TSTP Solution File: SWW328+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW328+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:31:14 EDT 2024
% Result : Theorem 5.09s 1.41s
% Output : Refutation 5.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 624
% Syntax : Number of formulae : 1518 ( 888 unt; 0 def)
% Number of atoms : 2829 ( 556 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 1951 ( 640 ~; 551 |; 275 &)
% ( 351 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 426 ( 424 usr; 313 prp; 0-4 aty)
% Number of functors : 106 ( 106 usr; 42 con; 0-3 aty)
% Number of variables : 976 ( 926 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29611,plain,
$false,
inference(avatar_sat_refutation,[],[f28120,f28129,f28134,f28139,f28144,f28149,f28154,f28159,f28164,f28169,f28174,f28179,f28184,f28189,f28194,f28199,f28204,f28209,f28214,f28219,f28224,f28229,f28234,f28239,f28244,f28249,f28254,f28259,f28264,f28269,f28274,f28279,f28284,f28289,f28294,f28299,f28304,f28309,f28314,f28319,f28324,f28329,f28334,f28339,f28344,f28349,f28354,f28359,f28364,f28369,f28374,f28379,f28384,f28389,f28394,f28399,f28404,f28409,f28414,f28419,f28424,f28429,f28434,f28439,f28444,f28449,f28454,f28459,f28464,f28469,f28474,f28479,f28484,f28489,f28494,f28499,f28504,f28509,f28514,f28519,f28524,f28529,f28534,f28539,f28544,f28549,f28554,f28559,f28564,f28569,f28574,f28579,f28584,f28589,f28594,f28599,f28604,f28609,f28614,f28619,f28624,f28629,f28634,f28639,f28644,f28649,f28654,f28659,f28664,f28669,f28674,f28679,f28684,f28689,f28694,f28699,f28704,f28709,f28714,f28719,f28724,f28729,f28734,f28739,f28744,f28749,f28754,f28759,f28764,f28769,f28774,f28779,f28784,f28789,f28794,f28799,f28804,f28809,f28814,f28819,f28824,f28829,f28834,f28839,f28844,f28849,f28854,f28859,f28864,f28869,f28874,f28879,f28884,f28889,f28894,f28899,f28904,f28909,f28914,f28919,f28924,f28929,f28934,f28939,f28944,f28949,f28954,f28959,f28964,f28969,f28974,f28979,f28984,f28989,f28994,f28999,f29004,f29009,f29014,f29019,f29024,f29029,f29034,f29039,f29047,f29051,f29056,f29061,f29066,f29072,f29077,f29082,f29086,f29091,f29095,f29100,f29112,f29117,f29122,f29127,f29132,f29137,f29142,f29146,f29150,f29155,f29160,f29165,f29170,f29175,f29180,f29186,f29191,f29196,f29201,f29206,f29211,f29217,f29222,f29226,f29230,f29234,f29238,f29242,f29246,f29250,f29254,f29258,f29262,f29266,f29270,f29275,f29279,f29283,f29287,f29292,f29297,f29302,f29307,f29312,f29317,f29322,f29327,f29331,f29335,f29340,f29344,f29350,f29355,f29361,f29365,f29369,f29373,f29377,f29381,f29385,f29389,f29393,f29398,f29402,f29406,f29410,f29414,f29418,f29422,f29426,f29430,f29434,f29438,f29442,f29446,f29450,f29454,f29458,f29462,f29466,f29470,f29474,f29478,f29483,f29487,f29491,f29495,f29499,f29503,f29507,f29511,f29515,f29519,f29520,f29525,f29529,f29533,f29537,f29541,f29546,f29551,f29556,f29561,f29566,f29570,f29574,f29578,f29582,f29586,f29591,f29595,f29599,f29600,f29604,f29606,f29609,f29610]) ).
fof(f29610,plain,
( ~ spl573_186
| spl573_312
| ~ spl573_3 ),
inference(avatar_split_clause,[],[f25198,f28126,f29602,f29041]) ).
fof(f29041,plain,
( spl573_186
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_186])]) ).
fof(f29602,plain,
( spl573_312
<=> ! [X0] : ~ v_P(X0,v_s1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_312])]) ).
fof(f28126,plain,
( spl573_3
<=> hBOOL(hAPP(v_ba,v_s2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_3])]) ).
fof(f25198,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87) ),
inference(trivial_inequality_removal,[],[f23754]) ).
fof(f23754,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87)
| c_Com_Ocom_OWhile(v_ba,v_ca) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f16647,f16632,f16632,f16633]) ).
fof(f16633,plain,
v_c = v_ca,
inference(cnf_transformation,[],[f14500]) ).
fof(f14500,plain,
( ( hBOOL(hAPP(v_b,v_s2))
| ~ v_P(sK85,v_s2) )
& v_P(sK85,v_s0)
& ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
& v_c = v_ca
& v_b = v_ba ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f14498,f14499]) ).
fof(f14499,plain,
( ? [X0] :
( ( hBOOL(hAPP(v_b,v_s2))
| ~ v_P(X0,v_s2) )
& v_P(X0,v_s0) )
=> ( ( hBOOL(hAPP(v_b,v_s2))
| ~ v_P(sK85,v_s2) )
& v_P(sK85,v_s0) ) ),
introduced(choice_axiom,[]) ).
fof(f14498,plain,
( ? [X0] :
( ( hBOOL(hAPP(v_b,v_s2))
| ~ v_P(X0,v_s2) )
& v_P(X0,v_s0) )
& ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
& v_c = v_ca
& v_b = v_ba ),
inference(rectify,[],[f10290]) ).
fof(f10290,plain,
( ? [X1] :
( ( hBOOL(hAPP(v_b,v_s2))
| ~ v_P(X1,v_s2) )
& v_P(X1,v_s0) )
& ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
& v_c = v_ca
& v_b = v_ba ),
inference(flattening,[],[f10289]) ).
fof(f10289,plain,
( ? [X1] :
( ( hBOOL(hAPP(v_b,v_s2))
| ~ v_P(X1,v_s2) )
& v_P(X1,v_s0) )
& ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
& v_c = v_ca
& v_b = v_ba ),
inference(ennf_transformation,[],[f5213]) ).
fof(f5213,plain,
~ ( ( v_c = v_ca
& v_b = v_ba )
=> ( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0) )
=> ! [X1] :
( v_P(X1,v_s0)
=> ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X1,v_s2) ) ) ) ),
inference(rectify,[],[f5212]) ).
fof(f5212,negated_conjecture,
~ ( ( v_c = v_ca
& v_b = v_ba )
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X2) )
=> ! [X26] :
( v_P(X26,v_s0)
=> ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X26,v_s2) ) ) ) ),
inference(negated_conjecture,[],[f5211]) ).
fof(f5211,conjecture,
( ( v_c = v_ca
& v_b = v_ba )
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X2) )
=> ! [X26] :
( v_P(X26,v_s0)
=> ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X26,v_s2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(f16632,plain,
v_b = v_ba,
inference(cnf_transformation,[],[f14500]) ).
fof(f16647,plain,
! [X0] :
( ~ hBOOL(hAPP(v_b,v_s2))
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87)
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(cnf_transformation,[],[f14506]) ).
fof(f14506,plain,
( ! [X0] :
( ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X0,v_s2) )
| ~ v_P(X0,v_s1) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G)) )
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87])],[f14504,f14505]) ).
fof(f14505,plain,
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G)) ) ),
introduced(choice_axiom,[]) ).
fof(f14504,plain,
( ! [X0] :
( ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X0,v_s2) )
| ~ v_P(X0,v_s1) )
| ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(rectify,[],[f10294]) ).
fof(f10294,plain,
( ! [X1] :
( ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X1,v_s2) )
| ~ v_P(X1,v_s1) )
| ? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(flattening,[],[f10293]) ).
fof(f10293,plain,
( ! [X1] :
( ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X1,v_s2) )
| ~ v_P(X1,v_s1) )
| ? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(ennf_transformation,[],[f5215]) ).
fof(f5215,plain,
( c_Com_Ocom_OWhile(v_b,v_c) = c_Com_Ocom_OWhile(v_ba,v_ca)
=> ( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0) )
=> ! [X1] :
( v_P(X1,v_s1)
=> ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X1,v_s2) ) ) ) ),
inference(rectify,[],[f5210]) ).
fof(f5210,axiom,
( c_Com_Ocom_OWhile(v_b,v_c) = c_Com_Ocom_OWhile(v_ba,v_ca)
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X2) )
=> ! [X26] :
( v_P(X26,v_s1)
=> ( ~ hBOOL(hAPP(v_b,v_s2))
& v_P(X26,v_s2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
fof(f29609,plain,
( spl573_186
| ~ spl573_188
| ~ spl573_198 ),
inference(avatar_split_clause,[],[f29608,f29097,f29049,f29041]) ).
fof(f29049,plain,
( spl573_188
<=> ! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_188])]) ).
fof(f29097,plain,
( spl573_198
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_198])]) ).
fof(f29608,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87)
| ~ spl573_188
| ~ spl573_198 ),
inference(resolution,[],[f29099,f29050]) ).
fof(f29050,plain,
( ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1) )
| ~ spl573_188 ),
inference(avatar_component_clause,[],[f29049]) ).
fof(f29099,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G))
| ~ spl573_198 ),
inference(avatar_component_clause,[],[f29097]) ).
fof(f29606,plain,
( ~ spl573_263
| ~ spl573_312 ),
inference(avatar_contradiction_clause,[],[f29605]) ).
fof(f29605,plain,
( $false
| ~ spl573_263
| ~ spl573_312 ),
inference(resolution,[],[f29603,f29397]) ).
fof(f29397,plain,
( v_P(sK85,v_s1)
| ~ spl573_263 ),
inference(avatar_component_clause,[],[f29395]) ).
fof(f29395,plain,
( spl573_263
<=> v_P(sK85,v_s1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_263])]) ).
fof(f29603,plain,
( ! [X0] : ~ v_P(X0,v_s1)
| ~ spl573_312 ),
inference(avatar_component_clause,[],[f29602]) ).
fof(f29604,plain,
( spl573_198
| spl573_312
| ~ spl573_3 ),
inference(avatar_split_clause,[],[f25197,f28126,f29602,f29097]) ).
fof(f25197,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G)) ),
inference(trivial_inequality_removal,[],[f23755]) ).
fof(f23755,plain,
! [X0] :
( ~ hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G))
| c_Com_Ocom_OWhile(v_ba,v_ca) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f16646,f16632,f16632,f16633]) ).
fof(f16646,plain,
! [X0] :
( ~ hBOOL(hAPP(v_b,v_s2))
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G))
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(cnf_transformation,[],[f14506]) ).
fof(f29600,plain,
( spl573_2
| ~ spl573_187
| ~ spl573_263 ),
inference(avatar_split_clause,[],[f29562,f29395,f29045,f28122]) ).
fof(f28122,plain,
( spl573_2
<=> v_P(sK85,v_s2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_2])]) ).
fof(f29045,plain,
( spl573_187
<=> ! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_187])]) ).
fof(f29562,plain,
( v_P(sK85,v_s2)
| ~ spl573_187
| ~ spl573_263 ),
inference(resolution,[],[f29397,f29046]) ).
fof(f29046,plain,
( ! [X0] :
( ~ v_P(X0,v_s1)
| v_P(X0,v_s2) )
| ~ spl573_187 ),
inference(avatar_component_clause,[],[f29045]) ).
fof(f29599,plain,
spl573_311,
inference(avatar_split_clause,[],[f26562,f29597]) ).
fof(f29597,plain,
( spl573_311
<=> ! [X1] :
( c_Int_OPls != X1
| sP7(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_311])]) ).
fof(f26562,plain,
! [X1] :
( c_Int_OPls != X1
| sP7(X1,X1) ),
inference(forward_demodulation,[],[f26561,f16844]) ).
fof(f16844,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f1333]) ).
fof(f1333,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(f26561,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| sP7(X1,X1) ),
inference(forward_demodulation,[],[f24695,f16994]) ).
fof(f16994,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f5247]) ).
fof(f5247,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f1211]) ).
fof(f1211,axiom,
! [X99] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X99) = X99,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f24695,plain,
! [X1] :
( sP7(X1,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(equality_resolution,[],[f18950]) ).
fof(f18950,plain,
! [X0,X1] :
( sP7(X0,X1)
| X0 != X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f14964]) ).
fof(f14964,plain,
! [X0,X1] :
( ( sP7(X0,X1)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
| ~ sP7(X0,X1) ) ),
inference(rectify,[],[f14963]) ).
fof(f14963,plain,
! [X1,X0] :
( ( sP7(X1,X0)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| ~ sP7(X1,X0) ) ),
inference(flattening,[],[f14962]) ).
fof(f14962,plain,
! [X1,X0] :
( ( sP7(X1,X0)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| ~ sP7(X1,X0) ) ),
inference(nnf_transformation,[],[f14361]) ).
fof(f14361,plain,
! [X1,X0] :
( sP7(X1,X0)
<=> ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f29595,plain,
spl573_310,
inference(avatar_split_clause,[],[f25797,f29593]) ).
fof(f29593,plain,
( spl573_310
<=> ! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_310])]) ).
fof(f25797,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f24568,f16856]) ).
fof(f16856,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f247]) ).
fof(f247,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(f24568,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(equality_resolution,[],[f17880]) ).
fof(f17880,plain,
! [X0,X1] :
( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f10436]) ).
fof(f10436,plain,
! [X0,X1] :
( ( c_Nitpick_Onat__gcd(X0,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f6039]) ).
fof(f6039,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> c_Nitpick_Onat__gcd(X0,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Nitpick_Onat__gcd(X0,X1) = X0 ) ),
inference(rectify,[],[f1119]) ).
fof(f1119,axiom,
! [X54,X53] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X53
=> c_Nitpick_Onat__gcd(X54,X53) = c_Nitpick_Onat__gcd(X53,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X54,X53)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53
=> c_Nitpick_Onat__gcd(X54,X53) = X54 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).
fof(f29591,plain,
spl573_309,
inference(avatar_split_clause,[],[f25386,f29588]) ).
fof(f29588,plain,
( spl573_309
<=> c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_309])]) ).
fof(f25386,plain,
c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f24545,f16844]) ).
fof(f24545,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(equality_resolution,[],[f17210]) ).
fof(f17210,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0 ),
inference(cnf_transformation,[],[f10298]) ).
fof(f10298,plain,
! [X0] :
( ( ( ( hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
& ( hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0 ) ),
inference(ennf_transformation,[],[f5462]) ).
fof(f5462,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0) ) ),
inference(rectify,[],[f1556]) ).
fof(f1556,axiom,
! [X99] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X99
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X99,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X99) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X99,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X99) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X99),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X99
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X99) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__of__code) ).
fof(f29586,plain,
spl573_308,
inference(avatar_split_clause,[],[f25382,f29584]) ).
fof(f29584,plain,
( spl573_308
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_308])]) ).
fof(f25382,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(forward_demodulation,[],[f17209,f16844]) ).
fof(f17209,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f5461]) ).
fof(f5461,plain,
! [X0] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f928]) ).
fof(f928,axiom,
! [X93] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X93
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X93),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(f29582,plain,
spl573_307,
inference(avatar_split_clause,[],[f25295,f29580]) ).
fof(f29580,plain,
( spl573_307
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_307])]) ).
fof(f25295,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f25294,f16844]) ).
fof(f25294,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f17071,f16994]) ).
fof(f17071,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(cnf_transformation,[],[f5324]) ).
fof(f5324,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(rectify,[],[f1316]) ).
fof(f1316,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).
fof(f29578,plain,
spl573_306,
inference(avatar_split_clause,[],[f25285,f29576]) ).
fof(f29576,plain,
( spl573_306
<=> ! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_306])]) ).
fof(f25285,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0,
inference(forward_demodulation,[],[f17053,f16994]) ).
fof(f17053,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f5306]) ).
fof(f5306,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0),
inference(rectify,[],[f1221]) ).
fof(f1221,axiom,
! [X129] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X129) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X129),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__number__of__def) ).
fof(f29574,plain,
spl573_305,
inference(avatar_split_clause,[],[f25276,f29572]) ).
fof(f29572,plain,
( spl573_305
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_305])]) ).
fof(f25276,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0),
inference(forward_demodulation,[],[f17021,f16844]) ).
fof(f17021,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f5274]) ).
fof(f5274,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(rectify,[],[f853]) ).
fof(f853,axiom,
! [X97] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X97),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(f29570,plain,
spl573_304,
inference(avatar_split_clause,[],[f25271,f29568]) ).
fof(f29568,plain,
( spl573_304
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_304])]) ).
fof(f25271,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(forward_demodulation,[],[f17002,f16844]) ).
fof(f17002,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f5255]) ).
fof(f5255,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(rectify,[],[f854]) ).
fof(f854,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X93,X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(f29566,plain,
spl573_303,
inference(avatar_split_clause,[],[f25264,f29564]) ).
fof(f29564,plain,
( spl573_303
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_303])]) ).
fof(f25264,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0),
inference(forward_demodulation,[],[f16983,f16856]) ).
fof(f16983,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5236]) ).
fof(f5236,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(rectify,[],[f156]) ).
fof(f156,axiom,
! [X90] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X90),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(f29561,plain,
~ spl573_302,
inference(avatar_split_clause,[],[f25228,f29558]) ).
fof(f29558,plain,
( spl573_302
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl573_302])]) ).
fof(f25228,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != c_Int_OPls,
inference(forward_demodulation,[],[f16914,f25207]) ).
fof(f25207,plain,
c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(forward_demodulation,[],[f16880,f16844]) ).
fof(f16880,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f1351]) ).
fof(f1351,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
fof(f16914,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f1357]) ).
fof(f1357,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(f29556,plain,
spl573_301,
inference(avatar_split_clause,[],[f25209,f29553]) ).
fof(f29553,plain,
( spl573_301
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_301])]) ).
fof(f25209,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f25208,f16856]) ).
fof(f25208,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f16881,f16844]) ).
fof(f16881,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f502]) ).
fof(f502,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0) ).
fof(f29551,plain,
spl573_300,
inference(avatar_split_clause,[],[f25205,f29548]) ).
fof(f29548,plain,
( spl573_300
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_300])]) ).
fof(f25205,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f16866,f16856]) ).
fof(f16866,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f252]) ).
fof(f252,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
fof(f29546,plain,
spl573_299,
inference(avatar_split_clause,[],[f25204,f29543]) ).
fof(f29543,plain,
( spl573_299
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_299])]) ).
fof(f25204,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f16865,f16856]) ).
fof(f16865,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f1673]) ).
fof(f1673,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I1_J) ).
fof(f29541,plain,
spl573_298,
inference(avatar_split_clause,[],[f24576,f29539]) ).
fof(f29539,plain,
( spl573_298
<=> ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_298])]) ).
fof(f24576,plain,
! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_resolution,[],[f17974]) ).
fof(f17974,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f6083]) ).
fof(f6083,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(rectify,[],[f5191]) ).
fof(f5191,axiom,
! [X125,X102] :
( hBOOL(hAPP(hAPP(c_fequal,X102),X125))
| X102 != X125 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(f29537,plain,
spl573_297,
inference(avatar_split_clause,[],[f24561,f29535]) ).
fof(f29535,plain,
( spl573_297
<=> ! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_297])]) ).
fof(f24561,plain,
! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1),
inference(equality_resolution,[],[f17868]) ).
fof(f17868,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f10431]) ).
fof(f10431,plain,
! [X0,X1] :
( ( c_Random_Oinc__shift(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X0),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| X0 = X1 )
& ( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ) ),
inference(ennf_transformation,[],[f6034]) ).
fof(f6034,plain,
! [X0,X1] :
( ( X0 != X1
=> c_Random_Oinc__shift(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X0),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X0 = X1
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0) ) ),
inference(rectify,[],[f1679]) ).
fof(f1679,axiom,
! [X99,X137] :
( ( X99 != X137
=> c_Random_Oinc__shift(X137,X99) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X99),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X99 = X137
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X137,X99) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inc__shift__def) ).
fof(f29533,plain,
spl573_296,
inference(avatar_split_clause,[],[f20018,f29531]) ).
fof(f29531,plain,
( spl573_296
<=> ! [X2,X0,X1] :
( sP17(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_296])]) ).
fof(f20018,plain,
! [X2,X0,X1] :
( sP17(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f14378]) ).
fof(f14378,plain,
! [X0,X1,X2] :
( sP17(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(definition_folding,[],[f11843,f14377,f14376]) ).
fof(f14376,plain,
! [X2,X0,X1] :
( sP16(X2,X0,X1)
<=> ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f14377,plain,
! [X1,X0,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> sP16(X2,X0,X1) )
| ~ sP17(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f11843,plain,
! [X0,X1,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7578]) ).
fof(f7578,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1)))
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4)) ) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) ) ),
inference(rectify,[],[f4857]) ).
fof(f4857,axiom,
! [X282,X283,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Oappend(X5),X283),X282))
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X5),X2),hAPP(c_List_Oset(X5),X283)))
=> ! [X202] :
( hBOOL(hAPP(hAPP(c_member(X5),X202),hAPP(c_List_Oset(X5),X282)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X2),X202)) ) )
& c_List_Olinorder__class_Osorted(X5,X282)
& c_List_Olinorder__class_Osorted(X5,X283) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__append) ).
fof(f29529,plain,
spl573_295,
inference(avatar_split_clause,[],[f19569,f29527]) ).
fof(f29527,plain,
( spl573_295
<=> ! [X2,X0,X1] :
( sP15(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_295])]) ).
fof(f19569,plain,
! [X2,X0,X1] :
( sP15(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14375]) ).
fof(f14375,plain,
! [X0,X1,X2] :
( sP15(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11307,f14374,f14373]) ).
fof(f14373,plain,
! [X0,X2,X1] :
( sP14(X0,X2,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f14374,plain,
! [X1,X2,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> sP14(X0,X2,X1) )
| ~ sP15(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f11307,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f7224]) ).
fof(f7224,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f704]) ).
fof(f704,axiom,
! [X10,X76,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),X10)),c_Groups_Ozero__class_Ozero(X5)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X10))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X76),c_Groups_Ozero__class_Ozero(X5))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X76)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(f29525,plain,
spl573_294,
inference(avatar_split_clause,[],[f19560,f29523]) ).
fof(f29523,plain,
( spl573_294
<=> ! [X2,X0,X1] :
( sP13(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_294])]) ).
fof(f19560,plain,
! [X2,X0,X1] :
( sP13(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14372]) ).
fof(f14372,plain,
! [X0,X1,X2] :
( sP13(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11306,f14371,f14370]) ).
fof(f14370,plain,
! [X2,X0,X1] :
( sP12(X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f14371,plain,
! [X1,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> sP12(X2,X0,X1) )
| ~ sP13(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f11306,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f7223]) ).
fof(f7223,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f705]) ).
fof(f705,axiom,
! [X10,X76,X5] :
( class_Rings_Olinordered__ring__strict(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X76),X10)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X10),c_Groups_Ozero__class_Ozero(X5)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X76),c_Groups_Ozero__class_Ozero(X5))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X10))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),X76)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(f29520,plain,
( spl573_222
| ~ spl573_188
| ~ spl573_253 ),
inference(avatar_split_clause,[],[f29479,f29352,f29049,f29214]) ).
fof(f29214,plain,
( spl573_222
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK88(v_na)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_222])]) ).
fof(f29352,plain,
( spl573_253
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(v_na)),v_G)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_253])]) ).
fof(f29479,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK88(v_na))
| ~ spl573_188
| ~ spl573_253 ),
inference(resolution,[],[f29354,f29050]) ).
fof(f29354,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(v_na)),v_G))
| ~ spl573_253 ),
inference(avatar_component_clause,[],[f29352]) ).
fof(f29519,plain,
spl573_293,
inference(avatar_split_clause,[],[f19204,f29517]) ).
fof(f29517,plain,
( spl573_293
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_293])]) ).
fof(f19204,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0),
inference(cnf_transformation,[],[f6872]) ).
fof(f6872,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X65,X66,X21] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X21,X66,X65),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).
fof(f29515,plain,
spl573_292,
inference(avatar_split_clause,[],[f19201,f29513]) ).
fof(f29513,plain,
( spl573_292
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_292])]) ).
fof(f19201,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0),
inference(cnf_transformation,[],[f6869]) ).
fof(f6869,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X20,X21,X80] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X80,X21,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).
fof(f29511,plain,
spl573_291,
inference(avatar_split_clause,[],[f19200,f29509]) ).
fof(f29509,plain,
( spl573_291
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_291])]) ).
fof(f19200,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X2,X1,X0),
inference(cnf_transformation,[],[f6868]) ).
fof(f6868,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X2,X1,X0),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X21,X81,X82] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X82,X81,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I20_J) ).
fof(f29507,plain,
spl573_290,
inference(avatar_split_clause,[],[f18745,f29505]) ).
fof(f29505,plain,
( spl573_290
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_290])]) ).
fof(f18745,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP1(X1,X0) ),
inference(cnf_transformation,[],[f14814]) ).
fof(f14814,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f14350]) ).
fof(f14350,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> sP1(X1,X0) ),
inference(definition_folding,[],[f11241,f14349]) ).
fof(f14349,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) )
| ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f11241,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) )
| ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ) ),
inference(ennf_transformation,[],[f6699]) ).
fof(f6699,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
=> ? [X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0))
=> ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ) ) ),
inference(rectify,[],[f4222]) ).
fof(f4222,axiom,
! [X170,X5] :
( c_Wellfounded_Owf(X5,X170)
<=> ! [X265] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X5),X2),X265))
=> ? [X2] :
( ! [X96] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X96),X2)),X170))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X96),X265)) )
& hBOOL(hAPP(hAPP(c_member(X5),X2),X265)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
fof(f29503,plain,
spl573_289,
inference(avatar_split_clause,[],[f18744,f29501]) ).
fof(f29501,plain,
( spl573_289
<=> ! [X0,X1] :
( sP1(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_289])]) ).
fof(f18744,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f14814]) ).
fof(f29499,plain,
spl573_288,
inference(avatar_split_clause,[],[f18351,f29497]) ).
fof(f29497,plain,
( spl573_288
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_288])]) ).
fof(f18351,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10842]) ).
fof(f10842,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6398]) ).
fof(f6398,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3828]) ).
fof(f3828,axiom,
! [X170,X5] :
( c_Wellfounded_Owf(X5,X170)
=> c_Wellfounded_Oacyclic(X5,X170) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acyclic) ).
fof(f29495,plain,
spl573_287,
inference(avatar_split_clause,[],[f18310,f29493]) ).
fof(f29493,plain,
( spl573_287
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_287])]) ).
fof(f18310,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f10788]) ).
fof(f10788,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f6365]) ).
fof(f6365,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4996]) ).
fof(f4996,axiom,
! [X326,X327] :
( class_Orderings_Oorder(X327)
=> class_Orderings_Oorder(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(f29491,plain,
spl573_286,
inference(avatar_split_clause,[],[f18309,f29489]) ).
fof(f29489,plain,
( spl573_286
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_286])]) ).
fof(f18309,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f10787]) ).
fof(f10787,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f6364]) ).
fof(f6364,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f4998]) ).
fof(f4998,axiom,
! [X326,X327] :
( class_Orderings_Oord(X327)
=> class_Orderings_Oord(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(f29487,plain,
spl573_285,
inference(avatar_split_clause,[],[f18306,f29485]) ).
fof(f29485,plain,
( spl573_285
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_285])]) ).
fof(f18306,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10784]) ).
fof(f10784,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6361]) ).
fof(f6361,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4993]) ).
fof(f4993,axiom,
! [X326,X327] :
( class_Orderings_Opreorder(X327)
=> class_Orderings_Opreorder(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(f29483,plain,
spl573_284,
inference(avatar_split_clause,[],[f18305,f29481]) ).
fof(f29481,plain,
( spl573_284
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_284])]) ).
fof(f18305,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f10783]) ).
fof(f10783,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f6360]) ).
fof(f6360,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5001]) ).
fof(f5001,axiom,
! [X326,X327] :
( class_Groups_Ominus(X327)
=> class_Groups_Ominus(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(f29478,plain,
spl573_283,
inference(avatar_split_clause,[],[f18295,f29476]) ).
fof(f29476,plain,
( spl573_283
<=> ! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_283])]) ).
fof(f18295,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10768]) ).
fof(f10768,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6350]) ).
fof(f6350,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Olattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4995]) ).
fof(f4995,axiom,
! [X326,X327] :
( class_Lattices_Olattice(X327)
=> class_Lattices_Olattice(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(f29474,plain,
spl573_282,
inference(avatar_split_clause,[],[f18294,f29472]) ).
fof(f29472,plain,
( spl573_282
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_282])]) ).
fof(f18294,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10767]) ).
fof(f10767,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6349]) ).
fof(f6349,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__inf(tc_fun(X0,X1)) ),
inference(rectify,[],[f4990]) ).
fof(f4990,axiom,
! [X326,X327] :
( class_Lattices_Olattice(X327)
=> class_Lattices_Osemilattice__inf(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(f29470,plain,
spl573_281,
inference(avatar_split_clause,[],[f18293,f29468]) ).
fof(f29468,plain,
( spl573_281
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_281])]) ).
fof(f18293,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10766]) ).
fof(f10766,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6348]) ).
fof(f6348,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(rectify,[],[f4989]) ).
fof(f4989,axiom,
! [X326,X327] :
( class_Lattices_Olattice(X327)
=> class_Lattices_Osemilattice__sup(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(f29466,plain,
spl573_280,
inference(avatar_split_clause,[],[f18288,f29464]) ).
fof(f29464,plain,
( spl573_280
<=> ! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_280])]) ).
fof(f18288,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(cnf_transformation,[],[f10761]) ).
fof(f10761,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(ennf_transformation,[],[f6343]) ).
fof(f6343,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(X1)
=> class_Lattices_Odistrib__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4991]) ).
fof(f4991,axiom,
! [X326,X327] :
( class_Lattices_Odistrib__lattice(X327)
=> class_Lattices_Odistrib__lattice(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(f29462,plain,
spl573_279,
inference(avatar_split_clause,[],[f18198,f29460]) ).
fof(f29460,plain,
( spl573_279
<=> ! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_279])]) ).
fof(f18198,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f10659]) ).
fof(f10659,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f6260]) ).
fof(f6260,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> class_Orderings_Obot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4999]) ).
fof(f4999,axiom,
! [X326,X327] :
( class_Orderings_Obot(X327)
=> class_Orderings_Obot(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(f29458,plain,
spl573_278,
inference(avatar_split_clause,[],[f18195,f29456]) ).
fof(f29456,plain,
( spl573_278
<=> ! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_278])]) ).
fof(f18195,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(cnf_transformation,[],[f10656]) ).
fof(f10656,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(ennf_transformation,[],[f6257]) ).
fof(f6257,plain,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5000]) ).
fof(f5000,axiom,
! [X326,X327] :
( class_Groups_Ouminus(X327)
=> class_Groups_Ouminus(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(f29454,plain,
spl573_277,
inference(avatar_split_clause,[],[f18180,f29452]) ).
fof(f29452,plain,
( spl573_277
<=> ! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_277])]) ).
fof(f18180,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10639]) ).
fof(f10639,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6244]) ).
fof(f6244,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4986]) ).
fof(f4986,axiom,
! [X326,X327] :
( class_Complete__Lattice_Ocomplete__lattice(X327)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f29450,plain,
spl573_276,
inference(avatar_split_clause,[],[f18174,f29448]) ).
fof(f29448,plain,
( spl573_276
<=> ! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_276])]) ).
fof(f18174,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10633]) ).
fof(f10633,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6238]) ).
fof(f6238,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(rectify,[],[f4992]) ).
fof(f4992,axiom,
! [X326,X327] :
( class_Lattices_Oboolean__algebra(X327)
=> class_Lattices_Oboolean__algebra(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(f29446,plain,
spl573_275,
inference(avatar_split_clause,[],[f18164,f29444]) ).
fof(f29444,plain,
( spl573_275
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_275])]) ).
fof(f18164,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10623]) ).
fof(f10623,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6228]) ).
fof(f6228,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__top(tc_fun(X0,X1)) ),
inference(rectify,[],[f4987]) ).
fof(f4987,axiom,
! [X326,X327] :
( class_Lattices_Obounded__lattice(X327)
=> class_Lattices_Obounded__lattice__top(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
fof(f29442,plain,
spl573_274,
inference(avatar_split_clause,[],[f18163,f29440]) ).
fof(f29440,plain,
( spl573_274
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_274])]) ).
fof(f18163,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10622]) ).
fof(f10622,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6227]) ).
fof(f6227,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4988]) ).
fof(f4988,axiom,
! [X326,X327] :
( class_Lattices_Obounded__lattice(X327)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(f29438,plain,
spl573_273,
inference(avatar_split_clause,[],[f18162,f29436]) ).
fof(f29436,plain,
( spl573_273
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_273])]) ).
fof(f18162,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10621]) ).
fof(f10621,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6226]) ).
fof(f6226,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4985]) ).
fof(f4985,axiom,
! [X326,X327] :
( class_Lattices_Obounded__lattice(X327)
=> class_Lattices_Obounded__lattice(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(f29434,plain,
spl573_272,
inference(avatar_split_clause,[],[f18161,f29432]) ).
fof(f29432,plain,
( spl573_272
<=> ! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_272])]) ).
fof(f18161,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(cnf_transformation,[],[f10620]) ).
fof(f10620,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(ennf_transformation,[],[f6225]) ).
fof(f6225,plain,
! [X0,X1] :
( class_Orderings_Otop(X1)
=> class_Orderings_Otop(tc_fun(X0,X1)) ),
inference(rectify,[],[f4997]) ).
fof(f4997,axiom,
! [X326,X327] :
( class_Orderings_Otop(X327)
=> class_Orderings_Otop(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(f29430,plain,
spl573_271,
inference(avatar_split_clause,[],[f17504,f29428]) ).
fof(f29428,plain,
( spl573_271
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_271])]) ).
fof(f17504,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(cnf_transformation,[],[f5670]) ).
fof(f5670,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(rectify,[],[f3367]) ).
fof(f3367,axiom,
! [X149,X5] : c_Fun_Oinj__on(X5,X5,c_COMBI(X5),X149),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(f29426,plain,
spl573_270,
inference(avatar_split_clause,[],[f17503,f29424]) ).
fof(f29424,plain,
( spl573_270
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_270])]) ).
fof(f17503,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(cnf_transformation,[],[f5669]) ).
fof(f5669,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(rectify,[],[f3703]) ).
fof(f3703,axiom,
! [X149,X5] : c_Fun_Oinj__on(X5,X5,c_Fun_Oid(X5),X149),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id) ).
fof(f29422,plain,
spl573_269,
inference(avatar_split_clause,[],[f17498,f29420]) ).
fof(f29420,plain,
( spl573_269
<=> ! [X0,X1] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_269])]) ).
fof(f17498,plain,
! [X0,X1] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X0))),
inference(cnf_transformation,[],[f5664]) ).
fof(f5664,plain,
! [X0,X1] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X0))),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X76,X78] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X78,X76))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OAssign) ).
fof(f29418,plain,
spl573_268,
inference(avatar_split_clause,[],[f17497,f29416]) ).
fof(f29416,plain,
( spl573_268
<=> ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_268])]) ).
fof(f17497,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5663]) ).
fof(f5663,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f3634]) ).
fof(f3634,axiom,
! [X25,X5] : hAPP(c_Set_OCollect(X5),X25) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(f29414,plain,
spl573_267,
inference(avatar_split_clause,[],[f17496,f29412]) ).
fof(f29412,plain,
( spl573_267
<=> ! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_267])]) ).
fof(f17496,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f5662]) ).
fof(f5662,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f5185]) ).
fof(f5185,axiom,
! [X88,X32] : hAPP(c_COMBI(X32),X88) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f29410,plain,
spl573_266,
inference(avatar_split_clause,[],[f17494,f29408]) ).
fof(f29408,plain,
( spl573_266
<=> ! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_266])]) ).
fof(f17494,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(cnf_transformation,[],[f5660]) ).
fof(f5660,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(rectify,[],[f3707]) ).
fof(f3707,axiom,
! [X254,X32] : hAPP(c_Fun_Oid(X32),X254) = X254,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).
fof(f29406,plain,
spl573_265,
inference(avatar_split_clause,[],[f17493,f29404]) ).
fof(f29404,plain,
( spl573_265
<=> ! [X0,X1] : ~ c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_265])]) ).
fof(f17493,plain,
! [X0,X1] : ~ c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(cnf_transformation,[],[f5659]) ).
fof(f5659,plain,
! [X0,X1] : ~ c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(rectify,[],[f249]) ).
fof(f249,axiom,
! [X54,X5] : ~ c_Option_Ois__none(X5,hAPP(c_Option_Ooption_OSome(X5),X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_is__none__code_I2_J) ).
fof(f29402,plain,
spl573_264,
inference(avatar_split_clause,[],[f17478,f29400]) ).
fof(f29400,plain,
( spl573_264
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,sK112(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_264])]) ).
fof(f17478,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,sK112(X0)) = X0,
inference(cnf_transformation,[],[f14622]) ).
fof(f14622,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK112(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK112(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112])],[f10429,f14621]) ).
fof(f14621,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,X1) = X0 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK112(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK112(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f10429,plain,
! [X0] :
? [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,X1) = X0 ),
inference(ennf_transformation,[],[f5645]) ).
fof(f5645,plain,
! [X0] :
~ ! [X1] :
( hAPP(c_Int_OAbs__Integ,X1) = X0
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg)) ),
inference(rectify,[],[f3839]) ).
fof(f3839,axiom,
! [X102] :
~ ! [X96] :
( hAPP(c_Int_OAbs__Integ,X96) = X102
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X96),c_Int_OInteg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).
fof(f29398,plain,
( spl573_263
| ~ spl573_1
| ~ spl573_201 ),
inference(avatar_split_clause,[],[f29356,f29110,f28117,f29395]) ).
fof(f28117,plain,
( spl573_1
<=> v_P(sK85,v_s0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_1])]) ).
fof(f29110,plain,
( spl573_201
<=> ! [X0] :
( v_P(X0,v_s1)
| ~ v_P(X0,v_s0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_201])]) ).
fof(f29356,plain,
( v_P(sK85,v_s1)
| ~ spl573_1
| ~ spl573_201 ),
inference(resolution,[],[f29111,f28119]) ).
fof(f28119,plain,
( v_P(sK85,v_s0)
| ~ spl573_1 ),
inference(avatar_component_clause,[],[f28117]) ).
fof(f29111,plain,
( ! [X0] :
( ~ v_P(X0,v_s0)
| v_P(X0,v_s1) )
| ~ spl573_201 ),
inference(avatar_component_clause,[],[f29110]) ).
fof(f29393,plain,
spl573_262,
inference(avatar_split_clause,[],[f17283,f29391]) ).
fof(f29391,plain,
( spl573_262
<=> ! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_262])]) ).
fof(f17283,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10356]) ).
fof(f10356,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5523]) ).
fof(f5523,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0)) ),
inference(rectify,[],[f4874]) ).
fof(f4874,axiom,
! [X32] :
( class_Orderings_Olinorder(X32)
=> c_List_Olinorder__class_Osorted(X32,c_List_Olist_ONil(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Oequations_I1_J) ).
fof(f29389,plain,
spl573_261,
inference(avatar_split_clause,[],[f17271,f29387]) ).
fof(f29387,plain,
( spl573_261
<=> ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_261])]) ).
fof(f17271,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10344]) ).
fof(f10344,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5511]) ).
fof(f5511,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f1305]) ).
fof(f1305,axiom,
! [X32] :
( class_Rings_Osemiring__1(X32)
=> c_Int_Oiszero(X32,c_Groups_Ozero__class_Ozero(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__0) ).
fof(f29385,plain,
spl573_260,
inference(avatar_split_clause,[],[f17270,f29383]) ).
fof(f29383,plain,
( spl573_260
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_260])]) ).
fof(f17270,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10343]) ).
fof(f10343,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5510]) ).
fof(f5510,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f1306]) ).
fof(f1306,axiom,
! [X32] :
( class_Rings_Osemiring__1(X32)
=> ~ c_Int_Oiszero(X32,c_Groups_Oone__class_Oone(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__1) ).
fof(f29381,plain,
spl573_259,
inference(avatar_split_clause,[],[f17235,f29379]) ).
fof(f29379,plain,
( spl573_259
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_259])]) ).
fof(f17235,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(cnf_transformation,[],[f5474]) ).
fof(f5474,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(rectify,[],[f5194]) ).
fof(f5194,axiom,
! [X25] :
( ~ hBOOL(X25)
| ~ hBOOL(hAPP(c_fNot,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(f29377,plain,
spl573_258,
inference(avatar_split_clause,[],[f17234,f29375]) ).
fof(f29375,plain,
( spl573_258
<=> ! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_258])]) ).
fof(f17234,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f5473]) ).
fof(f5473,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f5195]) ).
fof(f5195,axiom,
! [X25] :
( hBOOL(hAPP(c_fNot,X25))
| hBOOL(X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(f29373,plain,
spl573_257,
inference(avatar_split_clause,[],[f16995,f29371]) ).
fof(f29371,plain,
( spl573_257
<=> ! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_257])]) ).
fof(f16995,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(cnf_transformation,[],[f5248]) ).
fof(f5248,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(rectify,[],[f4449]) ).
fof(f4449,axiom,
! [X32] : hBOOL(hAPP(c_List_Odistinct(X32),c_List_Olist_ONil(X32))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(f29369,plain,
spl573_256,
inference(avatar_split_clause,[],[f16994,f29367]) ).
fof(f29367,plain,
( spl573_256
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_256])]) ).
fof(f29365,plain,
spl573_255,
inference(avatar_split_clause,[],[f16993,f29363]) ).
fof(f29363,plain,
( spl573_255
<=> ! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_255])]) ).
fof(f16993,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f5246]) ).
fof(f5246,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f250]) ).
fof(f250,axiom,
! [X31] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X31) = X31,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).
fof(f29361,plain,
spl573_254,
inference(avatar_split_clause,[],[f16863,f29358]) ).
fof(f29358,plain,
( spl573_254
<=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_254])]) ).
fof(f16863,plain,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f1340]) ).
fof(f1340,axiom,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls) ).
fof(f29355,plain,
( spl573_253
| ~ spl573_202
| spl573_201
| ~ spl573_215
| ~ spl573_251 ),
inference(avatar_split_clause,[],[f29345,f29342,f29177,f29110,f29114,f29352]) ).
fof(f29114,plain,
( spl573_202
<=> hBOOL(hAPP(v_ba,v_s0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_202])]) ).
fof(f29177,plain,
( spl573_215
<=> c_Natural_Oevaln(v_ca,v_s0,v_na,v_s1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_215])]) ).
fof(f29342,plain,
( spl573_251
<=> ! [X0,X3,X2,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| ~ hBOOL(hAPP(v_ba,X2))
| ~ v_P(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(X0)),v_G)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_251])]) ).
fof(f29345,plain,
( ! [X0] :
( v_P(X0,v_s1)
| ~ hBOOL(hAPP(v_ba,v_s0))
| ~ v_P(X0,v_s0)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(v_na)),v_G)) )
| ~ spl573_215
| ~ spl573_251 ),
inference(resolution,[],[f29343,f29179]) ).
fof(f29179,plain,
( c_Natural_Oevaln(v_ca,v_s0,v_na,v_s1)
| ~ spl573_215 ),
inference(avatar_component_clause,[],[f29177]) ).
fof(f29343,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| v_P(X1,X3)
| ~ hBOOL(hAPP(v_ba,X2))
| ~ v_P(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(X0)),v_G)) )
| ~ spl573_251 ),
inference(avatar_component_clause,[],[f29342]) ).
fof(f29350,plain,
spl573_252,
inference(avatar_split_clause,[],[f16862,f29347]) ).
fof(f29347,plain,
( spl573_252
<=> c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_252])]) ).
fof(f16862,plain,
c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
inference(cnf_transformation,[],[f4260]) ).
fof(f4260,axiom,
c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_body__def) ).
fof(f29344,plain,
spl573_251,
inference(avatar_split_clause,[],[f23759,f29342]) ).
fof(f23759,plain,
! [X2,X3,X0,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| ~ hBOOL(hAPP(v_ba,X2))
| ~ v_P(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(X0)),v_G)) ),
inference(definition_unfolding,[],[f16648,f16633,f16632]) ).
fof(f16648,plain,
! [X2,X3,X0,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_c,X2,X0,X3)
| ~ hBOOL(hAPP(v_b,X2))
| ~ v_P(X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(X0)),v_G)) ),
inference(cnf_transformation,[],[f14509]) ).
fof(f14509,plain,
! [X0] :
( ! [X1,X2] :
( ! [X3] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_c,X2,X0,X3) )
| ~ hBOOL(hAPP(v_b,X2))
| ~ v_P(X1,X2) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK88(X0))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(X0)),v_G)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88])],[f14507,f14508]) ).
fof(f14508,plain,
! [X0] :
( ? [X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X4),v_G)) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK88(X0))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK88(X0)),v_G)) ) ),
introduced(choice_axiom,[]) ).
fof(f14507,plain,
! [X0] :
( ! [X1,X2] :
( ! [X3] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_c,X2,X0,X3) )
| ~ hBOOL(hAPP(v_b,X2))
| ~ v_P(X1,X2) )
| ? [X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X4),v_G)) ) ),
inference(rectify,[],[f10296]) ).
fof(f10296,plain,
! [X0] :
( ! [X2,X3] :
( ! [X4] :
( v_P(X2,X4)
| ~ c_Natural_Oevaln(v_c,X3,X0,X4) )
| ~ hBOOL(hAPP(v_b,X3))
| ~ v_P(X2,X3) )
| ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ) ),
inference(flattening,[],[f10295]) ).
fof(f10295,plain,
! [X0] :
( ! [X2,X3] :
( ! [X4] :
( v_P(X2,X4)
| ~ c_Natural_Oevaln(v_c,X3,X0,X4) )
| ~ hBOOL(hAPP(v_b,X3))
| ~ v_P(X2,X3) )
| ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ) ),
inference(ennf_transformation,[],[f5216]) ).
fof(f5216,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X0,X1) )
=> ! [X2,X3] :
( ( hBOOL(hAPP(v_b,X3))
& v_P(X2,X3) )
=> ! [X4] :
( c_Natural_Oevaln(v_c,X3,X0,X4)
=> v_P(X2,X4) ) ) ),
inference(rectify,[],[f5205]) ).
fof(f5205,axiom,
! [X6] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X6,X2) )
=> ! [X26,X27] :
( ( hBOOL(hAPP(v_b,X27))
& v_P(X26,X27) )
=> ! [X28] :
( c_Natural_Oevaln(v_c,X27,X6,X28)
=> v_P(X26,X28) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f29340,plain,
( spl573_250
| ~ spl573_221 ),
inference(avatar_split_clause,[],[f29212,f29208,f29337]) ).
fof(f29337,plain,
( spl573_250
<=> c_Nat__Transfer_Onat__set(c_Option_Oset(tc_Int_Oint,c_Option_Ooption_ONone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_250])]) ).
fof(f29208,plain,
( spl573_221
<=> c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_221])]) ).
fof(f29212,plain,
( c_Nat__Transfer_Onat__set(c_Option_Oset(tc_Int_Oint,c_Option_Ooption_ONone(tc_Int_Oint)))
| ~ spl573_221 ),
inference(forward_demodulation,[],[f29210,f17052]) ).
fof(f17052,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5305]) ).
fof(f5305,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f2634]) ).
fof(f2634,axiom,
! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_Option_Oset(X5,c_Option_Ooption_ONone(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I1_J) ).
fof(f29210,plain,
( c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))
| ~ spl573_221 ),
inference(avatar_component_clause,[],[f29208]) ).
fof(f29335,plain,
spl573_249,
inference(avatar_split_clause,[],[f27405,f29333]) ).
fof(f29333,plain,
( spl573_249
<=> ! [X0,X1] : sP39(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_249])]) ).
fof(f27405,plain,
! [X0,X1] : sP39(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24880,f16856]) ).
fof(f24880,plain,
! [X0,X1] : sP39(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f20860]) ).
fof(f20860,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15627]) ).
fof(f15627,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK337(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK337(X0,X1,X2))),sK338(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK338(X0,X1,X2)),X2))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X5))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP39(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK337,sK338])],[f15625,f15626]) ).
fof(f15626,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
=> ( ~ hBOOL(hAPP(X0,sK337(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK337(X0,X1,X2))),sK338(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK338(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15625,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X5))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP39(X0,X1,X2) ) ),
inference(rectify,[],[f15624]) ).
fof(f15624,plain,
! [X2,X1,X0] :
( ( sP39(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP39(X2,X1,X0) ) ),
inference(flattening,[],[f15623]) ).
fof(f15623,plain,
! [X2,X1,X0] :
( ( sP39(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP39(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14412]) ).
fof(f14412,plain,
! [X2,X1,X0] :
( sP39(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
fof(f29331,plain,
spl573_248,
inference(avatar_split_clause,[],[f27379,f29329]) ).
fof(f29329,plain,
( spl573_248
<=> ! [X0,X1] : sP34(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_248])]) ).
fof(f27379,plain,
! [X0,X1] : sP34(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24854,f16856]) ).
fof(f24854,plain,
! [X0,X1] : sP34(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f20777]) ).
fof(f20777,plain,
! [X2,X0,X1] :
( sP34(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15569]) ).
fof(f15569,plain,
! [X0,X1,X2] :
( ( sP34(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK328(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK327(X0,X1,X2))),sK328(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK328(X0,X1,X2)),X2))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP34(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK327,sK328])],[f15567,f15568]) ).
fof(f15568,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
=> ( ~ hBOOL(hAPP(X0,sK328(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK327(X0,X1,X2))),sK328(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK328(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15567,plain,
! [X0,X1,X2] :
( ( sP34(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP34(X0,X1,X2) ) ),
inference(rectify,[],[f15566]) ).
fof(f15566,plain,
! [X2,X1,X0] :
( ( sP34(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP34(X2,X1,X0) ) ),
inference(flattening,[],[f15565]) ).
fof(f15565,plain,
! [X2,X1,X0] :
( ( sP34(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP34(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14404]) ).
fof(f14404,plain,
! [X2,X1,X0] :
( sP34(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP34])]) ).
fof(f29327,plain,
spl573_247,
inference(avatar_split_clause,[],[f26630,f29324]) ).
fof(f29324,plain,
( spl573_247
<=> sP11(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_247])]) ).
fof(f26630,plain,
sP11(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26629,f25217]) ).
fof(f25217,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f16888,f16856]) ).
fof(f16888,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f726]) ).
fof(f726,axiom,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(f26629,plain,
sP11(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24714,f16856]) ).
fof(f24714,plain,
sP11(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f24713]) ).
fof(f24713,plain,
! [X1] :
( sP11(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f19042]) ).
fof(f19042,plain,
! [X0,X1] :
( sP11(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f15015]) ).
fof(f15015,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP11(X0,X1) ) ),
inference(flattening,[],[f15014]) ).
fof(f15014,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP11(X0,X1) ) ),
inference(nnf_transformation,[],[f14368]) ).
fof(f14368,plain,
! [X0,X1] :
( sP11(X0,X1)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f29322,plain,
spl573_246,
inference(avatar_split_clause,[],[f26628,f29319]) ).
fof(f29319,plain,
( spl573_246
<=> sP11(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_246])]) ).
fof(f26628,plain,
sP11(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f26627,f25217]) ).
fof(f26627,plain,
sP11(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24712,f16856]) ).
fof(f24712,plain,
sP11(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f24711]) ).
fof(f24711,plain,
! [X1] :
( sP11(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f19043]) ).
fof(f19043,plain,
! [X0,X1] :
( sP11(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f15015]) ).
fof(f29317,plain,
spl573_245,
inference(avatar_split_clause,[],[f26610,f29314]) ).
fof(f29314,plain,
( spl573_245
<=> sP10(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_245])]) ).
fof(f26610,plain,
sP10(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26609,f25217]) ).
fof(f26609,plain,
sP10(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24710,f16856]) ).
fof(f24710,plain,
sP10(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f24709]) ).
fof(f24709,plain,
! [X1] :
( sP10(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f19034]) ).
fof(f19034,plain,
! [X0,X1] :
( sP10(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f15012]) ).
fof(f15012,plain,
! [X0,X1] :
( ( sP10(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP10(X0,X1) ) ),
inference(flattening,[],[f15011]) ).
fof(f15011,plain,
! [X0,X1] :
( ( sP10(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP10(X0,X1) ) ),
inference(nnf_transformation,[],[f14366]) ).
fof(f14366,plain,
! [X0,X1] :
( sP10(X0,X1)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f29312,plain,
spl573_244,
inference(avatar_split_clause,[],[f26608,f29309]) ).
fof(f29309,plain,
( spl573_244
<=> sP10(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_244])]) ).
fof(f26608,plain,
sP10(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f26607,f25217]) ).
fof(f26607,plain,
sP10(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24708,f16856]) ).
fof(f24708,plain,
sP10(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f24707]) ).
fof(f24707,plain,
! [X1] :
( sP10(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f19035]) ).
fof(f19035,plain,
! [X0,X1] :
( sP10(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f15012]) ).
fof(f29307,plain,
spl573_243,
inference(avatar_split_clause,[],[f25392,f29304]) ).
fof(f29304,plain,
( spl573_243
<=> c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_243])]) ).
fof(f25392,plain,
c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls),
inference(forward_demodulation,[],[f24546,f16844]) ).
fof(f24546,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f17213]) ).
fof(f17213,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(cnf_transformation,[],[f10299]) ).
fof(f10299,plain,
! [X0] :
( ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ),
inference(ennf_transformation,[],[f5463]) ).
fof(f5463,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ),
inference(rectify,[],[f552]) ).
fof(f552,axiom,
! [X112] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X112
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X112) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X112) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X112
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X112) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).
fof(f29302,plain,
spl573_242,
inference(avatar_split_clause,[],[f25203,f29299]) ).
fof(f29299,plain,
( spl573_242
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Orderings_Obot__class_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_242])]) ).
fof(f25203,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(forward_demodulation,[],[f16859,f16856]) ).
fof(f16859,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f2624]) ).
fof(f2624,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__nat__def) ).
fof(f29297,plain,
spl573_241,
inference(avatar_split_clause,[],[f25202,f29294]) ).
fof(f29294,plain,
( spl573_241
<=> c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_241])]) ).
fof(f25202,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f16858,f16856]) ).
fof(f16858,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f175]) ).
fof(f175,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I1_J) ).
fof(f29292,plain,
spl573_240,
inference(avatar_split_clause,[],[f25201,f29289]) ).
fof(f29289,plain,
( spl573_240
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_240])]) ).
fof(f25201,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse),
inference(forward_demodulation,[],[f16857,f16856]) ).
fof(f16857,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f248]) ).
fof(f248,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(f29287,plain,
spl573_239,
inference(avatar_split_clause,[],[f25110,f29285]) ).
fof(f29285,plain,
( spl573_239
<=> ! [X2,X3] : sP76(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_239])]) ).
fof(f25110,plain,
! [X2,X3] : sP76(X3,X2,X2,X3),
inference(equality_resolution,[],[f25109]) ).
fof(f25109,plain,
! [X2,X3,X1] :
( sP76(X3,X1,X2,X3)
| X1 != X2 ),
inference(equality_resolution,[],[f23164]) ).
fof(f23164,plain,
! [X2,X3,X0,X1] :
( sP76(X0,X1,X2,X3)
| X0 != X3
| X1 != X2 ),
inference(cnf_transformation,[],[f16467]) ).
fof(f16467,plain,
! [X0,X1,X2,X3] :
( ( sP76(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X0 != X3
| X1 != X2 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X0 = X3
& X1 = X2 )
| ~ sP76(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16466]) ).
fof(f16466,plain,
! [X2,X1,X3,X0] :
( ( sP76(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP76(X2,X1,X3,X0) ) ),
inference(flattening,[],[f16465]) ).
fof(f16465,plain,
! [X2,X1,X3,X0] :
( ( sP76(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP76(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f14480]) ).
fof(f14480,plain,
! [X2,X1,X3,X0] :
( sP76(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP76])]) ).
fof(f29283,plain,
spl573_238,
inference(avatar_split_clause,[],[f25108,f29281]) ).
fof(f29281,plain,
( spl573_238
<=> ! [X1,X3] : sP76(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_238])]) ).
fof(f25108,plain,
! [X3,X1] : sP76(X1,X1,X3,X3),
inference(equality_resolution,[],[f25107]) ).
fof(f25107,plain,
! [X2,X3,X1] :
( sP76(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f23165]) ).
fof(f23165,plain,
! [X2,X3,X0,X1] :
( sP76(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f16467]) ).
fof(f29279,plain,
spl573_237,
inference(avatar_split_clause,[],[f24894,f29277]) ).
fof(f29277,plain,
( spl573_237
<=> ! [X0,X1] : sP43(X0,X1,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_237])]) ).
fof(f24894,plain,
! [X0,X1] : sP43(X0,X1,c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f20936]) ).
fof(f20936,plain,
! [X2,X0,X1] :
( sP43(X0,X1,X2)
| c_List_Olist_ONil(X1) != X2 ),
inference(cnf_transformation,[],[f15682]) ).
fof(f15682,plain,
! [X0,X1,X2] :
( ( sP43(X0,X1,X2)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4) != X2 )
& c_List_Olist_ONil(X1) != X2 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK346(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK345(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK345(X0,X1,X2)),sK346(X0,X1,X2)) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP43(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK345,sK346])],[f15680,f15681]) ).
fof(f15681,plain,
! [X0,X1,X2] :
( ? [X5,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X6),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6) = X2 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK346(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK345(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK345(X0,X1,X2)),sK346(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f15680,plain,
! [X0,X1,X2] :
( ( sP43(X0,X1,X2)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4) != X2 )
& c_List_Olist_ONil(X1) != X2 ) )
& ( ? [X5,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X6),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP43(X0,X1,X2) ) ),
inference(rectify,[],[f15679]) ).
fof(f15679,plain,
! [X0,X2,X1] :
( ( sP43(X0,X2,X1)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X1 )
& c_List_Olist_ONil(X2) != X1 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1
| ~ sP43(X0,X2,X1) ) ),
inference(flattening,[],[f15678]) ).
fof(f15678,plain,
! [X0,X2,X1] :
( ( sP43(X0,X2,X1)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X1 )
& c_List_Olist_ONil(X2) != X1 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1
| ~ sP43(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f14420]) ).
fof(f14420,plain,
! [X0,X2,X1] :
( sP43(X0,X2,X1)
<=> ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP43])]) ).
fof(f29275,plain,
spl573_236,
inference(avatar_split_clause,[],[f24680,f29272]) ).
fof(f29272,plain,
( spl573_236
<=> sP5(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_236])]) ).
fof(f24680,plain,
sP5(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_resolution,[],[f24679]) ).
fof(f24679,plain,
! [X1] :
( sP5(c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(equality_resolution,[],[f18897]) ).
fof(f18897,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f14931]) ).
fof(f14931,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ) ) )
& ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| ~ sP5(X0,X1) ) ),
inference(flattening,[],[f14930]) ).
fof(f14930,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ) ) )
& ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| ~ sP5(X0,X1) ) ),
inference(nnf_transformation,[],[f14357]) ).
fof(f14357,plain,
! [X0,X1] :
( sP5(X0,X1)
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f29270,plain,
spl573_235,
inference(avatar_split_clause,[],[f24648,f29268]) ).
fof(f29268,plain,
( spl573_235
<=> ! [X1] : sP3(hAPP(c_Int_Onat,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_235])]) ).
fof(f24648,plain,
! [X1] : sP3(hAPP(c_Int_Onat,X1),X1),
inference(equality_resolution,[],[f18768]) ).
fof(f18768,plain,
! [X0,X1] :
( sP3(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ),
inference(cnf_transformation,[],[f14828]) ).
fof(f14828,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X1) = X0
| ~ sP3(X0,X1) )
& ( sP3(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ) ),
inference(nnf_transformation,[],[f14354]) ).
fof(f14354,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> sP3(X0,X1) ),
inference(definition_folding,[],[f11243,f14353]) ).
fof(f14353,plain,
! [X0,X1] :
( sP3(X0,X1)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f11243,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
inference(ennf_transformation,[],[f6705]) ).
fof(f6705,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1 ) ) ),
inference(rectify,[],[f797]) ).
fof(f797,axiom,
! [X100,X123] :
( hAPP(c_Int_Onat,X123) = X100
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X100 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X100) = X123 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff) ).
fof(f29266,plain,
spl573_234,
inference(avatar_split_clause,[],[f24643,f29264]) ).
fof(f29264,plain,
( spl573_234
<=> ! [X0] : sP2(hAPP(c_Int_Onat,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_234])]) ).
fof(f24643,plain,
! [X0] : sP2(hAPP(c_Int_Onat,X0),X0),
inference(equality_resolution,[],[f18760]) ).
fof(f18760,plain,
! [X0,X1] :
( sP2(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ),
inference(cnf_transformation,[],[f14825]) ).
fof(f14825,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X0) = X1
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ) ),
inference(nnf_transformation,[],[f14352]) ).
fof(f14352,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> sP2(X1,X0) ),
inference(definition_folding,[],[f11242,f14351]) ).
fof(f14351,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f11242,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ) ),
inference(ennf_transformation,[],[f6704]) ).
fof(f6704,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0 ) ) ),
inference(rectify,[],[f798]) ).
fof(f798,axiom,
! [X123,X100] :
( hAPP(c_Int_Onat,X123) = X100
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X100 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X123))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X100) = X123 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
fof(f29262,plain,
spl573_233,
inference(avatar_split_clause,[],[f17491,f29260]) ).
fof(f29260,plain,
( spl573_233
<=> ! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_233])]) ).
fof(f17491,plain,
! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1),
inference(cnf_transformation,[],[f5657]) ).
fof(f5657,plain,
! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X31,X41] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X41,X31,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
fof(f29258,plain,
spl573_232,
inference(avatar_split_clause,[],[f17489,f29256]) ).
fof(f29256,plain,
( spl573_232
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_232])]) ).
fof(f17489,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(cnf_transformation,[],[f5655]) ).
fof(f5655,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(rectify,[],[f4871]) ).
fof(f4871,axiom,
! [X111,X112] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X112,X111)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__upto) ).
fof(f29254,plain,
spl573_231,
inference(avatar_split_clause,[],[f17487,f29252]) ).
fof(f29252,plain,
( spl573_231
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_231])]) ).
fof(f17487,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0),
inference(cnf_transformation,[],[f5653]) ).
fof(f5653,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X20,X21] : c_Com_Ocom_OWhile(X21,X20) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).
fof(f29250,plain,
spl573_230,
inference(avatar_split_clause,[],[f17482,f29248]) ).
fof(f29248,plain,
( spl573_230
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_230])]) ).
fof(f17482,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0),
inference(cnf_transformation,[],[f5648]) ).
fof(f5648,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X68,X69] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X69,X68),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
fof(f29246,plain,
spl573_229,
inference(avatar_split_clause,[],[f17481,f29244]) ).
fof(f29244,plain,
( spl573_229
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_229])]) ).
fof(f17481,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0),
inference(cnf_transformation,[],[f5647]) ).
fof(f5647,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0),
inference(rectify,[],[f117]) ).
fof(f117,axiom,
! [X21,X82] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X82,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).
fof(f29242,plain,
spl573_228,
inference(avatar_split_clause,[],[f17295,f29240]) ).
fof(f29240,plain,
( spl573_228
<=> ! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_228])]) ).
fof(f17295,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[],[f10368]) ).
fof(f10368,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(ennf_transformation,[],[f5535]) ).
fof(f5535,plain,
! [X0] :
( class_Finite__Set_Ofinite(X0)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5139]) ).
fof(f5139,axiom,
! [X327] :
( class_Finite__Set_Ofinite(X327)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X327)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(f29238,plain,
spl573_227,
inference(avatar_split_clause,[],[f16982,f29236]) ).
fof(f29236,plain,
( spl573_227
<=> ! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_227])]) ).
fof(f16982,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5235]) ).
fof(f5235,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(rectify,[],[f3427]) ).
fof(f3427,axiom,
! [X211] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X211),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(f29234,plain,
spl573_226,
inference(avatar_split_clause,[],[f16980,f29232]) ).
fof(f29232,plain,
( spl573_226
<=> ! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_226])]) ).
fof(f16980,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5233]) ).
fof(f5233,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f1577]) ).
fof(f1577,axiom,
! [X98] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(f29230,plain,
spl573_225,
inference(avatar_split_clause,[],[f16977,f29228]) ).
fof(f29228,plain,
( spl573_225
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_225])]) ).
fof(f16977,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f5230]) ).
fof(f5230,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X31] : hAPP(c_Nat_OSuc,X31) != X31,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(f29226,plain,
spl573_224,
inference(avatar_split_clause,[],[f16973,f29224]) ).
fof(f29224,plain,
( spl573_224
<=> ! [X0] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_224])]) ).
fof(f16973,plain,
! [X0] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X0),
inference(cnf_transformation,[],[f5226]) ).
fof(f5226,plain,
! [X0] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X0),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X83] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X83),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I18_J) ).
fof(f29222,plain,
spl573_223,
inference(avatar_split_clause,[],[f16861,f29219]) ).
fof(f29219,plain,
( spl573_223
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_223])]) ).
fof(f16861,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3759]) ).
fof(f3759,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pair__less) ).
fof(f29217,plain,
( ~ spl573_222
| ~ spl573_202
| spl573_201
| ~ spl573_214
| ~ spl573_215 ),
inference(avatar_split_clause,[],[f29181,f29177,f29173,f29110,f29114,f29214]) ).
fof(f29173,plain,
( spl573_214
<=> ! [X0,X3,X2,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| ~ hBOOL(hAPP(v_ba,X2))
| ~ v_P(X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK88(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_214])]) ).
fof(f29181,plain,
( ! [X0] :
( v_P(X0,v_s1)
| ~ hBOOL(hAPP(v_ba,v_s0))
| ~ v_P(X0,v_s0)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK88(v_na)) )
| ~ spl573_214
| ~ spl573_215 ),
inference(resolution,[],[f29179,f29174]) ).
fof(f29174,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| v_P(X1,X3)
| ~ hBOOL(hAPP(v_ba,X2))
| ~ v_P(X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK88(X0)) )
| ~ spl573_214 ),
inference(avatar_component_clause,[],[f29173]) ).
fof(f29211,plain,
spl573_221,
inference(avatar_split_clause,[],[f16860,f29208]) ).
fof(f16860,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2621]) ).
fof(f2621,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
fof(f29206,plain,
spl573_220,
inference(avatar_split_clause,[],[f16856,f29203]) ).
fof(f29203,plain,
( spl573_220
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_220])]) ).
fof(f29201,plain,
spl573_219,
inference(avatar_split_clause,[],[f16854,f29198]) ).
fof(f29198,plain,
( spl573_219
<=> c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_219])]) ).
fof(f16854,plain,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
inference(cnf_transformation,[],[f3307]) ).
fof(f3307,axiom,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__nat__def) ).
fof(f29196,plain,
spl573_218,
inference(avatar_split_clause,[],[f16853,f29193]) ).
fof(f29193,plain,
( spl573_218
<=> c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_218])]) ).
fof(f16853,plain,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
inference(cnf_transformation,[],[f2379]) ).
fof(f2379,axiom,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__nat__def) ).
fof(f29191,plain,
spl573_217,
inference(avatar_split_clause,[],[f16852,f29188]) ).
fof(f29188,plain,
( spl573_217
<=> c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_217])]) ).
fof(f16852,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[],[f3710]) ).
fof(f3710,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__id) ).
fof(f29186,plain,
~ spl573_216,
inference(avatar_split_clause,[],[f16848,f29183]) ).
fof(f29183,plain,
( spl573_216
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_216])]) ).
fof(f16848,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f1278]) ).
fof(f1278,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__1) ).
fof(f29180,plain,
spl573_215,
inference(avatar_split_clause,[],[f16638,f29177]) ).
fof(f16638,plain,
c_Natural_Oevaln(v_ca,v_s0,v_na,v_s1),
inference(cnf_transformation,[],[f5207]) ).
fof(f5207,axiom,
c_Natural_Oevaln(v_ca,v_s0,v_na,v_s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f29175,plain,
spl573_214,
inference(avatar_split_clause,[],[f23758,f29173]) ).
fof(f23758,plain,
! [X2,X3,X0,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_ca,X2,X0,X3)
| ~ hBOOL(hAPP(v_ba,X2))
| ~ v_P(X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK88(X0)) ),
inference(definition_unfolding,[],[f16649,f16633,f16632]) ).
fof(f16649,plain,
! [X2,X3,X0,X1] :
( v_P(X1,X3)
| ~ c_Natural_Oevaln(v_c,X2,X0,X3)
| ~ hBOOL(hAPP(v_b,X2))
| ~ v_P(X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X0,sK88(X0)) ),
inference(cnf_transformation,[],[f14509]) ).
fof(f29170,plain,
spl573_213,
inference(avatar_split_clause,[],[f26471,f29167]) ).
fof(f29167,plain,
( spl573_213
<=> sP3(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_213])]) ).
fof(f26471,plain,
sP3(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f26470,f25221]) ).
fof(f25221,plain,
c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25220,f16844]) ).
fof(f25220,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f16907,f16856]) ).
fof(f16907,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f352]) ).
fof(f352,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0) ).
fof(f26470,plain,
sP3(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24645,f16856]) ).
fof(f24645,plain,
sP3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f24644]) ).
fof(f24644,plain,
! [X1] :
( sP3(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f18767]) ).
fof(f18767,plain,
! [X0,X1] :
( sP3(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 ),
inference(cnf_transformation,[],[f14827]) ).
fof(f14827,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| ~ sP3(X0,X1) ) ),
inference(flattening,[],[f14826]) ).
fof(f14826,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| ~ sP3(X0,X1) ) ),
inference(nnf_transformation,[],[f14353]) ).
fof(f29165,plain,
spl573_212,
inference(avatar_split_clause,[],[f26463,f29162]) ).
fof(f29162,plain,
( spl573_212
<=> sP2(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_212])]) ).
fof(f26463,plain,
sP2(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f26462,f25221]) ).
fof(f26462,plain,
sP2(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24640,f16856]) ).
fof(f24640,plain,
sP2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f24639]) ).
fof(f24639,plain,
! [X1] :
( sP2(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f18759]) ).
fof(f18759,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 ),
inference(cnf_transformation,[],[f14824]) ).
fof(f14824,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f14823]) ).
fof(f14823,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f14822]) ).
fof(f14822,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f14351]) ).
fof(f29160,plain,
~ spl573_211,
inference(avatar_split_clause,[],[f25200,f29157]) ).
fof(f29157,plain,
( spl573_211
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_211])]) ).
fof(f25200,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(forward_demodulation,[],[f16849,f16844]) ).
fof(f16849,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f1276]) ).
fof(f1276,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__0) ).
fof(f29155,plain,
~ spl573_210,
inference(avatar_split_clause,[],[f25199,f29152]) ).
fof(f29152,plain,
( spl573_210
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl573_210])]) ).
fof(f25199,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls,
inference(forward_demodulation,[],[f16847,f16844]) ).
fof(f16847,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f490]) ).
fof(f490,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f29150,plain,
spl573_209,
inference(avatar_split_clause,[],[f16972,f29148]) ).
fof(f29148,plain,
( spl573_209
<=> ! [X0] : c_Option_Ois__none(X0,c_Option_Ooption_ONone(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_209])]) ).
fof(f16972,plain,
! [X0] : c_Option_Ois__none(X0,c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5225]) ).
fof(f5225,plain,
! [X0] : c_Option_Ois__none(X0,c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f254]) ).
fof(f254,axiom,
! [X32] : c_Option_Ois__none(X32,c_Option_Ooption_ONone(X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_is__none__code_I1_J) ).
fof(f29146,plain,
spl573_208,
inference(avatar_split_clause,[],[f16968,f29144]) ).
fof(f29144,plain,
( spl573_208
<=> ! [X0] : c_Int_OPls != c_Int_OBit1(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_208])]) ).
fof(f16968,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(cnf_transformation,[],[f5221]) ).
fof(f5221,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(rectify,[],[f1390]) ).
fof(f1390,axiom,
! [X99] : c_Int_OPls != c_Int_OBit1(X99),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
fof(f29142,plain,
spl573_207,
inference(avatar_split_clause,[],[f16845,f29139]) ).
fof(f29139,plain,
( spl573_207
<=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_207])]) ).
fof(f16845,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
inference(cnf_transformation,[],[f101]) ).
fof(f101,axiom,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OSkip) ).
fof(f29137,plain,
spl573_206,
inference(avatar_split_clause,[],[f16844,f29134]) ).
fof(f29134,plain,
( spl573_206
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl573_206])]) ).
fof(f29132,plain,
spl573_205,
inference(avatar_split_clause,[],[f16843,f29129]) ).
fof(f29129,plain,
( spl573_205
<=> c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral ),
introduced(avatar_definition,[new_symbols(naming,[spl573_205])]) ).
fof(f16843,plain,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
inference(cnf_transformation,[],[f1683]) ).
fof(f1683,axiom,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subtract__code__numeral__def) ).
fof(f29127,plain,
spl573_204,
inference(avatar_split_clause,[],[f16840,f29124]) ).
fof(f29124,plain,
( spl573_204
<=> c_Int_OMin = c_Int_OBit1(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_204])]) ).
fof(f16840,plain,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
inference(cnf_transformation,[],[f1391]) ).
fof(f1391,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__Min) ).
fof(f29122,plain,
spl573_203,
inference(avatar_split_clause,[],[f16838,f29119]) ).
fof(f29119,plain,
( spl573_203
<=> c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_203])]) ).
fof(f16838,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f1697]) ).
fof(f1697,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).
fof(f29117,plain,
spl573_202,
inference(avatar_split_clause,[],[f16637,f29114]) ).
fof(f16637,plain,
hBOOL(hAPP(v_ba,v_s0)),
inference(cnf_transformation,[],[f5206]) ).
fof(f5206,axiom,
hBOOL(hAPP(v_ba,v_s0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f29112,plain,
( ~ spl573_199
| ~ spl573_200
| spl573_201 ),
inference(avatar_split_clause,[],[f23752,f29110,f29106,f29102]) ).
fof(f29102,plain,
( spl573_199
<=> v_ca = c_Com_Ocom_OWhile(v_ba,v_ca) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_199])]) ).
fof(f29106,plain,
( spl573_200
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK86) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_200])]) ).
fof(f23752,plain,
! [X0] :
( v_P(X0,v_s1)
| ~ v_P(X0,v_s0)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK86)
| v_ca != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f16641,f16632,f16633]) ).
fof(f16641,plain,
! [X0] :
( v_P(X0,v_s1)
| ~ v_P(X0,v_s0)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK86)
| v_ca != c_Com_Ocom_OWhile(v_b,v_c) ),
inference(cnf_transformation,[],[f14503]) ).
fof(f14503,plain,
( ! [X0] :
( ( ~ hBOOL(hAPP(v_b,v_s1))
& v_P(X0,v_s1) )
| ~ v_P(X0,v_s0) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK86)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK86),v_G)) )
| v_ca != c_Com_Ocom_OWhile(v_b,v_c) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f14501,f14502]) ).
fof(f14502,plain,
( ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK86)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK86),v_G)) ) ),
introduced(choice_axiom,[]) ).
fof(f14501,plain,
( ! [X0] :
( ( ~ hBOOL(hAPP(v_b,v_s1))
& v_P(X0,v_s1) )
| ~ v_P(X0,v_s0) )
| ? [X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) )
| v_ca != c_Com_Ocom_OWhile(v_b,v_c) ),
inference(rectify,[],[f10292]) ).
fof(f10292,plain,
( ! [X1] :
( ( ~ hBOOL(hAPP(v_b,v_s1))
& v_P(X1,v_s1) )
| ~ v_P(X1,v_s0) )
| ? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
| v_ca != c_Com_Ocom_OWhile(v_b,v_c) ),
inference(flattening,[],[f10291]) ).
fof(f10291,plain,
( ! [X1] :
( ( ~ hBOOL(hAPP(v_b,v_s1))
& v_P(X1,v_s1) )
| ~ v_P(X1,v_s0) )
| ? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G)) )
| v_ca != c_Com_Ocom_OWhile(v_b,v_c) ),
inference(ennf_transformation,[],[f5214]) ).
fof(f5214,plain,
( v_ca = c_Com_Ocom_OWhile(v_b,v_c)
=> ( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X0) )
=> ! [X1] :
( v_P(X1,v_s0)
=> ( ~ hBOOL(hAPP(v_b,v_s1))
& v_P(X1,v_s1) ) ) ) ),
inference(rectify,[],[f5208]) ).
fof(f5208,axiom,
( v_ca = c_Com_Ocom_OWhile(v_b,v_c)
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X2) )
=> ! [X26] :
( v_P(X26,v_s0)
=> ( ~ hBOOL(hAPP(v_b,v_s1))
& v_P(X26,v_s1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(f29100,plain,
( spl573_198
| spl573_187 ),
inference(avatar_split_clause,[],[f25195,f29045,f29097]) ).
fof(f25195,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G)) ),
inference(trivial_inequality_removal,[],[f23757]) ).
fof(f23757,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G))
| c_Com_Ocom_OWhile(v_ba,v_ca) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f16644,f16632,f16633]) ).
fof(f16644,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK87),v_G))
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(cnf_transformation,[],[f14506]) ).
fof(f29095,plain,
spl573_197,
inference(avatar_split_clause,[],[f26520,f29093]) ).
fof(f29093,plain,
( spl573_197
<=> ! [X0] : sP6(X0,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_197])]) ).
fof(f26520,plain,
! [X0] : sP6(X0,c_Int_OPls),
inference(forward_demodulation,[],[f24685,f16844]) ).
fof(f24685,plain,
! [X0] : sP6(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f18911]) ).
fof(f18911,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f14939]) ).
fof(f14939,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP6(X0,X1) ) ),
inference(rectify,[],[f14938]) ).
fof(f14938,plain,
! [X1,X0] :
( ( sP6(X1,X0)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ sP6(X1,X0) ) ),
inference(flattening,[],[f14937]) ).
fof(f14937,plain,
! [X1,X0] :
( ( sP6(X1,X0)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ sP6(X1,X0) ) ),
inference(nnf_transformation,[],[f14359]) ).
fof(f14359,plain,
! [X1,X0] :
( sP6(X1,X0)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f29091,plain,
spl573_196,
inference(avatar_split_clause,[],[f26513,f29088]) ).
fof(f29088,plain,
( spl573_196
<=> sP5(c_Int_OMin,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_196])]) ).
fof(f26513,plain,
sP5(c_Int_OMin,c_Int_OMin),
inference(forward_demodulation,[],[f24678,f16994]) ).
fof(f24678,plain,
sP5(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(equality_resolution,[],[f24677]) ).
fof(f24677,plain,
! [X1] :
( sP5(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 ),
inference(equality_resolution,[],[f18898]) ).
fof(f18898,plain,
! [X0,X1] :
( sP5(X0,X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 ),
inference(cnf_transformation,[],[f14931]) ).
fof(f29086,plain,
spl573_195,
inference(avatar_split_clause,[],[f16965,f29084]) ).
fof(f29084,plain,
( spl573_195
<=> ! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_195])]) ).
fof(f16965,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(cnf_transformation,[],[f5218]) ).
fof(f5218,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(rectify,[],[f3373]) ).
fof(f3373,axiom,
! [X5] : c_Equiv__Relations_Oequivp(X5,c_fequal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).
fof(f29082,plain,
spl573_194,
inference(avatar_split_clause,[],[f16837,f29079]) ).
fof(f29079,plain,
( spl573_194
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_194])]) ).
fof(f16837,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3741]) ).
fof(f3741,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less__than) ).
fof(f29077,plain,
spl573_193,
inference(avatar_split_clause,[],[f16836,f29074]) ).
fof(f29074,plain,
( spl573_193
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_193])]) ).
fof(f16836,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3779]) ).
fof(f3779,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
fof(f29072,plain,
( spl573_192
| ~ spl573_191 ),
inference(avatar_split_clause,[],[f29067,f29063,f29069]) ).
fof(f29069,plain,
( spl573_192
<=> c_Nat__Transfer_Ois__nat(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_192])]) ).
fof(f29063,plain,
( spl573_191
<=> c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_191])]) ).
fof(f29067,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OPls)
| ~ spl573_191 ),
inference(forward_demodulation,[],[f29065,f16844]) ).
fof(f29065,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl573_191 ),
inference(avatar_component_clause,[],[f29063]) ).
fof(f29066,plain,
spl573_191,
inference(avatar_split_clause,[],[f16835,f29063]) ).
fof(f16835,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1575]) ).
fof(f1575,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(f29061,plain,
spl573_190,
inference(avatar_split_clause,[],[f16834,f29058]) ).
fof(f29058,plain,
( spl573_190
<=> c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_190])]) ).
fof(f16834,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1578]) ).
fof(f1578,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(f29056,plain,
~ spl573_189,
inference(avatar_split_clause,[],[f16832,f29053]) ).
fof(f29053,plain,
( spl573_189
<=> c_Int_OMin = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl573_189])]) ).
fof(f16832,plain,
c_Int_OMin != c_Int_OPls,
inference(cnf_transformation,[],[f1341]) ).
fof(f1341,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
fof(f29051,plain,
spl573_188,
inference(avatar_split_clause,[],[f16634,f29049]) ).
fof(f16634,plain,
! [X1] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ),
inference(cnf_transformation,[],[f14500]) ).
fof(f29047,plain,
( ~ spl573_186
| spl573_187 ),
inference(avatar_split_clause,[],[f25196,f29045,f29041]) ).
fof(f25196,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87) ),
inference(trivial_inequality_removal,[],[f23756]) ).
fof(f23756,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87)
| c_Com_Ocom_OWhile(v_ba,v_ca) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(definition_unfolding,[],[f16645,f16632,f16633]) ).
fof(f16645,plain,
! [X0] :
( v_P(X0,v_s2)
| ~ v_P(X0,v_s1)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,sK87)
| c_Com_Ocom_OWhile(v_b,v_c) != c_Com_Ocom_OWhile(v_ba,v_ca) ),
inference(cnf_transformation,[],[f14506]) ).
fof(f29039,plain,
spl573_185,
inference(avatar_split_clause,[],[f16831,f29036]) ).
fof(f29036,plain,
( spl573_185
<=> hBOOL(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_185])]) ).
fof(f16831,plain,
hBOOL(c_fTrue),
inference(cnf_transformation,[],[f5193]) ).
fof(f5193,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(f29034,plain,
spl573_184,
inference(avatar_split_clause,[],[f16830,f29031]) ).
fof(f29031,plain,
( spl573_184
<=> class_Finite__Set_Ofinite(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_184])]) ).
fof(f16830,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f5130]) ).
fof(f5130,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(f29029,plain,
spl573_183,
inference(avatar_split_clause,[],[f16829,f29026]) ).
fof(f29026,plain,
( spl573_183
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_183])]) ).
fof(f16829,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5142]) ).
fof(f5142,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(f29024,plain,
spl573_182,
inference(avatar_split_clause,[],[f16828,f29021]) ).
fof(f29021,plain,
( spl573_182
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_182])]) ).
fof(f16828,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5132]) ).
fof(f5132,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f29019,plain,
spl573_181,
inference(avatar_split_clause,[],[f16827,f29016]) ).
fof(f29016,plain,
( spl573_181
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_181])]) ).
fof(f16827,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5112]) ).
fof(f5112,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f29014,plain,
spl573_180,
inference(avatar_split_clause,[],[f16826,f29011]) ).
fof(f29011,plain,
( spl573_180
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_180])]) ).
fof(f16826,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5057]) ).
fof(f5057,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(f29009,plain,
spl573_179,
inference(avatar_split_clause,[],[f16825,f29006]) ).
fof(f29006,plain,
( spl573_179
<=> class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_179])]) ).
fof(f16825,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5176]) ).
fof(f5176,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
fof(f29004,plain,
spl573_178,
inference(avatar_split_clause,[],[f16824,f29001]) ).
fof(f29001,plain,
( spl573_178
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_178])]) ).
fof(f16824,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f5134]) ).
fof(f5134,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f28999,plain,
spl573_177,
inference(avatar_split_clause,[],[f16823,f28996]) ).
fof(f28996,plain,
( spl573_177
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_177])]) ).
fof(f16823,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f5114]) ).
fof(f5114,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f28994,plain,
spl573_176,
inference(avatar_split_clause,[],[f16822,f28991]) ).
fof(f28991,plain,
( spl573_176
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_176])]) ).
fof(f16822,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f5061]) ).
fof(f5061,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(f28989,plain,
spl573_175,
inference(avatar_split_clause,[],[f16821,f28986]) ).
fof(f28986,plain,
( spl573_175
<=> class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_175])]) ).
fof(f16821,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5178]) ).
fof(f5178,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
fof(f28984,plain,
spl573_174,
inference(avatar_split_clause,[],[f16820,f28981]) ).
fof(f28981,plain,
( spl573_174
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_174])]) ).
fof(f16820,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5129]) ).
fof(f5129,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f28979,plain,
spl573_173,
inference(avatar_split_clause,[],[f16819,f28976]) ).
fof(f28976,plain,
( spl573_173
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_173])]) ).
fof(f16819,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5104]) ).
fof(f5104,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f28974,plain,
spl573_172,
inference(avatar_split_clause,[],[f16818,f28971]) ).
fof(f28971,plain,
( spl573_172
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_172])]) ).
fof(f16818,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5044]) ).
fof(f5044,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(f28969,plain,
spl573_171,
inference(avatar_split_clause,[],[f16817,f28966]) ).
fof(f28966,plain,
( spl573_171
<=> class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_171])]) ).
fof(f16817,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5169]) ).
fof(f5169,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
fof(f28964,plain,
spl573_170,
inference(avatar_split_clause,[],[f16816,f28961]) ).
fof(f28961,plain,
( spl573_170
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_170])]) ).
fof(f16816,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5137]) ).
fof(f5137,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(f28959,plain,
spl573_169,
inference(avatar_split_clause,[],[f16815,f28956]) ).
fof(f28956,plain,
( spl573_169
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_169])]) ).
fof(f16815,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f5116]) ).
fof(f5116,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(f28954,plain,
spl573_168,
inference(avatar_split_clause,[],[f16814,f28951]) ).
fof(f28951,plain,
( spl573_168
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_168])]) ).
fof(f16814,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f5066]) ).
fof(f5066,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(f28949,plain,
spl573_167,
inference(avatar_split_clause,[],[f16813,f28946]) ).
fof(f28946,plain,
( spl573_167
<=> class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_167])]) ).
fof(f16813,plain,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5179]) ).
fof(f5179,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(f28944,plain,
spl573_166,
inference(avatar_split_clause,[],[f16812,f28941]) ).
fof(f28941,plain,
( spl573_166
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_166])]) ).
fof(f16812,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5131]) ).
fof(f5131,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(f28939,plain,
spl573_165,
inference(avatar_split_clause,[],[f16811,f28936]) ).
fof(f28936,plain,
( spl573_165
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_165])]) ).
fof(f16811,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5110]) ).
fof(f5110,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(f28934,plain,
spl573_164,
inference(avatar_split_clause,[],[f16810,f28931]) ).
fof(f28931,plain,
( spl573_164
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_164])]) ).
fof(f16810,plain,
class_Lattices_Olattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5052]) ).
fof(f5052,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).
fof(f28929,plain,
spl573_163,
inference(avatar_split_clause,[],[f16809,f28926]) ).
fof(f28926,plain,
( spl573_163
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_163])]) ).
fof(f16809,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(cnf_transformation,[],[f5126]) ).
fof(f5126,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(f28924,plain,
spl573_162,
inference(avatar_split_clause,[],[f16808,f28921]) ).
fof(f28921,plain,
( spl573_162
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_162])]) ).
fof(f16808,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(cnf_transformation,[],[f5089]) ).
fof(f5089,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(f28919,plain,
spl573_161,
inference(avatar_split_clause,[],[f16807,f28916]) ).
fof(f28916,plain,
( spl573_161
<=> class_Lattices_Osemilattice__inf(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_161])]) ).
fof(f16807,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(cnf_transformation,[],[f5025]) ).
fof(f5025,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(f28914,plain,
spl573_160,
inference(avatar_split_clause,[],[f16806,f28911]) ).
fof(f28911,plain,
( spl573_160
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_160])]) ).
fof(f16806,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f5125]) ).
fof(f5125,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(f28909,plain,
spl573_159,
inference(avatar_split_clause,[],[f16805,f28906]) ).
fof(f28906,plain,
( spl573_159
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_159])]) ).
fof(f16805,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f5088]) ).
fof(f5088,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(f28904,plain,
spl573_158,
inference(avatar_split_clause,[],[f16804,f28901]) ).
fof(f28901,plain,
( spl573_158
<=> class_Lattices_Osemilattice__sup(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_158])]) ).
fof(f16804,plain,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
inference(cnf_transformation,[],[f5024]) ).
fof(f5024,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(f28899,plain,
spl573_157,
inference(avatar_split_clause,[],[f16803,f28896]) ).
fof(f28896,plain,
( spl573_157
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_157])]) ).
fof(f16803,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5127]) ).
fof(f5127,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(f28894,plain,
spl573_156,
inference(avatar_split_clause,[],[f16802,f28891]) ).
fof(f28891,plain,
( spl573_156
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_156])]) ).
fof(f16802,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5090]) ).
fof(f5090,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(f28889,plain,
spl573_155,
inference(avatar_split_clause,[],[f16801,f28886]) ).
fof(f28886,plain,
( spl573_155
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_155])]) ).
fof(f16801,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5026]) ).
fof(f5026,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(f28884,plain,
spl573_154,
inference(avatar_split_clause,[],[f16800,f28881]) ).
fof(f28881,plain,
( spl573_154
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_154])]) ).
fof(f16800,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5105]) ).
fof(f5105,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f28879,plain,
spl573_153,
inference(avatar_split_clause,[],[f16799,f28876]) ).
fof(f28876,plain,
( spl573_153
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_153])]) ).
fof(f16799,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5045]) ).
fof(f5045,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(f28874,plain,
spl573_152,
inference(avatar_split_clause,[],[f16798,f28871]) ).
fof(f28871,plain,
( spl573_152
<=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_152])]) ).
fof(f16798,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5170]) ).
fof(f5170,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
fof(f28869,plain,
spl573_151,
inference(avatar_split_clause,[],[f16797,f28866]) ).
fof(f28866,plain,
( spl573_151
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_151])]) ).
fof(f16797,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5096]) ).
fof(f5096,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f28864,plain,
spl573_150,
inference(avatar_split_clause,[],[f16796,f28861]) ).
fof(f28861,plain,
( spl573_150
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_150])]) ).
fof(f16796,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5033]) ).
fof(f5033,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f28859,plain,
spl573_149,
inference(avatar_split_clause,[],[f16795,f28856]) ).
fof(f28856,plain,
( spl573_149
<=> class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_149])]) ).
fof(f16795,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5162]) ).
fof(f5162,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(f28854,plain,
spl573_148,
inference(avatar_split_clause,[],[f16794,f28851]) ).
fof(f28851,plain,
( spl573_148
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_148])]) ).
fof(f16794,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5097]) ).
fof(f5097,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f28849,plain,
spl573_147,
inference(avatar_split_clause,[],[f16793,f28846]) ).
fof(f28846,plain,
( spl573_147
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_147])]) ).
fof(f16793,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f5099]) ).
fof(f5099,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f28844,plain,
spl573_146,
inference(avatar_split_clause,[],[f16792,f28841]) ).
fof(f28841,plain,
( spl573_146
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_146])]) ).
fof(f16792,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5036]) ).
fof(f5036,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f28839,plain,
spl573_145,
inference(avatar_split_clause,[],[f16791,f28836]) ).
fof(f28836,plain,
( spl573_145
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_145])]) ).
fof(f16791,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5038]) ).
fof(f5038,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f28834,plain,
spl573_144,
inference(avatar_split_clause,[],[f16790,f28831]) ).
fof(f28831,plain,
( spl573_144
<=> class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_144])]) ).
fof(f16790,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5163]) ).
fof(f5163,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(f28829,plain,
spl573_143,
inference(avatar_split_clause,[],[f16789,f28826]) ).
fof(f28826,plain,
( spl573_143
<=> class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_143])]) ).
fof(f16789,plain,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5165]) ).
fof(f5165,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(f28824,plain,
spl573_142,
inference(avatar_split_clause,[],[f16788,f28821]) ).
fof(f28821,plain,
( spl573_142
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_142])]) ).
fof(f16788,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5092]) ).
fof(f5092,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f28819,plain,
spl573_141,
inference(avatar_split_clause,[],[f16787,f28816]) ).
fof(f28816,plain,
( spl573_141
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_141])]) ).
fof(f16787,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5028]) ).
fof(f5028,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f28814,plain,
spl573_140,
inference(avatar_split_clause,[],[f16786,f28811]) ).
fof(f28811,plain,
( spl573_140
<=> class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_140])]) ).
fof(f16786,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5158]) ).
fof(f5158,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
fof(f28809,plain,
spl573_139,
inference(avatar_split_clause,[],[f16785,f28806]) ).
fof(f28806,plain,
( spl573_139
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_139])]) ).
fof(f16785,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f5087]) ).
fof(f5087,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f28804,plain,
spl573_138,
inference(avatar_split_clause,[],[f16784,f28801]) ).
fof(f28801,plain,
( spl573_138
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_138])]) ).
fof(f16784,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5023]) ).
fof(f5023,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f28799,plain,
spl573_137,
inference(avatar_split_clause,[],[f16783,f28796]) ).
fof(f28796,plain,
( spl573_137
<=> class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_137])]) ).
fof(f16783,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5156]) ).
fof(f5156,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
fof(f28794,plain,
spl573_136,
inference(avatar_split_clause,[],[f16782,f28791]) ).
fof(f28791,plain,
( spl573_136
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_136])]) ).
fof(f16782,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5108]) ).
fof(f5108,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(f28789,plain,
spl573_135,
inference(avatar_split_clause,[],[f16781,f28786]) ).
fof(f28786,plain,
( spl573_135
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_135])]) ).
fof(f16781,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5050]) ).
fof(f5050,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(f28784,plain,
spl573_134,
inference(avatar_split_clause,[],[f16780,f28781]) ).
fof(f28781,plain,
( spl573_134
<=> class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_134])]) ).
fof(f16780,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5173]) ).
fof(f5173,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
fof(f28779,plain,
spl573_133,
inference(avatar_split_clause,[],[f16779,f28776]) ).
fof(f28776,plain,
( spl573_133
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_133])]) ).
fof(f16779,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f5119]) ).
fof(f5119,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(f28774,plain,
spl573_132,
inference(avatar_split_clause,[],[f16778,f28771]) ).
fof(f28771,plain,
( spl573_132
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_132])]) ).
fof(f16778,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f5071]) ).
fof(f5071,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(f28769,plain,
spl573_131,
inference(avatar_split_clause,[],[f16777,f28766]) ).
fof(f28766,plain,
( spl573_131
<=> class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_131])]) ).
fof(f16777,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5182]) ).
fof(f5182,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(f28764,plain,
spl573_130,
inference(avatar_split_clause,[],[f16776,f28761]) ).
fof(f28761,plain,
( spl573_130
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_130])]) ).
fof(f16776,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5079]) ).
fof(f5079,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f28759,plain,
spl573_129,
inference(avatar_split_clause,[],[f16775,f28756]) ).
fof(f28756,plain,
( spl573_129
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_129])]) ).
fof(f16775,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5008]) ).
fof(f5008,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f28754,plain,
spl573_128,
inference(avatar_split_clause,[],[f16774,f28751]) ).
fof(f28751,plain,
( spl573_128
<=> class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_128])]) ).
fof(f16774,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5148]) ).
fof(f5148,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
fof(f28749,plain,
spl573_127,
inference(avatar_split_clause,[],[f16773,f28746]) ).
fof(f28746,plain,
( spl573_127
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_127])]) ).
fof(f16773,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5081]) ).
fof(f5081,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f28744,plain,
spl573_126,
inference(avatar_split_clause,[],[f16772,f28741]) ).
fof(f28741,plain,
( spl573_126
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_126])]) ).
fof(f16772,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5011]) ).
fof(f5011,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f28739,plain,
spl573_125,
inference(avatar_split_clause,[],[f16771,f28736]) ).
fof(f28736,plain,
( spl573_125
<=> class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_125])]) ).
fof(f16771,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5150]) ).
fof(f5150,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
fof(f28734,plain,
spl573_124,
inference(avatar_split_clause,[],[f16770,f28731]) ).
fof(f28731,plain,
( spl573_124
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_124])]) ).
fof(f16770,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5106]) ).
fof(f5106,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f28729,plain,
spl573_123,
inference(avatar_split_clause,[],[f16769,f28726]) ).
fof(f28726,plain,
( spl573_123
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_123])]) ).
fof(f16769,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5046]) ).
fof(f5046,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f28724,plain,
spl573_122,
inference(avatar_split_clause,[],[f16768,f28721]) ).
fof(f28721,plain,
( spl573_122
<=> class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_122])]) ).
fof(f16768,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5171]) ).
fof(f5171,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
fof(f28719,plain,
spl573_121,
inference(avatar_split_clause,[],[f16767,f28716]) ).
fof(f28716,plain,
( spl573_121
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_121])]) ).
fof(f16767,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5091]) ).
fof(f5091,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f28714,plain,
spl573_120,
inference(avatar_split_clause,[],[f16766,f28711]) ).
fof(f28711,plain,
( spl573_120
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_120])]) ).
fof(f16766,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5107]) ).
fof(f5107,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f28709,plain,
spl573_119,
inference(avatar_split_clause,[],[f16765,f28706]) ).
fof(f28706,plain,
( spl573_119
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_119])]) ).
fof(f16765,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5027]) ).
fof(f5027,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f28704,plain,
spl573_118,
inference(avatar_split_clause,[],[f16764,f28701]) ).
fof(f28701,plain,
( spl573_118
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_118])]) ).
fof(f16764,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5048]) ).
fof(f5048,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f28699,plain,
spl573_117,
inference(avatar_split_clause,[],[f16763,f28696]) ).
fof(f28696,plain,
( spl573_117
<=> class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_117])]) ).
fof(f16763,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5157]) ).
fof(f5157,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
fof(f28694,plain,
spl573_116,
inference(avatar_split_clause,[],[f16762,f28691]) ).
fof(f28691,plain,
( spl573_116
<=> class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_116])]) ).
fof(f16762,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5172]) ).
fof(f5172,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(f28689,plain,
spl573_115,
inference(avatar_split_clause,[],[f16761,f28686]) ).
fof(f28686,plain,
( spl573_115
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_115])]) ).
fof(f16761,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f5076]) ).
fof(f5076,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28684,plain,
spl573_114,
inference(avatar_split_clause,[],[f16760,f28681]) ).
fof(f28681,plain,
( spl573_114
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_114])]) ).
fof(f16760,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f5004]) ).
fof(f5004,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28679,plain,
spl573_113,
inference(avatar_split_clause,[],[f16759,f28676]) ).
fof(f28676,plain,
( spl573_113
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_113])]) ).
fof(f16759,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5145]) ).
fof(f5145,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28674,plain,
spl573_112,
inference(avatar_split_clause,[],[f16758,f28671]) ).
fof(f28671,plain,
( spl573_112
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_112])]) ).
fof(f16758,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5109]) ).
fof(f5109,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f28669,plain,
spl573_111,
inference(avatar_split_clause,[],[f16757,f28666]) ).
fof(f28666,plain,
( spl573_111
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_111])]) ).
fof(f16757,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5051]) ).
fof(f5051,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f28664,plain,
spl573_110,
inference(avatar_split_clause,[],[f16756,f28661]) ).
fof(f28661,plain,
( spl573_110
<=> class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_110])]) ).
fof(f16756,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5174]) ).
fof(f5174,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(f28659,plain,
spl573_109,
inference(avatar_split_clause,[],[f16755,f28656]) ).
fof(f28656,plain,
( spl573_109
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_109])]) ).
fof(f16755,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5080]) ).
fof(f5080,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f28654,plain,
spl573_108,
inference(avatar_split_clause,[],[f16754,f28651]) ).
fof(f28651,plain,
( spl573_108
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_108])]) ).
fof(f16754,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f5117]) ).
fof(f5117,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(f28649,plain,
spl573_107,
inference(avatar_split_clause,[],[f16753,f28646]) ).
fof(f28646,plain,
( spl573_107
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_107])]) ).
fof(f16753,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5075]) ).
fof(f5075,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28644,plain,
spl573_106,
inference(avatar_split_clause,[],[f16752,f28641]) ).
fof(f28641,plain,
( spl573_106
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_106])]) ).
fof(f16752,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5003]) ).
fof(f5003,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28639,plain,
spl573_105,
inference(avatar_split_clause,[],[f16751,f28636]) ).
fof(f28636,plain,
( spl573_105
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_105])]) ).
fof(f16751,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f5067]) ).
fof(f5067,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(f28634,plain,
spl573_104,
inference(avatar_split_clause,[],[f16750,f28631]) ).
fof(f28631,plain,
( spl573_104
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_104])]) ).
fof(f16750,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5009]) ).
fof(f5009,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f28629,plain,
spl573_103,
inference(avatar_split_clause,[],[f16749,f28626]) ).
fof(f28626,plain,
( spl573_103
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_103])]) ).
fof(f16749,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5144]) ).
fof(f5144,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28624,plain,
spl573_102,
inference(avatar_split_clause,[],[f16748,f28621]) ).
fof(f28621,plain,
( spl573_102
<=> class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_102])]) ).
fof(f16748,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5180]) ).
fof(f5180,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(f28619,plain,
spl573_101,
inference(avatar_split_clause,[],[f16747,f28616]) ).
fof(f28616,plain,
( spl573_101
<=> class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_101])]) ).
fof(f16747,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5149]) ).
fof(f5149,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
fof(f28614,plain,
spl573_100,
inference(avatar_split_clause,[],[f16746,f28611]) ).
fof(f28611,plain,
( spl573_100
<=> class_Rings_Odvd(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_100])]) ).
fof(f16746,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f5121]) ).
fof(f5121,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(f28609,plain,
spl573_99,
inference(avatar_split_clause,[],[f16745,f28606]) ).
fof(f28606,plain,
( spl573_99
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_99])]) ).
fof(f16745,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5083]) ).
fof(f5083,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f28604,plain,
spl573_98,
inference(avatar_split_clause,[],[f16744,f28601]) ).
fof(f28601,plain,
( spl573_98
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_98])]) ).
fof(f16744,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5015]) ).
fof(f5015,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f28599,plain,
spl573_97,
inference(avatar_split_clause,[],[f16743,f28596]) ).
fof(f28596,plain,
( spl573_97
<=> class_Rings_Odvd(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_97])]) ).
fof(f16743,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f5073]) ).
fof(f5073,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(f28594,plain,
spl573_96,
inference(avatar_split_clause,[],[f16742,f28591]) ).
fof(f28591,plain,
( spl573_96
<=> class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_96])]) ).
fof(f16742,plain,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5184]) ).
fof(f5184,axiom,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).
fof(f28589,plain,
spl573_95,
inference(avatar_split_clause,[],[f16741,f28586]) ).
fof(f28586,plain,
( spl573_95
<=> class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_95])]) ).
fof(f16741,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5152]) ).
fof(f5152,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
fof(f28584,plain,
spl573_94,
inference(avatar_split_clause,[],[f16740,f28581]) ).
fof(f28581,plain,
( spl573_94
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_94])]) ).
fof(f16740,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5135]) ).
fof(f5135,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(f28579,plain,
spl573_93,
inference(avatar_split_clause,[],[f16739,f28576]) ).
fof(f28576,plain,
( spl573_93
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_93])]) ).
fof(f16739,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5085]) ).
fof(f5085,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f28574,plain,
spl573_92,
inference(avatar_split_clause,[],[f16738,f28571]) ).
fof(f28571,plain,
( spl573_92
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_92])]) ).
fof(f16738,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f5115]) ).
fof(f5115,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(f28569,plain,
spl573_91,
inference(avatar_split_clause,[],[f16737,f28566]) ).
fof(f28566,plain,
( spl573_91
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_91])]) ).
fof(f16737,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f5095]) ).
fof(f5095,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f28564,plain,
spl573_90,
inference(avatar_split_clause,[],[f16736,f28561]) ).
fof(f28561,plain,
( spl573_90
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_90])]) ).
fof(f16736,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5094]) ).
fof(f5094,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f28559,plain,
spl573_89,
inference(avatar_split_clause,[],[f16735,f28556]) ).
fof(f28556,plain,
( spl573_89
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_89])]) ).
fof(f16735,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5032]) ).
fof(f5032,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f28554,plain,
spl573_88,
inference(avatar_split_clause,[],[f16734,f28551]) ).
fof(f28551,plain,
( spl573_88
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_88])]) ).
fof(f16734,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5021]) ).
fof(f5021,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f28549,plain,
spl573_87,
inference(avatar_split_clause,[],[f16733,f28546]) ).
fof(f28546,plain,
( spl573_87
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_87])]) ).
fof(f16733,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5030]) ).
fof(f5030,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f28544,plain,
spl573_86,
inference(avatar_split_clause,[],[f16732,f28541]) ).
fof(f28541,plain,
( spl573_86
<=> class_Smallcheck_Osmall(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_86])]) ).
fof(f16732,plain,
class_Smallcheck_Osmall(tc_Int_Oint),
inference(cnf_transformation,[],[f5049]) ).
fof(f5049,axiom,
class_Smallcheck_Osmall(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Smallcheck_Osmall) ).
fof(f28539,plain,
spl573_85,
inference(avatar_split_clause,[],[f16731,f28536]) ).
fof(f28536,plain,
( spl573_85
<=> class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_85])]) ).
fof(f16731,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5154]) ).
fof(f5154,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(f28534,plain,
spl573_84,
inference(avatar_split_clause,[],[f16730,f28531]) ).
fof(f28531,plain,
( spl573_84
<=> class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_84])]) ).
fof(f16730,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5160]) ).
fof(f5160,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(f28529,plain,
spl573_83,
inference(avatar_split_clause,[],[f16729,f28526]) ).
fof(f28526,plain,
( spl573_83
<=> class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_83])]) ).
fof(f16729,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5161]) ).
fof(f5161,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
fof(f28524,plain,
spl573_82,
inference(avatar_split_clause,[],[f16728,f28521]) ).
fof(f28521,plain,
( spl573_82
<=> class_Smallcheck_Osmall(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_82])]) ).
fof(f16728,plain,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5143]) ).
fof(f5143,axiom,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Smallcheck_Osmall) ).
fof(f28519,plain,
spl573_81,
inference(avatar_split_clause,[],[f16727,f28516]) ).
fof(f28516,plain,
( spl573_81
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_81])]) ).
fof(f16727,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5136]) ).
fof(f5136,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(f28514,plain,
spl573_80,
inference(avatar_split_clause,[],[f16726,f28511]) ).
fof(f28511,plain,
( spl573_80
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_80])]) ).
fof(f16726,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5111]) ).
fof(f5111,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f28509,plain,
spl573_79,
inference(avatar_split_clause,[],[f16725,f28506]) ).
fof(f28506,plain,
( spl573_79
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_79])]) ).
fof(f16725,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5113]) ).
fof(f5113,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(f28504,plain,
spl573_78,
inference(avatar_split_clause,[],[f16724,f28501]) ).
fof(f28501,plain,
( spl573_78
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_78])]) ).
fof(f16724,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f5103]) ).
fof(f5103,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f28499,plain,
spl573_77,
inference(avatar_split_clause,[],[f16723,f28496]) ).
fof(f28496,plain,
( spl573_77
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_77])]) ).
fof(f16723,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f5062]) ).
fof(f5062,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(f28494,plain,
spl573_76,
inference(avatar_split_clause,[],[f16722,f28491]) ).
fof(f28491,plain,
( spl573_76
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_76])]) ).
fof(f16722,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f5055]) ).
fof(f5055,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(f28489,plain,
spl573_75,
inference(avatar_split_clause,[],[f16721,f28486]) ).
fof(f28486,plain,
( spl573_75
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_75])]) ).
fof(f16721,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f5042]) ).
fof(f5042,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f28484,plain,
spl573_74,
inference(avatar_split_clause,[],[f16720,f28481]) ).
fof(f28481,plain,
( spl573_74
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_74])]) ).
fof(f16720,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5060]) ).
fof(f5060,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(f28479,plain,
spl573_73,
inference(avatar_split_clause,[],[f16719,f28476]) ).
fof(f28476,plain,
( spl573_73
<=> class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_73])]) ).
fof(f16719,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5177]) ).
fof(f5177,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
fof(f28474,plain,
spl573_72,
inference(avatar_split_clause,[],[f16718,f28471]) ).
fof(f28471,plain,
( spl573_72
<=> class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_72])]) ).
fof(f16718,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5168]) ).
fof(f5168,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
fof(f28469,plain,
spl573_71,
inference(avatar_split_clause,[],[f16717,f28466]) ).
fof(f28466,plain,
( spl573_71
<=> class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_71])]) ).
fof(f16717,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5175]) ).
fof(f5175,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
fof(f28464,plain,
spl573_70,
inference(avatar_split_clause,[],[f16716,f28461]) ).
fof(f28461,plain,
( spl573_70
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_70])]) ).
fof(f16716,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5078]) ).
fof(f5078,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).
fof(f28459,plain,
spl573_69,
inference(avatar_split_clause,[],[f16715,f28456]) ).
fof(f28456,plain,
( spl573_69
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_69])]) ).
fof(f16715,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5086]) ).
fof(f5086,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f28454,plain,
spl573_68,
inference(avatar_split_clause,[],[f16714,f28451]) ).
fof(f28451,plain,
( spl573_68
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_68])]) ).
fof(f16714,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5093]) ).
fof(f5093,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f28449,plain,
spl573_67,
inference(avatar_split_clause,[],[f16713,f28446]) ).
fof(f28446,plain,
( spl573_67
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_67])]) ).
fof(f16713,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5102]) ).
fof(f5102,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(f28444,plain,
spl573_66,
inference(avatar_split_clause,[],[f16712,f28441]) ).
fof(f28441,plain,
( spl573_66
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_66])]) ).
fof(f16712,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5040]) ).
fof(f5040,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f28439,plain,
spl573_65,
inference(avatar_split_clause,[],[f16711,f28436]) ).
fof(f28436,plain,
( spl573_65
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_65])]) ).
fof(f16711,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5007]) ).
fof(f5007,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
fof(f28434,plain,
spl573_64,
inference(avatar_split_clause,[],[f16710,f28431]) ).
fof(f28431,plain,
( spl573_64
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_64])]) ).
fof(f16710,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5029]) ).
fof(f5029,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f28429,plain,
spl573_63,
inference(avatar_split_clause,[],[f16709,f28426]) ).
fof(f28426,plain,
( spl573_63
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_63])]) ).
fof(f16709,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5022]) ).
fof(f5022,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f28424,plain,
spl573_62,
inference(avatar_split_clause,[],[f16708,f28421]) ).
fof(f28421,plain,
( spl573_62
<=> class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_62])]) ).
fof(f16708,plain,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5167]) ).
fof(f5167,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).
fof(f28419,plain,
spl573_61,
inference(avatar_split_clause,[],[f16707,f28416]) ).
fof(f28416,plain,
( spl573_61
<=> class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_61])]) ).
fof(f16707,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5159]) ).
fof(f5159,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(f28414,plain,
spl573_60,
inference(avatar_split_clause,[],[f16706,f28411]) ).
fof(f28411,plain,
( spl573_60
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_60])]) ).
fof(f16706,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5147]) ).
fof(f5147,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(f28409,plain,
spl573_59,
inference(avatar_split_clause,[],[f16705,f28406]) ).
fof(f28406,plain,
( spl573_59
<=> class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_59])]) ).
fof(f16705,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5155]) ).
fof(f5155,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(f28404,plain,
spl573_58,
inference(avatar_split_clause,[],[f16704,f28401]) ).
fof(f28401,plain,
( spl573_58
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_58])]) ).
fof(f16704,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5084]) ).
fof(f5084,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f28399,plain,
spl573_57,
inference(avatar_split_clause,[],[f16703,f28396]) ).
fof(f28396,plain,
( spl573_57
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_57])]) ).
fof(f16703,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f5120]) ).
fof(f5120,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(f28394,plain,
spl573_56,
inference(avatar_split_clause,[],[f16702,f28391]) ).
fof(f28391,plain,
( spl573_56
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_56])]) ).
fof(f16702,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5118]) ).
fof(f5118,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(f28389,plain,
spl573_55,
inference(avatar_split_clause,[],[f16701,f28386]) ).
fof(f28386,plain,
( spl573_55
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_55])]) ).
fof(f16701,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5082]) ).
fof(f5082,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f28384,plain,
spl573_54,
inference(avatar_split_clause,[],[f16700,f28381]) ).
fof(f28381,plain,
( spl573_54
<=> class_Groups_Osemigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_54])]) ).
fof(f16700,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5098]) ).
fof(f5098,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).
fof(f28379,plain,
spl573_53,
inference(avatar_split_clause,[],[f16699,f28376]) ).
fof(f28376,plain,
( spl573_53
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_53])]) ).
fof(f16699,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5077]) ).
fof(f5077,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f28374,plain,
spl573_52,
inference(avatar_split_clause,[],[f16698,f28371]) ).
fof(f28371,plain,
( spl573_52
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_52])]) ).
fof(f16698,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5100]) ).
fof(f5100,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f28369,plain,
spl573_51,
inference(avatar_split_clause,[],[f16697,f28366]) ).
fof(f28366,plain,
( spl573_51
<=> class_Groups_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_51])]) ).
fof(f16697,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5037]) ).
fof(f5037,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(f28364,plain,
spl573_50,
inference(avatar_split_clause,[],[f16696,f28361]) ).
fof(f28361,plain,
( spl573_50
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_50])]) ).
fof(f16696,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5039]) ).
fof(f5039,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f28359,plain,
spl573_49,
inference(avatar_split_clause,[],[f16695,f28356]) ).
fof(f28356,plain,
( spl573_49
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_49])]) ).
fof(f16695,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f5068]) ).
fof(f5068,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(f28354,plain,
spl573_48,
inference(avatar_split_clause,[],[f16694,f28351]) ).
fof(f28351,plain,
( spl573_48
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_48])]) ).
fof(f16694,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5005]) ).
fof(f5005,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f28349,plain,
spl573_47,
inference(avatar_split_clause,[],[f16693,f28346]) ).
fof(f28346,plain,
( spl573_47
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_47])]) ).
fof(f16693,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5013]) ).
fof(f5013,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f28344,plain,
spl573_46,
inference(avatar_split_clause,[],[f16692,f28341]) ).
fof(f28341,plain,
( spl573_46
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_46])]) ).
fof(f16692,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5018]) ).
fof(f5018,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f28339,plain,
spl573_45,
inference(avatar_split_clause,[],[f16691,f28336]) ).
fof(f28336,plain,
( spl573_45
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_45])]) ).
fof(f16691,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f5072]) ).
fof(f5072,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(f28334,plain,
spl573_44,
inference(avatar_split_clause,[],[f16690,f28331]) ).
fof(f28331,plain,
( spl573_44
<=> class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_44])]) ).
fof(f16690,plain,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5164]) ).
fof(f5164,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(f28329,plain,
spl573_43,
inference(avatar_split_clause,[],[f16689,f28326]) ).
fof(f28326,plain,
( spl573_43
<=> class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_43])]) ).
fof(f16689,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5166]) ).
fof(f5166,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
fof(f28324,plain,
spl573_42,
inference(avatar_split_clause,[],[f16688,f28321]) ).
fof(f28321,plain,
( spl573_42
<=> class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_42])]) ).
fof(f16688,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5153]) ).
fof(f5153,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(f28319,plain,
spl573_41,
inference(avatar_split_clause,[],[f16687,f28316]) ).
fof(f28316,plain,
( spl573_41
<=> class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_41])]) ).
fof(f16687,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5181]) ).
fof(f5181,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(f28314,plain,
spl573_40,
inference(avatar_split_clause,[],[f16686,f28311]) ).
fof(f28311,plain,
( spl573_40
<=> class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_40])]) ).
fof(f16686,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5183]) ).
fof(f5183,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
fof(f28309,plain,
spl573_39,
inference(avatar_split_clause,[],[f16685,f28306]) ).
fof(f28306,plain,
( spl573_39
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_39])]) ).
fof(f16685,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5151]) ).
fof(f5151,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(f28304,plain,
spl573_38,
inference(avatar_split_clause,[],[f16684,f28301]) ).
fof(f28301,plain,
( spl573_38
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_38])]) ).
fof(f16684,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5146]) ).
fof(f5146,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
fof(f28299,plain,
spl573_37,
inference(avatar_split_clause,[],[f16683,f28296]) ).
fof(f28296,plain,
( spl573_37
<=> class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_37])]) ).
fof(f16683,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5122]) ).
fof(f5122,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(f28294,plain,
spl573_36,
inference(avatar_split_clause,[],[f16682,f28291]) ).
fof(f28291,plain,
( spl573_36
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_36])]) ).
fof(f16682,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f5128]) ).
fof(f5128,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f28289,plain,
spl573_35,
inference(avatar_split_clause,[],[f16681,f28286]) ).
fof(f28286,plain,
( spl573_35
<=> class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_35])]) ).
fof(f16681,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(cnf_transformation,[],[f5123]) ).
fof(f5123,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(f28284,plain,
spl573_34,
inference(avatar_split_clause,[],[f16680,f28281]) ).
fof(f28281,plain,
( spl573_34
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_34])]) ).
fof(f16680,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5124]) ).
fof(f5124,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(f28279,plain,
spl573_33,
inference(avatar_split_clause,[],[f16679,f28276]) ).
fof(f28276,plain,
( spl573_33
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_33])]) ).
fof(f16679,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f5074]) ).
fof(f5074,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f28274,plain,
spl573_32,
inference(avatar_split_clause,[],[f16678,f28271]) ).
fof(f28271,plain,
( spl573_32
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_32])]) ).
fof(f16678,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f5002]) ).
fof(f5002,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f28269,plain,
spl573_31,
inference(avatar_split_clause,[],[f16677,f28266]) ).
fof(f28266,plain,
( spl573_31
<=> class_Orderings_Otop(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_31])]) ).
fof(f16677,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(cnf_transformation,[],[f5133]) ).
fof(f5133,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(f28264,plain,
spl573_30,
inference(avatar_split_clause,[],[f16676,f28261]) ).
fof(f28261,plain,
( spl573_30
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_30])]) ).
fof(f16676,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f4984]) ).
fof(f4984,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(f28259,plain,
spl573_29,
inference(avatar_split_clause,[],[f16675,f28256]) ).
fof(f28256,plain,
( spl573_29
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_29])]) ).
fof(f16675,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5059]) ).
fof(f5059,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(f28254,plain,
spl573_28,
inference(avatar_split_clause,[],[f16674,f28251]) ).
fof(f28251,plain,
( spl573_28
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_28])]) ).
fof(f16674,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f5035]) ).
fof(f5035,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f28249,plain,
spl573_27,
inference(avatar_split_clause,[],[f16673,f28246]) ).
fof(f28246,plain,
( spl573_27
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_27])]) ).
fof(f16673,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5010]) ).
fof(f5010,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(f28244,plain,
spl573_26,
inference(avatar_split_clause,[],[f16672,f28241]) ).
fof(f28241,plain,
( spl573_26
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_26])]) ).
fof(f16672,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5065]) ).
fof(f5065,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(f28239,plain,
spl573_25,
inference(avatar_split_clause,[],[f16671,f28236]) ).
fof(f28236,plain,
( spl573_25
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_25])]) ).
fof(f16671,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5020]) ).
fof(f5020,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f28234,plain,
spl573_24,
inference(avatar_split_clause,[],[f16670,f28231]) ).
fof(f28231,plain,
( spl573_24
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_24])]) ).
fof(f16670,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5053]) ).
fof(f5053,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f28229,plain,
spl573_23,
inference(avatar_split_clause,[],[f16669,f28226]) ).
fof(f28226,plain,
( spl573_23
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_23])]) ).
fof(f16669,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5041]) ).
fof(f5041,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f28224,plain,
spl573_22,
inference(avatar_split_clause,[],[f16668,f28221]) ).
fof(f28221,plain,
( spl573_22
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_22])]) ).
fof(f16668,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5012]) ).
fof(f5012,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f28219,plain,
spl573_21,
inference(avatar_split_clause,[],[f16667,f28216]) ).
fof(f28216,plain,
( spl573_21
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_21])]) ).
fof(f16667,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5016]) ).
fof(f5016,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f28214,plain,
spl573_20,
inference(avatar_split_clause,[],[f16666,f28211]) ).
fof(f28211,plain,
( spl573_20
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_20])]) ).
fof(f16666,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f5069]) ).
fof(f5069,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(f28209,plain,
spl573_19,
inference(avatar_split_clause,[],[f16665,f28206]) ).
fof(f28206,plain,
( spl573_19
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_19])]) ).
fof(f16665,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5043]) ).
fof(f5043,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f28204,plain,
spl573_18,
inference(avatar_split_clause,[],[f16664,f28201]) ).
fof(f28201,plain,
( spl573_18
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_18])]) ).
fof(f16664,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5058]) ).
fof(f5058,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(f28199,plain,
spl573_17,
inference(avatar_split_clause,[],[f16663,f28196]) ).
fof(f28196,plain,
( spl573_17
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_17])]) ).
fof(f16663,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5054]) ).
fof(f5054,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(f28194,plain,
spl573_16,
inference(avatar_split_clause,[],[f16662,f28191]) ).
fof(f28191,plain,
( spl573_16
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_16])]) ).
fof(f16662,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5047]) ).
fof(f5047,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f28189,plain,
spl573_15,
inference(avatar_split_clause,[],[f16661,f28186]) ).
fof(f28186,plain,
( spl573_15
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_15])]) ).
fof(f16661,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5014]) ).
fof(f5014,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f28184,plain,
spl573_14,
inference(avatar_split_clause,[],[f16660,f28181]) ).
fof(f28181,plain,
( spl573_14
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_14])]) ).
fof(f16660,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5034]) ).
fof(f5034,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f28179,plain,
spl573_13,
inference(avatar_split_clause,[],[f16659,f28176]) ).
fof(f28176,plain,
( spl573_13
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_13])]) ).
fof(f16659,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5070]) ).
fof(f5070,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(f28174,plain,
spl573_12,
inference(avatar_split_clause,[],[f16658,f28171]) ).
fof(f28171,plain,
( spl573_12
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_12])]) ).
fof(f16658,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5056]) ).
fof(f5056,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(f28169,plain,
spl573_11,
inference(avatar_split_clause,[],[f16657,f28166]) ).
fof(f28166,plain,
( spl573_11
<=> class_Groups_Osgn__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_11])]) ).
fof(f16657,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5063]) ).
fof(f5063,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
fof(f28164,plain,
spl573_10,
inference(avatar_split_clause,[],[f16656,f28161]) ).
fof(f28161,plain,
( spl573_10
<=> class_Orderings_Owellorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_10])]) ).
fof(f16656,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5101]) ).
fof(f5101,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
fof(f28159,plain,
spl573_9,
inference(avatar_split_clause,[],[f16655,f28156]) ).
fof(f28156,plain,
( spl573_9
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_9])]) ).
fof(f16655,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5017]) ).
fof(f5017,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f28154,plain,
spl573_8,
inference(avatar_split_clause,[],[f16654,f28151]) ).
fof(f28151,plain,
( spl573_8
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_8])]) ).
fof(f16654,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5031]) ).
fof(f5031,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(f28149,plain,
spl573_7,
inference(avatar_split_clause,[],[f16653,f28146]) ).
fof(f28146,plain,
( spl573_7
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_7])]) ).
fof(f16653,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5006]) ).
fof(f5006,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f28144,plain,
spl573_6,
inference(avatar_split_clause,[],[f16652,f28141]) ).
fof(f28141,plain,
( spl573_6
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_6])]) ).
fof(f16652,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5064]) ).
fof(f5064,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(f28139,plain,
spl573_5,
inference(avatar_split_clause,[],[f16651,f28136]) ).
fof(f28136,plain,
( spl573_5
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_5])]) ).
fof(f16651,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5019]) ).
fof(f5019,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f28134,plain,
~ spl573_4,
inference(avatar_split_clause,[],[f16650,f28131]) ).
fof(f28131,plain,
( spl573_4
<=> hBOOL(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_4])]) ).
fof(f16650,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[],[f5192]) ).
fof(f5192,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(f28129,plain,
( ~ spl573_2
| spl573_3 ),
inference(avatar_split_clause,[],[f23749,f28126,f28122]) ).
fof(f23749,plain,
( hBOOL(hAPP(v_ba,v_s2))
| ~ v_P(sK85,v_s2) ),
inference(definition_unfolding,[],[f16636,f16632]) ).
fof(f16636,plain,
( hBOOL(hAPP(v_b,v_s2))
| ~ v_P(sK85,v_s2) ),
inference(cnf_transformation,[],[f14500]) ).
fof(f28120,plain,
spl573_1,
inference(avatar_split_clause,[],[f16635,f28117]) ).
fof(f16635,plain,
v_P(sK85,v_s0),
inference(cnf_transformation,[],[f14500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW328+1 : TPTP v8.1.2. Released v5.2.0.
% 0.15/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 03:22:10 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.22/0.36 % (1660)Running in auto input_syntax mode. Trying TPTP
% 0.50/0.73 % (1776)WARNING: value z3 for option sas not known
% 0.56/0.73 % (1774)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.56/0.73 % (1776)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)
% 0.56/0.73 % (1775)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.56/0.73 % (1777)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.56/0.73 % (1778)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)
% 0.56/0.73 % (1779)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)
% 0.56/0.73 % (1780)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)
% 5.09/1.40 % (1778)First to succeed.
% 5.09/1.41 % (1778)Refutation found. Thanks to Tanya!
% 5.09/1.41 % SZS status Theorem for theBenchmark
% 5.09/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 5.09/1.42 % (1778)------------------------------
% 5.09/1.42 % (1778)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 5.09/1.42 % (1778)Termination reason: Refutation
% 5.09/1.42
% 5.09/1.42 % (1778)Memory used [KB]: 20570
% 5.09/1.42 % (1778)Time elapsed: 0.680 s
% 5.09/1.42 % (1778)Instructions burned: 2015 (million)
% 5.09/1.42 % (1778)------------------------------
% 5.09/1.42 % (1778)------------------------------
% 5.09/1.42 % (1660)Success in time 1.039 s
%------------------------------------------------------------------------------