) ).
thf(f123,plain,
! [X0: d,X1: d,X2: u,X3: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0))),combin_k_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X3))) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: d,X1: d,X5: u,X6: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0))),combin_k_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))),vAPP(u,du,vAPP(d,sTfun(u,du),s,X1),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).
thf(f1905,plain,
spl32_111,
inference(avatar_split_clause,[],[f269,f1903]) ).
thf(f1903,plain,
( spl32_111
<=> ! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(du,sTfun($o,sTfun($o,$o)),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_111])]) ).
thf(f269,plain,
! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(du,sTfun($o,sTfun($o,$o)),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X0)))) ),
inference(cnf_transformation,[],[f114]) ).
thf(f114,plain,
! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(du,sTfun($o,sTfun($o,$o)),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X0)))) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X10: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(du,sTfun($o,sTfun($o,$o)),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).
thf(f1892,plain,
spl32_110,
inference(avatar_split_clause,[],[f343,f1890]) ).
thf(f1890,plain,
( spl32_110
<=> ! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(u,sTfun(d,u),sK20,X1),X0))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_110])]) ).
thf(f343,plain,
! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(u,sTfun(d,u),sK20,X1),X0))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ),
inference(cnf_transformation,[],[f203]) ).
thf(f203,plain,
! [X0: d,X1: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ! [X2: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) )
& ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(u,sTfun(d,u),sK20,X1),X0))))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f201,f202]) ).
thf(f202,plain,
! [X0: d,X1: u] :
( ? [X3: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X3)))) )
=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(u,sTfun(d,u),sK20,X1),X0))))) ) ),
introduced(choice_axiom,[]) ).
thf(f201,plain,
! [X0: d,X1: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ! [X2: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) )
& ( ? [X3: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X3)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ) ),
inference(rectify,[],[f200]) ).
thf(f200,plain,
! [X0: d,X1: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ! [X2: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) )
& ( ? [X2: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ) ),
inference(nnf_transformation,[],[f90]) ).
thf(f90,plain,
! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
<=> ? [X2: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f89,plain,
! [X0: d,X1: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1))))
<=> ? [X2: u] : vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
! [X0: d,X2: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X2))))
<=> ? [X12: u] : vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(f1888,plain,
spl32_109,
inference(avatar_split_clause,[],[f342,f1886]) ).
thf(f1886,plain,
( spl32_109
<=> ! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(u,sTfun(d,u),sK19,X1),X0))))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_109])]) ).
thf(f342,plain,
! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(u,sTfun(d,u),sK19,X1),X0))))) ) ),
inference(cnf_transformation,[],[f199]) ).
thf(f199,plain,
! [X0: d,X1: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(u,sTfun(d,u),sK19,X1),X0))))) ) )
& ( ! [X3: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X3)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f197,f198]) ).
thf(f198,plain,
! [X0: d,X1: u] :
( ? [X2: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
=> ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(d,u,vAPP(u,sTfun(d,u),sK19,X1),X0))))) ) ),
introduced(choice_axiom,[]) ).
thf(f197,plain,
! [X0: d,X1: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ? [X2: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) )
& ( ! [X3: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X3)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ) ),
inference(rectify,[],[f196]) ).
thf(f196,plain,
! [X0: d,X1: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ? [X2: u] : ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) )
& ( ! [X2: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ) ),
inference(nnf_transformation,[],[f88]) ).
thf(f88,plain,
! [X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
<=> ! [X2: u] : ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f87,plain,
! [X0: d,X1: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1))))
<=> ! [X2: u] : vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
! [X0: d,X2: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X2))))
<=> ! [X12: u] : vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(f1870,plain,
( spl32_108
| ~ spl32_3
| ~ spl32_6 ),
inference(avatar_split_clause,[],[f780,f754,f713,f1868]) ).
thf(f1868,plain,
( spl32_108
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_108])]) ).
thf(f754,plain,
( spl32_6
<=> ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,$true),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_6])]) ).
thf(f780,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_6 ),
inference(duplicate_literal_removal,[],[f778]) ).
thf(f778,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_6 ),
inference(binary_proxy_clausification,[],[f777]) ).
thf(f777,plain,
( ! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_6 ),
inference(superposition,[],[f755,f714]) ).
thf(f755,plain,
( ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,$true),X1) )
| ~ spl32_6 ),
inference(avatar_component_clause,[],[f754]) ).
thf(f1866,plain,
spl32_107,
inference(avatar_split_clause,[],[f344,f1864]) ).
thf(f1864,plain,
( spl32_107
<=> ! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_107])]) ).
thf(f344,plain,
! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_3F_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ),
inference(cnf_transformation,[],[f203]) ).
thf(f1862,plain,
spl32_106,
inference(avatar_split_clause,[],[f341,f1860]) ).
thf(f1860,plain,
( spl32_106
<=> ! [X0: d,X1: u,X3: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X3)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_106])]) ).
thf(f341,plain,
! [X3: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X3)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,c_2Ebool_2E_21_2E1,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X1)))) ) ),
inference(cnf_transformation,[],[f199]) ).
thf(f1840,plain,
spl32_105,
inference(avatar_split_clause,[],[f616,f1838]) ).
thf(f616,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,[],[f361]) ).
thf(f361,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,[],[f210]) ).
thf(f210,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,[],[f209]) ).
thf(f209,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) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != vAPP($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,vNOT,X2) )
| ( $true = vAPP($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,[],[f208]) ).
thf(f208,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) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != vAPP($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,vNOT,X2) )
| ( $true = vAPP($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,[],[f161]) ).
thf(f1836,plain,
spl32_104,
inference(avatar_split_clause,[],[f615,f1834]) ).
thf(f1834,plain,
( spl32_104
<=> ! [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,[spl32_104])]) ).
thf(f615,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,[],[f360]) ).
thf(f360,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,[],[f210]) ).
thf(f1766,plain,
spl32_103,
inference(avatar_split_clause,[],[f518,f1764]) ).
thf(f518,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,[],[f359]) ).
thf(f359,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,[],[f210]) ).
thf(f1754,plain,
spl32_102,
inference(avatar_split_clause,[],[f303,f1752]) ).
thf(f1752,plain,
( spl32_102
<=> ! [X0: $o > $o,X1: $o] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP($o,$o,X0,X1))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X0))),vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_102])]) ).
thf(f303,plain,
! [X0: $o > $o,X1: $o] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP($o,$o,X0,X1))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X0))),vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X1)))) ),
inference(cnf_transformation,[],[f118]) ).
thf(f118,plain,
! [X0: $o > $o,X1: $o] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP($o,$o,X0,X1))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X0))),vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X1)))) ),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
! [X8: $o > $o,X9: $o] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP($o,$o,X8,X9))) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X8))),vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,X9)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) ).
thf(f1750,plain,
( spl32_101
| ~ spl32_3
| ~ spl32_5 ),
inference(avatar_split_clause,[],[f776,f750,f713,f1748]) ).
thf(f1748,plain,
( spl32_101
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X1),X0) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_101])]) ).
thf(f750,plain,
( spl32_5
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_5])]) ).
thf(f776,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X1),X0) )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_5 ),
inference(duplicate_literal_removal,[],[f774]) ).
thf(f774,plain,
( ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X1),X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_5 ),
inference(binary_proxy_clausification,[],[f773]) ).
thf(f773,plain,
( ! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X1),X0) = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_5 ),
inference(superposition,[],[f751,f714]) ).
thf(f751,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),$true) )
| ~ spl32_5 ),
inference(avatar_component_clause,[],[f750]) ).
thf(f1738,plain,
spl32_100,
inference(avatar_split_clause,[],[f268,f1736]) ).
thf(f1736,plain,
( spl32_100
<=> ! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(du,sTfun($o,$o),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_100])]) ).
thf(f268,plain,
! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(du,sTfun($o,$o),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0)))) ),
inference(cnf_transformation,[],[f113]) ).
thf(f113,plain,
! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(du,sTfun($o,$o),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0)))) ),
inference(rectify,[],[f13]) ).
thf(f13,axiom,
! [X10: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(du,sTfun($o,$o),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(f1723,plain,
spl32_99,
inference(avatar_split_clause,[],[f417,f1721]) ).
thf(f417,plain,
! [X2: u,X0: d,X1: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) ) ),
inference(cnf_transformation,[],[f238]) ).
thf(f238,plain,
! [X0: d,X1: u,X2: u] :
( ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
| ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) != vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) ) )
& ( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ) ),
inference(nnf_transformation,[],[f102]) ).
thf(f102,plain,
! [X0: d,X1: u,X2: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) )
<=> ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) ) ),
inference(fool_elimination,[],[f101]) ).
thf(f101,plain,
! [X0: d,X1: u,X2: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2))))
<=> ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) ) ),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
! [X0: d,X10: u,X11: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X10)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11))))
<=> ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(f1719,plain,
spl32_98,
inference(avatar_split_clause,[],[f416,f1717]) ).
thf(f1717,plain,
( spl32_98
<=> ! [X2: u,X0: d,X1: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_98])]) ).
thf(f416,plain,
! [X2: u,X0: d,X1: u] :
( ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2Emin_2E_3D_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X2)))) ) ),
inference(cnf_transformation,[],[f238]) ).
thf(f1711,plain,
spl32_97,
inference(avatar_split_clause,[],[f302,f1709]) ).
thf(f1709,plain,
( spl32_97
<=> ! [X0: d,X1: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X0)),combin_i_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_97])]) ).
thf(f302,plain,
! [X0: d,X1: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X0)),combin_i_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1))) ),
inference(cnf_transformation,[],[f117]) ).
thf(f117,plain,
! [X0: d,X1: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X0)),combin_i_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X1))) ),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
! [X0: d,X5: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5) = vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),X0)),combin_i_2E0)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).
thf(f1707,plain,
spl32_96,
inference(avatar_split_clause,[],[f267,f1705]) ).
thf(f1705,plain,
( spl32_96
<=> ! [X0: $o > $o > $o] : ( vAPP(du,sTfun($o,sTfun($o,$o)),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_96])]) ).
thf(f267,plain,
! [X0: $o > $o > $o] : ( vAPP(du,sTfun($o,sTfun($o,$o)),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X0))) = X0 ),
inference(cnf_transformation,[],[f112]) ).
thf(f112,plain,
! [X0: $o > $o > $o] : ( vAPP(du,sTfun($o,sTfun($o,$o)),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X0))) = X0 ),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X8: $o > $o > $o] : ( vAPP(du,sTfun($o,sTfun($o,$o)),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),vAPP(sTfun($o,sTfun($o,$o)),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X8))) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).
thf(f1703,plain,
( spl32_95
| ~ spl32_3
| ~ spl32_4 ),
inference(avatar_split_clause,[],[f768,f745,f713,f1701]) ).
thf(f1701,plain,
( spl32_95
<=> ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X0) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_95])]) ).
thf(f745,plain,
( spl32_4
<=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,$true),$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_4])]) ).
thf(f768,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X0) )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_4 ),
inference(duplicate_literal_removal,[],[f766]) ).
thf(f766,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_4 ),
inference(binary_proxy_clausification,[],[f765]) ).
thf(f765,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X0) = X0 )
| ( $false = X0 ) )
| ~ spl32_3
| ~ spl32_4 ),
inference(superposition,[],[f747,f714]) ).
thf(f747,plain,
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,$true),$true) )
| ~ spl32_4 ),
inference(avatar_component_clause,[],[f745]) ).
thf(f1693,plain,
spl32_94,
inference(avatar_split_clause,[],[f600,f1691]) ).
thf(f1691,plain,
( spl32_94
<=> ! [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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true = X1 )
| ( $true = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_94])]) ).
thf(f600,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true = X1 )
| ( $true = X2 ) ),
inference(not_proxy_clausification,[],[f599]) ).
thf(f599,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vNOT,X2) ) ),
inference(not_proxy_clausification,[],[f384]) ).
thf(f384,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) )
| ( $true != vAPP($o,$o,vNOT,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)),sP9,X2),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X1) )
& ( $true != X0 ) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != X0 ) ) )
& ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
& ( ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true = X0 ) )
& ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = X0 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ) ),
inference(rectify,[],[f221]) ).
thf(f221,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)),sP7,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)),sP7,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)),sP9,X1),X0),X2) ) ) ),
inference(flattening,[],[f220]) ).
thf(f220,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)),sP7,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)),sP7,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)),sP9,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f165]) ).
thf(f165,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)),sP7,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(f1657,plain,
spl32_93,
inference(avatar_split_clause,[],[f591,f1655]) ).
thf(f591,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,$true),X1),X0) )
| ( $true = X1 ) ),
inference(not_proxy_clausification,[],[f540]) ).
thf(f540,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,$true),X1),X0) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,$true),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X1) ) ),
inference(equality_resolution,[],[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)),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 != X2 ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f231,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 ) )
| ( ( $true != X2 )
& ( $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 ) )
& ( ( $true = X2 )
| ( $true = X0 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP12,X2),X1),X0) ) ) ),
inference(rectify,[],[f230]) ).
thf(f230,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 != 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 = 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,[],[f229]) ).
thf(f229,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 != 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 = 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,[],[f169]) ).
thf(f169,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 = X1 )
| ( $true = X2 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1569,plain,
spl32_92,
inference(avatar_split_clause,[],[f596,f1567]) ).
thf(f596,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),$true) ) ),
inference(trivial_inequality_removal,[],[f530]) ).
thf(f530,plain,
! [X2: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),$true) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),$true) )
| ( $true != $true ) ),
inference(equality_resolution,[],[f381]) ).
thf(f381,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),X1),X0) )
| ( $true != X0 )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f1565,plain,
spl32_91,
inference(avatar_split_clause,[],[f589,f1563]) ).
thf(f589,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,[],[f544]) ).
thf(f544,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,[],[f400]) ).
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)),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,[],[f231]) ).
thf(f1561,plain,
spl32_90,
inference(avatar_split_clause,[],[f415,f1559]) ).
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)),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,[],[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)),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,[],[f170]) ).
thf(f170,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,[],[f148,f169,f168,f167]) ).
thf(f167,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) )
<=> ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f168,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(f148,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( ( $true = X0 )
| ( $true != X1 ) ) )
<=> ( ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $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 ) ) )
<=> ( ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $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,[],[f47]) ).
thf(f47,axiom,
! [X46: $o,X47: $o,X48: $o] :
( ( X48
<=> ( X47
=> X46 ) )
<=> ( ( vAPP($o,$o,vNOT,X48)
| X46
| vAPP($o,$o,vNOT,X47) )
& ( vAPP($o,$o,vNOT,X46)
| X48 )
& ( X47
| X48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__imp) ).
thf(f1557,plain,
spl32_89,
inference(avatar_split_clause,[],[f414,f1555]) ).
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)),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,[],[f237]) ).
thf(f1553,plain,
spl32_88,
inference(avatar_split_clause,[],[f399,f1551]) ).
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)),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,[],[f231]) ).
thf(f1542,plain,
spl32_87,
inference(avatar_split_clause,[],[f396,f1540]) ).
thf(f396,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,[],[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)),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,[],[f166]) ).
thf(f166,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,[],[f98,f165,f164,f163]) ).
thf(f163,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X1),X0),X2) )
<=> ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = X0 )
| ( $true = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f164,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(f98,plain,
! [X0: $o,X1: $o,X2: $o] :
( ( ( $true = X2 )
<=> ( ( $true = X0 )
| ( $true = X1 ) ) )
<=> ( ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $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,[],[f46]) ).
thf(f46,axiom,
! [X46: $o,X47: $o,X48: $o] :
( ( X48
<=> ( X46
| X47 ) )
<=> ( ( vAPP($o,$o,vNOT,X48)
| X46
| X47 )
& ( vAPP($o,$o,vNOT,X46)
| X48 )
& ( vAPP($o,$o,vNOT,X47)
| X48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__disj) ).
thf(f1538,plain,
spl32_86,
inference(avatar_split_clause,[],[f395,f1536]) ).
thf(f395,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,[],[f228]) ).
thf(f1534,plain,
spl32_85,
inference(avatar_split_clause,[],[f380,f1532]) ).
thf(f380,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,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f1530,plain,
spl32_84,
inference(avatar_split_clause,[],[f357,f1528]) ).
thf(f357,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,[],[f210]) ).
thf(f1526,plain,
spl32_83,
inference(avatar_split_clause,[],[f356,f1524]) ).
thf(f356,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,[],[f210]) ).
thf(f1522,plain,
spl32_82,
inference(avatar_split_clause,[],[f355,f1520]) ).
thf(f355,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,[],[f210]) ).
thf(f1512,plain,
spl32_81,
inference(avatar_split_clause,[],[f266,f1510]) ).
thf(f266,plain,
! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0)))) ),
inference(cnf_transformation,[],[f111]) ).
thf(f111,plain,
! [X0: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X0)))) ),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
! [X10: u] : ( vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X10) = vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP($o,u,i_mono_2Etyop_2Emin_2Ebool,vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).
thf(f1441,plain,
spl32_80,
inference(avatar_split_clause,[],[f558,f1439]) ).
thf(f558,plain,
! [X2: $o,X3: $o,X0: $o] :
( ( $true = X0 )
| ( $true = X3 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),$true),X0) ) ),
inference(equality_resolution,[],[f442]) ).
thf(f442,plain,
! [X2: $o,X3: $o,X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != X1 )
| ( $true = X3 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),X1),X0) ) ),
inference(cnf_transformation,[],[f255]) ).
thf(f255,plain,
! [X0: $o,X1: $o,X2: $o,X3: $o] :
( ( ( ( $true = X2 )
| ( $true != X3 )
| ( ( $true != X0 )
& ( $true = X1 ) ) )
& ( ( $true = X0 )
| ( $true != X1 )
| ( ( $true != X2 )
& ( $true = X3 ) ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),X1),X0) ) ),
inference(rectify,[],[f254]) ).
thf(f254,plain,
! [X3: $o,X1: $o,X2: $o,X0: $o] :
( ( ( ( $true = X2 )
| ( $true != X0 )
| ( ( $true != X3 )
& ( $true = X1 ) ) )
& ( ( $true = X3 )
| ( $true != X1 )
| ( ( $true != X2 )
& ( $true = X0 ) ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X2),X1),X3) ) ),
inference(flattening,[],[f253]) ).
thf(f253,plain,
! [X3: $o,X1: $o,X2: $o,X0: $o] :
( ( ( ( $true = X2 )
| ( $true != X0 )
| ( ( $true != X3 )
& ( $true = X1 ) ) )
& ( ( $true = X3 )
| ( $true != X1 )
| ( ( $true != X2 )
& ( $true = X0 ) ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X2),X1),X3) ) ),
inference(nnf_transformation,[],[f171]) ).
thf(f171,plain,
! [X3: $o,X1: $o,X2: $o,X0: $o] :
( ( ( ( $true = X2 )
| ( $true != X0 ) )
<=> ( ( $true = X3 )
| ( $true != X1 ) ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X2),X1),X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1437,plain,
spl32_79,
inference(avatar_split_clause,[],[f555,f1435]) ).
thf(f555,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)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X2),X1),X0) ) ),
inference(equality_resolution,[],[f444]) ).
thf(f444,plain,
! [X2: $o,X3: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true != X3 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),X1),X0) ) ),
inference(cnf_transformation,[],[f255]) ).
thf(f1433,plain,
spl32_78,
inference(avatar_split_clause,[],[f265,f1431]) ).
thf(f1431,plain,
( spl32_78
<=> ! [X0: $o > $o] : ( vAPP(du,sTfun($o,$o),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_78])]) ).
thf(f265,plain,
! [X0: $o > $o] : ( vAPP(du,sTfun($o,$o),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X0))) = X0 ),
inference(cnf_transformation,[],[f110]) ).
thf(f110,plain,
! [X0: $o > $o] : ( vAPP(du,sTfun($o,$o),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X0))) = X0 ),
inference(rectify,[],[f16]) ).
thf(f16,axiom,
! [X8: $o > $o] : ( vAPP(du,sTfun($o,$o),j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),vAPP(sTfun($o,$o),u,i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X8))) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(f1399,plain,
spl32_77,
inference(avatar_split_clause,[],[f561,f1397]) ).
thf(f1397,plain,
( spl32_77
<=> ! [X2: $o,X1: $o,X3: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X1),X2),X1),X3) )
| ( $true = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_77])]) ).
thf(f561,plain,
! [X2: $o,X3: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X1),X2),X1),X3) )
| ( $true = X1 ) ),
inference(equality_resolution,[],[f446]) ).
thf(f446,plain,
! [X2: $o,X3: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X2),X1),X3) )
| ( $true = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f172]) ).
thf(f172,plain,
! [X0: $o,X1: $o,X2: $o,X3: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X2),X1),X3) )
| ( ( X2 != X3 )
& ( $true = X1 ) )
| ( X0 != X1 ) ),
inference(definition_folding,[],[f151,f171]) ).
thf(f151,plain,
! [X0: $o,X1: $o,X2: $o,X3: $o] :
( ( ( ( $true = X2 )
| ( $true != X0 ) )
<=> ( ( $true = X3 )
| ( $true != X1 ) ) )
| ( ( X2 != X3 )
& ( $true = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f150]) ).
thf(f150,plain,
! [X0: $o,X1: $o,X2: $o,X3: $o] :
( ( ( ( $true = X2 )
| ( $true != X0 ) )
<=> ( ( $true = X3 )
| ( $true != X1 ) ) )
| ( ( X2 != X3 )
& ( $true = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f106]) ).
thf(f106,plain,
! [X0: $o,X1: $o,X2: $o,X3: $o] :
( ( ( ( $true = X1 )
=> ( X2 = X3 ) )
& ( X0 = X1 ) )
=> ( ( ( $true = X0 )
=> ( $true = X2 ) )
<=> ( ( $true = X1 )
=> ( $true = X3 ) ) ) ),
inference(fool_elimination,[],[f105]) ).
thf(f105,plain,
! [X0: $o,X1: $o,X2: $o,X3: $o] :
( ( ( X1
=> ( X2 = X3 ) )
& ( X0 = X1 ) )
=> ( ( X0
=> X2 )
<=> ( X1
=> X3 ) ) ),
inference(rectify,[],[f38]) ).
thf(f38,axiom,
! [X19: $o,X20: $o,X21: $o,X22: $o] :
( ( ( X20
=> ( X21 = X22 ) )
& ( X19 = X20 ) )
=> ( ( X19
=> X21 )
<=> ( X20
=> X22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CONG) ).
thf(f1395,plain,
spl32_76,
inference(avatar_split_clause,[],[f557,f1393]) ).
thf(f557,plain,
! [X3: $o,X0: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),$true),$true),X0) ) ),
inference(equality_resolution,[],[f556]) ).
thf(f556,plain,
! [X2: $o,X3: $o,X0: $o] :
( ( $true = X0 )
| ( $true != X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),$true),X0) ) ),
inference(equality_resolution,[],[f443]) ).
thf(f443,plain,
! [X2: $o,X3: $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)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),X1),X0) ) ),
inference(cnf_transformation,[],[f255]) ).
thf(f1391,plain,
spl32_75,
inference(avatar_split_clause,[],[f554,f1389]) ).
thf(f554,plain,
! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X2),X1),$true) ) ),
inference(equality_resolution,[],[f553]) ).
thf(f553,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)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,$true),X2),X1),X0) ) ),
inference(equality_resolution,[],[f445]) ).
thf(f445,plain,
! [X2: $o,X3: $o,X0: $o,X1: $o] :
( ( $true = X2 )
| ( $true != X3 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X3),X2),X1),X0) ) ),
inference(cnf_transformation,[],[f255]) ).
thf(f1383,plain,
spl32_74,
inference(avatar_split_clause,[],[f560,f1381]) ).
thf(f1381,plain,
( spl32_74
<=> ! [X1: $o,X3: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X1),X3),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_74])]) ).
thf(f560,plain,
! [X3: $o,X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X1),X3),X1),X3) ),
inference(equality_resolution,[],[f559]) ).
thf(f559,plain,
! [X3: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X3),X1),X3) )
| ( X0 != X1 ) ),
inference(equality_resolution,[],[f447]) ).
thf(f447,plain,
! [X2: $o,X3: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),vAPP($o,sTfun($o,sTfun($o,sTfun($o,$o))),sP13,X0),X2),X1),X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f172]) ).
thf(f1340,plain,
spl32_73,
inference(avatar_split_clause,[],[f614,f1338]) ).
thf(f614,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,[],[f613]) ).
thf(f613,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,[],[f358]) ).
thf(f358,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,[],[f210]) ).
thf(f1332,plain,
spl32_72,
inference(avatar_split_clause,[],[f610,f1330]) ).
thf(f610,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,[],[f609]) ).
thf(f609,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,[],[f362]) ).
thf(f362,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,[],[f213]) ).
thf(f213,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,[],[f212]) ).
thf(f212,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) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X1 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = vAPP($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,[],[f211]) ).
thf(f211,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) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X1 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = vAPP($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,[],[f160]) ).
thf(f1328,plain,
spl32_71,
inference(avatar_split_clause,[],[f606,f1326]) ).
thf(f606,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,[],[f605]) ).
thf(f605,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,[],[f366]) ).
thf(f366,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,[],[f216]) ).
thf(f216,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,[],[f215]) ).
thf(f215,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,[],[f214]) ).
thf(f214,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,[],[f159]) ).
thf(f1324,plain,
spl32_70,
inference(avatar_split_clause,[],[f592,f1322]) ).
thf(f592,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)),sP7,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f391]) ).
thf(f391,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)),sP7,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f227]) ).
thf(f227,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 != 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)),sP7,X2),X1),X0) ) ) ),
inference(rectify,[],[f226]) ).
thf(f226,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X1),X0),X2) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != X0 )
& ( $true != X1 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X1),X0),X2) ) ) ),
inference(flattening,[],[f225]) ).
thf(f225,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X1),X0),X2) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != X0 )
& ( $true != X1 ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f163]) ).
thf(f1320,plain,
spl32_69,
inference(avatar_split_clause,[],[f585,f1318]) ).
thf(f585,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)),sP10,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f584]) ).
thf(f584,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $false = X0 )
| ( $true = X1 )
| ( $true = vAPP($o,$o,vNOT,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,[],[f410]) ).
thf(f410,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) ) ),
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)),sP10,X2),X1),X0) )
| ( ( $true != vAPP($o,$o,vNOT,X0) )
& ( $true != X1 )
& ( $true != vAPP($o,$o,vNOT,X2) ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $true = X1 )
| ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X2),X1),X0) ) ) ),
inference(rectify,[],[f235]) ).
thf(f235,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) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != X0 )
& ( $true != vAPP($o,$o,vNOT,X1) ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) ) ) ),
inference(flattening,[],[f234]) ).
thf(f234,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) )
| ( ( $true != vAPP($o,$o,vNOT,X2) )
& ( $true != X0 )
& ( $true != vAPP($o,$o,vNOT,X1) ) ) )
& ( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = X0 )
| ( $true = vAPP($o,$o,vNOT,X1) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP10,X1),X0),X2) ) ) ),
inference(nnf_transformation,[],[f167]) ).
thf(f1316,plain,
spl32_68,
inference(avatar_split_clause,[],[f388,f1314]) ).
thf(f388,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,[],[f224]) ).
thf(f224,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,[],[f223]) ).
thf(f223,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,[],[f164]) ).
thf(f1312,plain,
spl32_67,
inference(avatar_split_clause,[],[f370,f1310]) ).
thf(f370,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,[],[f218]) ).
thf(f218,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,[],[f217]) ).
thf(f217,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,[],[f158]) ).
thf(f1306,plain,
spl32_66,
inference(avatar_split_clause,[],[f258,f1304]) ).
thf(f258,plain,
! [X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) ) ),
inference(cnf_transformation,[],[f174]) ).
thf(f174,plain,
( ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)))) )
& ! [X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18])],[f133,f173]) ).
thf(f173,plain,
( ? [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)))) )
& ! [X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) ) ) )
=> ( ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)))) )
& ! [X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)),vAPP(u,du,vAPP(d,sTfun(u,du),s,sK14),X5)))) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f133,plain,
? [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)))) )
& ! [X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) ) ) ),
inference(flattening,[],[f132]) ).
thf(f132,plain,
? [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)))) )
& ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)))) )
& ! [X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) )
| ( $true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) ) ) ),
inference(ennf_transformation,[],[f56]) ).
thf(f56,plain,
~ ! [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ! [X5: u] :
( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) )
=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) ) )
=> ( ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)))) )
=> ( $true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)))) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f55,plain,
~ ! [X0: d,X1: d,X2: u,X3: u,X4: u] :
( ! [X5: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5))))
=> vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X5)))) )
=> ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X3))))
=> vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X2)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X4)))) ) ),
inference(rectify,[],[f52]) ).
thf(f52,negated_conjecture,
~ ! [X0: d,X1: d,X23: u,X24: u,X51: u] :
( ! [X52: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X51)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X52))))
=> vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X24)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X52)))) )
=> ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X23)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X24))))
=> vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X23)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X51)))) ) ),
inference(negated_conjecture,[],[f51]) ).
thf(f51,conjecture,
! [X0: d,X1: d,X23: u,X24: u,X51: u] :
( ! [X52: u] :
( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X51)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X52))))
=> vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),app_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X24)),vAPP(u,du,vAPP(d,sTfun(u,du),s,X0),X52)))) )
=> ( vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X23)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X24))))
=> vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X1),X0)),X23)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,X0),tyop_2Emin_2Ebool)),X51)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
thf(f1224,plain,
spl32_65,
inference(avatar_split_clause,[],[f595,f1222]) ).
thf(f595,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)),sP9,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f379]) ).
thf(f379,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)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f1220,plain,
spl32_64,
inference(avatar_split_clause,[],[f594,f1218]) ).
thf(f594,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)),sP9,X2),X1),X0) ) ),
inference(not_proxy_clausification,[],[f378]) ).
thf(f378,plain,
! [X2: $o,X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vNOT,X2) )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP9,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f1216,plain,
spl32_63,
inference(avatar_split_clause,[],[f588,f1214]) ).
thf(f588,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,[],[f398]) ).
thf(f398,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,[],[f231]) ).
thf(f1212,plain,
spl32_62,
inference(avatar_split_clause,[],[f548,f1210]) ).
thf(f548,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 = X0 )
| ( $true = X2 ) ),
inference(equality_resolution,[],[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)),sP11,X2),X1),X0) )
| ( $true = X0 )
| ( $true != X1 )
| ( $true = X2 ) ),
inference(cnf_transformation,[],[f233]) ).
thf(f233,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,[],[f232]) ).
thf(f232,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,[],[f168]) ).
thf(f1208,plain,
spl32_61,
inference(avatar_split_clause,[],[f537,f1206]) ).
thf(f537,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)),sP8,$true),X1),X0) ) ),
inference(equality_resolution,[],[f385]) ).
thf(f385,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)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f224]) ).
thf(f1204,plain,
( spl32_60
| ~ spl32_8
| ~ spl32_57 ),
inference(avatar_split_clause,[],[f1192,f1182,f762,f1202]) ).
thf(f1202,plain,
( spl32_60
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_60])]) ).
thf(f1192,plain,
( ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,$true),X0) )
| ~ spl32_8
| ~ spl32_57 ),
inference(trivial_inequality_removal,[],[f1187]) ).
thf(f1187,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,$true),X0) ) )
| ~ spl32_8
| ~ spl32_57 ),
inference(superposition,[],[f1183,f763]) ).
thf(f1200,plain,
spl32_59,
inference(avatar_split_clause,[],[f405,f1198]) ).
thf(f405,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,[],[f233]) ).
thf(f1196,plain,
spl32_58,
inference(avatar_split_clause,[],[f397,f1194]) ).
thf(f397,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)),sP12,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f1184,plain,
spl32_57,
inference(avatar_split_clause,[],[f318,f1182]) ).
thf(f318,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,[],[f183]) ).
thf(f183,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,[],[f155]) ).
thf(f155,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,[],[f142,f154,f153]) ).
thf(f153,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
<=> ( ( mono_2Ec_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(f154,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
<=> ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f142,plain,
! [X0: $o,X1: $o] :
( ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) )
<=> ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = X1 ) ) ) ),
inference(flattening,[],[f141]) ).
thf(f141,plain,
! [X0: $o,X1: $o] :
( ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) )
<=> ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = X1 ) ) ) ),
inference(ennf_transformation,[],[f76]) ).
thf(f76,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) )
=> ( mono_2Ec_2Ebool_2EF = $true ) )
<=> ( ( ( $true = X1 )
=> ( mono_2Ec_2Ebool_2EF = $true ) )
=> ( ( $true = vAPP($o,$o,vNOT,X0) )
=> ( mono_2Ec_2Ebool_2EF = $true ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f75,plain,
! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,
( X0
| X1 ))
=> mono_2Ec_2Ebool_2EF )
<=> ( ( X1
=> mono_2Ec_2Ebool_2EF )
=> ( vAPP($o,$o,vNOT,X0)
=> mono_2Ec_2Ebool_2EF ) ) ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
! [X44: $o,X45: $o] :
( ( vAPP($o,$o,vNOT,
( X44
| X45 ))
=> mono_2Ec_2Ebool_2EF )
<=> ( ( X45
=> mono_2Ec_2Ebool_2EF )
=> ( vAPP($o,$o,vNOT,X44)
=> mono_2Ec_2Ebool_2EF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).
thf(f1180,plain,
spl32_56,
inference(avatar_split_clause,[],[f317,f1178]) ).
thf(f317,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,[],[f183]) ).
thf(f1176,plain,
( spl32_55
| ~ spl32_3
| ~ spl32_13 ),
inference(avatar_split_clause,[],[f831,f802,f713,f1174]) ).
thf(f1174,plain,
( spl32_55
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,$true),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_55])]) ).
thf(f831,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,$true),X0) ) )
| ~ spl32_3
| ~ spl32_13 ),
inference(trivial_inequality_removal,[],[f830]) ).
thf(f830,plain,
( ! [X0: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,$true),X0) ) )
| ~ spl32_3
| ~ spl32_13 ),
inference(superposition,[],[f803,f714]) ).
thf(f1098,plain,
spl32_54,
inference(avatar_split_clause,[],[f612,f1096]) ).
thf(f1096,plain,
( spl32_54
<=> ! [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,[spl32_54])]) ).
thf(f612,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,[],[f365]) ).
thf(f365,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,[],[f213]) ).
thf(f1094,plain,
( spl32_53
| ~ spl32_3
| ~ spl32_11 ),
inference(avatar_split_clause,[],[f826,f794,f713,f1092]) ).
thf(f1092,plain,
( spl32_53
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_53])]) ).
thf(f794,plain,
( spl32_11
<=> ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_11])]) ).
thf(f826,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) )
| ~ spl32_3
| ~ spl32_11 ),
inference(trivial_inequality_removal,[],[f825]) ).
thf(f825,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) )
| ~ spl32_3
| ~ spl32_11 ),
inference(superposition,[],[f795,f714]) ).
thf(f795,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) )
| ( $true = X1 ) )
| ~ spl32_11 ),
inference(avatar_component_clause,[],[f794]) ).
thf(f1090,plain,
spl32_52,
inference(avatar_split_clause,[],[f611,f1088]) ).
thf(f1088,plain,
( spl32_52
<=> ! [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,[spl32_52])]) ).
thf(f611,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,[],[f364]) ).
thf(f364,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,[],[f213]) ).
thf(f1086,plain,
spl32_51,
inference(avatar_split_clause,[],[f608,f1084]) ).
thf(f1084,plain,
( spl32_51
<=> ! [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,[spl32_51])]) ).
thf(f608,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,[],[f369]) ).
thf(f369,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,[],[f216]) ).
thf(f1082,plain,
spl32_50,
inference(avatar_split_clause,[],[f607,f1080]) ).
thf(f1080,plain,
( spl32_50
<=> ! [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,[spl32_50])]) ).
thf(f607,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,[],[f368]) ).
thf(f368,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,[],[f216]) ).
thf(f1078,plain,
spl32_49,
inference(avatar_split_clause,[],[f593,f1076]) ).
thf(f1076,plain,
( spl32_49
<=> ! [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,[spl32_49])]) ).
thf(f593,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,[],[f394]) ).
thf(f394,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,[],[f227]) ).
thf(f1074,plain,
spl32_48,
inference(avatar_split_clause,[],[f587,f1072]) ).
thf(f1072,plain,
( spl32_48
<=> ! [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,[spl32_48])]) ).
thf(f587,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,[],[f413]) ).
thf(f413,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,[],[f236]) ).
thf(f1070,plain,
spl32_47,
inference(avatar_split_clause,[],[f586,f1068]) ).
thf(f1068,plain,
( spl32_47
<=> ! [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 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_47])]) ).
thf(f586,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(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)),sP10,X2),X1),X0) )
| ( $true != vAPP($o,$o,vNOT,X2) ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f1066,plain,
spl32_46,
inference(avatar_split_clause,[],[f551,f1064]) ).
thf(f551,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),$true),X0) ) ),
inference(equality_resolution,[],[f550]) ).
thf(f550,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)),sP11,X2),$true),X0) ) ),
inference(equality_resolution,[],[f404]) ).
thf(f404,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,[],[f233]) ).
thf(f1062,plain,
spl32_45,
inference(avatar_split_clause,[],[f549,f1060]) ).
thf(f549,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,[],[f406]) ).
thf(f406,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,[],[f233]) ).
thf(f1058,plain,
spl32_44,
inference(avatar_split_clause,[],[f547,f1056]) ).
thf(f547,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP11,$true),X1),X0) )
| ( $true = X1 ) ),
inference(equality_resolution,[],[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)),sP11,X2),X1),X0) )
| ( $true = X1 )
| ( $true != X2 ) ),
inference(cnf_transformation,[],[f233]) ).
thf(f1054,plain,
spl32_43,
inference(avatar_split_clause,[],[f536,f1052]) ).
thf(f536,plain,
! [X2: $o,X0: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),$true),X0) ) ),
inference(equality_resolution,[],[f386]) ).
thf(f386,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)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f224]) ).
thf(f1050,plain,
( spl32_42
| ~ spl32_3
| ~ spl32_10 ),
inference(avatar_split_clause,[],[f823,f790,f713,f1048]) ).
thf(f1048,plain,
( spl32_42
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_42])]) ).
thf(f790,plain,
( spl32_10
<=> ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_10])]) ).
thf(f823,plain,
( ! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) )
| ~ spl32_3
| ~ spl32_10 ),
inference(trivial_inequality_removal,[],[f822]) ).
thf(f822,plain,
( ! [X0: $o,X1: $o] :
( ( $true != $true )
| ( $true = X0 )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) )
| ~ spl32_3
| ~ spl32_10 ),
inference(superposition,[],[f791,f714]) ).
thf(f791,plain,
( ! [X0: $o,X1: $o] :
( ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) )
| ( $true = X0 ) )
| ~ spl32_10 ),
inference(avatar_component_clause,[],[f790]) ).
thf(f1046,plain,
spl32_41,
inference(avatar_split_clause,[],[f535,f1044]) ).
thf(f535,plain,
! [X2: $o,X1: $o] :
( ( $true = X2 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),X1),$true) ) ),
inference(equality_resolution,[],[f387]) ).
thf(f387,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)),sP8,X2),X1),X0) ) ),
inference(cnf_transformation,[],[f224]) ).
thf(f1042,plain,
spl32_40,
inference(avatar_split_clause,[],[f524,f1040]) ).
thf(f524,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,[],[f377]) ).
thf(f377,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,[],[f219]) ).
thf(f1006,plain,
spl32_39,
inference(avatar_split_clause,[],[f643,f1004]) ).
thf(f1004,plain,
( spl32_39
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $false = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_39])]) ).
thf(f643,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[],[f641]) ).
thf(f641,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0) ) ),
inference(not_proxy_clausification,[],[f315]) ).
thf(f315,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) ),
inference(cnf_transformation,[],[f182]) ).
thf(f182,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) ) )
& ( ( mono_2Ec_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,[],[f181]) ).
thf(f181,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = vAPP($o,$o,vNOT,vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X1),X0)) ) ) )
& ( ( mono_2Ec_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,[],[f153]) ).
thf(f986,plain,
spl32_38,
inference(avatar_split_clause,[],[f552,f984]) ).
thf(f984,plain,
( spl32_38
<=> ! [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,[spl32_38])]) ).
thf(f552,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,[],[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)),sP10,X2),X1),X0) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f982,plain,
spl32_37,
inference(avatar_split_clause,[],[f546,f980]) ).
thf(f546,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,[],[f545]) ).
thf(f545,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,[],[f409]) ).
thf(f409,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,[],[f233]) ).
thf(f978,plain,
spl32_36,
inference(avatar_split_clause,[],[f539,f976]) ).
thf(f976,plain,
( spl32_36
<=> ! [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,[spl32_36])]) ).
thf(f539,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,[],[f392]) ).
thf(f392,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,[],[f227]) ).
thf(f974,plain,
spl32_35,
inference(avatar_split_clause,[],[f538,f972]) ).
thf(f972,plain,
( spl32_35
<=> ! [X2: $o,X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),$true),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_35])]) ).
thf(f538,plain,
! [X2: $o,X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP7,X2),$true),X0) ),
inference(equality_resolution,[],[f393]) ).
thf(f393,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(cnf_transformation,[],[f227]) ).
thf(f970,plain,
spl32_34,
inference(avatar_split_clause,[],[f534,f968]) ).
thf(f534,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),$true),X0) ),
inference(equality_resolution,[],[f533]) ).
thf(f533,plain,
! [X2: $o,X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,X2),$true),X0) )
| ( $true != X2 ) ),
inference(equality_resolution,[],[f389]) ).
thf(f389,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,[],[f224]) ).
thf(f966,plain,
spl32_33,
inference(avatar_split_clause,[],[f532,f964]) ).
thf(f532,plain,
! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP($o,sTfun($o,sTfun($o,$o)),sP8,$true),X1),$true) ),
inference(equality_resolution,[],[f531]) ).
thf(f531,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 != X2 ) ),
inference(equality_resolution,[],[f390]) ).
thf(f390,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,[],[f224]) ).
thf(f962,plain,
spl32_32,
inference(avatar_split_clause,[],[f642,f960]) ).
thf(f960,plain,
( spl32_32
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_32])]) ).
thf(f642,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $false = X0 ) ),
inference(binary_proxy_clausification,[],[f641]) ).
thf(f958,plain,
spl32_31,
inference(avatar_split_clause,[],[f527,f956]) ).
thf(f527,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,[],[f526]) ).
thf(f526,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,[],[f375]) ).
thf(f375,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,[],[f219]) ).
thf(f954,plain,
spl32_30,
inference(avatar_split_clause,[],[f523,f952]) ).
thf(f952,plain,
( spl32_30
<=> ! [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,[spl32_30])]) ).
thf(f523,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,[],[f371]) ).
thf(f371,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,[],[f218]) ).
thf(f950,plain,
spl32_29,
inference(avatar_split_clause,[],[f522,f948]) ).
thf(f522,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,[],[f372]) ).
thf(f372,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,[],[f218]) ).
thf(f946,plain,
spl32_28,
inference(avatar_split_clause,[],[f521,f944]) ).
thf(f521,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,[],[f373]) ).
thf(f373,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,[],[f218]) ).
thf(f942,plain,
spl32_27,
inference(avatar_split_clause,[],[f520,f940]) ).
thf(f940,plain,
( spl32_27
<=> ! [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,[spl32_27])]) ).
thf(f520,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,[],[f367]) ).
thf(f367,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,[],[f216]) ).
thf(f938,plain,
spl32_26,
inference(avatar_split_clause,[],[f519,f936]) ).
thf(f519,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,[],[f363]) ).
thf(f363,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,[],[f213]) ).
thf(f901,plain,
spl32_25,
inference(avatar_split_clause,[],[f701,f899]) ).
thf(f701,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,[],[f700]) ).
thf(f700,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,[],[f640,f684]) ).
thf(f684,plain,
mono_2Ec_2Ebool_2ET = $true,
inference(boolean_simplification,[],[f476]) ).
thf(f476,plain,
$true = vAPP($o,$o,vNOT,vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2ET)),
inference(equality_resolution,[],[f453]) ).
thf(f453,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2ET) != X0 ) ),
inference(definition_unfolding,[],[f276,f262]) ).
thf(f262,plain,
mono_2Ec_2Ebool_2EF = vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2ET),
inference(cnf_transformation,[],[f58]) ).
thf(f58,plain,
( ( mono_2Ec_2Ebool_2ET = vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2EF) )
& ( mono_2Ec_2Ebool_2EF = vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2ET) )
& ! [X0: $o] : ( vAPP($o,$o,vNOT,vAPP($o,$o,vNOT,X0)) = X0 ) ),
inference(fool_elimination,[],[f57]) ).
thf(f57,plain,
( ( vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2EF)
<=> mono_2Ec_2Ebool_2ET )
& ( vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2ET)
<=> mono_2Ec_2Ebool_2EF )
& ! [X0: $o] :
( vAPP($o,$o,vNOT,vAPP($o,$o,vNOT,X0))
<=> X0 ) ),
inference(rectify,[],[f34]) ).
thf(f34,axiom,
( ( vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2EF)
<=> mono_2Ec_2Ebool_2ET )
& ( vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2ET)
<=> mono_2Ec_2Ebool_2EF )
& ! [X15: $o] :
( vAPP($o,$o,vNOT,vAPP($o,$o,vNOT,X15))
<=> X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(f276,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( mono_2Ec_2Ebool_2EF != X0 ) ),
inference(cnf_transformation,[],[f176]) ).
thf(f176,plain,
! [X0: $o] :
( ( ( mono_2Ec_2Ebool_2EF = X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( mono_2Ec_2Ebool_2EF != X0 ) )
& ( ( mono_2Ec_2Ebool_2EF = X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( mono_2Ec_2Ebool_2EF != X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( mono_2Ec_2Ebool_2ET != X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( mono_2Ec_2Ebool_2ET != X0 ) ) ),
inference(flattening,[],[f175]) ).
thf(f175,plain,
! [X0: $o] :
( ( ( mono_2Ec_2Ebool_2EF = X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( mono_2Ec_2Ebool_2EF != X0 ) )
& ( ( mono_2Ec_2Ebool_2EF = X0 )
| ( $true != vAPP($o,$o,vNOT,X0) ) )
& ( ( $true = vAPP($o,$o,vNOT,X0) )
| ( mono_2Ec_2Ebool_2EF != X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( mono_2Ec_2Ebool_2ET != X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
| ( $true != X0 ) )
& ( ( $true = X0 )
| ( mono_2Ec_2Ebool_2ET != X0 ) ) ),
inference(nnf_transformation,[],[f60]) ).
thf(f60,plain,
! [X0: $o] :
( ( ( mono_2Ec_2Ebool_2EF = X0 )
<=> ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( mono_2Ec_2Ebool_2EF = X0 )
<=> ( $true = vAPP($o,$o,vNOT,X0) ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
<=> ( $true = X0 ) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
<=> ( $true = X0 ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f59,plain,
! [X0: $o] :
( ( ( mono_2Ec_2Ebool_2EF = X0 )
<=> vAPP($o,$o,vNOT,X0) )
& ( ( mono_2Ec_2Ebool_2EF = X0 )
<=> vAPP($o,$o,vNOT,X0) )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
<=> X0 )
& ( ( mono_2Ec_2Ebool_2ET = X0 )
<=> X0 ) ),
inference(rectify,[],[f36]) ).
thf(f36,axiom,
! [X15: $o] :
( ( ( mono_2Ec_2Ebool_2EF = X15 )
<=> vAPP($o,$o,vNOT,X15) )
& ( ( mono_2Ec_2Ebool_2EF = X15 )
<=> vAPP($o,$o,vNOT,X15) )
& ( ( mono_2Ec_2Ebool_2ET = X15 )
<=> X15 )
& ( ( mono_2Ec_2Ebool_2ET = X15 )
<=> X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(f640,plain,
! [X0: $o,X1: $o] :
( ( mono_2Ec_2Ebool_2ET = $false )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP0,X1),X0) )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[],[f639]) ).
thf(f639,plain,
! [X0: $o,X1: $o] :
( ( mono_2Ec_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,[],[f638]) ).
thf(f638,plain,
! [X0: $o,X1: $o] :
( ( mono_2Ec_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,[],[f470]) ).
thf(f470,plain,
! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,mono_2Ec_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,[],[f314,f262]) ).
thf(f314,plain,
! [X0: $o,X1: $o] :
( ( mono_2Ec_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,[],[f182]) ).
thf(f897,plain,
spl32_24,
inference(avatar_split_clause,[],[f699,f895]) ).
thf(f699,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,[],[f698]) ).
thf(f698,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,[],[f646,f684]) ).
thf(f646,plain,
! [X0: $o,X1: $o] :
( ( mono_2Ec_2Ebool_2ET = $false )
| ( $true = X0 )
| ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ),
inference(not_proxy_clausification,[],[f645]) ).
thf(f645,plain,
! [X0: $o,X1: $o] :
( ( mono_2Ec_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,[],[f468]) ).
thf(f468,plain,
! [X0: $o,X1: $o] :
( ( vAPP($o,$o,vNOT,mono_2Ec_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,[],[f309,f262]) ).
thf(f309,plain,
! [X0: $o,X1: $o] :
( ( mono_2Ec_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,[],[f180]) ).
thf(f180,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = vAPP($o,$o,vNOT,X0) )
& ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != X1 ) ) ) )
& ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = X1 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ) ),
inference(flattening,[],[f179]) ).
thf(f179,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = vAPP($o,$o,vNOT,X0) )
& ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != X1 ) ) ) )
& ( ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != vAPP($o,$o,vNOT,X0) )
| ( ( mono_2Ec_2Ebool_2EF != $true )
& ( $true = X1 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) ) ) ),
inference(nnf_transformation,[],[f154]) ).
thf(f893,plain,
spl32_23,
inference(avatar_split_clause,[],[f622,f891]) ).
thf(f622,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,[],[f621]) ).
thf(f621,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,[],[f325]) ).
thf(f325,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,[],[f188]) ).
thf(f188,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,[],[f187]) ).
thf(f187,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,[],[f186]) ).
thf(f186,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,[],[f156]) ).
thf(f156,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(f889,plain,
spl32_22,
inference(avatar_split_clause,[],[f335,f887]) ).
thf(f335,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) ) ),
inference(cnf_transformation,[],[f193]) ).
thf(f193,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
| ( ( $true != X1 )
& ( $true != X0 ) ) )
& ( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) ) ) ),
inference(flattening,[],[f192]) ).
thf(f192,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
| ( ( $true != X1 )
& ( $true != X0 ) ) )
& ( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) ) ) ),
inference(nnf_transformation,[],[f84]) ).
thf(f84,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
<=> ( ( $true = X1 )
| ( $true = X0 ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f83,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1)
<=> ( X1
| X0 ) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X8: $o,X9: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X8),X9)
<=> ( X9
| X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(f885,plain,
spl32_21,
inference(avatar_split_clause,[],[f324,f883]) ).
thf(f324,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),X0) ) ),
inference(cnf_transformation,[],[f188]) ).
thf(f879,plain,
spl32_20,
inference(avatar_split_clause,[],[f497,f877]) ).
thf(f877,plain,
( spl32_20
<=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),vAPP($o,$o,vNOT,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_20])]) ).
thf(f497,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X0),vAPP($o,$o,vNOT,X0)) ),
inference(equality_resolution,[],[f330]) ).
thf(f330,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,[],[f189]) ).
thf(f189,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,[],[f157]) ).
thf(f157,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,[],[f80,f156]) ).
thf(f80,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,[],[f79]) ).
thf(f79,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,[],[f48]) ).
thf(f48,axiom,
! [X49: $o,X50: $o] :
( ( X50
<=> vAPP($o,$o,vNOT,X49) )
<=> ( ( vAPP($o,$o,vNOT,X50)
| vAPP($o,$o,vNOT,X49) )
& ( X49
| X50 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__neg) ).
thf(f873,plain,
~ spl32_19,
inference(avatar_split_clause,[],[f260,f870]) ).
thf(f260,plain,
$true != vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK18)))),
inference(cnf_transformation,[],[f174]) ).
thf(f868,plain,
spl32_18,
inference(avatar_split_clause,[],[f259,f865]) ).
thf(f259,plain,
$true = vAPP(du,$o,j_mono_2Etyop_2Emin_2Ebool,vAPP(u,du,vAPP(d,sTfun(u,du),s,tyop_2Emin_2Ebool),vAPP(du,u,vAPP(du,sTfun(du,u),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2,vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK15),sK14)),sK16)),vAPP(u,du,vAPP(d,sTfun(u,du),s,vAPP(d,d,vAPP(d,sTfun(d,d),tyop_2Emin_2Efun,sK14),tyop_2Emin_2Ebool)),sK17)))),
inference(cnf_transformation,[],[f174]) ).
thf(f820,plain,
spl32_17,
inference(avatar_split_clause,[],[f648,f818]) ).
thf(f818,plain,
( spl32_17
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_17])]) ).
thf(f648,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( $false = X0 ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f312,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,[],[f180]) ).
thf(f816,plain,
spl32_16,
inference(avatar_split_clause,[],[f663,f814]) ).
thf(f814,plain,
( spl32_16
<=> ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_16])]) ).
thf(f663,plain,
! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0) ) ),
inference(not_proxy_clausification,[],[f660]) ).
thf(f660,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vNOT,X0) )
| ( $false = vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0) ) ),
inference(binary_proxy_clausification,[],[f298]) ).
thf(f298,plain,
! [X0: $o] : ( vAPP($o,$o,vNOT,X0) = vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0) ),
inference(cnf_transformation,[],[f68]) ).
thf(f68,plain,
! [X0: $o] : ( vAPP($o,$o,vNOT,X0) = vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0) ),
inference(fool_elimination,[],[f67]) ).
thf(f67,plain,
! [X0: $o] :
( vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0)
<=> vAPP($o,$o,vNOT,X0) ),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
! [X8: $o] :
( vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X8)
<=> vAPP($o,$o,vNOT,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(f812,plain,
spl32_15,
inference(avatar_split_clause,[],[f626,f810]) ).
thf(f626,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,$true),X0) )
| ( $true = X0 ) ),
inference(not_proxy_clausification,[],[f493]) ).
thf(f493,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,$true),X0) )
| ( $true != vAPP($o,$o,vNOT,X0) ) ),
inference(equality_resolution,[],[f329]) ).
thf(f329,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,[],[f188]) ).
thf(f808,plain,
spl32_14,
inference(avatar_split_clause,[],[f623,f806]) ).
thf(f623,plain,
! [X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),$true) )
| ( $true = X1 ) ),
inference(not_proxy_clausification,[],[f496]) ).
thf(f496,plain,
! [X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP2,X1),$true) )
| ( $true != vAPP($o,$o,vNOT,X1) ) ),
inference(equality_resolution,[],[f326]) ).
thf(f326,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,[],[f188]) ).
thf(f804,plain,
spl32_13,
inference(avatar_split_clause,[],[f503,f802]) ).
thf(f503,plain,
! [X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,$true),X1) ) ),
inference(equality_resolution,[],[f338]) ).
thf(f338,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) ) ),
inference(cnf_transformation,[],[f195]) ).
thf(f195,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( ( $true != X1 )
& ( $true = X0 ) ) )
& ( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) ) ) ),
inference(flattening,[],[f194]) ).
thf(f194,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( ( $true != X1 )
& ( $true = X0 ) ) )
& ( ( $true = X1 )
| ( $true != X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) ) ) ),
inference(nnf_transformation,[],[f145]) ).
thf(f145,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
<=> ( ( $true = X1 )
| ( $true != X0 ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f86,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
<=> ( ( $true = X0 )
=> ( $true = X1 ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f85,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1)
<=> ( X0
=> X1 ) ),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
! [X8: $o,X9: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X8),X9)
<=> ( X8
=> X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(f800,plain,
spl32_12,
inference(avatar_split_clause,[],[f339,f798]) ).
thf(f798,plain,
( spl32_12
<=> ! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_12])]) ).
thf(f339,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true = X0 ) ),
inference(cnf_transformation,[],[f195]) ).
thf(f796,plain,
spl32_11,
inference(avatar_split_clause,[],[f333,f794]) ).
thf(f333,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) ),
inference(cnf_transformation,[],[f191]) ).
thf(f191,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) )
& ( ( ( $true = X1 )
& ( $true = X0 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) ) ),
inference(flattening,[],[f190]) ).
thf(f190,plain,
! [X0: $o,X1: $o] :
( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) )
& ( ( ( $true = X1 )
& ( $true = X0 ) )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) ) ),
inference(nnf_transformation,[],[f82]) ).
thf(f82,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) )
<=> ( ( $true = X1 )
& ( $true = X0 ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f81,plain,
! [X0: $o,X1: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1)
<=> ( X1
& X0 ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X8: $o,X9: $o] :
( vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X8),X9)
<=> ( X9
& X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(f792,plain,
spl32_10,
inference(avatar_split_clause,[],[f332,f790]) ).
thf(f332,plain,
! [X0: $o,X1: $o] :
( ( $true = X0 )
| ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) ) ),
inference(cnf_transformation,[],[f191]) ).
thf(f772,plain,
spl32_9,
inference(avatar_split_clause,[],[f662,f770]) ).
thf(f770,plain,
( spl32_9
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_9])]) ).
thf(f662,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $true = vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0) ) ),
inference(not_proxy_clausification,[],[f661]) ).
thf(f661,plain,
! [X0: $o] :
( ( $false = vAPP($o,$o,vNOT,X0) )
| ( $true = vAPP($o,$o,mono_2Ec_2Ebool_2E_7E,X0) ) ),
inference(binary_proxy_clausification,[],[f298]) ).
thf(f764,plain,
spl32_8,
inference(avatar_split_clause,[],[f697,f762]) ).
thf(f697,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) ),
inference(trivial_inequality_removal,[],[f696]) ).
thf(f696,plain,
! [X0: $o] :
( ( $true = $false )
| ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) ) ),
inference(forward_demodulation,[],[f647,f684]) ).
thf(f647,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) )
| ( mono_2Ec_2Ebool_2ET = $false ) ),
inference(not_proxy_clausification,[],[f490]) ).
thf(f490,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,$true),X0) )
| ( vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2ET) = $true ) ),
inference(equality_resolution,[],[f466]) ).
thf(f466,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( vAPP($o,$o,vNOT,mono_2Ec_2Ebool_2ET) = $true )
| ( $true != X1 ) ),
inference(definition_unfolding,[],[f311,f262]) ).
thf(f311,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),sP1,X1),X0) )
| ( mono_2Ec_2Ebool_2EF = $true )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f180]) ).
thf(f760,plain,
spl32_7,
inference(avatar_split_clause,[],[f502,f758]) ).
thf(f502,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),$true) ),
inference(equality_resolution,[],[f340]) ).
thf(f340,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Emin_2E_3D_3D_3E,X0),X1) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f195]) ).
thf(f756,plain,
spl32_6,
inference(avatar_split_clause,[],[f501,f754]) ).
thf(f501,plain,
! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,$true),X1) ),
inference(equality_resolution,[],[f336]) ).
thf(f336,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f193]) ).
thf(f752,plain,
spl32_5,
inference(avatar_split_clause,[],[f500,f750]) ).
thf(f500,plain,
! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),$true) ),
inference(equality_resolution,[],[f337]) ).
thf(f337,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_5C_2F,X0),X1) )
| ( $true != X1 ) ),
inference(cnf_transformation,[],[f193]) ).
thf(f748,plain,
spl32_4,
inference(avatar_split_clause,[],[f499,f745]) ).
thf(f499,plain,
$true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,$true),$true),
inference(equality_resolution,[],[f498]) ).
thf(f498,plain,
! [X0: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),$true) )
| ( $true != X0 ) ),
inference(equality_resolution,[],[f334]) ).
thf(f334,plain,
! [X0: $o,X1: $o] :
( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),mono_2Ec_2Ebool_2E_2F_5C,X0),X1) )
| ( $true != X1 )
| ( $true != X0 ) ),
inference(cnf_transformation,[],[f191]) ).
thf(f715,plain,
spl32_3,
inference(avatar_split_clause,[],[f54,f713]) ).
thf(f54,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f711,plain,
spl32_2,
inference(avatar_split_clause,[],[f684,f708]) ).
thf(f708,plain,
( spl32_2
<=> ( mono_2Ec_2Ebool_2ET = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_2])]) ).
thf(f706,plain,
~ spl32_1,
inference(avatar_split_clause,[],[f53,f703]) ).
thf(f703,plain,
( spl32_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl32_1])]) ).
thf(f53,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP006^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 17:44:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (26584)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (26587)WARNING: value z3 for option sas not known
% 0.14/0.37 % (26585)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (26586)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (26588)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (26589)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (26587)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (26590)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (26591)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.39 % (26591)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.41 % (26592)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.41 % (26593)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)
% 0.14/0.41 % (26594)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)
% 0.20/0.42 % (26592)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.42 % Exception at run slice level
% 0.20/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.42 % (26593)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.44 % (26596)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.71/0.59 % (26589)First to succeed.
% 1.71/0.61 % (26589)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26584"
% 1.71/0.61 % (26589)Refutation found. Thanks to Tanya!
% 1.71/0.61 % SZS status Theorem for theBenchmark
% 1.71/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.71/0.62 % (26589)------------------------------
% 1.71/0.62 % (26589)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.71/0.62 % (26589)Termination reason: Refutation
% 1.71/0.62
% 1.71/0.62 % (26589)Memory used [KB]: 3577
% 1.71/0.62 % (26589)Time elapsed: 0.238 s
% 1.71/0.62 % (26589)Instructions burned: 711 (million)
% 1.71/0.62 % (26584)Success in time 0.275 s
%------------------------------------------------------------------------------