TSTP Solution File: LCL785-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL785-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n008.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 : Fri Sep 1 18:55:38 EDT 2023
% Result : Unsatisfiable 0.24s 0.50s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 353
% Syntax : Number of formulae : 576 ( 254 unt; 0 def)
% Number of atoms : 1054 ( 298 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 800 ( 322 ~; 296 |; 0 &)
% ( 182 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 212 ( 210 usr; 183 prp; 0-4 aty)
% Number of functors : 53 ( 53 usr; 21 con; 0-5 aty)
% Number of variables : 811 (; 811 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1518,plain,
$false,
inference(avatar_sat_refutation,[],[f459,f464,f469,f474,f479,f484,f489,f494,f499,f504,f509,f514,f519,f524,f529,f534,f539,f544,f549,f554,f559,f563,f568,f573,f578,f586,f590,f594,f598,f602,f606,f610,f614,f618,f622,f626,f630,f635,f639,f643,f649,f653,f657,f661,f665,f669,f673,f677,f681,f685,f689,f693,f697,f704,f708,f712,f716,f720,f724,f728,f732,f736,f740,f746,f750,f754,f758,f762,f766,f770,f774,f778,f782,f786,f790,f794,f798,f802,f806,f828,f833,f837,f841,f845,f849,f853,f857,f861,f866,f870,f874,f878,f882,f886,f908,f912,f916,f920,f924,f928,f932,f936,f940,f944,f948,f952,f956,f960,f964,f968,f972,f976,f980,f984,f988,f992,f996,f1000,f1004,f1008,f1012,f1016,f1028,f1083,f1087,f1091,f1095,f1099,f1103,f1108,f1113,f1118,f1123,f1128,f1132,f1136,f1140,f1144,f1148,f1152,f1201,f1205,f1209,f1213,f1217,f1221,f1225,f1229,f1233,f1237,f1241,f1245,f1249,f1253,f1257,f1261,f1265,f1269,f1309,f1420,f1430,f1434,f1438,f1442,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1495,f1499,f1503,f1507,f1511,f1516,f1517]) ).
fof(f1517,plain,
spl0_26,
inference(avatar_split_clause,[],[f422,f583]) ).
fof(f583,plain,
( spl0_26
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f422,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(forward_demodulation,[],[f395,f350]) ).
fof(f350,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_True_0) ).
fof(f395,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_CHAINED_0_01) ).
fof(f1516,plain,
spl0_182,
inference(avatar_split_clause,[],[f421,f1513]) ).
fof(f1513,plain,
( spl0_182
<=> c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f421,plain,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
inference(forward_demodulation,[],[f356,f350]) ).
fof(f356,axiom,
c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Var_I2_J_0) ).
fof(f1511,plain,
spl0_181,
inference(avatar_split_clause,[],[f389,f1509]) ).
fof(f1509,plain,
( spl0_181
<=> ! [X3,X24,X8,X23] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23)),X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X24,tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f389,axiom,
! [X3,X8,X24,X23] : hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X23)),X3) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X24,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Abs__App__neq__Var__apps_0) ).
fof(f1507,plain,
spl0_180,
inference(avatar_split_clause,[],[f335,f1505]) ).
fof(f1505,plain,
( spl0_180
<=> ! [X54,X55,X62,X63] :
( X55 = X63
| hAPP(hAPP(c_Lambda_OdB_OApp,X54),X55) != hAPP(hAPP(c_Lambda_OdB_OApp,X62),X63) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f335,axiom,
! [X54,X55,X62,X63] :
( X55 = X63
| hAPP(hAPP(c_Lambda_OdB_OApp,X54),X55) != hAPP(hAPP(c_Lambda_OdB_OApp,X62),X63) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I2_J_1) ).
fof(f1503,plain,
spl0_179,
inference(avatar_split_clause,[],[f334,f1501]) ).
fof(f1501,plain,
( spl0_179
<=> ! [X55,X54,X63,X62] :
( X54 = X62
| hAPP(hAPP(c_Lambda_OdB_OApp,X54),X55) != hAPP(hAPP(c_Lambda_OdB_OApp,X62),X63) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f334,axiom,
! [X54,X55,X62,X63] :
( X54 = X62
| hAPP(hAPP(c_Lambda_OdB_OApp,X54),X55) != hAPP(hAPP(c_Lambda_OdB_OApp,X62),X63) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I2_J_0) ).
fof(f1499,plain,
spl0_178,
inference(avatar_split_clause,[],[f333,f1497]) ).
fof(f1497,plain,
( spl0_178
<=> ! [X8,X58] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X58,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X58,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f333,axiom,
! [X58,X8] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X58,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X8),X58,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_IT_OVar_0) ).
fof(f1495,plain,
spl0_177,
inference(avatar_split_clause,[],[f317,f1493]) ).
fof(f1493,plain,
( spl0_177
<=> ! [X43,X3,X2,X39] :
( ~ c_Type_Otyping(X2,X3,X43)
| c_Type_Otyping(X2,X39,X43)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f317,axiom,
! [X2,X3,X39,X43] :
( ~ c_Type_Otyping(X2,X3,X43)
| c_Type_Otyping(X2,X39,X43)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X39)) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_subject__reduction_0) ).
fof(f1490,plain,
spl0_176,
inference(avatar_split_clause,[],[f304,f1488]) ).
fof(f1488,plain,
( spl0_176
<=> ! [X43,X19,X3,X2,X52] :
( ~ c_Type_Otyping(X2,X3,X43)
| c_Type_Otyping(c_Type_Oshift(X2,X19,X52,tc_Type_Otype),c_Lambda_Olift(X3,X19),X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f304,axiom,
! [X2,X3,X19,X52,X43] :
( ~ c_Type_Otyping(X2,X3,X43)
| c_Type_Otyping(c_Type_Oshift(X2,X19,X52,tc_Type_Otype),c_Lambda_Olift(X3,X19),X43) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_lift__type_0) ).
fof(f1486,plain,
spl0_175,
inference(avatar_split_clause,[],[f279,f1484]) ).
fof(f1484,plain,
( spl0_175
<=> ! [X48,X47,X50,X49] :
( X47 = X49
| hAPP(hAPP(c_Type_Otype_OFun,X47),X48) != hAPP(hAPP(c_Type_Otype_OFun,X49),X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f279,axiom,
! [X50,X48,X49,X47] :
( X47 = X49
| hAPP(hAPP(c_Type_Otype_OFun,X47),X48) != hAPP(hAPP(c_Type_Otype_OFun,X49),X50) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_type_Osimps_I2_J_0) ).
fof(f1482,plain,
spl0_174,
inference(avatar_split_clause,[],[f278,f1480]) ).
fof(f1480,plain,
( spl0_174
<=> ! [X50,X48,X47,X49] :
( X48 = X50
| hAPP(hAPP(c_Type_Otype_OFun,X47),X48) != hAPP(hAPP(c_Type_Otype_OFun,X49),X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f278,axiom,
! [X50,X48,X49,X47] :
( X48 = X50
| hAPP(hAPP(c_Type_Otype_OFun,X47),X48) != hAPP(hAPP(c_Type_Otype_OFun,X49),X50) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_type_Osimps_I2_J_1) ).
fof(f1478,plain,
spl0_173,
inference(avatar_split_clause,[],[f223,f1476]) ).
fof(f1476,plain,
( spl0_173
<=> ! [X10,X13,X0,X9] :
( ~ hBOOL(hAPP(hAPP(X13,X9),X10))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X0),X9),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f223,axiom,
! [X10,X0,X9,X13] :
( ~ hBOOL(hAPP(hAPP(X13,X9),X10))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X0),X9),X10)) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_r__into__rtranclp_0) ).
fof(f1474,plain,
spl0_172,
inference(avatar_split_clause,[],[f199,f1472]) ).
fof(f1472,plain,
( spl0_172
<=> ! [X23,X3] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X23),X3))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X23)),c_Lambda_OdB_OAbs(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f199,axiom,
! [X3,X23] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X23),X3))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X23)),c_Lambda_OdB_OAbs(X3))) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_abs_0) ).
fof(f1470,plain,
spl0_171,
inference(avatar_split_clause,[],[f144,f1468]) ).
fof(f1468,plain,
( spl0_171
<=> ! [X10,X0,X12,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X12,X10,X0)
| c_HOL_Oord__class_Oless(X12,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f144,axiom,
! [X10,X0,X9,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X12,X10,X0)
| c_HOL_Oord__class_Oless(X12,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_xt1_I10_J_0) ).
fof(f1466,plain,
spl0_170,
inference(avatar_split_clause,[],[f143,f1464]) ).
fof(f1464,plain,
( spl0_170
<=> ! [X10,X0,X12,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X12,X0)
| c_HOL_Oord__class_Oless(X9,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f143,axiom,
! [X10,X0,X9,X12] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X12,X0)
| c_HOL_Oord__class_Oless(X9,X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_order__less__trans_0) ).
fof(f1462,plain,
spl0_169,
inference(avatar_split_clause,[],[f120,f1460]) ).
fof(f1460,plain,
( spl0_169
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f120,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_of__nat__0__less__iff_1) ).
fof(f1458,plain,
spl0_168,
inference(avatar_split_clause,[],[f119,f1456]) ).
fof(f1456,plain,
( spl0_168
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f119,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_of__nat__0__less__iff_0) ).
fof(f1454,plain,
spl0_167,
inference(avatar_split_clause,[],[f117,f1452]) ).
fof(f1452,plain,
( spl0_167
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X1,X0) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X0),X1,c_HOL_Ozero__class_Ozero(X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X1,X0) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X0),X1,c_HOL_Ozero__class_Ozero(X0),X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_listsum__foldr_0) ).
fof(f1450,plain,
spl0_166,
inference(avatar_split_clause,[],[f101,f1448]) ).
fof(f1448,plain,
( spl0_166
<=> ! [X6,X0,X1] :
( c_List_Olist_ONil(X0) = X6
| c_List_Olast(c_List_Oappend(X1,X6,X0),X0) = c_List_Olast(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f101,axiom,
! [X0,X1,X6] :
( c_List_Olist_ONil(X0) = X6
| c_List_Olast(c_List_Oappend(X1,X6,X0),X0) = c_List_Olast(X6,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_last__append_1) ).
fof(f1446,plain,
spl0_165,
inference(avatar_split_clause,[],[f88,f1444]) ).
fof(f1444,plain,
( spl0_165
<=> ! [X9,X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_List_Olast(X1,X0) = c_List_Olast(c_List_Olist_OCons(X9,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f88,axiom,
! [X0,X1,X9] :
( c_List_Olist_ONil(X0) = X1
| c_List_Olast(X1,X0) = c_List_Olast(c_List_Olist_OCons(X9,X1,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_last_Osimps_1) ).
fof(f1442,plain,
spl0_164,
inference(avatar_split_clause,[],[f74,f1440]) ).
fof(f1440,plain,
( spl0_164
<=> ! [X0,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X7,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f74,axiom,
! [X0,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X7,X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_of__nat__less__iff_0) ).
fof(f1438,plain,
spl0_163,
inference(avatar_split_clause,[],[f73,f1436]) ).
fof(f1436,plain,
( spl0_163
<=> ! [X0,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f73,axiom,
! [X0,X8,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X0),c_Nat_Osemiring__1__class_Oof__nat(X8,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_of__nat__less__iff_1) ).
fof(f1434,plain,
spl0_162,
inference(avatar_split_clause,[],[f69,f1432]) ).
fof(f1432,plain,
( spl0_162
<=> ! [X13,X0,X14,X15] :
( ~ c_Wellfounded_Oaccp(X13,X14,X0)
| c_Wellfounded_Oaccp(X13,X15,X0)
| ~ hBOOL(hAPP(hAPP(X13,X15),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f69,axiom,
! [X0,X14,X15,X13] :
( ~ c_Wellfounded_Oaccp(X13,X14,X0)
| c_Wellfounded_Oaccp(X13,X15,X0)
| ~ hBOOL(hAPP(hAPP(X13,X15),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_accp__downward_0) ).
fof(f1430,plain,
spl0_161,
inference(avatar_split_clause,[],[f1,f1428]) ).
fof(f1428,plain,
( spl0_161
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X1,X0) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0),X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_List_Olistsum(X1,X0) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0),X1,X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_listsum_0) ).
fof(f1420,plain,
( spl0_160
| ~ spl0_58
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1346,f1231,f718,f1418]) ).
fof(f1418,plain,
( spl0_160
<=> ! [X2,X4,X3] : c_Lambda_Osubstn(c_Lambda_Olift(X2,X3),X4,X3) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f718,plain,
( spl0_58
<=> ! [X11,X23,X3] : c_Lambda_Osubst(c_Lambda_Olift(X3,X11),X23,X11) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1231,plain,
( spl0_149
<=> ! [X8,X3,X23] : c_Lambda_Osubstn(X3,X23,X8) = c_Lambda_Osubst(X3,c_Lambda_Oliftn(X8,X23,c_HOL_Ozero__class_Ozero(tc_nat)),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1346,plain,
( ! [X2,X3,X4] : c_Lambda_Osubstn(c_Lambda_Olift(X2,X3),X4,X3) = X2
| ~ spl0_58
| ~ spl0_149 ),
inference(superposition,[],[f1232,f719]) ).
fof(f719,plain,
( ! [X3,X11,X23] : c_Lambda_Osubst(c_Lambda_Olift(X3,X11),X23,X11) = X3
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f1232,plain,
( ! [X3,X8,X23] : c_Lambda_Osubstn(X3,X23,X8) = c_Lambda_Osubst(X3,c_Lambda_Oliftn(X8,X23,c_HOL_Ozero__class_Ozero(tc_nat)),X8)
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1231]) ).
fof(f1309,plain,
( spl0_159
| ~ spl0_9
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1023,f922,f496,f1307]) ).
fof(f1307,plain,
( spl0_159
<=> ! [X0] : c_List_Olistsum(X0,tc_nat) = c_List_Olistsum(c_List_Orev(X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f496,plain,
( spl0_9
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f922,plain,
( spl0_99
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_List_Olistsum(X1,X0) = c_List_Olistsum(c_List_Orev(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1023,plain,
( ! [X0] : c_List_Olistsum(X0,tc_nat) = c_List_Olistsum(c_List_Orev(X0,tc_nat),tc_nat)
| ~ spl0_9
| ~ spl0_99 ),
inference(resolution,[],[f923,f498]) ).
fof(f498,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f923,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_List_Olistsum(X1,X0) = c_List_Olistsum(c_List_Orev(X1,X0),X0) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f1269,plain,
spl0_158,
inference(avatar_split_clause,[],[f386,f1267]) ).
fof(f1267,plain,
( spl0_158
<=> ! [X19,X3] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X3))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X3),c_Lambda_OdB_OVar(X19)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f386,axiom,
! [X3,X19] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X3))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X3),c_Lambda_OdB_OVar(X19)))) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_app__Var__IT_0) ).
fof(f1265,plain,
spl0_157,
inference(avatar_split_clause,[],[f384,f1263]) ).
fof(f1263,plain,
( spl0_157
<=> ! [X24,X7,X23] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X24
| c_Lambda_OdB_OVar(X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X24,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f384,axiom,
! [X7,X24,X23] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X24
| c_Lambda_OdB_OVar(X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X24,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Var__eq__apps__conv_1) ).
fof(f1261,plain,
spl0_156,
inference(avatar_split_clause,[],[f376,f1259]) ).
fof(f1259,plain,
( spl0_156
<=> ! [X13,X24,X23] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X24
| c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X24,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f376,axiom,
! [X24,X23,X13] :
( c_List_Olist_ONil(tc_Lambda_OdB) = X24
| c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X24,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_apps__eq__Abs__conv_1) ).
fof(f1257,plain,
spl0_155,
inference(avatar_split_clause,[],[f373,f1255]) ).
fof(f1255,plain,
( spl0_155
<=> ! [X13,X24,X23] :
( c_Lambda_OdB_OAbs(X13) = X23
| c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X24,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f373,axiom,
! [X24,X23,X13] :
( c_Lambda_OdB_OAbs(X13) = X23
| c_Lambda_OdB_OAbs(X13) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X24,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Abs__eq__apps__conv_0) ).
fof(f1253,plain,
spl0_154,
inference(avatar_split_clause,[],[f340,f1251]) ).
fof(f1251,plain,
( spl0_154
<=> ! [X24,X23,X7] :
( c_Lambda_OdB_OVar(X7) = X23
| c_Lambda_OdB_OVar(X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X24,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f340,axiom,
! [X7,X24,X23] :
( c_Lambda_OdB_OVar(X7) = X23
| c_Lambda_OdB_OVar(X7) != c_List_Ofoldl(c_Lambda_OdB_OApp,X23,X24,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Var__eq__apps__conv_0) ).
fof(f1249,plain,
spl0_153,
inference(avatar_split_clause,[],[f256,f1247]) ).
fof(f1247,plain,
( spl0_153
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f256,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X10,X9,X0)
| c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_linorder__antisym__conv3_0) ).
fof(f1245,plain,
spl0_152,
inference(avatar_split_clause,[],[f249,f1243]) ).
fof(f1243,plain,
( spl0_152
<=> ! [X9,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f249,axiom,
! [X10,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X9 = X10
| c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(X10,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_linorder__neqE__ordered__idom_0) ).
fof(f1241,plain,
spl0_151,
inference(avatar_split_clause,[],[f193,f1239]) ).
fof(f1239,plain,
( spl0_151
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_HOL_Ozero__class_Ozero(X0)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f193,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X9),c_HOL_Ozero__class_Ozero(X0)) = X9 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f1237,plain,
spl0_150,
inference(avatar_split_clause,[],[f142,f1235]) ).
fof(f1235,plain,
( spl0_150
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f142,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_double__eq__0__iff_1) ).
fof(f1233,plain,
spl0_149,
inference(avatar_split_clause,[],[f141,f1231]) ).
fof(f141,axiom,
! [X3,X8,X23] : c_Lambda_Osubstn(X3,X23,X8) = c_Lambda_Osubst(X3,c_Lambda_Oliftn(X8,X23,c_HOL_Ozero__class_Ozero(tc_nat)),X8),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_substn__subst__n_0) ).
fof(f1229,plain,
spl0_148,
inference(avatar_split_clause,[],[f89,f1227]) ).
fof(f1227,plain,
( spl0_148
<=> ! [X9,X0] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f89,axiom,
! [X0,X9] : c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rev__singleton__conv_1) ).
fof(f1225,plain,
spl0_147,
inference(avatar_split_clause,[],[f47,f1223]) ).
fof(f1223,plain,
( spl0_147
<=> ! [X8,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f47,axiom,
! [X8,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_add__is__0_1) ).
fof(f1221,plain,
spl0_146,
inference(avatar_split_clause,[],[f46,f1219]) ).
fof(f1219,plain,
( spl0_146
<=> ! [X7,X8] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f46,axiom,
! [X8,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_add__is__0_0) ).
fof(f1217,plain,
spl0_145,
inference(avatar_split_clause,[],[f40,f1215]) ).
fof(f1215,plain,
( spl0_145
<=> ! [X7,X8] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f40,axiom,
! [X8,X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X8),X7),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_nat__add__commute_0) ).
fof(f1213,plain,
spl0_144,
inference(avatar_split_clause,[],[f39,f1211]) ).
fof(f1211,plain,
( spl0_144
<=> ! [X20,X7,X19] :
( ~ c_HOL_Oord__class_Oless(X19,X20,tc_nat)
| c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X20),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f39,axiom,
! [X19,X7,X20] :
( ~ c_HOL_Oord__class_Oless(X19,X20,tc_nat)
| c_HOL_Oord__class_Oless(X19,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X20),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_trans__less__add2_0) ).
fof(f1209,plain,
spl0_143,
inference(avatar_split_clause,[],[f37,f1207]) ).
fof(f1207,plain,
( spl0_143
<=> ! [X20,X11,X19] :
( c_HOL_Oord__class_Oless(X19,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X20),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f37,axiom,
! [X11,X19,X20] :
( c_HOL_Oord__class_Oless(X19,X11,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X20),X11,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_add__lessD1_0) ).
fof(f1205,plain,
spl0_142,
inference(avatar_split_clause,[],[f35,f1203]) ).
fof(f1203,plain,
( spl0_142
<=> ! [X9,X12,X10] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X12),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f35,axiom,
! [X10,X9,X12] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X12),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_termination__basic__simps_I1_J_0) ).
fof(f1201,plain,
( spl0_141
| ~ spl0_38
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1124,f1116,f632,f1198]) ).
fof(f1198,plain,
( spl0_141
<=> v_as____ = c_List_Obutlast(c_List_Orotate1(v_rs____,tc_Lambda_OdB),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f632,plain,
( spl0_38
<=> v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1116,plain,
( spl0_132
<=> ! [X9,X0,X1] : c_List_Obutlast(c_List_Orotate1(c_List_Olist_OCons(X9,X1,X0),X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1124,plain,
( v_as____ = c_List_Obutlast(c_List_Orotate1(v_rs____,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ spl0_38
| ~ spl0_132 ),
inference(superposition,[],[f1117,f634]) ).
fof(f634,plain,
( v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f1117,plain,
( ! [X0,X1,X9] : c_List_Obutlast(c_List_Orotate1(c_List_Olist_OCons(X9,X1,X0),X0),X0) = X1
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1152,plain,
spl0_140,
inference(avatar_split_clause,[],[f288,f1150]) ).
fof(f1150,plain,
( spl0_140
<=> ! [X42,X41,X51,X0,X15] :
( X42 = X51
| c_List_Olist_OCons(X41,X42,X0) != c_List_Olist_OCons(X15,X51,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f288,axiom,
! [X51,X41,X0,X15,X42] :
( X42 = X51
| c_List_Olist_OCons(X41,X42,X0) != c_List_Olist_OCons(X15,X51,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_list_Oinject_1) ).
fof(f1148,plain,
spl0_139,
inference(avatar_split_clause,[],[f287,f1146]) ).
fof(f1146,plain,
( spl0_139
<=> ! [X41,X51,X0,X42,X15] :
( X15 = X41
| c_List_Olist_OCons(X41,X42,X0) != c_List_Olist_OCons(X15,X51,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f287,axiom,
! [X51,X41,X0,X15,X42] :
( X15 = X41
| c_List_Olist_OCons(X41,X42,X0) != c_List_Olist_OCons(X15,X51,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_list_Oinject_0) ).
fof(f1144,plain,
spl0_138,
inference(avatar_split_clause,[],[f273,f1142]) ).
fof(f1142,plain,
( spl0_138
<=> ! [X13,X20,X19] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X13))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X13,c_Lambda_OdB_OVar(X19),X20))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f273,axiom,
! [X19,X13,X20] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X13))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(X13,c_Lambda_OdB_OVar(X19),X20))) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_subst__Var__IT_0) ).
fof(f1140,plain,
spl0_137,
inference(avatar_split_clause,[],[f269,f1138]) ).
fof(f1138,plain,
( spl0_137
<=> ! [X20,X25,X19] :
( ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat)
| c_Lambda_OdB_OVar(X20) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X20),X25,X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f269,axiom,
! [X19,X25,X20] :
( ~ c_HOL_Oord__class_Oless(X20,X19,tc_nat)
| c_Lambda_OdB_OVar(X20) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X20),X25,X19) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_subst__lt_0) ).
fof(f1136,plain,
spl0_136,
inference(avatar_split_clause,[],[f179,f1134]) ).
fof(f1134,plain,
( spl0_136
<=> ! [X11,X8,X19] :
( ~ c_HOL_Oord__class_Oless(X19,X11,tc_nat)
| c_Lambda_OdB_OVar(X19) = c_Lambda_Oliftn(X8,c_Lambda_OdB_OVar(X19),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f179,axiom,
! [X11,X8,X19] :
( ~ c_HOL_Oord__class_Oless(X19,X11,tc_nat)
| c_Lambda_OdB_OVar(X19) = c_Lambda_Oliftn(X8,c_Lambda_OdB_OVar(X19),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_liftn_Osimps_I1_J_0) ).
fof(f1132,plain,
spl0_135,
inference(avatar_split_clause,[],[f128,f1130]) ).
fof(f1130,plain,
( spl0_135
<=> ! [X0,X6,X22,X1] :
( X6 = X22
| c_List_Oappend(X6,X1,X0) != c_List_Oappend(X22,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f128,axiom,
! [X0,X1,X6,X22] :
( X6 = X22
| c_List_Oappend(X6,X1,X0) != c_List_Oappend(X22,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_append__same__eq_0) ).
fof(f1128,plain,
spl0_134,
inference(avatar_split_clause,[],[f127,f1126]) ).
fof(f1126,plain,
( spl0_134
<=> ! [X0,X6,X22,X1] :
( X6 = X22
| c_List_Oappend(X1,X6,X0) != c_List_Oappend(X1,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f127,axiom,
! [X0,X1,X6,X22] :
( X6 = X22
| c_List_Oappend(X1,X6,X0) != c_List_Oappend(X1,X22,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_same__append__eq_0) ).
fof(f1123,plain,
( spl0_133
| ~ spl0_38
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1109,f1106,f632,f1120]) ).
fof(f1120,plain,
( spl0_133
<=> v_a____ = c_List_Olast(c_List_Orotate1(v_rs____,tc_Lambda_OdB),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1106,plain,
( spl0_130
<=> ! [X9,X0,X1] : c_List_Olast(c_List_Orotate1(c_List_Olist_OCons(X9,X1,X0),X0),X0) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1109,plain,
( v_a____ = c_List_Olast(c_List_Orotate1(v_rs____,tc_Lambda_OdB),tc_Lambda_OdB)
| ~ spl0_38
| ~ spl0_130 ),
inference(superposition,[],[f1107,f634]) ).
fof(f1107,plain,
( ! [X0,X1,X9] : c_List_Olast(c_List_Orotate1(c_List_Olist_OCons(X9,X1,X0),X0),X0) = X9
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1106]) ).
fof(f1118,plain,
( spl0_132
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1114,f1111,f1116]) ).
fof(f1111,plain,
( spl0_131
<=> ! [X9,X0,X1] : c_List_Obutlast(c_List_Oappend(X1,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1114,plain,
( ! [X0,X1,X9] : c_List_Obutlast(c_List_Orotate1(c_List_Olist_OCons(X9,X1,X0),X0),X0) = X1
| ~ spl0_131 ),
inference(forward_demodulation,[],[f1112,f114]) ).
fof(f114,axiom,
! [X1,X9,X16] : c_List_Orotate1(c_List_Olist_OCons(X9,X1,X16),X16) = c_List_Oappend(X1,c_List_Olist_OCons(X9,c_List_Olist_ONil(X16),X16),X16),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rotate__simps_1) ).
fof(f1112,plain,
( ! [X0,X1,X9] : c_List_Obutlast(c_List_Oappend(X1,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) = X1
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f1113,plain,
spl0_131,
inference(avatar_split_clause,[],[f108,f1111]) ).
fof(f108,axiom,
! [X0,X1,X9] : c_List_Obutlast(c_List_Oappend(X1,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) = X1,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_butlast__snoc_0) ).
fof(f1108,plain,
( spl0_130
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1104,f1101,f1106]) ).
fof(f1101,plain,
( spl0_129
<=> ! [X9,X0,X1] : c_List_Olast(c_List_Oappend(X1,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1104,plain,
( ! [X0,X1,X9] : c_List_Olast(c_List_Orotate1(c_List_Olist_OCons(X9,X1,X0),X0),X0) = X9
| ~ spl0_129 ),
inference(forward_demodulation,[],[f1102,f114]) ).
fof(f1102,plain,
( ! [X0,X1,X9] : c_List_Olast(c_List_Oappend(X1,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) = X9
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1101]) ).
fof(f1103,plain,
spl0_129,
inference(avatar_split_clause,[],[f107,f1101]) ).
fof(f107,axiom,
! [X0,X1,X9] : c_List_Olast(c_List_Oappend(X1,c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),X0) = X9,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_last__snoc_0) ).
fof(f1099,plain,
spl0_128,
inference(avatar_split_clause,[],[f44,f1097]) ).
fof(f1097,plain,
( spl0_128
<=> ! [X8,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) != X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f44,axiom,
! [X8,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8) != X7 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_add__eq__self__zero_0) ).
fof(f1095,plain,
spl0_127,
inference(avatar_split_clause,[],[f43,f1093]) ).
fof(f1093,plain,
( spl0_127
<=> ! [X0,X8,X7] :
( ~ class_Nat_Osemiring__char__0(X0)
| X7 = X8
| c_Nat_Osemiring__1__class_Oof__nat(X7,X0) != c_Nat_Osemiring__1__class_Oof__nat(X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f43,axiom,
! [X0,X8,X7] :
( ~ class_Nat_Osemiring__char__0(X0)
| X7 = X8
| c_Nat_Osemiring__1__class_Oof__nat(X7,X0) != c_Nat_Osemiring__1__class_Oof__nat(X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_of__nat__eq__iff_0) ).
fof(f1091,plain,
spl0_126,
inference(avatar_split_clause,[],[f26,f1089]) ).
fof(f1089,plain,
( spl0_126
<=> ! [X9,X0,X10,X8,X7] :
( X7 = X8
| c_List_Oreplicate(X7,X9,X0) != c_List_Oreplicate(X8,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f26,axiom,
! [X10,X0,X8,X9,X7] :
( X7 = X8
| c_List_Oreplicate(X7,X9,X0) != c_List_Oreplicate(X8,X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_replicate__eq__replicate_0) ).
fof(f1087,plain,
spl0_125,
inference(avatar_split_clause,[],[f12,f1085]) ).
fof(f1085,plain,
( spl0_125
<=> ! [X9,X0,X8] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_List_Olast(c_List_Oreplicate(X8,X9,X0),X0) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f12,axiom,
! [X0,X8,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_List_Olast(c_List_Oreplicate(X8,X9,X0),X0) = X9 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_last__replicate_0) ).
fof(f1083,plain,
spl0_124,
inference(avatar_split_clause,[],[f2,f1081]) ).
fof(f1081,plain,
( spl0_124
<=> ! [X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f2,axiom,
! [X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X1,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_length__greater__0__conv_1) ).
fof(f1028,plain,
( spl0_123
| ~ spl0_52
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f829,f800,f691,f1026]) ).
fof(f1026,plain,
( spl0_123
<=> ! [X2,X0,X1,X3] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f691,plain,
( spl0_52
<=> ! [X61,X9] : c_Type_Otyping(X61,c_Lambda_OdB_OVar(X9),hAPP(X61,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f800,plain,
( spl0_78
<=> ! [X9,X0,X43,X2] : hAPP(c_Type_Oshift(X2,X9,X43,X0),X9) = X43 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f829,plain,
( ! [X2,X3,X0,X1] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2)
| ~ spl0_52
| ~ spl0_78 ),
inference(superposition,[],[f692,f801]) ).
fof(f801,plain,
( ! [X2,X0,X9,X43] : hAPP(c_Type_Oshift(X2,X9,X43,X0),X9) = X43
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f692,plain,
( ! [X9,X61] : c_Type_Otyping(X61,c_Lambda_OdB_OVar(X9),hAPP(X61,X9))
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f1016,plain,
spl0_122,
inference(avatar_split_clause,[],[f367,f1014]) ).
fof(f1014,plain,
( spl0_122
<=> ! [X31,X53,X0,X30,X29] : hAPP(X29,X53) = c_Lambda_OdB_OdB__case(X29,X30,X31,c_Lambda_OdB_OVar(X53),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f367,axiom,
! [X31,X29,X0,X53,X30] : hAPP(X29,X53) = c_Lambda_OdB_OdB__case(X29,X30,X31,c_Lambda_OdB_OVar(X53),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I10_J_0) ).
fof(f1012,plain,
spl0_121,
inference(avatar_split_clause,[],[f342,f1010]) ).
fof(f1010,plain,
( spl0_121
<=> ! [X31,X53,X0,X30,X29] : hAPP(X29,X53) = c_Lambda_OdB_OdB__rec(X29,X30,X31,c_Lambda_OdB_OVar(X53),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f342,axiom,
! [X31,X29,X0,X53,X30] : hAPP(X29,X53) = c_Lambda_OdB_OdB__rec(X29,X30,X31,c_Lambda_OdB_OVar(X53),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Orecs_I1_J_0) ).
fof(f1008,plain,
spl0_120,
inference(avatar_split_clause,[],[f267,f1006]) ).
fof(f1006,plain,
( spl0_120
<=> ! [X23,X3] : c_Lambda_Osubstn(X3,X23,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X3,X23,c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f267,axiom,
! [X3,X23] : c_Lambda_Osubstn(X3,X23,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(X3,X23,c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_substn__subst__0_0) ).
fof(f1004,plain,
spl0_119,
inference(avatar_split_clause,[],[f253,f1002]) ).
fof(f1002,plain,
( spl0_119
<=> ! [X9,X10] :
( X9 = X10
| c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f253,axiom,
! [X10,X9] :
( X9 = X10
| c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X10,X9,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_linorder__neqE__nat_0) ).
fof(f1000,plain,
( spl0_118
| ~ spl0_52
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f808,f748,f691,f998]) ).
fof(f998,plain,
( spl0_118
<=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f748,plain,
( spl0_65
<=> ! [X8] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f808,plain,
( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_OdB_OVar(X0),X0)
| ~ spl0_52
| ~ spl0_65 ),
inference(superposition,[],[f692,f749]) ).
fof(f749,plain,
( ! [X8] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X8) = X8
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f996,plain,
spl0_117,
inference(avatar_split_clause,[],[f235,f994]) ).
fof(f994,plain,
( spl0_117
<=> ! [X6,X0,X1] :
( c_List_Olist_ONil(X0) = X6
| c_List_Olist_ONil(X0) != c_List_Oappend(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f235,axiom,
! [X0,X1,X6] :
( c_List_Olist_ONil(X0) = X6
| c_List_Olist_ONil(X0) != c_List_Oappend(X1,X6,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Nil__is__append__conv_1) ).
fof(f992,plain,
spl0_116,
inference(avatar_split_clause,[],[f234,f990]) ).
fof(f990,plain,
( spl0_116
<=> ! [X6,X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_List_Olist_ONil(X0) != c_List_Oappend(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f234,axiom,
! [X0,X1,X6] :
( c_List_Olist_ONil(X0) = X1
| c_List_Olist_ONil(X0) != c_List_Oappend(X1,X6,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Nil__is__append__conv_0) ).
fof(f988,plain,
spl0_115,
inference(avatar_split_clause,[],[f201,f986]) ).
fof(f986,plain,
( spl0_115
<=> ! [X15,X44,X0,X45] :
( ~ c_OrderedGroup_Omonoid__add(X45,X44,X0)
| hAPP(hAPP(X44,X45),X15) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f201,axiom,
! [X0,X44,X45,X15] :
( ~ c_OrderedGroup_Omonoid__add(X45,X44,X0)
| hAPP(hAPP(X44,X45),X15) = X15 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_monoid__add_Oadd__0__left_0) ).
fof(f984,plain,
spl0_114,
inference(avatar_split_clause,[],[f200,f982]) ).
fof(f982,plain,
( spl0_114
<=> ! [X15,X44,X0,X45] :
( ~ c_OrderedGroup_Omonoid__add(X45,X44,X0)
| hAPP(hAPP(X44,X15),X45) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f200,axiom,
! [X0,X44,X45,X15] :
( ~ c_OrderedGroup_Omonoid__add(X45,X44,X0)
| hAPP(hAPP(X44,X15),X45) = X15 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_monoid__add_Oadd__0__right_0) ).
fof(f980,plain,
spl0_113,
inference(avatar_split_clause,[],[f198,f978]) ).
fof(f978,plain,
( spl0_113
<=> ! [X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X15) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f198,axiom,
! [X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X15) = X15 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f976,plain,
spl0_112,
inference(avatar_split_clause,[],[f197,f974]) ).
fof(f974,plain,
( spl0_112
<=> ! [X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),c_HOL_Ozero__class_Ozero(X0)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f197,axiom,
! [X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),c_HOL_Ozero__class_Ozero(X0)) = X15 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f972,plain,
spl0_111,
inference(avatar_split_clause,[],[f196,f970]) ).
fof(f970,plain,
( spl0_111
<=> ! [X0,X15] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),c_HOL_Ozero__class_Ozero(X0)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f196,axiom,
! [X0,X15] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),c_HOL_Ozero__class_Ozero(X0)) = X15 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f968,plain,
spl0_110,
inference(avatar_split_clause,[],[f195,f966]) ).
fof(f966,plain,
( spl0_110
<=> ! [X0,X15] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X15) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f195,axiom,
! [X0,X15] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X15) = X15 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_add__0__left_0) ).
fof(f964,plain,
spl0_109,
inference(avatar_split_clause,[],[f194,f962]) ).
fof(f962,plain,
( spl0_109
<=> ! [X0,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),c_HOL_Ozero__class_Ozero(X0)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f194,axiom,
! [X0,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X15),c_HOL_Ozero__class_Ozero(X0)) = X15 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f960,plain,
spl0_108,
inference(avatar_split_clause,[],[f192,f958]) ).
fof(f958,plain,
( spl0_108
<=> ! [X0,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X15) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f192,axiom,
! [X0,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X15) = X15 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_comm__monoid__add_Omult__1_0) ).
fof(f956,plain,
( spl0_107
| ~ spl0_52
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f807,f744,f691,f954]) ).
fof(f954,plain,
( spl0_107
<=> ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f744,plain,
( spl0_64
<=> ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f807,plain,
( ! [X0] : c_Type_Otyping(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
| ~ spl0_52
| ~ spl0_64 ),
inference(superposition,[],[f692,f745]) ).
fof(f745,plain,
( ! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X7
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f952,plain,
spl0_106,
inference(avatar_split_clause,[],[f182,f950]) ).
fof(f950,plain,
( spl0_106
<=> ! [X11,X19] :
( ~ c_HOL_Oord__class_Oless(X19,X11,tc_nat)
| c_Lambda_OdB_OVar(X19) = c_Lambda_Olift(c_Lambda_OdB_OVar(X19),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f182,axiom,
! [X11,X19] :
( ~ c_HOL_Oord__class_Oless(X19,X11,tc_nat)
| c_Lambda_OdB_OVar(X19) = c_Lambda_Olift(c_Lambda_OdB_OVar(X19),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_lift_Osimps_I1_J_0) ).
fof(f948,plain,
spl0_105,
inference(avatar_split_clause,[],[f135,f946]) ).
fof(f946,plain,
( spl0_105
<=> ! [X28,X0,X6,X1] :
( c_List_Olistsp(X28,X1,X0)
| ~ c_List_Olistsp(X28,c_List_Oappend(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f135,axiom,
! [X28,X0,X1,X6] :
( c_List_Olistsp(X28,X1,X0)
| ~ c_List_Olistsp(X28,c_List_Oappend(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_append__in__listsp__conv_0) ).
fof(f944,plain,
spl0_104,
inference(avatar_split_clause,[],[f134,f942]) ).
fof(f942,plain,
( spl0_104
<=> ! [X0,X6,X28,X1] :
( c_List_Olistsp(X28,X6,X0)
| ~ c_List_Olistsp(X28,c_List_Oappend(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f134,axiom,
! [X28,X0,X1,X6] :
( c_List_Olistsp(X28,X6,X0)
| ~ c_List_Olistsp(X28,c_List_Oappend(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_append__in__listsp__conv_1) ).
fof(f940,plain,
spl0_103,
inference(avatar_split_clause,[],[f133,f938]) ).
fof(f938,plain,
( spl0_103
<=> ! [X31,X29,X0,X30,X32] : c_Lambda_OdB_OdB__case(X29,X30,X31,c_Lambda_OdB_OAbs(X32),X0) = hAPP(X31,X32) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f133,axiom,
! [X31,X29,X0,X32,X30] : c_Lambda_OdB_OdB__case(X29,X30,X31,c_Lambda_OdB_OAbs(X32),X0) = hAPP(X31,X32),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I12_J_0) ).
fof(f936,plain,
spl0_102,
inference(avatar_split_clause,[],[f85,f934]) ).
fof(f934,plain,
( spl0_102
<=> ! [X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X1,tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f85,axiom,
! [X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X1,tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_length__0__conv_0) ).
fof(f932,plain,
spl0_101,
inference(avatar_split_clause,[],[f84,f930]) ).
fof(f930,plain,
( spl0_101
<=> ! [X9,X0,X8] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X8,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f84,axiom,
! [X0,X8,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X8,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_empty__replicate_0) ).
fof(f928,plain,
spl0_100,
inference(avatar_split_clause,[],[f66,f926]) ).
fof(f926,plain,
( spl0_100
<=> ! [X0,X1] : c_Nat_Osize__class_Osize(X1,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orev(X1,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f66,axiom,
! [X0,X1] : c_Nat_Osize__class_Osize(X1,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orev(X1,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_length__rev_0) ).
fof(f924,plain,
spl0_99,
inference(avatar_split_clause,[],[f55,f922]) ).
fof(f55,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_List_Olistsum(X1,X0) = c_List_Olistsum(c_List_Orev(X1,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_listsum__rev_0) ).
fof(f920,plain,
spl0_98,
inference(avatar_split_clause,[],[f49,f918]) ).
fof(f918,plain,
( spl0_98
<=> ! [X0,X1] : c_Nat_Osize__class_Osize(X1,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate1(X1,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f49,axiom,
! [X0,X1] : c_Nat_Osize__class_Osize(X1,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate1(X1,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_length__rotate1_0) ).
fof(f916,plain,
spl0_97,
inference(avatar_split_clause,[],[f42,f914]) ).
fof(f914,plain,
( spl0_97
<=> ! [X9,X0,X8] : c_List_Oreplicate(X8,X9,X0) = c_List_Orev(c_List_Oreplicate(X8,X9,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f42,axiom,
! [X0,X8,X9] : c_List_Oreplicate(X8,X9,X0) = c_List_Orev(c_List_Oreplicate(X8,X9,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rev__replicate_0) ).
fof(f912,plain,
spl0_96,
inference(avatar_split_clause,[],[f30,f910]) ).
fof(f910,plain,
( spl0_96
<=> ! [X13] :
( hBOOL(hAPP(c_InductTermi_OIT,X13))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X13,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f30,axiom,
! [X13] :
( hBOOL(hAPP(c_InductTermi_OIT,X13))
| ~ c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X13,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_termi__implies__IT_0) ).
fof(f908,plain,
spl0_95,
inference(avatar_split_clause,[],[f29,f906]) ).
fof(f906,plain,
( spl0_95
<=> ! [X3] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X3))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X3,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f29,axiom,
! [X3] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X3))
| c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),X3,tc_Lambda_OdB) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_IT__implies__termi_0) ).
fof(f886,plain,
spl0_94,
inference(avatar_split_clause,[],[f418,f884]) ).
fof(f884,plain,
( spl0_94
<=> ! [X0,X72,X71] :
( X71 = X72
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X71),X72)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f418,axiom,
! [X72,X0,X71] :
( X71 = X72
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X71),X72)) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f882,plain,
spl0_93,
inference(avatar_split_clause,[],[f375,f880]) ).
fof(f880,plain,
( spl0_93
<=> ! [X3] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X3),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f375,axiom,
! [X3] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(X3),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(X3),tc_Lambda_OdB,tc_Lambda_OdB) = X3,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_ex__head__tail_0) ).
fof(f878,plain,
spl0_92,
inference(avatar_split_clause,[],[f353,f876]) ).
fof(f876,plain,
( spl0_92
<=> ! [X2,X43,X19] :
( ~ c_Type_Otyping(X2,c_Lambda_OdB_OVar(X19),X43)
| hAPP(X2,X19) = X43 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f353,axiom,
! [X2,X19,X43] :
( ~ c_Type_Otyping(X2,c_Lambda_OdB_OVar(X19),X43)
| hAPP(X2,X19) = X43 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_typing__elims_I1_J_0) ).
fof(f874,plain,
spl0_91,
inference(avatar_split_clause,[],[f302,f872]) ).
fof(f872,plain,
( spl0_91
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f302,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_order__less__asym_0) ).
fof(f870,plain,
spl0_90,
inference(avatar_split_clause,[],[f301,f868]) ).
fof(f868,plain,
( spl0_90
<=> ! [X9,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f301,axiom,
! [X10,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_not__less__iff__gr__or__eq_1) ).
fof(f866,plain,
( spl0_89
| ~ spl0_12
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f816,f776,f511,f863]) ).
fof(f863,plain,
( spl0_89
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f511,plain,
( spl0_12
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f776,plain,
( spl0_72
<=> ! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f816,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat)
| ~ spl0_12
| ~ spl0_72 ),
inference(resolution,[],[f777,f513]) ).
fof(f513,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f777,plain,
( ! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f861,plain,
spl0_88,
inference(avatar_split_clause,[],[f298,f859]) ).
fof(f859,plain,
( spl0_88
<=> ! [X0,X14,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X15,X0)
| ~ c_HOL_Oord__class_Oless(X15,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f298,axiom,
! [X0,X14,X15] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X14,X15,X0)
| ~ c_HOL_Oord__class_Oless(X15,X14,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_xt1_I9_J_0) ).
fof(f857,plain,
spl0_87,
inference(avatar_split_clause,[],[f276,f855]) ).
fof(f855,plain,
( spl0_87
<=> ! [X6,X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_List_Oappend(X1,X6,X0) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f276,axiom,
! [X0,X1,X6] :
( c_List_Olist_ONil(X0) = X1
| c_List_Oappend(X1,X6,X0) != X6 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_append__self__conv2_0) ).
fof(f853,plain,
spl0_86,
inference(avatar_split_clause,[],[f274,f851]) ).
fof(f851,plain,
( spl0_86
<=> ! [X6,X0,X1] :
( c_List_Olist_ONil(X0) = X6
| c_List_Oappend(X1,X6,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f274,axiom,
! [X0,X1,X6] :
( c_List_Olist_ONil(X0) = X6
| c_List_Oappend(X1,X6,X0) != X1 ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_append__self__conv_0) ).
fof(f849,plain,
spl0_85,
inference(avatar_split_clause,[],[f233,f847]) ).
fof(f847,plain,
( spl0_85
<=> ! [X19,X3] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X3))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X3,X19))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f233,axiom,
! [X3,X19] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X3))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Olift(X3,X19))) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_lift__IT_0) ).
fof(f845,plain,
spl0_84,
inference(avatar_split_clause,[],[f92,f843]) ).
fof(f843,plain,
( spl0_84
<=> ! [X9,X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f92,axiom,
! [X0,X9] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_butlast_Osimps_I2_J_0) ).
fof(f841,plain,
spl0_83,
inference(avatar_split_clause,[],[f54,f839]) ).
fof(f839,plain,
( spl0_83
<=> ! [X6,X0,X1] :
( X1 = X6
| c_List_Orev(X6,X0) != c_List_Orev(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f54,axiom,
! [X0,X1,X6] :
( X1 = X6
| c_List_Orev(X6,X0) != c_List_Orev(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rev__is__rev__conv_0) ).
fof(f837,plain,
spl0_82,
inference(avatar_split_clause,[],[f31,f835]) ).
fof(f835,plain,
( spl0_82
<=> ! [X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_List_Olist_ONil(X0) != c_List_Orotate1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f31,axiom,
! [X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_List_Olist_ONil(X0) != c_List_Orotate1(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rotate1__is__Nil__conv_0) ).
fof(f833,plain,
spl0_81,
inference(avatar_split_clause,[],[f10,f831]) ).
fof(f831,plain,
( spl0_81
<=> ! [X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_List_Olist_ONil(X0) != c_List_Orev(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f10,axiom,
! [X0,X1] :
( c_List_Olist_ONil(X0) = X1
| c_List_Olist_ONil(X0) != c_List_Orev(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rev__is__Nil__conv_0) ).
fof(f828,plain,
( spl0_80
| ~ spl0_11
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f815,f772,f506,f825]) ).
fof(f825,plain,
( spl0_80
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f506,plain,
( spl0_11
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f772,plain,
( spl0_71
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f815,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_11
| ~ spl0_71 ),
inference(resolution,[],[f773,f508]) ).
fof(f508,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f773,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f806,plain,
spl0_79,
inference(avatar_split_clause,[],[f348,f804]) ).
fof(f804,plain,
( spl0_79
<=> ! [X38,X16,X0,X15] : c_List_Ofoldl(X38,X15,c_List_Olist_ONil(X16),X0,X16) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f348,axiom,
! [X38,X0,X16,X15] : c_List_Ofoldl(X38,X15,c_List_Olist_ONil(X16),X0,X16) = X15,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_foldl__Nil_0) ).
fof(f802,plain,
spl0_78,
inference(avatar_split_clause,[],[f347,f800]) ).
fof(f347,axiom,
! [X2,X0,X9,X43] : hAPP(c_Type_Oshift(X2,X9,X43,X0),X9) = X43,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_shift__eq_0) ).
fof(f798,plain,
spl0_77,
inference(avatar_split_clause,[],[f261,f796]) ).
fof(f796,plain,
( spl0_77
<=> ! [X8] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f261,axiom,
! [X8] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_gr0I_0) ).
fof(f794,plain,
spl0_76,
inference(avatar_split_clause,[],[f190,f792]) ).
fof(f792,plain,
( spl0_76
<=> ! [X13,X0] : c_Transitive__Closure_Ortranclp(X13,X0) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f190,axiom,
! [X0,X13] : c_Transitive__Closure_Ortranclp(X13,X0) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X13,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rtranclp__idemp_0) ).
fof(f790,plain,
spl0_75,
inference(avatar_split_clause,[],[f175,f788]) ).
fof(f788,plain,
( spl0_75
<=> ! [X13] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X13))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f175,axiom,
! [X13] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X13))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X13))) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Lambda_0) ).
fof(f786,plain,
spl0_74,
inference(avatar_split_clause,[],[f158,f784]) ).
fof(f784,plain,
( spl0_74
<=> ! [X38,X0,X16,X15] : c_List_Ofoldr(X38,c_List_Olist_ONil(X16),X15,X16,X0) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f158,axiom,
! [X38,X0,X16,X15] : c_List_Ofoldr(X38,c_List_Olist_ONil(X16),X15,X16,X0) = X15,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_foldr_Osimps_I1_J_0) ).
fof(f782,plain,
spl0_73,
inference(avatar_split_clause,[],[f93,f780]) ).
fof(f780,plain,
( spl0_73
<=> ! [X9,X0] : c_List_Olast(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f93,axiom,
! [X0,X9] : c_List_Olast(c_List_Olist_OCons(X9,c_List_Olist_ONil(X0),X0),X0) = X9,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_last_Osimps_0) ).
fof(f778,plain,
spl0_72,
inference(avatar_split_clause,[],[f75,f776]) ).
fof(f75,axiom,
! [X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_List_Olistsum(c_List_Olist_ONil(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_listsum_Osimps_I1_J_0) ).
fof(f774,plain,
spl0_71,
inference(avatar_split_clause,[],[f72,f772]) ).
fof(f72,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_of__nat__0_0) ).
fof(f770,plain,
spl0_70,
inference(avatar_split_clause,[],[f71,f768]) ).
fof(f768,plain,
( spl0_70
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f71,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X7,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_of__nat__less__0__iff_0) ).
fof(f766,plain,
spl0_69,
inference(avatar_split_clause,[],[f60,f764]) ).
fof(f764,plain,
( spl0_69
<=> ! [X20,X19] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f60,axiom,
! [X19,X20] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X20),X19),X19,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_not__add__less2_0) ).
fof(f762,plain,
spl0_68,
inference(avatar_split_clause,[],[f59,f760]) ).
fof(f760,plain,
( spl0_68
<=> ! [X20,X19] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X20),X19,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f59,axiom,
! [X19,X20] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X19),X20),X19,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_not__add__less1_0) ).
fof(f758,plain,
spl0_67,
inference(avatar_split_clause,[],[f58,f756]) ).
fof(f756,plain,
( spl0_67
<=> ! [X13,X0,X16] : c_Predicate_Oconversep(c_Predicate_Oconversep(X13,X0,X16),X16,X0) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f58,axiom,
! [X0,X16,X13] : c_Predicate_Oconversep(c_Predicate_Oconversep(X13,X0,X16),X16,X0) = X13,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_conversep__conversep_0) ).
fof(f754,plain,
spl0_66,
inference(avatar_split_clause,[],[f56,f752]) ).
fof(f752,plain,
( spl0_66
<=> ! [X9,X0,X8] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X8,X9,X0),tc_List_Olist(X0)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f56,axiom,
! [X0,X8,X9] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X8,X9,X0),tc_List_Olist(X0)) = X8,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_length__replicate_0) ).
fof(f750,plain,
spl0_65,
inference(avatar_split_clause,[],[f7,f748]) ).
fof(f7,axiom,
! [X8] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X8) = X8,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_plus__nat_Oadd__0_0) ).
fof(f746,plain,
spl0_64,
inference(avatar_split_clause,[],[f6,f744]) ).
fof(f6,axiom,
! [X7] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),c_HOL_Ozero__class_Ozero(tc_nat)) = X7,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Nat_Oadd__0__right_0) ).
fof(f740,plain,
spl0_63,
inference(avatar_split_clause,[],[f393,f738]) ).
fof(f738,plain,
( spl0_63
<=> ! [X53,X62,X63] : c_Lambda_OdB_OVar(X53) != hAPP(hAPP(c_Lambda_OdB_OApp,X62),X63) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f393,axiom,
! [X62,X63,X53] : c_Lambda_OdB_OVar(X53) != hAPP(hAPP(c_Lambda_OdB_OApp,X62),X63),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I5_J_0) ).
fof(f736,plain,
spl0_62,
inference(avatar_split_clause,[],[f316,f734]) ).
fof(f734,plain,
( spl0_62
<=> ! [X54,X55,X46] : c_Lambda_OdB_OAbs(X46) != hAPP(hAPP(c_Lambda_OdB_OApp,X54),X55) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f316,axiom,
! [X46,X54,X55] : c_Lambda_OdB_OAbs(X46) != hAPP(hAPP(c_Lambda_OdB_OApp,X54),X55),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I9_J_0) ).
fof(f732,plain,
spl0_61,
inference(avatar_split_clause,[],[f313,f730]) ).
fof(f730,plain,
( spl0_61
<=> ! [X53,X56] :
( X53 = X56
| c_Lambda_OdB_OVar(X53) != c_Lambda_OdB_OVar(X56) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f313,axiom,
! [X56,X53] :
( X53 = X56
| c_Lambda_OdB_OVar(X53) != c_Lambda_OdB_OVar(X56) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I1_J_0) ).
fof(f728,plain,
spl0_60,
inference(avatar_split_clause,[],[f236,f726]) ).
fof(f726,plain,
( spl0_60
<=> ! [X32,X46] :
( X32 = X46
| c_Lambda_OdB_OAbs(X32) != c_Lambda_OdB_OAbs(X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f236,axiom,
! [X46,X32] :
( X32 = X46
| c_Lambda_OdB_OAbs(X32) != c_Lambda_OdB_OAbs(X46) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I3_J_0) ).
fof(f724,plain,
spl0_59,
inference(avatar_split_clause,[],[f204,f722]) ).
fof(f722,plain,
( spl0_59
<=> ! [X13,X0,X15] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X0),X15),X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f204,axiom,
! [X0,X15,X13] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X13,X0),X15),X15)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rtranclp_Ortrancl__refl_0) ).
fof(f720,plain,
spl0_58,
inference(avatar_split_clause,[],[f181,f718]) ).
fof(f181,axiom,
! [X3,X11,X23] : c_Lambda_Osubst(c_Lambda_Olift(X3,X11),X23,X11) = X3,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_subst__lift_0) ).
fof(f716,plain,
spl0_57,
inference(avatar_split_clause,[],[f82,f714]) ).
fof(f714,plain,
( spl0_57
<=> ! [X9,X0] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f82,axiom,
! [X0,X9] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X9,X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_empty__replicate_1) ).
fof(f712,plain,
spl0_56,
inference(avatar_split_clause,[],[f81,f710]) ).
fof(f710,plain,
( spl0_56
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f81,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_length__0__conv_1) ).
fof(f708,plain,
spl0_55,
inference(avatar_split_clause,[],[f48,f706]) ).
fof(f706,plain,
( spl0_55
<=> ! [X0] : c_fequal(X0) = c_Predicate_Oconversep(c_fequal(X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f48,axiom,
! [X0] : c_fequal(X0) = c_Predicate_Oconversep(c_fequal(X0),X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_conversep__eq_0) ).
fof(f704,plain,
( ~ spl0_54
| ~ spl0_38
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f699,f675,f632,f701]) ).
fof(f701,plain,
( spl0_54
<=> c_List_Olist_ONil(tc_Lambda_OdB) = v_rs____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f675,plain,
( spl0_48
<=> ! [X41,X0,X42] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X41,X42,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f699,plain,
( c_List_Olist_ONil(tc_Lambda_OdB) != v_rs____
| ~ spl0_38
| ~ spl0_48 ),
inference(superposition,[],[f676,f634]) ).
fof(f676,plain,
( ! [X41,X0,X42] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X41,X42,X0)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f697,plain,
spl0_53,
inference(avatar_split_clause,[],[f417,f695]) ).
fof(f695,plain,
( spl0_53
<=> ! [X9,X0] : hBOOL(hAPP(hAPP(c_fequal(X0),X9),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f417,axiom,
! [X0,X9] : hBOOL(hAPP(hAPP(c_fequal(X0),X9),X9)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f693,plain,
spl0_52,
inference(avatar_split_clause,[],[f372,f691]) ).
fof(f372,axiom,
! [X9,X61] : c_Type_Otyping(X61,c_Lambda_OdB_OVar(X9),hAPP(X61,X9)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_typing_OVar_0) ).
fof(f689,plain,
spl0_51,
inference(avatar_split_clause,[],[f328,f687]) ).
fof(f687,plain,
( spl0_51
<=> ! [X19,X3] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X19)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f328,axiom,
! [X3,X19] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X19)),X3)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_beta__cases_I1_J_0) ).
fof(f685,plain,
spl0_50,
inference(avatar_split_clause,[],[f320,f683]) ).
fof(f683,plain,
( spl0_50
<=> ! [X25,X11] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X25,X11) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f320,axiom,
! [X11,X25] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X25,X11) = X25,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_subst__eq_0) ).
fof(f681,plain,
spl0_49,
inference(avatar_split_clause,[],[f264,f679]) ).
fof(f679,plain,
( spl0_49
<=> ! [X11,X3] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X3,X11) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f264,axiom,
! [X3,X11] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X3,X11) = X3,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_liftn__0_0) ).
fof(f677,plain,
spl0_48,
inference(avatar_split_clause,[],[f258,f675]) ).
fof(f258,axiom,
! [X41,X0,X42] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X41,X42,X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_list_Osimps_I2_J_0) ).
fof(f673,plain,
spl0_47,
inference(avatar_split_clause,[],[f210,f671]) ).
fof(f671,plain,
( spl0_47
<=> ! [X6,X0] : c_List_Oappend(c_List_Olist_ONil(X0),X6,X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f210,axiom,
! [X0,X6] : c_List_Oappend(c_List_Olist_ONil(X0),X6,X0) = X6,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_append__Nil_0) ).
fof(f669,plain,
spl0_46,
inference(avatar_split_clause,[],[f207,f667]) ).
fof(f667,plain,
( spl0_46
<=> ! [X0,X1] : c_List_Oappend(X1,c_List_Olist_ONil(X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f207,axiom,
! [X0,X1] : c_List_Oappend(X1,c_List_Olist_ONil(X0),X0) = X1,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_append__Nil2_0) ).
fof(f665,plain,
spl0_45,
inference(avatar_split_clause,[],[f64,f663]) ).
fof(f663,plain,
( spl0_45
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f64,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_butlast_Osimps_I1_J_0) ).
fof(f661,plain,
spl0_44,
inference(avatar_split_clause,[],[f34,f659]) ).
fof(f659,plain,
( spl0_44
<=> ! [X0,X1] : c_List_Orev(c_List_Orev(X1,X0),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f34,axiom,
! [X0,X1] : c_List_Orev(c_List_Orev(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rev__rev__ident_0) ).
fof(f657,plain,
spl0_43,
inference(avatar_split_clause,[],[f25,f655]) ).
fof(f655,plain,
( spl0_43
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Orotate1(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f25,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Orotate1(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rotate__simps_0) ).
fof(f653,plain,
spl0_42,
inference(avatar_split_clause,[],[f5,f651]) ).
fof(f651,plain,
( spl0_42
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f5,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_rev__is__Nil__conv_1) ).
fof(f649,plain,
( ~ spl0_41
| ~ spl0_31
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f644,f632,f604,f646]) ).
fof(f646,plain,
( spl0_41
<=> v_rs____ = v_as____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f604,plain,
( spl0_31
<=> ! [X9,X0,X3] : c_List_Olist_OCons(X9,X3,X0) != X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f644,plain,
( v_rs____ != v_as____
| ~ spl0_31
| ~ spl0_38 ),
inference(superposition,[],[f605,f634]) ).
fof(f605,plain,
( ! [X3,X0,X9] : c_List_Olist_OCons(X9,X3,X0) != X3
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f643,plain,
spl0_40,
inference(avatar_split_clause,[],[f398,f641]) ).
fof(f641,plain,
( spl0_40
<=> ! [X70,X69] :
( ~ class_Orderings_Oorder(X70)
| class_Orderings_Oorder(tc_fun(X69,X70)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f398,axiom,
! [X70,X69] :
( ~ class_Orderings_Oorder(X70)
| class_Orderings_Oorder(tc_fun(X69,X70)) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_fun__Orderings_Oorder) ).
fof(f639,plain,
spl0_39,
inference(avatar_split_clause,[],[f397,f637]) ).
fof(f637,plain,
( spl0_39
<=> ! [X70,X69] :
( ~ class_Orderings_Opreorder(X70)
| class_Orderings_Opreorder(tc_fun(X69,X70)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f397,axiom,
! [X70,X69] :
( ~ class_Orderings_Opreorder(X70)
| class_Orderings_Opreorder(tc_fun(X69,X70)) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_fun__Orderings_Opreorder) ).
fof(f635,plain,
spl0_38,
inference(avatar_split_clause,[],[f382,f632]) ).
fof(f382,axiom,
v_rs____ = c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Cons_0) ).
fof(f630,plain,
spl0_37,
inference(avatar_split_clause,[],[f266,f628]) ).
fof(f628,plain,
( spl0_37
<=> ! [X0] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f266,axiom,
! [X0] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_semigroup__add__class_Oaxioms_0) ).
fof(f626,plain,
spl0_36,
inference(avatar_split_clause,[],[f243,f624]) ).
fof(f624,plain,
( spl0_36
<=> ! [X9,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f243,axiom,
! [X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_order__less__irrefl_0) ).
fof(f622,plain,
spl0_35,
inference(avatar_split_clause,[],[f242,f620]) ).
fof(f620,plain,
( spl0_35
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f242,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_linorder__neq__iff_1) ).
fof(f618,plain,
spl0_34,
inference(avatar_split_clause,[],[f241,f616]) ).
fof(f616,plain,
( spl0_34
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f241,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_order__less__le_1) ).
fof(f614,plain,
spl0_33,
inference(avatar_split_clause,[],[f225,f612]) ).
fof(f612,plain,
( spl0_33
<=> ! [X13,X0,X1] : ~ c_ListOrder_Ostep1(X13,X1,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f225,axiom,
! [X0,X1,X13] : ~ c_ListOrder_Ostep1(X13,X1,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_not__step1__Nil_0) ).
fof(f610,plain,
spl0_32,
inference(avatar_split_clause,[],[f224,f608]) ).
fof(f608,plain,
( spl0_32
<=> ! [X13,X0,X1] : ~ c_ListOrder_Ostep1(X13,c_List_Olist_ONil(X0),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f224,axiom,
! [X0,X1,X13] : ~ c_ListOrder_Ostep1(X13,c_List_Olist_ONil(X0),X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_not__Nil__step1_0) ).
fof(f606,plain,
spl0_31,
inference(avatar_split_clause,[],[f184,f604]) ).
fof(f184,axiom,
! [X3,X0,X9] : c_List_Olist_OCons(X9,X3,X0) != X3,
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_not__Cons__self2_0) ).
fof(f602,plain,
spl0_30,
inference(avatar_split_clause,[],[f352,f600]) ).
fof(f600,plain,
( spl0_30
<=> ! [X8] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f352,axiom,
! [X8] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X8))),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Var__IT_0) ).
fof(f598,plain,
spl0_29,
inference(avatar_split_clause,[],[f351,f596]) ).
fof(f596,plain,
( spl0_29
<=> ! [X53,X46] : c_Lambda_OdB_OAbs(X46) != c_Lambda_OdB_OVar(X53) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f351,axiom,
! [X46,X53] : c_Lambda_OdB_OAbs(X46) != c_Lambda_OdB_OVar(X53),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_dB_Osimps_I6_J_0) ).
fof(f594,plain,
spl0_28,
inference(avatar_split_clause,[],[f154,f592]) ).
fof(f592,plain,
( spl0_28
<=> ! [X7] : ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f154,axiom,
! [X7] : ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_gr__implies__not0_0) ).
fof(f590,plain,
spl0_27,
inference(avatar_split_clause,[],[f129,f588]) ).
fof(f588,plain,
( spl0_27
<=> ! [X0,X28] : c_List_Olistsp(X28,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f129,axiom,
! [X28,X0] : c_List_Olistsp(X28,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_listsp_ONil_0) ).
fof(f586,plain,
( ~ spl0_26
| ~ spl0_19
| spl0_25 ),
inference(avatar_split_clause,[],[f581,f575,f546,f583]) ).
fof(f546,plain,
( spl0_19
<=> v_n____ = v_i____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f575,plain,
( spl0_25
<=> c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f581,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ spl0_19
| spl0_25 ),
inference(forward_demodulation,[],[f580,f548]) ).
fof(f548,plain,
( v_n____ = v_i____
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f580,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| spl0_25 ),
inference(forward_demodulation,[],[f579,f382]) ).
fof(f579,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| spl0_25 ),
inference(forward_demodulation,[],[f577,f369]) ).
fof(f369,axiom,
! [X38,X0,X1,X9,X16,X15] : c_List_Ofoldl(X38,X15,c_List_Olist_OCons(X9,X1,X16),X0,X16) = c_List_Ofoldl(X38,hAPP(hAPP(X38,X15),X9),X1,X0,X16),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_foldl__Cons_0) ).
fof(f577,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| spl0_25 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f578,plain,
~ spl0_25,
inference(avatar_split_clause,[],[f396,f575]) ).
fof(f396,axiom,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_conjecture_0) ).
fof(f573,plain,
spl0_24,
inference(avatar_split_clause,[],[f358,f570]) ).
fof(f570,plain,
( spl0_24
<=> c_Type_Otyping(v_ea______,v_ua______,v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f358,axiom,
c_Type_Otyping(v_ea______,v_ua______,v_T____),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Var_I4_J_0) ).
fof(f568,plain,
spl0_23,
inference(avatar_split_clause,[],[f307,f565]) ).
fof(f565,plain,
( spl0_23
<=> c_Type_Otyping(v_e____,v_u____,v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f307,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_uT_0) ).
fof(f563,plain,
spl0_22,
inference(avatar_split_clause,[],[f239,f561]) ).
fof(f561,plain,
( spl0_22
<=> ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f239,axiom,
! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_nat__less__le_1) ).
fof(f559,plain,
spl0_21,
inference(avatar_split_clause,[],[f178,f556]) ).
fof(f556,plain,
( spl0_21
<=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f178,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_uIT_0) ).
fof(f554,plain,
spl0_20,
inference(avatar_split_clause,[],[f138,f551]) ).
fof(f551,plain,
( spl0_20
<=> hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f138,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',cls_Var_I3_J_0) ).
fof(f549,plain,
spl0_19,
inference(avatar_split_clause,[],[f350,f546]) ).
fof(f544,plain,
spl0_18,
inference(avatar_split_clause,[],[f416,f541]) ).
fof(f541,plain,
( spl0_18
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f416,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_bool__Orderings_Oorder) ).
fof(f539,plain,
spl0_17,
inference(avatar_split_clause,[],[f415,f536]) ).
fof(f536,plain,
( spl0_17
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f415,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_bool__Orderings_Opreorder) ).
fof(f534,plain,
spl0_16,
inference(avatar_split_clause,[],[f414,f531]) ).
fof(f531,plain,
( spl0_16
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f414,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__Orderings_Oorder) ).
fof(f529,plain,
spl0_15,
inference(avatar_split_clause,[],[f413,f526]) ).
fof(f526,plain,
( spl0_15
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f413,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__Orderings_Olinorder) ).
fof(f524,plain,
spl0_14,
inference(avatar_split_clause,[],[f412,f521]) ).
fof(f521,plain,
( spl0_14
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f412,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__Orderings_Opreorder) ).
fof(f519,plain,
spl0_13,
inference(avatar_split_clause,[],[f411,f516]) ).
fof(f516,plain,
( spl0_13
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f411,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f514,plain,
spl0_12,
inference(avatar_split_clause,[],[f410,f511]) ).
fof(f410,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f509,plain,
spl0_11,
inference(avatar_split_clause,[],[f409,f506]) ).
fof(f409,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f504,plain,
spl0_10,
inference(avatar_split_clause,[],[f408,f501]) ).
fof(f501,plain,
( spl0_10
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f408,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(f499,plain,
spl0_9,
inference(avatar_split_clause,[],[f407,f496]) ).
fof(f407,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f494,plain,
spl0_8,
inference(avatar_split_clause,[],[f406,f491]) ).
fof(f491,plain,
( spl0_8
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f406,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f489,plain,
spl0_7,
inference(avatar_split_clause,[],[f405,f486]) ).
fof(f486,plain,
( spl0_7
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f405,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f484,plain,
spl0_6,
inference(avatar_split_clause,[],[f404,f481]) ).
fof(f481,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f404,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f479,plain,
spl0_5,
inference(avatar_split_clause,[],[f403,f476]) ).
fof(f476,plain,
( spl0_5
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f403,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f474,plain,
spl0_4,
inference(avatar_split_clause,[],[f402,f471]) ).
fof(f471,plain,
( spl0_4
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f402,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f469,plain,
spl0_3,
inference(avatar_split_clause,[],[f401,f466]) ).
fof(f466,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f401,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f464,plain,
spl0_2,
inference(avatar_split_clause,[],[f400,f461]) ).
fof(f461,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f400,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f459,plain,
spl0_1,
inference(avatar_split_clause,[],[f399,f456]) ).
fof(f456,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f399,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.3O4yfByldk/Vampire---4.8_16364',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : LCL785-1 : TPTP v8.1.2. Released v4.1.0.
% 0.16/0.17 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.18/0.38 % Computer : n008.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Wed Aug 30 14:56:33 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.24/0.44 % (16618)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.46 % (16627)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.24/0.46 % (16628)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.24/0.46 % (16630)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.24/0.46 % (16629)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 Vampire---4 for (569ds/0Mi)
% 0.24/0.46 % (16631)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 Vampire---4 for (531ds/0Mi)
% 0.24/0.46 % (16632)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 Vampire---4 for (522ds/0Mi)
% 0.24/0.46 % (16633)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 Vampire---4 for (497ds/0Mi)
% 0.24/0.50 % (16631)First to succeed.
% 0.24/0.50 % (16631)Refutation found. Thanks to Tanya!
% 0.24/0.50 % SZS status Unsatisfiable for Vampire---4
% 0.24/0.50 % SZS output start Proof for Vampire---4
% See solution above
% 0.24/0.51 % (16631)------------------------------
% 0.24/0.51 % (16631)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.51 % (16631)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.51 % (16631)Termination reason: Refutation
% 0.24/0.51
% 0.24/0.51 % (16631)Memory used [KB]: 6652
% 0.24/0.51 % (16631)Time elapsed: 0.043 s
% 0.24/0.51 % (16631)------------------------------
% 0.24/0.51 % (16631)------------------------------
% 0.24/0.51 % (16618)Success in time 0.12 s
% 0.24/0.51 % Vampire---4.8 exiting
%------------------------------------------------------------------------------