TSTP Solution File: ITP015_3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP015_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 06:58:43 EDT 2024
% Result : Theorem 2.39s 0.75s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 229
% Syntax : Number of formulae : 690 ( 150 unt; 55 typ; 0 def)
% Number of atoms : 1731 ( 394 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 1831 ( 735 ~; 846 |; 69 &)
% ( 157 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 39 ( 26 >; 13 *; 0 +; 0 <<)
% Number of predicates : 130 ( 128 usr; 128 prp; 0-2 aty)
% Number of functors : 50 ( 50 usr; 13 con; 0-4 aty)
% Number of variables : 1043 (1002 !; 12 ?;1043 :)
% ( 29 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(type_def_6,type,
tyop_2Efcp_2Ecart: ( $tType * $tType ) > $tType ).
tff(type_def_7,type,
tyop_2Einteger_2Eint: $tType ).
tff(type_def_8,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_9,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_10,type,
tyop_2Enum_2Enum: $tType ).
tff(type_def_11,type,
sK0: $tType ).
tff(func_def_0,type,
app_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
combin_i_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).
tff(func_def_2,type,
combin_k_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).
tff(func_def_3,type,
combin_s_2E0:
!>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).
tff(func_def_4,type,
c_2Ebool_2E_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_5,type,
c_2Ebool_2E_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_6,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_7,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_8,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(func_def_9,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(func_def_10,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(func_def_11,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_12,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_13,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_14,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_15,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_16,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_17,type,
c_2Ebool_2ECOND_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0))) ).
tff(func_def_18,type,
c_2Ebool_2ECOND_2E3:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * X0 * X0 ) > X0 ) ).
tff(func_def_19,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_20,type,
c_2Earithmetic_2EMOD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(func_def_21,type,
c_2Earithmetic_2EMOD_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(func_def_22,type,
c_2Einteger_2ENum_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Enum_2Enum) ).
tff(func_def_23,type,
c_2Einteger_2ENum_2E1: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).
tff(func_def_24,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_25,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_26,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_27,type,
c_2Ewords_2Edimword_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum) ).
tff(func_def_28,type,
c_2Ewords_2Edimword_2E1:
!>[X0: $tType] : ( tyop_2Ebool_2Eitself(X0) > tyop_2Enum_2Enum ) ).
tff(func_def_29,type,
c_2Einteger__word_2Ei2w_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)) ).
tff(func_def_30,type,
c_2Einteger__word_2Ei2w_2E1:
!>[X0: $tType] : ( tyop_2Einteger_2Eint > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_31,type,
c_2Einteger_2Eint__lt_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(func_def_32,type,
c_2Einteger_2Eint__lt_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(func_def_33,type,
c_2Einteger_2Eint__neg_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint) ).
tff(func_def_34,type,
c_2Einteger_2Eint__neg_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
tff(func_def_35,type,
c_2Einteger_2Eint__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint) ).
tff(func_def_36,type,
c_2Einteger_2Eint__of__num_2E1: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
tff(func_def_37,type,
c_2Ewords_2En2w_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)) ).
tff(func_def_38,type,
c_2Ewords_2En2w_2E1:
!>[X0: $tType] : ( tyop_2Enum_2Enum > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_39,type,
c_2Ebool_2Ethe__value_2E0:
!>[X0: $tType] : tyop_2Ebool_2Eitself(X0) ).
tff(func_def_40,type,
c_2Ewords_2Eword__2comp_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)) ).
tff(func_def_41,type,
c_2Ewords_2Eword__2comp_2E1:
!>[X0: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_42,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_43,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_44,type,
sK1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_45,type,
sK2:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_46,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(f5509,plain,
$false,
inference(avatar_sat_refutation,[],[f280,f285,f289,f293,f297,f303,f307,f311,f315,f319,f323,f327,f331,f344,f351,f355,f377,f381,f385,f394,f398,f402,f406,f434,f443,f447,f453,f457,f461,f465,f469,f486,f510,f515,f519,f527,f531,f552,f556,f560,f564,f592,f596,f618,f624,f634,f638,f642,f653,f657,f674,f681,f685,f689,f704,f708,f714,f723,f727,f731,f784,f830,f834,f840,f881,f885,f890,f943,f947,f951,f955,f960,f964,f968,f972,f1442,f1473,f1477,f1481,f1485,f1489,f1493,f1497,f1505,f1519,f1520,f1524,f2670,f2719,f2791,f2807,f2812,f2878,f2906,f2949,f2953,f2957,f2961,f2975,f2979,f2983,f3009,f3010,f3011,f3012,f3013,f3055,f3090,f3707,f4012,f4081,f4122,f4126,f4493,f4497,f4501,f4671,f4675,f4704,f4708,f4712,f4716,f4720,f5072,f5076,f5080,f5308,f5324,f5328,f5332,f5336,f5415,f5508]) ).
tff(f5508,plain,
( spl4_6
| ~ spl4_126 ),
inference(avatar_contradiction_clause,[],[f5507]) ).
tff(f5507,plain,
( $false
| spl4_6
| ~ spl4_126 ),
inference(trivial_inequality_removal,[],[f5505]) ).
tff(f5505,plain,
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),c_2Enum_2E0_2E0) != app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),c_2Enum_2E0_2E0) )
| spl4_6
| ~ spl4_126 ),
inference(superposition,[],[f302,f5335]) ).
tff(f5335,plain,
( ! [X1: $tType,X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X0) )
| ~ spl4_126 ),
inference(avatar_component_clause,[],[f5334]) ).
tff(f5334,plain,
( spl4_126
<=> ! [X1: $tType,X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_126])]) ).
tff(f302,plain,
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),c_2Enum_2E0_2E0) != app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Einteger__word_2Ei2w_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) )
| spl4_6 ),
inference(avatar_component_clause,[],[f300]) ).
tff(f300,plain,
( spl4_6
<=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),c_2Enum_2E0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Einteger__word_2Ei2w_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
tff(f5415,plain,
( spl4_127
| ~ spl4_14
| spl4_93 ),
inference(avatar_split_clause,[],[f2813,f2804,f342,f5412]) ).
tff(f5412,plain,
( spl4_127
<=> ( c_2Ebool_2EF_2E0 = sK1(tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_127])]) ).
tff(f342,plain,
( spl4_14
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
tff(f2804,plain,
( spl4_93
<=> p(sK1(tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_93])]) ).
tff(f2813,plain,
( ( c_2Ebool_2EF_2E0 = sK1(tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool)) )
| ~ spl4_14
| spl4_93 ),
inference(resolution,[],[f2806,f343]) ).
tff(f343,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f342]) ).
tff(f2806,plain,
( ~ p(sK1(tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool)))
| spl4_93 ),
inference(avatar_component_clause,[],[f2804]) ).
tff(f5336,plain,
( spl4_126
| ~ spl4_25
| ~ spl4_34
| ~ spl4_48
| ~ spl4_52
| ~ spl4_57
| ~ spl4_58
| ~ spl4_65 ),
inference(avatar_split_clause,[],[f871,f838,f712,f706,f672,f636,f512,f441,f5334]) ).
tff(f441,plain,
( spl4_25
<=> ! [X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).
tff(f512,plain,
( spl4_34
<=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_34])]) ).
tff(f636,plain,
( spl4_48
<=> ! [X0: $tType,X2: X0,X1: X0] : ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),c_2Ebool_2EF_2E0),X1),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_48])]) ).
tff(f672,plain,
( spl4_52
<=> ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_52])]) ).
tff(f706,plain,
( spl4_57
<=> ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_57])]) ).
tff(f712,plain,
( spl4_58
<=> ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_58])]) ).
tff(f838,plain,
( spl4_65
<=> ! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X1) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X1))))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_65])]) ).
tff(f871,plain,
( ! [X1: $tType,X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X0) )
| ~ spl4_25
| ~ spl4_34
| ~ spl4_48
| ~ spl4_52
| ~ spl4_57
| ~ spl4_58
| ~ spl4_65 ),
inference(forward_demodulation,[],[f870,f637]) ).
tff(f637,plain,
( ! [X0: $tType,X2: X0,X1: X0] : ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),c_2Ebool_2EF_2E0),X1),X2) = X2 )
| ~ spl4_48 ),
inference(avatar_component_clause,[],[f636]) ).
tff(f870,plain,
( ! [X1: $tType,X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),c_2Ebool_2EF_2E0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)))))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X0)) )
| ~ spl4_25
| ~ spl4_34
| ~ spl4_52
| ~ spl4_57
| ~ spl4_58
| ~ spl4_65 ),
inference(forward_demodulation,[],[f869,f719]) ).
tff(f719,plain,
( ! [X0: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),c_2Enum_2E0_2E0) )
| ~ spl4_34
| ~ spl4_52
| ~ spl4_58 ),
inference(forward_demodulation,[],[f715,f673]) ).
tff(f673,plain,
( ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))) )
| ~ spl4_52 ),
inference(avatar_component_clause,[],[f672]) ).
tff(f715,plain,
( ! [X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),c_2Enum_2E0_2E0) )
| ~ spl4_34
| ~ spl4_58 ),
inference(superposition,[],[f713,f514]) ).
tff(f514,plain,
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) )
| ~ spl4_34 ),
inference(avatar_component_clause,[],[f512]) ).
tff(f713,plain,
( ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))) )
| ~ spl4_58 ),
inference(avatar_component_clause,[],[f712]) ).
tff(f869,plain,
( ! [X1: $tType,X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),c_2Enum_2E0_2E0)),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)))))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X0)) )
| ~ spl4_25
| ~ spl4_57
| ~ spl4_65 ),
inference(forward_demodulation,[],[f864,f442]) ).
tff(f442,plain,
( ! [X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = X0 )
| ~ spl4_25 ),
inference(avatar_component_clause,[],[f441]) ).
tff(f864,plain,
( ! [X1: $tType,X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Einteger__word_2Ei2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),c_2Enum_2E0_2E0)),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)))))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)))) )
| ~ spl4_57
| ~ spl4_65 ),
inference(superposition,[],[f839,f707]) ).
tff(f707,plain,
( ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)) )
| ~ spl4_57 ),
inference(avatar_component_clause,[],[f706]) ).
tff(f839,plain,
( ! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X1) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X1))))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X1))) )
| ~ spl4_65 ),
inference(avatar_component_clause,[],[f838]) ).
tff(f5332,plain,
( spl4_125
| ~ spl4_19
| ~ spl4_50 ),
inference(avatar_split_clause,[],[f665,f651,f383,f5330]) ).
tff(f5330,plain,
( spl4_125
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,X0)] :
( ( sK3(X0,X0,X1,combin_i_2E0(X0)) != app_2E2(X0,X0,X1,sK3(X0,X0,X1,combin_i_2E0(X0))) )
| ( combin_i_2E0(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_125])]) ).
tff(f383,plain,
( spl4_19
<=> ! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
tff(f651,plain,
( spl4_50
<=> ! [X1: $tType,X0: $tType,X3: tyop_2Emin_2Efun(X0,X1),X2: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK3(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK3(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_50])]) ).
tff(f665,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,X0)] :
( ( sK3(X0,X0,X1,combin_i_2E0(X0)) != app_2E2(X0,X0,X1,sK3(X0,X0,X1,combin_i_2E0(X0))) )
| ( combin_i_2E0(X0) = X1 ) )
| ~ spl4_19
| ~ spl4_50 ),
inference(superposition,[],[f652,f384]) ).
tff(f384,plain,
( ! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 )
| ~ spl4_19 ),
inference(avatar_component_clause,[],[f383]) ).
tff(f652,plain,
( ! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( app_2E2(X0,X1,X2,sK3(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK3(X0,X1,X2,X3)) )
| ( X2 = X3 ) )
| ~ spl4_50 ),
inference(avatar_component_clause,[],[f651]) ).
tff(f5328,plain,
( spl4_124
| ~ spl4_7
| ~ spl4_50 ),
inference(avatar_split_clause,[],[f664,f651,f305,f5326]) ).
tff(f5326,plain,
( spl4_124
<=> ! [X0: $tType,X2: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,X0),X1: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,X0)] :
( ( app_2E2(tyop_2Emin_2Ebool,X0,X1,c_2Ebool_2ET_2E0) != app_2E2(tyop_2Emin_2Ebool,X0,X2,c_2Ebool_2ET_2E0) )
| ( X1 = X2 )
| ( c_2Ebool_2EF_2E0 = sK3(tyop_2Emin_2Ebool,X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_124])]) ).
tff(f305,plain,
( spl4_7
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
tff(f664,plain,
( ! [X0: $tType,X2: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,X0),X1: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,X0)] :
( ( app_2E2(tyop_2Emin_2Ebool,X0,X1,c_2Ebool_2ET_2E0) != app_2E2(tyop_2Emin_2Ebool,X0,X2,c_2Ebool_2ET_2E0) )
| ( X1 = X2 )
| ( c_2Ebool_2EF_2E0 = sK3(tyop_2Emin_2Ebool,X0,X1,X2) ) )
| ~ spl4_7
| ~ spl4_50 ),
inference(superposition,[],[f652,f306]) ).
tff(f306,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f305]) ).
tff(f5324,plain,
( spl4_123
| ~ spl4_19
| ~ spl4_50 ),
inference(avatar_split_clause,[],[f659,f651,f383,f5322]) ).
tff(f5322,plain,
( spl4_123
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,X0)] :
( ( sK3(X0,X0,combin_i_2E0(X0),X1) != app_2E2(X0,X0,X1,sK3(X0,X0,combin_i_2E0(X0),X1)) )
| ( combin_i_2E0(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_123])]) ).
tff(f659,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,X0)] :
( ( sK3(X0,X0,combin_i_2E0(X0),X1) != app_2E2(X0,X0,X1,sK3(X0,X0,combin_i_2E0(X0),X1)) )
| ( combin_i_2E0(X0) = X1 ) )
| ~ spl4_19
| ~ spl4_50 ),
inference(superposition,[],[f652,f384]) ).
tff(f5308,plain,
( spl4_122
| ~ spl4_34
| ~ spl4_52 ),
inference(avatar_split_clause,[],[f675,f672,f512,f5306]) ).
tff(f5306,plain,
( spl4_122
<=> ! [X0: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_122])]) ).
tff(f675,plain,
( ! [X0: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) )
| ~ spl4_34
| ~ spl4_52 ),
inference(superposition,[],[f673,f514]) ).
tff(f5080,plain,
( spl4_121
| ~ spl4_15
| ~ spl4_44 ),
inference(avatar_split_clause,[],[f611,f594,f349,f5078]) ).
tff(f5078,plain,
( spl4_121
<=> ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1)))
| p(X2)
| ( app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_121])]) ).
tff(f349,plain,
( spl4_15
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| p(X1)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
tff(f594,plain,
( spl4_44
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1)))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_44])]) ).
tff(f611,plain,
( ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1)))
| p(X2)
| ( app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) = X2 ) )
| ~ spl4_15
| ~ spl4_44 ),
inference(resolution,[],[f595,f350]) ).
tff(f350,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ( X0 = X1 ) )
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f349]) ).
tff(f595,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1))) )
| ~ spl4_44 ),
inference(avatar_component_clause,[],[f594]) ).
tff(f5076,plain,
( spl4_120
| ~ spl4_7
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f606,f590,f305,f5074]) ).
tff(f5074,plain,
( spl4_120
<=> ! [X0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0,c_2Ebool_2ET_2E0))
| p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),X0))
| ( c_2Ebool_2EF_2E0 = sK1(tyop_2Emin_2Ebool,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_120])]) ).
tff(f590,plain,
( spl4_43
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK1(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_43])]) ).
tff(f606,plain,
( ! [X0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0,c_2Ebool_2ET_2E0))
| p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),X0))
| ( c_2Ebool_2EF_2E0 = sK1(tyop_2Emin_2Ebool,X0) ) )
| ~ spl4_7
| ~ spl4_43 ),
inference(superposition,[],[f591,f306]) ).
tff(f591,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK1(X0,X1)))
| p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1)) )
| ~ spl4_43 ),
inference(avatar_component_clause,[],[f590]) ).
tff(f5072,plain,
( spl4_119
| ~ spl4_15
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f604,f590,f349,f5070]) ).
tff(f5070,plain,
( spl4_119
<=> ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1))
| p(X2)
| ( app_2E2(X0,tyop_2Emin_2Ebool,X1,sK1(X0,X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_119])]) ).
tff(f604,plain,
( ! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1))
| p(X2)
| ( app_2E2(X0,tyop_2Emin_2Ebool,X1,sK1(X0,X1)) = X2 ) )
| ~ spl4_15
| ~ spl4_43 ),
inference(resolution,[],[f591,f350]) ).
tff(f4720,plain,
( spl4_118
| ~ spl4_33
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f609,f590,f508,f4718]) ).
tff(f4718,plain,
( spl4_118
<=> ! [X0: $tType,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),combin_k_2E0(tyop_2Emin_2Ebool,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_118])]) ).
tff(f508,plain,
( spl4_33
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_33])]) ).
tff(f609,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),combin_k_2E0(tyop_2Emin_2Ebool,X0),X1))) )
| ~ spl4_33
| ~ spl4_43 ),
inference(superposition,[],[f591,f509]) ).
tff(f509,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 )
| ~ spl4_33 ),
inference(avatar_component_clause,[],[f508]) ).
tff(f4716,plain,
( spl4_117
| ~ spl4_15
| ~ spl4_42 ),
inference(avatar_split_clause,[],[f586,f562,f349,f4714]) ).
tff(f4714,plain,
( spl4_117
<=> ! [X2: $tType,X0: X2,X3: tyop_2Emin_2Ebool,X1: X2] :
( ( X0 = X1 )
| p(X3)
| ( app_2E2(X2,tyop_2Emin_2Ebool,app_2E2(X2,tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X2),X0),X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_117])]) ).
tff(f562,plain,
( spl4_42
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_42])]) ).
tff(f586,plain,
( ! [X2: $tType,X3: tyop_2Emin_2Ebool,X0: X2,X1: X2] :
( ( X0 = X1 )
| p(X3)
| ( app_2E2(X2,tyop_2Emin_2Ebool,app_2E2(X2,tyop_2Emin_2Efun(X2,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X2),X0),X1) = X3 ) )
| ~ spl4_15
| ~ spl4_42 ),
inference(resolution,[],[f563,f350]) ).
tff(f563,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
| ( X1 = X2 ) )
| ~ spl4_42 ),
inference(avatar_component_clause,[],[f562]) ).
tff(f4712,plain,
( spl4_116
| ~ spl4_15
| ~ spl4_41 ),
inference(avatar_split_clause,[],[f581,f558,f349,f4710]) ).
tff(f4710,plain,
( spl4_116
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_116])]) ).
tff(f558,plain,
( spl4_41
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_41])]) ).
tff(f581,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1) = X2 ) )
| ~ spl4_15
| ~ spl4_41 ),
inference(resolution,[],[f559,f350]) ).
tff(f559,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ~ p(X0)
| p(X1) )
| ~ spl4_41 ),
inference(avatar_component_clause,[],[f558]) ).
tff(f4708,plain,
( spl4_115
| ~ spl4_15
| ~ spl4_40 ),
inference(avatar_split_clause,[],[f575,f554,f349,f4706]) ).
tff(f4706,plain,
( spl4_115
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_115])]) ).
tff(f554,plain,
( spl4_40
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_40])]) ).
tff(f575,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1) = X2 ) )
| ~ spl4_15
| ~ spl4_40 ),
inference(resolution,[],[f555,f350]) ).
tff(f555,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| p(X0)
| p(X1) )
| ~ spl4_40 ),
inference(avatar_component_clause,[],[f554]) ).
tff(f4704,plain,
( spl4_114
| ~ spl4_16
| ~ spl4_39 ),
inference(avatar_split_clause,[],[f569,f550,f353,f4702]) ).
tff(f4702,plain,
( spl4_114
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ~ p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X1),X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_114])]) ).
tff(f353,plain,
( spl4_16
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ~ p(X0)
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
tff(f550,plain,
( spl4_39
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_39])]) ).
tff(f569,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ~ p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X1),X0) = X2 ) )
| ~ spl4_16
| ~ spl4_39 ),
inference(resolution,[],[f551,f354]) ).
tff(f354,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| ~ p(X0)
| ( X0 = X1 ) )
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f353]) ).
tff(f551,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) )
| ~ spl4_39 ),
inference(avatar_component_clause,[],[f550]) ).
tff(f4675,plain,
( spl4_113
| spl4_88
| ~ spl4_38
| ~ spl4_39 ),
inference(avatar_split_clause,[],[f567,f550,f529,f2668,f4673]) ).
tff(f4673,plain,
( spl4_113
<=> ! [X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_113])]) ).
tff(f2668,plain,
( spl4_88
<=> ! [X0: tyop_2Emin_2Ebool] : ~ p(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_88])]) ).
tff(f529,plain,
( spl4_38
<=> ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_38])]) ).
tff(f567,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X1))) )
| ~ spl4_38
| ~ spl4_39 ),
inference(resolution,[],[f551,f530]) ).
tff(f530,plain,
( ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) )
| ~ spl4_38 ),
inference(avatar_component_clause,[],[f529]) ).
tff(f4671,plain,
( spl4_112
| ~ spl4_33
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f548,f529,f508,f4669]) ).
tff(f4669,plain,
( spl4_112
<=> ! [X0: $tType,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),combin_k_2E0(tyop_2Emin_2Ebool,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_112])]) ).
tff(f548,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),combin_k_2E0(tyop_2Emin_2Ebool,X0),X1))) )
| ~ spl4_33
| ~ spl4_38 ),
inference(superposition,[],[f530,f509]) ).
tff(f4501,plain,
( spl4_111
| ~ spl4_15
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f544,f529,f349,f4499]) ).
tff(f4499,plain,
( spl4_111
<=> ! [X0: $tType,X3: tyop_2Emin_2Ebool,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| p(X3)
| ( app_2E2(X0,tyop_2Emin_2Ebool,X1,X2) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_111])]) ).
tff(f544,plain,
( ! [X0: $tType,X2: X0,X3: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| p(X3)
| ( app_2E2(X0,tyop_2Emin_2Ebool,X1,X2) = X3 ) )
| ~ spl4_15
| ~ spl4_38 ),
inference(resolution,[],[f530,f350]) ).
tff(f4497,plain,
( spl4_110
| ~ spl4_15
| ~ spl4_35 ),
inference(avatar_split_clause,[],[f534,f517,f349,f4495]) ).
tff(f4495,plain,
( spl4_110
<=> ! [X0: $tType,X3: tyop_2Emin_2Ebool,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| p(X3)
| ( app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_110])]) ).
tff(f517,plain,
( spl4_35
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).
tff(f534,plain,
( ! [X0: $tType,X2: X0,X3: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| p(X3)
| ( app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) = X3 ) )
| ~ spl4_15
| ~ spl4_35 ),
inference(resolution,[],[f518,f350]) ).
tff(f518,plain,
( ! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1))
| p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3)) )
| ~ spl4_35 ),
inference(avatar_component_clause,[],[f517]) ).
tff(f4493,plain,
( spl4_109
| ~ spl4_7
| ~ spl4_33 ),
inference(avatar_split_clause,[],[f532,f508,f305,f4491]) ).
tff(f4491,plain,
( spl4_109
<=> ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X1 )
| ( c_2Ebool_2EF_2E0 = app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),combin_k_2E0(tyop_2Emin_2Ebool,X0),X1),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_109])]) ).
tff(f532,plain,
( ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X1 )
| ( c_2Ebool_2EF_2E0 = app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),combin_k_2E0(tyop_2Emin_2Ebool,X0),X1),X2) ) )
| ~ spl4_7
| ~ spl4_33 ),
inference(superposition,[],[f509,f306]) ).
tff(f4126,plain,
( spl4_108
| ~ spl4_31
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f601,f590,f467,f4124]) ).
tff(f4124,plain,
( spl4_108
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0)))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_108])]) ).
tff(f467,plain,
( spl4_31
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).
tff(f601,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0)))
| p(X0) )
| ~ spl4_31
| ~ spl4_43 ),
inference(resolution,[],[f591,f468]) ).
tff(f468,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| p(X0) )
| ~ spl4_31 ),
inference(avatar_component_clause,[],[f467]) ).
tff(f4122,plain,
( spl4_107
| ~ spl4_29
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f599,f590,f459,f4120]) ).
tff(f4120,plain,
( spl4_107
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0)))
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_107])]) ).
tff(f459,plain,
( spl4_29
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).
tff(f599,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0)))
| ~ p(X0) )
| ~ spl4_29
| ~ spl4_43 ),
inference(resolution,[],[f591,f460]) ).
tff(f460,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X0) )
| ~ spl4_29 ),
inference(avatar_component_clause,[],[f459]) ).
tff(f4081,plain,
( spl4_88
| spl4_106
| ~ spl4_32
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f540,f529,f484,f4079,f2668]) ).
tff(f4079,plain,
( spl4_106
<=> ! [X0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_106])]) ).
tff(f484,plain,
( spl4_32
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).
tff(f540,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0)))
| ~ p(X1) )
| ~ spl4_32
| ~ spl4_38 ),
inference(resolution,[],[f530,f485]) ).
tff(f485,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ~ p(X1) )
| ~ spl4_32 ),
inference(avatar_component_clause,[],[f484]) ).
tff(f4012,plain,
( spl4_105
| ~ spl4_24
| ~ spl4_89 ),
inference(avatar_split_clause,[],[f2721,f2712,f432,f4009]) ).
tff(f4009,plain,
( spl4_105
<=> ( c_2Ebool_2ET_2E0 = sK1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_105])]) ).
tff(f432,plain,
( spl4_24
<=> ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).
tff(f2712,plain,
( spl4_89
<=> p(sK1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_89])]) ).
tff(f2721,plain,
( ( c_2Ebool_2ET_2E0 = sK1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0) )
| ~ spl4_24
| ~ spl4_89 ),
inference(resolution,[],[f2714,f433]) ).
tff(f433,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = X0 ) )
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f432]) ).
tff(f2714,plain,
( p(sK1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
| ~ spl4_89 ),
inference(avatar_component_clause,[],[f2712]) ).
tff(f3707,plain,
( spl4_104
| ~ spl4_19
| ~ spl4_44
| ~ spl4_87 ),
inference(avatar_split_clause,[],[f2693,f2664,f594,f383,f3704]) ).
tff(f3704,plain,
( spl4_104
<=> p(sK2(tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_104])]) ).
tff(f2664,plain,
( spl4_87
<=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),combin_i_2E0(tyop_2Emin_2Ebool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_87])]) ).
tff(f2693,plain,
( p(sK2(tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool)))
| ~ spl4_19
| ~ spl4_44
| ~ spl4_87 ),
inference(forward_demodulation,[],[f2671,f384]) ).
tff(f2671,plain,
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool),sK2(tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool))))
| ~ spl4_44
| ~ spl4_87 ),
inference(resolution,[],[f2666,f595]) ).
tff(f2666,plain,
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),combin_i_2E0(tyop_2Emin_2Ebool)))
| ~ spl4_87 ),
inference(avatar_component_clause,[],[f2664]) ).
tff(f3090,plain,
( ~ spl4_1
| ~ spl4_14
| spl4_90 ),
inference(avatar_split_clause,[],[f3026,f2716,f342,f277]) ).
tff(f277,plain,
( spl4_1
<=> p(c_2Ebool_2EF_2E0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f2716,plain,
( spl4_90
<=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_90])]) ).
tff(f3026,plain,
( ~ p(c_2Ebool_2EF_2E0)
| ~ spl4_14
| spl4_90 ),
inference(forward_demodulation,[],[f2717,f2757]) ).
tff(f2757,plain,
( ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0) )
| ~ spl4_14
| spl4_90 ),
inference(resolution,[],[f2717,f343]) ).
tff(f2717,plain,
( ~ p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0))
| spl4_90 ),
inference(avatar_component_clause,[],[f2716]) ).
tff(f3055,plain,
( spl4_2
| ~ spl4_24
| ~ spl4_96 ),
inference(avatar_split_clause,[],[f3018,f2904,f432,f282]) ).
tff(f282,plain,
( spl4_2
<=> p(c_2Ebool_2ET_2E0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f2904,plain,
( spl4_96
<=> ! [X0: $tType,X1: X0] : p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_96])]) ).
tff(f3018,plain,
( p(c_2Ebool_2ET_2E0)
| ~ spl4_24
| ~ spl4_96 ),
inference(forward_demodulation,[],[f2905,f2910]) ).
tff(f2910,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1)) )
| ~ spl4_24
| ~ spl4_96 ),
inference(resolution,[],[f2905,f433]) ).
tff(f2905,plain,
( ! [X0: $tType,X1: X0] : p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1)))
| ~ spl4_96 ),
inference(avatar_component_clause,[],[f2904]) ).
tff(f3013,plain,
( ~ spl4_86
| ~ spl4_88 ),
inference(avatar_contradiction_clause,[],[f3001]) ).
tff(f3001,plain,
( $false
| ~ spl4_86
| ~ spl4_88 ),
inference(resolution,[],[f2669,f1504]) ).
tff(f1504,plain,
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0))
| ~ spl4_86 ),
inference(avatar_component_clause,[],[f1502]) ).
tff(f1502,plain,
( spl4_86
<=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_86])]) ).
tff(f2669,plain,
( ! [X0: tyop_2Emin_2Ebool] : ~ p(X0)
| ~ spl4_88 ),
inference(avatar_component_clause,[],[f2668]) ).
tff(f3012,plain,
( ~ spl4_87
| ~ spl4_88 ),
inference(avatar_contradiction_clause,[],[f3002]) ).
tff(f3002,plain,
( $false
| ~ spl4_87
| ~ spl4_88 ),
inference(resolution,[],[f2669,f2666]) ).
tff(f3011,plain,
( ~ spl4_88
| ~ spl4_96 ),
inference(avatar_contradiction_clause,[],[f3003]) ).
tff(f3003,plain,
( $false
| ~ spl4_88
| ~ spl4_96 ),
inference(resolution,[],[f2669,f2905]) ).
tff(f3010,plain,
( ~ spl4_2
| ~ spl4_88 ),
inference(avatar_contradiction_clause,[],[f3006]) ).
tff(f3006,plain,
( $false
| ~ spl4_2
| ~ spl4_88 ),
inference(resolution,[],[f2669,f284]) ).
tff(f284,plain,
( p(c_2Ebool_2ET_2E0)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f282]) ).
tff(f3009,plain,
( ~ spl4_88
| ~ spl4_89 ),
inference(avatar_contradiction_clause,[],[f3008]) ).
tff(f3008,plain,
( $false
| ~ spl4_88
| ~ spl4_89 ),
inference(resolution,[],[f2669,f2714]) ).
tff(f2983,plain,
( spl4_88
| spl4_103
| ~ spl4_30
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f538,f529,f463,f2981,f2668]) ).
tff(f2981,plain,
( spl4_103
<=> ! [X0: tyop_2Emin_2Ebool] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_103])]) ).
tff(f463,plain,
( spl4_30
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).
tff(f538,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0)))
| ~ p(X1) )
| ~ spl4_30
| ~ spl4_38 ),
inference(resolution,[],[f530,f464]) ).
tff(f464,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X1) )
| ~ spl4_30 ),
inference(avatar_component_clause,[],[f463]) ).
tff(f2979,plain,
( spl4_102
| ~ spl4_16
| ~ spl4_32 ),
inference(avatar_split_clause,[],[f505,f484,f353,f2977]) ).
tff(f2977,plain,
( spl4_102
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X2),X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_102])]) ).
tff(f505,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X2),X0) = X1 ) )
| ~ spl4_16
| ~ spl4_32 ),
inference(resolution,[],[f485,f354]) ).
tff(f2975,plain,
( spl4_101
| ~ spl4_16
| ~ spl4_31 ),
inference(avatar_split_clause,[],[f502,f467,f353,f2973]) ).
tff(f2973,plain,
( spl4_101
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X2) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_101])]) ).
tff(f502,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X2) = X1 ) )
| ~ spl4_16
| ~ spl4_31 ),
inference(resolution,[],[f468,f354]) ).
tff(f2961,plain,
( spl4_100
| ~ spl4_16
| ~ spl4_30 ),
inference(avatar_split_clause,[],[f499,f463,f353,f2959]) ).
tff(f2959,plain,
( spl4_100
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X2),X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_100])]) ).
tff(f499,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X2),X0) = X1 ) )
| ~ spl4_16
| ~ spl4_30 ),
inference(resolution,[],[f464,f354]) ).
tff(f2957,plain,
( spl4_99
| ~ spl4_16
| ~ spl4_29 ),
inference(avatar_split_clause,[],[f496,f459,f353,f2955]) ).
tff(f2955,plain,
( spl4_99
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X2) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_99])]) ).
tff(f496,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X2) = X1 ) )
| ~ spl4_16
| ~ spl4_29 ),
inference(resolution,[],[f460,f354]) ).
tff(f2953,plain,
( spl4_98
| ~ spl4_15
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f492,f455,f349,f2951]) ).
tff(f2951,plain,
( spl4_98
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X1),X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_98])]) ).
tff(f455,plain,
( spl4_28
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
tff(f492,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X1),X0) = X2 ) )
| ~ spl4_15
| ~ spl4_28 ),
inference(resolution,[],[f456,f350]) ).
tff(f456,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| p(X1) )
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f455]) ).
tff(f2949,plain,
( spl4_97
| ~ spl4_15
| ~ spl4_27 ),
inference(avatar_split_clause,[],[f488,f451,f349,f2947]) ).
tff(f2947,plain,
( spl4_97
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_97])]) ).
tff(f451,plain,
( spl4_27
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).
tff(f488,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X2)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1) = X2 ) )
| ~ spl4_15
| ~ spl4_27 ),
inference(resolution,[],[f452,f350]) ).
tff(f452,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| p(X0) )
| ~ spl4_27 ),
inference(avatar_component_clause,[],[f451]) ).
tff(f2906,plain,
( spl4_96
| ~ spl4_26
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f542,f529,f445,f2904]) ).
tff(f445,plain,
( spl4_26
<=> ! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).
tff(f542,plain,
( ! [X0: $tType,X1: X0] : p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1)))
| ~ spl4_26
| ~ spl4_38 ),
inference(resolution,[],[f530,f446]) ).
tff(f446,plain,
( ! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2))
| ~ spl4_26 ),
inference(avatar_component_clause,[],[f445]) ).
tff(f2878,plain,
( spl4_95
| ~ spl4_34
| ~ spl4_53 ),
inference(avatar_split_clause,[],[f695,f679,f512,f2876]) ).
tff(f2876,plain,
( spl4_95
<=> ! [X0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,c_2Enum_2E0_2E0),X0))
| ( c_2Enum_2E0_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_95])]) ).
tff(f679,plain,
( spl4_53
<=> ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)))
| ( c_2Enum_2E0_2E0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_53])]) ).
tff(f695,plain,
( ! [X0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,c_2Enum_2E0_2E0),X0))
| ( c_2Enum_2E0_2E0 = X0 ) )
| ~ spl4_34
| ~ spl4_53 ),
inference(forward_demodulation,[],[f693,f275]) ).
tff(f275,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)) ),
inference(forward_demodulation,[],[f246,f240]) ).
tff(f240,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))) ),
inference(definition_unfolding,[],[f169,f232]) ).
tff(f232,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X1,X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))) ),
inference(definition_unfolding,[],[f174,f170,f151,f152,f151,f152]) ).
tff(f152,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__of__num_2E1(X0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0) ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__of__num_2E1(X0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X12: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__of__num_2E1(X12) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__of__num_2E1) ).
tff(f151,plain,
! [X0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__neg_2E1(X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X0) ),
inference(cnf_transformation,[],[f55]) ).
tff(f55,plain,
! [X0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__neg_2E1(X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X0) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X12: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__neg_2E1(X12) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__neg_2E1) ).
tff(f170,plain,
! [X0: tyop_2Einteger_2Eint,X1: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__lt_2E2(X0,X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X0),X1) ),
inference(cnf_transformation,[],[f70]) ).
tff(f70,plain,
! [X0: tyop_2Einteger_2Eint,X1: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__lt_2E2(X0,X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X0),X1) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X12: tyop_2Einteger_2Eint,X13: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__lt_2E2(X12,X13) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X12),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Einteger_2Eint__lt_2E2) ).
tff(f174,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) = c_2Eprim__rec_2E_3C_2E2(X1,X0) ),
inference(cnf_transformation,[],[f112]) ).
tff(f112,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( c_2Ebool_2EF_2E0 = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) )
& ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1)))
| ( ( c_2Enum_2E0_2E0 = X1 )
& ( c_2Enum_2E0_2E0 = X0 ) ) )
& ( ( c_2Enum_2E0_2E0 != X1 )
| ( c_2Enum_2E0_2E0 != X0 )
| ~ p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1))) )
& ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) = c_2Eprim__rec_2E_3C_2E2(X1,X0) )
& ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(X1)) ) ),
inference(flattening,[],[f111]) ).
tff(f111,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( c_2Ebool_2EF_2E0 = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) )
& ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1)))
| ( ( c_2Enum_2E0_2E0 = X1 )
& ( c_2Enum_2E0_2E0 = X0 ) ) )
& ( ( c_2Enum_2E0_2E0 != X1 )
| ( c_2Enum_2E0_2E0 != X0 )
| ~ p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1))) )
& ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) = c_2Eprim__rec_2E_3C_2E2(X1,X0) )
& ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(X1)) ) ),
inference(nnf_transformation,[],[f73]) ).
tff(f73,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( c_2Ebool_2EF_2E0 = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) )
& ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1)))
<=> ( ( c_2Enum_2E0_2E0 != X1 )
| ( c_2Enum_2E0_2E0 != X0 ) ) )
& ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) = c_2Eprim__rec_2E_3C_2E2(X1,X0) )
& ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(X1)) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X25: tyop_2Enum_2Enum,X26: tyop_2Enum_2Enum] :
( ( c_2Ebool_2EF_2E0 = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X25),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X26))) )
& ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X25)),c_2Einteger_2Eint__of__num_2E1(X26)))
<=> ( ( c_2Enum_2E0_2E0 != X26 )
| ( c_2Enum_2E0_2E0 != X25 ) ) )
& ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X25)),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X26))) = c_2Eprim__rec_2E_3C_2E2(X26,X25) )
& ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X25),c_2Einteger_2Eint__of__num_2E1(X26)) = c_2Eprim__rec_2E_3C_2E2(X25,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
tff(f169,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) ),
inference(cnf_transformation,[],[f69]) ).
tff(f69,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X12: tyop_2Enum_2Enum,X13: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X12,X13) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X12),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) ).
tff(f246,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)) ),
inference(definition_unfolding,[],[f173,f232,f170,f152,f152]) ).
tff(f173,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(X1)) ),
inference(cnf_transformation,[],[f112]) ).
tff(f693,plain,
( ! [X0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)))
| ( c_2Enum_2E0_2E0 = X0 ) )
| ~ spl4_34
| ~ spl4_53 ),
inference(superposition,[],[f680,f514]) ).
tff(f680,plain,
( ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)))
| ( c_2Enum_2E0_2E0 = X1 ) )
| ~ spl4_53 ),
inference(avatar_component_clause,[],[f679]) ).
tff(f2812,plain,
( spl4_94
| ~ spl4_34
| spl4_46
| ~ spl4_52
| ~ spl4_58
| ~ spl4_60 ),
inference(avatar_split_clause,[],[f2599,f725,f712,f672,f621,f512,f2809]) ).
tff(f2809,plain,
( spl4_94
<=> ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2EF_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_94])]) ).
tff(f621,plain,
( spl4_46
<=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,c_2Enum_2E0_2E0),c_2Enum_2E0_2E0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_46])]) ).
tff(f725,plain,
( spl4_60
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) )
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_60])]) ).
tff(f2599,plain,
( ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2EF_2E0) )
| ~ spl4_34
| spl4_46
| ~ spl4_52
| ~ spl4_58
| ~ spl4_60 ),
inference(forward_demodulation,[],[f2591,f719]) ).
tff(f2591,plain,
( ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,c_2Enum_2E0_2E0),c_2Enum_2E0_2E0)) )
| spl4_46
| ~ spl4_60 ),
inference(resolution,[],[f726,f623]) ).
tff(f623,plain,
( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,c_2Enum_2E0_2E0),c_2Enum_2E0_2E0))
| spl4_46 ),
inference(avatar_component_clause,[],[f621]) ).
tff(f726,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
| ~ spl4_60 ),
inference(avatar_component_clause,[],[f725]) ).
tff(f2807,plain,
( spl4_92
| ~ spl4_93
| ~ spl4_19
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f608,f590,f383,f2804,f2800]) ).
tff(f2800,plain,
( spl4_92
<=> p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),combin_i_2E0(tyop_2Emin_2Ebool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_92])]) ).
tff(f608,plain,
( ~ p(sK1(tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool)))
| p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),combin_i_2E0(tyop_2Emin_2Ebool)))
| ~ spl4_19
| ~ spl4_43 ),
inference(superposition,[],[f591,f384]) ).
tff(f2791,plain,
( spl4_91
| ~ spl4_34
| ~ spl4_52
| ~ spl4_58 ),
inference(avatar_split_clause,[],[f719,f712,f672,f512,f2789]) ).
tff(f2789,plain,
( spl4_91
<=> ! [X0: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),c_2Enum_2E0_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_91])]) ).
tff(f2719,plain,
( spl4_89
| spl4_90
| ~ spl4_17
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f597,f590,f375,f2716,f2712]) ).
tff(f375,plain,
( spl4_17
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
tff(f597,plain,
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0))
| p(sK1(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0))
| ~ spl4_17
| ~ spl4_43 ),
inference(resolution,[],[f591,f376]) ).
tff(f376,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) )
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f375]) ).
tff(f2670,plain,
( spl4_87
| spl4_88
| ~ spl4_19
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f547,f529,f383,f2668,f2664]) ).
tff(f547,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),combin_i_2E0(tyop_2Emin_2Ebool))) )
| ~ spl4_19
| ~ spl4_38 ),
inference(superposition,[],[f530,f384]) ).
tff(f1524,plain,
( spl4_2
| ~ spl4_24
| ~ spl4_26 ),
inference(avatar_split_clause,[],[f1522,f445,f432,f282]) ).
tff(f1522,plain,
( p(c_2Ebool_2ET_2E0)
| ~ spl4_24
| ~ spl4_26 ),
inference(forward_demodulation,[],[f446,f474]) ).
tff(f474,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X1) )
| ~ spl4_24
| ~ spl4_26 ),
inference(resolution,[],[f433,f446]) ).
tff(f1520,plain,
( spl4_46
| ~ spl4_85 ),
inference(avatar_contradiction_clause,[],[f1515]) ).
tff(f1515,plain,
( $false
| spl4_46
| ~ spl4_85 ),
inference(resolution,[],[f1500,f623]) ).
tff(f1500,plain,
( ! [X0: tyop_2Emin_2Ebool] : p(X0)
| ~ spl4_85 ),
inference(avatar_component_clause,[],[f1499]) ).
tff(f1499,plain,
( spl4_85
<=> ! [X0: tyop_2Emin_2Ebool] : p(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_85])]) ).
tff(f1519,plain,
( spl4_1
| ~ spl4_85 ),
inference(avatar_contradiction_clause,[],[f1517]) ).
tff(f1517,plain,
( $false
| spl4_1
| ~ spl4_85 ),
inference(resolution,[],[f1500,f279]) ).
tff(f279,plain,
( ~ p(c_2Ebool_2EF_2E0)
| spl4_1 ),
inference(avatar_component_clause,[],[f277]) ).
tff(f1505,plain,
( spl4_85
| spl4_86
| ~ spl4_17
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f537,f529,f375,f1502,f1499]) ).
tff(f537,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0))
| p(X0) )
| ~ spl4_17
| ~ spl4_38 ),
inference(resolution,[],[f530,f376]) ).
tff(f1497,plain,
( spl4_84
| ~ spl4_15
| ~ spl4_23 ),
inference(avatar_split_clause,[],[f437,f404,f349,f1495]) ).
tff(f1495,plain,
( spl4_84
<=> ! [X2: $tType,X0: X2,X3: tyop_2Emin_2Ebool,X1: X2] :
( ( X0 = X1 )
| p(X3)
| ( c_2Emin_2E_3D_2E2(X2,X0,X1) = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_84])]) ).
tff(f404,plain,
( spl4_23
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).
tff(f437,plain,
( ! [X2: $tType,X3: tyop_2Emin_2Ebool,X0: X2,X1: X2] :
( ( X0 = X1 )
| p(X3)
| ( c_2Emin_2E_3D_2E2(X2,X0,X1) = X3 ) )
| ~ spl4_15
| ~ spl4_23 ),
inference(resolution,[],[f405,f350]) ).
tff(f405,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2))
| ( X1 = X2 ) )
| ~ spl4_23 ),
inference(avatar_component_clause,[],[f404]) ).
tff(f1493,plain,
( spl4_83
| ~ spl4_15
| ~ spl4_22 ),
inference(avatar_split_clause,[],[f428,f400,f349,f1491]) ).
tff(f1491,plain,
( spl4_83
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| p(X2)
| ( c_2Emin_2E_3D_3D_3E_2E2(X0,X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_83])]) ).
tff(f400,plain,
( spl4_22
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
tff(f428,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| p(X2)
| ( c_2Emin_2E_3D_3D_3E_2E2(X0,X1) = X2 ) )
| ~ spl4_15
| ~ spl4_22 ),
inference(resolution,[],[f401,f350]) ).
tff(f401,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ~ p(X0)
| p(X1) )
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f400]) ).
tff(f1489,plain,
( spl4_82
| ~ spl4_15
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f422,f396,f349,f1487]) ).
tff(f1487,plain,
( spl4_82
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| p(X2)
| ( c_2Ebool_2E_5C_2F_2E2(X0,X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_82])]) ).
tff(f396,plain,
( spl4_21
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
tff(f422,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| p(X1)
| p(X2)
| ( c_2Ebool_2E_5C_2F_2E2(X0,X1) = X2 ) )
| ~ spl4_15
| ~ spl4_21 ),
inference(resolution,[],[f397,f350]) ).
tff(f397,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| p(X0)
| p(X1) )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f396]) ).
tff(f1485,plain,
( spl4_81
| ~ spl4_16
| ~ spl4_20 ),
inference(avatar_split_clause,[],[f417,f392,f353,f1483]) ).
tff(f1483,plain,
( spl4_81
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ~ p(X2)
| ( c_2Ebool_2E_2F_5C_2E2(X1,X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_81])]) ).
tff(f392,plain,
( spl4_20
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
tff(f417,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(X1)
| ~ p(X2)
| ( c_2Ebool_2E_2F_5C_2E2(X1,X0) = X2 ) )
| ~ spl4_16
| ~ spl4_20 ),
inference(resolution,[],[f393,f354]) ).
tff(f393,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f392]) ).
tff(f1481,plain,
( spl4_80
| ~ spl4_7
| ~ spl4_19 ),
inference(avatar_split_clause,[],[f414,f383,f305,f1479]) ).
tff(f1479,plain,
( spl4_80
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_80])]) ).
tff(f414,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,combin_i_2E0(tyop_2Emin_2Ebool),X0) ) )
| ~ spl4_7
| ~ spl4_19 ),
inference(superposition,[],[f384,f306]) ).
tff(f1477,plain,
( spl4_79
| ~ spl4_15
| ~ spl4_18 ),
inference(avatar_split_clause,[],[f411,f379,f349,f1475]) ).
tff(f1475,plain,
( spl4_79
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_79])]) ).
tff(f379,plain,
( spl4_18
<=> ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
tff(f411,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0) = X1 ) )
| ~ spl4_15
| ~ spl4_18 ),
inference(resolution,[],[f380,f350]) ).
tff(f380,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| ~ p(X0) )
| ~ spl4_18 ),
inference(avatar_component_clause,[],[f379]) ).
tff(f1473,plain,
( spl4_78
| ~ spl4_16
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f407,f375,f353,f1471]) ).
tff(f1471,plain,
( spl4_78
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_78])]) ).
tff(f407,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(X1)
| ( app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0) = X1 ) )
| ~ spl4_16
| ~ spl4_17 ),
inference(resolution,[],[f376,f354]) ).
tff(f1442,plain,
( spl4_77
| ~ spl4_15
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f365,f353,f349,f1440]) ).
tff(f1440,plain,
( spl4_77
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( X0 = X1 )
| p(X2)
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_77])]) ).
tff(f365,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( X0 = X1 )
| p(X2)
| ( X1 = X2 ) )
| ~ spl4_15
| ~ spl4_16 ),
inference(resolution,[],[f354,f350]) ).
tff(f972,plain,
( spl4_76
| ~ spl4_10
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f372,f353,f317,f970]) ).
tff(f970,plain,
( spl4_76
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2E_5C_2F_2E2(X1,X2) = X0 )
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_76])]) ).
tff(f317,plain,
( spl4_10
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
tff(f372,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2E_5C_2F_2E2(X1,X2) = X0 )
| ~ p(X1) )
| ~ spl4_10
| ~ spl4_16 ),
inference(resolution,[],[f354,f318]) ).
tff(f318,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X0) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f317]) ).
tff(f968,plain,
( spl4_75
| ~ spl4_11
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f371,f353,f321,f966]) ).
tff(f966,plain,
( spl4_75
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2E_5C_2F_2E2(X1,X2) = X0 )
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_75])]) ).
tff(f321,plain,
( spl4_11
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
tff(f371,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2E_5C_2F_2E2(X1,X2) = X0 )
| ~ p(X2) )
| ~ spl4_11
| ~ spl4_16 ),
inference(resolution,[],[f354,f322]) ).
tff(f322,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X1) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f321]) ).
tff(f964,plain,
( spl4_74
| ~ spl4_12
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f369,f353,f325,f962]) ).
tff(f962,plain,
( spl4_74
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Emin_2E_3D_3D_3E_2E2(X1,X2) = X0 )
| p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_74])]) ).
tff(f325,plain,
( spl4_12
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
tff(f369,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Emin_2E_3D_3D_3E_2E2(X1,X2) = X0 )
| p(X1) )
| ~ spl4_12
| ~ spl4_16 ),
inference(resolution,[],[f354,f326]) ).
tff(f326,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| p(X0) )
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f325]) ).
tff(f960,plain,
( spl4_73
| ~ spl4_24
| ~ spl4_26
| ~ spl4_47 ),
inference(avatar_split_clause,[],[f862,f632,f445,f432,f957]) ).
tff(f957,plain,
( spl4_73
<=> ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2ET_2E0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_73])]) ).
tff(f632,plain,
( spl4_47
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) )
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_47])]) ).
tff(f862,plain,
( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(c_2Ebool_2ET_2E0) )
| ~ spl4_24
| ~ spl4_26
| ~ spl4_47 ),
inference(forward_demodulation,[],[f851,f474]) ).
tff(f851,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X1)) )
| ~ spl4_26
| ~ spl4_47 ),
inference(resolution,[],[f633,f446]) ).
tff(f633,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) ) )
| ~ spl4_47 ),
inference(avatar_component_clause,[],[f632]) ).
tff(f955,plain,
( spl4_72
| ~ spl4_13
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f368,f353,f329,f953]) ).
tff(f953,plain,
( spl4_72
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Emin_2E_3D_3D_3E_2E2(X1,X2) = X0 )
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_72])]) ).
tff(f329,plain,
( spl4_13
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
tff(f368,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Emin_2E_3D_3D_3E_2E2(X1,X2) = X0 )
| ~ p(X2) )
| ~ spl4_13
| ~ spl4_16 ),
inference(resolution,[],[f354,f330]) ).
tff(f330,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ~ p(X1) )
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f329]) ).
tff(f951,plain,
( spl4_71
| ~ spl4_8
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f359,f349,f309,f949]) ).
tff(f949,plain,
( spl4_71
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ( c_2Ebool_2E_2F_5C_2E2(X0,X1) = X2 )
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_71])]) ).
tff(f309,plain,
( spl4_8
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
tff(f359,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ( c_2Ebool_2E_2F_5C_2E2(X0,X1) = X2 )
| p(X0) )
| ~ spl4_8
| ~ spl4_15 ),
inference(resolution,[],[f350,f310]) ).
tff(f310,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| p(X0) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f309]) ).
tff(f947,plain,
( spl4_70
| ~ spl4_9
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f358,f349,f313,f945]) ).
tff(f945,plain,
( spl4_70
<=> ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ( c_2Ebool_2E_2F_5C_2E2(X0,X1) = X2 )
| p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_70])]) ).
tff(f313,plain,
( spl4_9
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
tff(f358,plain,
( ! [X2: tyop_2Emin_2Ebool,X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X2)
| ( c_2Ebool_2E_2F_5C_2E2(X0,X1) = X2 )
| p(X1) )
| ~ spl4_9
| ~ spl4_15 ),
inference(resolution,[],[f350,f314]) ).
tff(f314,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| p(X1) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f313]) ).
tff(f943,plain,
( spl4_69
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f332,f305,f941]) ).
tff(f941,plain,
( spl4_69
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( c_2Ebool_2EF_2E0 = X1 )
| ( c_2Ebool_2EF_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_69])]) ).
tff(f332,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( c_2Ebool_2EF_2E0 = X1 )
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl4_7 ),
inference(superposition,[],[f306,f306]) ).
tff(f890,plain,
( spl4_68
| ~ spl4_4
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f373,f353,f291,f888]) ).
tff(f888,plain,
( spl4_68
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2E_7E_2E1(X1) = X0 )
| p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_68])]) ).
tff(f291,plain,
( spl4_4
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
tff(f373,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2E_7E_2E1(X1) = X0 )
| p(X1) )
| ~ spl4_4
| ~ spl4_16 ),
inference(resolution,[],[f354,f292]) ).
tff(f292,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f291]) ).
tff(f885,plain,
( spl4_67
| ~ spl4_5
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f367,f353,f295,f883]) ).
tff(f883,plain,
( spl4_67
<=> ! [X1: $tType,X2: X1,X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Emin_2E_3D_2E2(X1,X2,X2) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_67])]) ).
tff(f295,plain,
( spl4_5
<=> ! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
tff(f367,plain,
( ! [X1: $tType,X2: X1,X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Emin_2E_3D_2E2(X1,X2,X2) = X0 ) )
| ~ spl4_5
| ~ spl4_16 ),
inference(resolution,[],[f354,f296]) ).
tff(f296,plain,
( ! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f295]) ).
tff(f881,plain,
( spl4_66
| ~ spl4_3
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f357,f349,f287,f879]) ).
tff(f879,plain,
( spl4_66
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ( c_2Ebool_2E_7E_2E1(X0) = X1 )
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_66])]) ).
tff(f287,plain,
( spl4_3
<=> ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
tff(f357,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ( c_2Ebool_2E_7E_2E1(X0) = X1 )
| ~ p(X0) )
| ~ spl4_3
| ~ spl4_15 ),
inference(resolution,[],[f350,f288]) ).
tff(f288,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(c_2Ebool_2E_7E_2E1(X0))
| ~ p(X0) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f287]) ).
tff(f840,plain,
spl4_65,
inference(avatar_split_clause,[],[f241,f838]) ).
tff(f241,plain,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X1) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X1))))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X1))) ),
inference(definition_unfolding,[],[f172,f166,f224,f170,f152,f171,f167,f150,f151,f167,f150]) ).
tff(f150,plain,
! [X0: tyop_2Einteger_2Eint] : ( c_2Einteger_2ENum_2E1(X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X0) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: tyop_2Einteger_2Eint] : ( c_2Einteger_2ENum_2E1(X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X0) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X12: tyop_2Einteger_2Eint] : ( c_2Einteger_2ENum_2E1(X12) = app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2ENum_2E1) ).
tff(f167,plain,
! [X0: $tType,X1: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X1) ),
inference(cnf_transformation,[],[f67]) ).
tff(f67,plain,
! [X0: $tType,X1: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X1) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType,X12: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(X0,X12) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).
tff(f171,plain,
! [X0: $tType,X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__2comp_2E1(X0,X1) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),X1) ),
inference(cnf_transformation,[],[f71]) ).
tff(f71,plain,
! [X0: $tType,X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__2comp_2E1(X0,X1) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),X1) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X12: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__2comp_2E1(X0,X12) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).
tff(f224,plain,
! [X0: $tType,X2: X0,X3: X0,X1: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(X0,X1,X2,X3) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X1),X2),X3) ),
inference(cnf_transformation,[],[f91]) ).
tff(f91,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: X0,X3: X0] : ( c_2Ebool_2ECOND_2E3(X0,X1,X2,X3) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X1),X2),X3) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType,X12: tyop_2Emin_2Ebool,X13: X0,X14: X0] : ( c_2Ebool_2ECOND_2E3(X0,X12,X13,X14) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X12),X13),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).
tff(f166,plain,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X1) ),
inference(cnf_transformation,[],[f66]) ).
tff(f66,plain,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X1) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X0: $tType,X12: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X12) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a) ).
tff(f172,plain,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X1) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger_2Eint__lt_2E2(X1,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(X1)))),c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(X1))) ),
inference(cnf_transformation,[],[f72]) ).
tff(f72,plain,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X1) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger_2Eint__lt_2E2(X1,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(X1)))),c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(X1))) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType,X27: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X27) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger_2Eint__lt_2E2(X27,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(X27)))),c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(X27))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
tff(f834,plain,
spl4_64,
inference(avatar_split_clause,[],[f252,f832]) ).
tff(f832,plain,
( spl4_64
<=> ! [X0: $tType,X2: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X1),app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),c_2Ebool_2Ethe__value_2E0(X0))) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X2),app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),c_2Ebool_2Ethe__value_2E0(X0))) )
| ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X1) != app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_64])]) ).
tff(f252,plain,
! [X0: $tType,X2: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X1),app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),c_2Ebool_2Ethe__value_2E0(X0))) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X2),app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),c_2Ebool_2Ethe__value_2E0(X0))) )
| ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X1) != app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X2) ) ),
inference(definition_unfolding,[],[f215,f168,f163,f168,f163,f167,f167]) ).
tff(f163,plain,
! [X0: $tType,X1: tyop_2Ebool_2Eitself(X0)] : ( c_2Ewords_2Edimword_2E1(X0,X1) = app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),X1) ),
inference(cnf_transformation,[],[f63]) ).
tff(f63,plain,
! [X0: $tType,X1: tyop_2Ebool_2Eitself(X0)] : ( c_2Ewords_2Edimword_2E1(X0,X1) = app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),X1) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType,X12: tyop_2Ebool_2Eitself(X0)] : ( c_2Ewords_2Edimword_2E1(X0,X12) = app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a) ).
tff(f168,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X0),X1) ),
inference(cnf_transformation,[],[f68]) ).
tff(f68,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X0),X1) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X12: tyop_2Enum_2Enum,X13: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(X12,X13) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X12),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2EMOD_2E2) ).
tff(f215,plain,
! [X0: $tType,X2: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD_2E2(X1,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) = c_2Earithmetic_2EMOD_2E2(X2,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) )
| ( c_2Ewords_2En2w_2E1(X0,X1) != c_2Ewords_2En2w_2E1(X0,X2) ) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: $tType,X1: tyop_2Enum_2Enum,X2: tyop_2Enum_2Enum] :
( ( ( c_2Ewords_2En2w_2E1(X0,X1) = c_2Ewords_2En2w_2E1(X0,X2) )
| ( c_2Earithmetic_2EMOD_2E2(X1,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) != c_2Earithmetic_2EMOD_2E2(X2,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) ) )
& ( ( c_2Earithmetic_2EMOD_2E2(X1,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) = c_2Earithmetic_2EMOD_2E2(X2,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) )
| ( c_2Ewords_2En2w_2E1(X0,X1) != c_2Ewords_2En2w_2E1(X0,X2) ) ) ),
inference(nnf_transformation,[],[f88]) ).
tff(f88,plain,
! [X0: $tType,X1: tyop_2Enum_2Enum,X2: tyop_2Enum_2Enum] :
( ( c_2Ewords_2En2w_2E1(X0,X1) = c_2Ewords_2En2w_2E1(X0,X2) )
<=> ( c_2Earithmetic_2EMOD_2E2(X1,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) = c_2Earithmetic_2EMOD_2E2(X2,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType,X28: tyop_2Enum_2Enum,X29: tyop_2Enum_2Enum] :
( ( c_2Ewords_2En2w_2E1(X0,X28) = c_2Ewords_2En2w_2E1(X0,X29) )
<=> ( c_2Earithmetic_2EMOD_2E2(X28,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) = c_2Earithmetic_2EMOD_2E2(X29,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__11) ).
tff(f830,plain,
spl4_63,
inference(avatar_split_clause,[],[f251,f828]) ).
tff(f828,plain,
( spl4_63
<=> ! [X0: $tType,X2: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X2) )
| ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X1),app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),c_2Ebool_2Ethe__value_2E0(X0))) != app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X2),app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),c_2Ebool_2Ethe__value_2E0(X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_63])]) ).
tff(f251,plain,
! [X0: $tType,X2: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X2) )
| ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X1),app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),c_2Ebool_2Ethe__value_2E0(X0))) != app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMOD_2E0,X2),app_2E2(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(X0),c_2Ebool_2Ethe__value_2E0(X0))) ) ),
inference(definition_unfolding,[],[f216,f167,f167,f168,f163,f168,f163]) ).
tff(f216,plain,
! [X0: $tType,X2: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( c_2Ewords_2En2w_2E1(X0,X1) = c_2Ewords_2En2w_2E1(X0,X2) )
| ( c_2Earithmetic_2EMOD_2E2(X1,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) != c_2Earithmetic_2EMOD_2E2(X2,c_2Ewords_2Edimword_2E1(X0,c_2Ebool_2Ethe__value_2E0(X0))) ) ),
inference(cnf_transformation,[],[f138]) ).
tff(f784,plain,
spl4_62,
inference(avatar_split_clause,[],[f227,f782]) ).
tff(f782,plain,
( spl4_62
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_62])]) ).
tff(f227,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),X4: tyop_2Emin_2Efun(X0,X1),X5: X0] : ( app_2E2(X0,X2,app_2E2(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2)),combin_s_2E0(X0,X1,X2),X3),X4),X5) = app_2E2(X1,X2,app_2E2(X0,tyop_2Emin_2Efun(X1,X2),X3,X5),app_2E2(X0,X1,X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Es__thm) ).
tff(f731,plain,
spl4_61,
inference(avatar_split_clause,[],[f270,f729]) ).
tff(f729,plain,
( spl4_61
<=> ! [X0: $tType,X6: X0,X4: X0,X5: X0,X2: tyop_2Emin_2Ebool] :
( ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X6) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X5) )
| ~ p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_61])]) ).
tff(f270,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X6: X0,X4: X0,X5: X0] :
( ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X6) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X5) )
| ~ p(X2) ),
inference(equality_resolution,[],[f269]) ).
tff(f269,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool,X6: X0,X4: X0,X5: X0] :
( ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X6) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X1),X4),X5) )
| ~ p(X2)
| ( X1 != X2 ) ),
inference(equality_resolution,[],[f256]) ).
tff(f256,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X3: X0,X1: tyop_2Emin_2Ebool,X6: X0,X4: X0,X5: X0] :
( ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X1),X3),X5) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X6) )
| ~ p(X2)
| ( X3 != X4 )
| ( X1 != X2 ) ),
inference(definition_unfolding,[],[f229,f224,f224]) ).
tff(f229,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X3: X0,X1: tyop_2Emin_2Ebool,X6: X0,X4: X0,X5: X0] :
( ( c_2Ebool_2ECOND_2E3(X0,X1,X3,X5) = c_2Ebool_2ECOND_2E3(X0,X2,X4,X6) )
| ~ p(X2)
| ( X3 != X4 )
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f106]) ).
tff(f106,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool,X3: X0,X4: X0,X5: X0,X6: X0] :
( ( c_2Ebool_2ECOND_2E3(X0,X1,X3,X5) = c_2Ebool_2ECOND_2E3(X0,X2,X4,X6) )
| ( ( X5 != X6 )
& ~ p(X2) )
| ( ( X3 != X4 )
& p(X2) )
| ( X1 != X2 ) ),
inference(flattening,[],[f105]) ).
tff(f105,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool,X3: X0,X4: X0,X5: X0,X6: X0] :
( ( c_2Ebool_2ECOND_2E3(X0,X1,X3,X5) = c_2Ebool_2ECOND_2E3(X0,X2,X4,X6) )
| ( ( X5 != X6 )
& ~ p(X2) )
| ( ( X3 != X4 )
& p(X2) )
| ( X1 != X2 ) ),
inference(ennf_transformation,[],[f94]) ).
tff(f94,plain,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: tyop_2Emin_2Ebool,X3: X0,X4: X0,X5: X0,X6: X0] :
( ( ( ~ p(X2)
=> ( X5 = X6 ) )
& ( p(X2)
=> ( X3 = X4 ) )
& ( X1 = X2 ) )
=> ( c_2Ebool_2ECOND_2E3(X0,X1,X3,X5) = c_2Ebool_2ECOND_2E3(X0,X2,X4,X6) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType,X18: tyop_2Emin_2Ebool,X19: tyop_2Emin_2Ebool,X5: X0,X20: X0,X21: X0,X22: X0] :
( ( ( ~ p(X19)
=> ( X21 = X22 ) )
& ( p(X19)
=> ( X5 = X20 ) )
& ( X18 = X19 ) )
=> ( c_2Ebool_2ECOND_2E3(X0,X18,X5,X21) = c_2Ebool_2ECOND_2E3(X0,X19,X20,X22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
tff(f727,plain,
( spl4_60
| ~ spl4_4
| ~ spl4_24 ),
inference(avatar_split_clause,[],[f482,f432,f291,f725]) ).
tff(f482,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = c_2Ebool_2E_7E_2E1(X0) )
| p(X0) )
| ~ spl4_4
| ~ spl4_24 ),
inference(resolution,[],[f433,f292]) ).
tff(f723,plain,
spl4_59,
inference(avatar_split_clause,[],[f268,f721]) ).
tff(f721,plain,
( spl4_59
<=> ! [X0: $tType,X3: X0,X4: X0,X6: X0,X2: tyop_2Emin_2Ebool] :
( ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X6) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X3),X6) )
| p(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_59])]) ).
tff(f268,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X3: X0,X6: X0,X4: X0] :
( ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X6) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X3),X6) )
| p(X2) ),
inference(equality_resolution,[],[f267]) ).
tff(f267,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X3: X0,X1: tyop_2Emin_2Ebool,X6: X0,X4: X0] :
( ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X6) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X1),X3),X6) )
| p(X2)
| ( X1 != X2 ) ),
inference(equality_resolution,[],[f255]) ).
tff(f255,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X3: X0,X1: tyop_2Emin_2Ebool,X6: X0,X4: X0,X5: X0] :
( ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X1),X3),X5) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X2),X4),X6) )
| ( X5 != X6 )
| p(X2)
| ( X1 != X2 ) ),
inference(definition_unfolding,[],[f230,f224,f224]) ).
tff(f230,plain,
! [X0: $tType,X2: tyop_2Emin_2Ebool,X3: X0,X1: tyop_2Emin_2Ebool,X6: X0,X4: X0,X5: X0] :
( ( c_2Ebool_2ECOND_2E3(X0,X1,X3,X5) = c_2Ebool_2ECOND_2E3(X0,X2,X4,X6) )
| ( X5 != X6 )
| p(X2)
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f106]) ).
tff(f714,plain,
spl4_58,
inference(avatar_split_clause,[],[f240,f712]) ).
tff(f708,plain,
spl4_57,
inference(avatar_split_clause,[],[f275,f706]) ).
tff(f704,plain,
spl4_56,
inference(avatar_split_clause,[],[f237,f702]) ).
tff(f702,plain,
( spl4_56
<=> ! [X0: $tType] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_56])]) ).
tff(f237,plain,
! [X0: $tType] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)) ),
inference(definition_unfolding,[],[f153,f167,f171,f167]) ).
tff(f153,plain,
! [X0: $tType] : ( c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) = c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0)) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] : ( c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) = c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).
tff(f689,plain,
spl4_55,
inference(avatar_split_clause,[],[f244,f687]) ).
tff(f687,plain,
( spl4_55
<=> ! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)))
| ( c_2Enum_2E0_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_55])]) ).
tff(f244,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)))
| ( c_2Enum_2E0_2E0 = X0 ) ),
inference(definition_unfolding,[],[f176,f170,f151,f152,f152]) ).
tff(f176,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1)))
| ( c_2Enum_2E0_2E0 = X0 ) ),
inference(cnf_transformation,[],[f112]) ).
tff(f685,plain,
( spl4_54
| ~ spl4_5
| ~ spl4_24 ),
inference(avatar_split_clause,[],[f476,f432,f295,f683]) ).
tff(f683,plain,
( spl4_54
<=> ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = c_2Emin_2E_3D_2E2(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_54])]) ).
tff(f476,plain,
( ! [X0: $tType,X1: X0] : ( c_2Ebool_2ET_2E0 = c_2Emin_2E_3D_2E2(X0,X1,X1) )
| ~ spl4_5
| ~ spl4_24 ),
inference(resolution,[],[f433,f296]) ).
tff(f681,plain,
spl4_53,
inference(avatar_split_clause,[],[f243,f679]) ).
tff(f243,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)))
| ( c_2Enum_2E0_2E0 = X1 ) ),
inference(definition_unfolding,[],[f177,f170,f151,f152,f152]) ).
tff(f177,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1)))
| ( c_2Enum_2E0_2E0 = X1 ) ),
inference(cnf_transformation,[],[f112]) ).
tff(f674,plain,
spl4_52,
inference(avatar_split_clause,[],[f242,f672]) ).
tff(f242,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))) ),
inference(definition_unfolding,[],[f178,f170,f152,f151,f152]) ).
tff(f178,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) ),
inference(cnf_transformation,[],[f112]) ).
tff(f657,plain,
spl4_51,
inference(avatar_split_clause,[],[f273,f655]) ).
tff(f655,plain,
( spl4_51
<=> ! [X0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_51])]) ).
tff(f273,plain,
! [X0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)))),
inference(forward_demodulation,[],[f235,f234]) ).
tff(f234,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),
inference(definition_unfolding,[],[f147,f152,f151,f152]) ).
tff(f147,plain,
c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),
inference(cnf_transformation,[],[f43]) ).
tff(f43,axiom,
c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
tff(f235,plain,
! [X0: tyop_2Enum_2Enum] : ~ p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)))),
inference(definition_unfolding,[],[f148,f232]) ).
tff(f148,plain,
! [X0: tyop_2Enum_2Enum] : ~ p(c_2Eprim__rec_2E_3C_2E2(X0,c_2Enum_2E0_2E0)),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: tyop_2Enum_2Enum] : ~ p(c_2Eprim__rec_2E_3C_2E2(X0,c_2Enum_2E0_2E0)),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X25: tyop_2Enum_2Enum] : ~ p(c_2Eprim__rec_2E_3C_2E2(X25,c_2Enum_2E0_2E0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).
tff(f653,plain,
spl4_50,
inference(avatar_split_clause,[],[f226,f651]) ).
tff(f226,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK3(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK3(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK3(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK3(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f104,f141]) ).
tff(f141,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ? [X4: X0] : ( app_2E2(X0,X1,X2,X4) != app_2E2(X0,X1,X3,X4) )
=> ( app_2E2(X0,X1,X2,sK3(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK3(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f104,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ? [X4: X0] : ( app_2E2(X0,X1,X2,X4) != app_2E2(X0,X1,X3,X4) ) ),
inference(ennf_transformation,[],[f93]) ).
tff(f93,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ! [X4: X0] : ( app_2E2(X0,X1,X2,X4) = app_2E2(X0,X1,X3,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X0: $tType,X1: $tType,X3: tyop_2Emin_2Efun(X0,X1),X4: tyop_2Emin_2Efun(X0,X1)] :
( ! [X5: X0] : ( app_2E2(X0,X1,X3,X5) = app_2E2(X0,X1,X4,X5) )
=> ( X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).
tff(f642,plain,
spl4_49,
inference(avatar_split_clause,[],[f239,f640]) ).
tff(f640,plain,
( spl4_49
<=> ! [X0: $tType,X4: X0,X3: X0] : ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),c_2Ebool_2ET_2E0),X3),X4) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_49])]) ).
tff(f239,plain,
! [X0: $tType,X3: X0,X4: X0] : ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),c_2Ebool_2ET_2E0),X3),X4) = X3 ),
inference(definition_unfolding,[],[f154,f224]) ).
tff(f154,plain,
! [X0: $tType,X3: X0,X4: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2ET_2E0,X3,X4) = X3 ),
inference(cnf_transformation,[],[f57]) ).
tff(f57,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2EF_2E0,X1,X2) = X2 )
& ! [X3: X0,X4: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2ET_2E0,X3,X4) = X3 ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( ! [X23: X0,X24: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2EF_2E0,X23,X24) = X24 )
& ! [X15: X0,X16: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2ET_2E0,X15,X16) = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
tff(f638,plain,
spl4_48,
inference(avatar_split_clause,[],[f238,f636]) ).
tff(f238,plain,
! [X0: $tType,X2: X0,X1: X0] : ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),c_2Ebool_2EF_2E0),X1),X2) = X2 ),
inference(definition_unfolding,[],[f155,f224]) ).
tff(f155,plain,
! [X0: $tType,X2: X0,X1: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2EF_2E0,X1,X2) = X2 ),
inference(cnf_transformation,[],[f57]) ).
tff(f634,plain,
( spl4_47
| ~ spl4_3
| ~ spl4_14 ),
inference(avatar_split_clause,[],[f390,f342,f287,f632]) ).
tff(f390,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = c_2Ebool_2E_7E_2E1(X0) )
| ~ p(X0) )
| ~ spl4_3
| ~ spl4_14 ),
inference(resolution,[],[f343,f288]) ).
tff(f624,plain,
( ~ spl4_46
| spl4_45 ),
inference(avatar_split_clause,[],[f619,f615,f621]) ).
tff(f615,plain,
( spl4_45
<=> p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_45])]) ).
tff(f619,plain,
( ~ p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,c_2Enum_2E0_2E0),c_2Enum_2E0_2E0))
| spl4_45 ),
inference(forward_demodulation,[],[f617,f275]) ).
tff(f617,plain,
( ~ p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)))
| spl4_45 ),
inference(avatar_component_clause,[],[f615]) ).
tff(f618,plain,
~ spl4_45,
inference(avatar_split_clause,[],[f274,f615]) ).
tff(f274,plain,
~ p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),
inference(forward_demodulation,[],[f259,f234]) ).
tff(f259,plain,
~ p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),
inference(equality_resolution,[],[f258]) ).
tff(f258,plain,
! [X0: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 != X0 )
| ~ p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))) ),
inference(equality_resolution,[],[f245]) ).
tff(f245,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 != X1 )
| ( c_2Enum_2E0_2E0 != X0 )
| ~ p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))) ),
inference(definition_unfolding,[],[f175,f170,f151,f152,f152]) ).
tff(f175,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 != X1 )
| ( c_2Enum_2E0_2E0 != X0 )
| ~ p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1))) ),
inference(cnf_transformation,[],[f112]) ).
tff(f596,plain,
spl4_44,
inference(avatar_split_clause,[],[f250,f594]) ).
tff(f250,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1)))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) ),
inference(definition_unfolding,[],[f198,f164]) ).
tff(f164,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) ),
inference(cnf_transformation,[],[f64]) ).
tff(f64,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType,X12: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X12) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
tff(f198,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1)))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1)))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f126,f127]) ).
tff(f127,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f126,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(rectify,[],[f125]) ).
tff(f125,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(nnf_transformation,[],[f81]) ).
tff(f81,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X1))
<=> ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X3))
<=> ? [X11: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).
tff(f592,plain,
spl4_43,
inference(avatar_split_clause,[],[f247,f590]) ).
tff(f247,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK1(X0,X1))) ),
inference(definition_unfolding,[],[f197,f165]) ).
tff(f165,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ),
inference(cnf_transformation,[],[f65]) ).
tff(f65,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType,X12: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X12) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
tff(f197,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK1(X0,X1))) ),
inference(cnf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK1(X0,X1))) )
& ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f122,f123]) ).
tff(f123,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
=> ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK1(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f122,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(rectify,[],[f121]) ).
tff(f121,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ! [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(nnf_transformation,[],[f80]) ).
tff(f80,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X1))
<=> ! [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X3))
<=> ! [X11: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X3,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).
tff(f564,plain,
spl4_42,
inference(avatar_split_clause,[],[f212,f562]) ).
tff(f212,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) )
& ( p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
| ( X1 != X2 ) ) ),
inference(nnf_transformation,[],[f86]) ).
tff(f86,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
<=> p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType,X12: X0,X13: X0] :
( ( X12 = X13 )
<=> p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X12),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
tff(f560,plain,
spl4_41,
inference(avatar_split_clause,[],[f208,f558]) ).
tff(f208,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ( ~ p(X1)
& p(X0) ) ) ),
inference(flattening,[],[f133]) ).
tff(f133,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ( ~ p(X1)
& p(X0) ) ) ),
inference(nnf_transformation,[],[f101]) ).
tff(f101,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(ennf_transformation,[],[f84]) ).
tff(f84,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X0)
=> p(X1) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
( ( p(X12)
=> p(X13) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X12),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
tff(f556,plain,
spl4_40,
inference(avatar_split_clause,[],[f205,f554]) ).
tff(f205,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ( ~ p(X1)
& ~ p(X0) ) ) ),
inference(flattening,[],[f131]) ).
tff(f131,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ( ~ p(X1)
& ~ p(X0) ) ) ),
inference(nnf_transformation,[],[f83]) ).
tff(f83,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
( ( p(X13)
| p(X12) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X12),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
tff(f552,plain,
spl4_39,
inference(avatar_split_clause,[],[f200,f550]) ).
tff(f200,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( ( p(X1)
& p(X0) )
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
inference(flattening,[],[f129]) ).
tff(f129,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( ( p(X1)
& p(X0) )
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
inference(nnf_transformation,[],[f82]) ).
tff(f82,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
& p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X12: tyop_2Emin_2Ebool,X13: tyop_2Emin_2Ebool] :
( ( p(X13)
& p(X12) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X12),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
tff(f531,plain,
spl4_38,
inference(avatar_split_clause,[],[f249,f529]) ).
tff(f249,plain,
! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(definition_unfolding,[],[f199,f164]) ).
tff(f199,plain,
! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(cnf_transformation,[],[f128]) ).
tff(f527,plain,
( spl4_36
| ~ spl4_37
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f337,f305,f524,f521]) ).
tff(f521,plain,
( spl4_36
<=> ! [X0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EF_2E0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_36])]) ).
tff(f524,plain,
( spl4_37
<=> ( c_2Ebool_2ET_2E0 = c_2Ebool_2EF_2E0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_37])]) ).
tff(f337,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl4_7 ),
inference(equality_factoring,[],[f306]) ).
tff(f519,plain,
spl4_35,
inference(avatar_split_clause,[],[f248,f517]) ).
tff(f248,plain,
! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1)) ),
inference(definition_unfolding,[],[f196,f165]) ).
tff(f196,plain,
! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ),
inference(cnf_transformation,[],[f124]) ).
tff(f515,plain,
spl4_34,
inference(avatar_split_clause,[],[f234,f512]) ).
tff(f510,plain,
spl4_33,
inference(avatar_split_clause,[],[f223,f508]) ).
tff(f223,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ),
inference(cnf_transformation,[],[f90]) ).
tff(f90,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X1: $tType,X9: X0,X10: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X9),X10) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).
tff(f486,plain,
spl4_32,
inference(avatar_split_clause,[],[f207,f484]) ).
tff(f207,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f134]) ).
tff(f469,plain,
spl4_31,
inference(avatar_split_clause,[],[f206,f467]) ).
tff(f206,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| p(X0) ),
inference(cnf_transformation,[],[f134]) ).
tff(f465,plain,
spl4_30,
inference(avatar_split_clause,[],[f204,f463]) ).
tff(f204,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f132]) ).
tff(f461,plain,
spl4_29,
inference(avatar_split_clause,[],[f203,f459]) ).
tff(f203,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X0) ),
inference(cnf_transformation,[],[f132]) ).
tff(f457,plain,
spl4_28,
inference(avatar_split_clause,[],[f202,f455]) ).
tff(f202,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f130]) ).
tff(f453,plain,
spl4_27,
inference(avatar_split_clause,[],[f201,f451]) ).
tff(f201,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f130]) ).
tff(f447,plain,
spl4_26,
inference(avatar_split_clause,[],[f262,f445]) ).
tff(f262,plain,
! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2)),
inference(equality_resolution,[],[f211]) ).
tff(f211,plain,
! [X0: $tType,X2: X0,X1: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f136]) ).
tff(f443,plain,
spl4_25,
inference(avatar_split_clause,[],[f236,f441]) ).
tff(f236,plain,
! [X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = X0 ),
inference(definition_unfolding,[],[f149,f150,f152]) ).
tff(f149,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__of__num_2E1(X0)) = X0 ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__of__num_2E1(X0)) = X0 ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X25: tyop_2Enum_2Enum] : ( c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__of__num_2E1(X25)) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
tff(f434,plain,
( spl4_24
| ~ spl4_2
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f370,f353,f282,f432]) ).
tff(f370,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = X0 ) )
| ~ spl4_2
| ~ spl4_16 ),
inference(resolution,[],[f354,f284]) ).
tff(f406,plain,
spl4_23,
inference(avatar_split_clause,[],[f213,f404]) ).
tff(f213,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f87]) ).
tff(f87,plain,
! [X0: $tType,X1: X0,X2: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
<=> ( X1 = X2 ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType,X6: X0,X7: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X6,X7))
<=> ( X6 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).
tff(f402,plain,
spl4_22,
inference(avatar_split_clause,[],[f193,f400]) ).
tff(f193,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ( ~ p(X1)
& p(X0) ) )
& ( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
inference(flattening,[],[f119]) ).
tff(f119,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ( ~ p(X1)
& p(X0) ) )
& ( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f100]) ).
tff(f100,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
<=> ( p(X1)
| ~ p(X0) ) ),
inference(ennf_transformation,[],[f79]) ).
tff(f79,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
<=> ( p(X0)
=> p(X1) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X6,X7))
<=> ( p(X6)
=> p(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
tff(f398,plain,
spl4_21,
inference(avatar_split_clause,[],[f190,f396]) ).
tff(f190,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ( ~ p(X1)
& ~ p(X0) ) )
& ( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
inference(flattening,[],[f117]) ).
tff(f117,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ( ~ p(X1)
& ~ p(X0) ) )
& ( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f78]) ).
tff(f78,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
<=> ( p(X1)
| p(X0) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X6,X7))
<=> ( p(X7)
| p(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
tff(f394,plain,
spl4_20,
inference(avatar_split_clause,[],[f189,f392]) ).
tff(f189,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) )
& ( ( p(X1)
& p(X0) )
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
inference(flattening,[],[f115]) ).
tff(f115,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) )
& ( ( p(X1)
& p(X0) )
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f77]) ).
tff(f77,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
<=> ( p(X1)
& p(X0) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X6,X7))
<=> ( p(X7)
& p(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
tff(f385,plain,
spl4_19,
inference(avatar_split_clause,[],[f162,f383]) ).
tff(f162,plain,
! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ),
inference(cnf_transformation,[],[f62]) ).
tff(f62,plain,
! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType,X9: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X9) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).
tff(f381,plain,
spl4_18,
inference(avatar_split_clause,[],[f159,f379]) ).
tff(f159,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ),
inference(cnf_transformation,[],[f109]) ).
tff(f109,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ) ),
inference(nnf_transformation,[],[f60]) ).
tff(f60,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X12: tyop_2Emin_2Ebool] :
( ~ p(X12)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
tff(f377,plain,
spl4_17,
inference(avatar_split_clause,[],[f158,f375]) ).
tff(f158,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ),
inference(cnf_transformation,[],[f109]) ).
tff(f355,plain,
spl4_16,
inference(avatar_split_clause,[],[f182,f353]) ).
tff(f182,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ~ p(X0)
| ~ p(X1) ),
inference(cnf_transformation,[],[f98]) ).
tff(f98,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( ~ p(X0)
& p(X1) )
| ( ~ p(X1)
& p(X0) ) ),
inference(flattening,[],[f97]) ).
tff(f97,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( ~ p(X0)
& p(X1) )
| ( ~ p(X1)
& p(X0) ) ),
inference(ennf_transformation,[],[f74]) ).
tff(f74,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X0)
=> p(X1) )
=> ( ( p(X1)
=> p(X0) )
=> ( X0 = X1 ) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X15: tyop_2Emin_2Ebool,X16: tyop_2Emin_2Ebool] :
( ( p(X15)
=> p(X16) )
=> ( ( p(X16)
=> p(X15) )
=> ( X15 = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
tff(f351,plain,
spl4_15,
inference(avatar_split_clause,[],[f179,f349]) ).
tff(f179,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| p(X1)
| p(X0) ),
inference(cnf_transformation,[],[f98]) ).
tff(f344,plain,
( spl4_14
| ~ spl4_2
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f333,f305,f282,f342]) ).
tff(f333,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(superposition,[],[f284,f306]) ).
tff(f331,plain,
spl4_13,
inference(avatar_split_clause,[],[f195,f329]) ).
tff(f195,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f120]) ).
tff(f327,plain,
spl4_12,
inference(avatar_split_clause,[],[f194,f325]) ).
tff(f194,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| p(X0) ),
inference(cnf_transformation,[],[f120]) ).
tff(f323,plain,
spl4_11,
inference(avatar_split_clause,[],[f192,f321]) ).
tff(f192,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f118]) ).
tff(f319,plain,
spl4_10,
inference(avatar_split_clause,[],[f191,f317]) ).
tff(f191,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X0) ),
inference(cnf_transformation,[],[f118]) ).
tff(f315,plain,
spl4_9,
inference(avatar_split_clause,[],[f188,f313]) ).
tff(f188,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
tff(f311,plain,
spl4_8,
inference(avatar_split_clause,[],[f187,f309]) ).
tff(f187,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f116]) ).
tff(f307,plain,
spl4_7,
inference(avatar_split_clause,[],[f156,f305]) ).
tff(f156,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(cnf_transformation,[],[f58]) ).
tff(f58,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X8 )
| ( c_2Ebool_2ET_2E0 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
tff(f303,plain,
~ spl4_6,
inference(avatar_split_clause,[],[f233,f300]) ).
tff(f233,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),c_2Enum_2E0_2E0) != app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Einteger__word_2Ei2w_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),
inference(definition_unfolding,[],[f143,f167,f166,f152]) ).
tff(f143,plain,
c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(sK0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),
inference(cnf_transformation,[],[f108]) ).
tff(f108,plain,
c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(sK0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f107]) ).
tff(f107,plain,
( ? [X0: $tType] : ( c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(X0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) )
=> ( c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(sK0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ),
introduced(choice_axiom,[]) ).
tff(f95,plain,
? [X0: $tType] : ( c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(X0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ),
inference(ennf_transformation,[],[f51]) ).
tff(f51,negated_conjecture,
~ ! [X0: $tType] : ( c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) = c_2Einteger__word_2Ei2w_2E1(X0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ),
inference(negated_conjecture,[],[f50]) ).
tff(f50,conjecture,
! [X0: $tType] : ( c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) = c_2Einteger__word_2Ei2w_2E1(X0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
tff(f297,plain,
spl4_5,
inference(avatar_split_clause,[],[f263,f295]) ).
tff(f263,plain,
! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2)),
inference(equality_resolution,[],[f214]) ).
tff(f214,plain,
! [X0: $tType,X2: X0,X1: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f137]) ).
tff(f293,plain,
spl4_4,
inference(avatar_split_clause,[],[f161,f291]) ).
tff(f161,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) ),
inference(cnf_transformation,[],[f110]) ).
tff(f110,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) )
& ( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ) ),
inference(nnf_transformation,[],[f61]) ).
tff(f61,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
<=> ~ p(X0) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X6: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X6))
<=> ~ p(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).
tff(f289,plain,
spl4_3,
inference(avatar_split_clause,[],[f160,f287]) ).
tff(f160,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ),
inference(cnf_transformation,[],[f110]) ).
tff(f285,plain,
spl4_2,
inference(avatar_split_clause,[],[f145,f282]) ).
tff(f145,plain,
p(c_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
p(c_2Ebool_2ET_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).
tff(f280,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f144,f277]) ).
tff(f144,plain,
~ p(c_2Ebool_2EF_2E0),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
~ p(c_2Ebool_2EF_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP015_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 19:09:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (5227)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (5230)WARNING: value z3 for option sas not known
% 0.14/0.38 % (5231)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (5229)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (5230)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 % (5232)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 % (5228)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (5233)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 % (5234)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 % (5234)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
% 0.21/0.40 % (5235)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.40 % (5237)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)
% 0.21/0.40 % (5236)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)
% 0.21/0.40 % (5235)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41 % Exception at run slice level
% 0.21/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41 % (5236)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42 % (5238)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)
% 2.39/0.74 % (5232)First to succeed.
% 2.39/0.75 % (5232)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5227"
% 2.39/0.75 % (5232)Refutation found. Thanks to Tanya!
% 2.39/0.75 % SZS status Theorem for theBenchmark
% 2.39/0.75 % SZS output start Proof for theBenchmark
% See solution above
% 2.39/0.76 % (5232)------------------------------
% 2.39/0.76 % (5232)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.39/0.76 % (5232)Termination reason: Refutation
% 2.39/0.76
% 2.39/0.76 % (5232)Memory used [KB]: 3368
% 2.39/0.76 % (5232)Time elapsed: 0.368 s
% 2.39/0.76 % (5232)Instructions burned: 1091 (million)
% 2.39/0.76 % (5227)Success in time 0.378 s
%------------------------------------------------------------------------------