TSTP Solution File: ALG377-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG377-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:37:20 EDT 2024
% Result : Unsatisfiable 3.32s 0.88s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 956
% Syntax : Number of formulae : 1576 ( 551 unt; 0 def)
% Number of atoms : 3807 ( 561 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 3905 (1674 ~;1730 |; 0 &)
% ( 501 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 540 ( 538 usr; 502 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 2119 (2119 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9138,plain,
$false,
inference(avatar_sat_refutation,[],[f570,f575,f580,f585,f590,f595,f600,f605,f610,f615,f620,f625,f630,f635,f640,f645,f650,f655,f660,f665,f670,f675,f680,f685,f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f740,f745,f750,f755,f760,f765,f770,f775,f780,f785,f790,f795,f800,f805,f810,f815,f820,f825,f829,f833,f837,f841,f845,f849,f854,f858,f862,f867,f871,f876,f880,f884,f888,f892,f896,f900,f904,f908,f912,f916,f920,f924,f929,f940,f944,f948,f952,f956,f960,f964,f968,f972,f976,f981,f985,f989,f1008,f1014,f1018,f1022,f1027,f1031,f1035,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1072,f1076,f1080,f1085,f1089,f1093,f1097,f1101,f1105,f1109,f1113,f1117,f1121,f1125,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1160,f1201,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1285,f1291,f1295,f1299,f1303,f1307,f1311,f1315,f1319,f1323,f1328,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1360,f1364,f1368,f1372,f1378,f1382,f1386,f1415,f1523,f1567,f1633,f1638,f1652,f1658,f1662,f1666,f1670,f1674,f1678,f1682,f1686,f1690,f1694,f1699,f1703,f1707,f1711,f1715,f1719,f1723,f1727,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1763,f1767,f1792,f1891,f1969,f2030,f2034,f2038,f2042,f2046,f2050,f2054,f2059,f2063,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2095,f2099,f2103,f2107,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2139,f2143,f2147,f2151,f2238,f2314,f2437,f2442,f2446,f2450,f2454,f2458,f2462,f2466,f2470,f2474,f2478,f2482,f2487,f2491,f2495,f2499,f2503,f2507,f2511,f2515,f2519,f2523,f2527,f2532,f2536,f2540,f2544,f2548,f2552,f2556,f2560,f2564,f2609,f2713,f2960,f3034,f3038,f3042,f3046,f3050,f3054,f3058,f3062,f3066,f3070,f3074,f3078,f3082,f3086,f3092,f3096,f3100,f3104,f3108,f3112,f3116,f3120,f3124,f3128,f3132,f3136,f3140,f3144,f3148,f3152,f3156,f3160,f3164,f3168,f3172,f3182,f3186,f3190,f3194,f3198,f3202,f3206,f3210,f3214,f3218,f3222,f3226,f3230,f3234,f3238,f3242,f3246,f3250,f3254,f3258,f3262,f3271,f3275,f3279,f3283,f3287,f3291,f3295,f3519,f4457,f4461,f4465,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4518,f4522,f4526,f4644,f4996,f5009,f5013,f5017,f5021,f5025,f5029,f5035,f5039,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5072,f5076,f5080,f5084,f5088,f5111,f5420,f5424,f6050,f6054,f6058,f6064,f6070,f6098,f6102,f6106,f6111,f6115,f6119,f6123,f6127,f6131,f6135,f6144,f6148,f6152,f6156,f6181,f6185,f6242,f6319,f6323,f6327,f6331,f6335,f6349,f6353,f6357,f6361,f6365,f6369,f6373,f6380,f6384,f6388,f6402,f6406,f6410,f6414,f6418,f6422,f6426,f6430,f6434,f6438,f6805,f7108,f7112,f7116,f7120,f7134,f7138,f7142,f7146,f7150,f7154,f7162,f7166,f7170,f7174,f7178,f7182,f7186,f7190,f7194,f7198,f7202,f7206,f7210,f7214,f7218,f7222,f7226,f7230,f7234,f7238,f7242,f7246,f7250,f7254,f7258,f7262,f7329,f8144,f8245,f8249,f8253,f8257,f8261,f8265,f8270,f8274,f8438,f8442,f8474,f8478,f8482,f8486,f8490,f8494,f8498,f8502,f8506,f8510,f8532,f8536,f8540,f8544,f8548,f8552,f8556,f8560,f8564,f8568,f8574,f8699,f9001,f9005,f9009,f9013,f9017,f9021,f9025,f9029,f9137]) ).
fof(f9137,plain,
spl0_335,
inference(avatar_split_clause,[],[f506,f4467]) ).
fof(f4467,plain,
( spl0_335
<=> c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f506,axiom,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f9029,plain,
spl0_501,
inference(avatar_split_clause,[],[f456,f9027]) ).
fof(f9027,plain,
( spl0_501
<=> ! [X18,X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(X7,X18,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f456,axiom,
! [X3,X18,X7,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(X7,X18,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f9025,plain,
( spl0_500
| ~ spl0_225
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4997,f4641,f2129,f9023]) ).
fof(f9023,plain,
( spl0_500
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2129,plain,
( spl0_225
<=> ! [X13,X14,X15] :
( ~ c_lessequals(X13,X15,tc_RealDef_Oreal)
| ~ c_lessequals(X15,X14,tc_RealDef_Oreal)
| c_lessequals(X13,X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f4641,plain,
( spl0_349
<=> c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f4997,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_225
| ~ spl0_349 ),
inference(resolution,[],[f4643,f2130]) ).
fof(f2130,plain,
( ! [X14,X15,X13] :
( ~ c_lessequals(X15,X14,tc_RealDef_Oreal)
| ~ c_lessequals(X13,X15,tc_RealDef_Oreal)
| c_lessequals(X13,X14,tc_RealDef_Oreal) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2129]) ).
fof(f4643,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f4641]) ).
fof(f9021,plain,
spl0_499,
inference(avatar_split_clause,[],[f252,f9019]) ).
fof(f9019,plain,
( spl0_499
<=> ! [X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X7,X3),c_HOL_Oinverse__class_Odivide(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f252,axiom,
! [X3,X7,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X7,X3),c_HOL_Oinverse__class_Odivide(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
fof(f9017,plain,
spl0_498,
inference(avatar_split_clause,[],[f251,f9015]) ).
fof(f9015,plain,
( spl0_498
<=> ! [X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X3),c_HOL_Oinverse__class_Odivide(X4,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f251,axiom,
! [X3,X7,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X7,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X3),c_HOL_Oinverse__class_Odivide(X4,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
fof(f9013,plain,
spl0_497,
inference(avatar_split_clause,[],[f219,f9011]) ).
fof(f9011,plain,
( spl0_497
<=> ! [X9,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f219,axiom,
! [X3,X0,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f9009,plain,
spl0_496,
inference(avatar_split_clause,[],[f218,f9007]) ).
fof(f9007,plain,
( spl0_496
<=> ! [X9,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f218,axiom,
! [X3,X0,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f9005,plain,
spl0_495,
inference(avatar_split_clause,[],[f104,f9003]) ).
fof(f9003,plain,
( spl0_495
<=> ! [X9,X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| c_RComplete_Onatfloor(c_HOL_Oinverse__class_Odivide(X0,c_RealDef_Oreal(X9,tc_nat),tc_RealDef_Oreal)) = c_Divides_Odiv__class_Odiv(c_RComplete_Onatfloor(X0),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f104,axiom,
! [X0,X9] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X9,tc_nat)
| c_RComplete_Onatfloor(c_HOL_Oinverse__class_Odivide(X0,c_RealDef_Oreal(X9,tc_nat),tc_RealDef_Oreal)) = c_Divides_Odiv__class_Odiv(c_RComplete_Onatfloor(X0),X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__div__nat_0) ).
fof(f9001,plain,
spl0_494,
inference(avatar_split_clause,[],[f10,f8999]) ).
fof(f8999,plain,
( spl0_494
<=> ! [X4,X7,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X7,X3),c_Divides_Odiv__class_Omod(X5,X7,X3),X3),X7,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f10,axiom,
! [X3,X7,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X7,X3),c_Divides_Odiv__class_Omod(X5,X7,X3),X3),X7,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
fof(f8699,plain,
( spl0_493
| ~ spl0_101
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1373,f1330,f1050,f8697]) ).
fof(f8697,plain,
( spl0_493
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f1050,plain,
( spl0_101
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1330,plain,
( spl0_149
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1373,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_101
| ~ spl0_149 ),
inference(resolution,[],[f1331,f1051]) ).
fof(f1051,plain,
( ! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f1331,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f8574,plain,
spl0_492,
inference(avatar_split_clause,[],[f339,f8572]) ).
fof(f8572,plain,
( spl0_492
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f339,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
fof(f8568,plain,
spl0_491,
inference(avatar_split_clause,[],[f338,f8566]) ).
fof(f8566,plain,
( spl0_491
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f338,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
fof(f8564,plain,
spl0_490,
inference(avatar_split_clause,[],[f337,f8562]) ).
fof(f8562,plain,
( spl0_490
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f337,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
fof(f8560,plain,
spl0_489,
inference(avatar_split_clause,[],[f336,f8558]) ).
fof(f8558,plain,
( spl0_489
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f336,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
fof(f8556,plain,
spl0_488,
inference(avatar_split_clause,[],[f322,f8554]) ).
fof(f8554,plain,
( spl0_488
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X0,X3),X9,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f322,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X0,X3),X9,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
fof(f8552,plain,
spl0_487,
inference(avatar_split_clause,[],[f258,f8550]) ).
fof(f8550,plain,
( spl0_487
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f258,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
fof(f8548,plain,
spl0_486,
inference(avatar_split_clause,[],[f257,f8546]) ).
fof(f8546,plain,
( spl0_486
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f257,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
fof(f8544,plain,
spl0_485,
inference(avatar_split_clause,[],[f256,f8542]) ).
fof(f8542,plain,
( spl0_485
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f256,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
fof(f8540,plain,
spl0_484,
inference(avatar_split_clause,[],[f255,f8538]) ).
fof(f8538,plain,
( spl0_484
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f255,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
fof(f8536,plain,
spl0_483,
inference(avatar_split_clause,[],[f254,f8534]) ).
fof(f8534,plain,
( spl0_483
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f254,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
fof(f8532,plain,
spl0_482,
inference(avatar_split_clause,[],[f253,f8530]) ).
fof(f8530,plain,
( spl0_482
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f253,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
fof(f8510,plain,
spl0_481,
inference(avatar_split_clause,[],[f250,f8508]) ).
fof(f8508,plain,
( spl0_481
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f250,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
fof(f8506,plain,
spl0_480,
inference(avatar_split_clause,[],[f249,f8504]) ).
fof(f8504,plain,
( spl0_480
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f249,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
fof(f8502,plain,
spl0_479,
inference(avatar_split_clause,[],[f248,f8500]) ).
fof(f8500,plain,
( spl0_479
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f248,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
fof(f8498,plain,
spl0_478,
inference(avatar_split_clause,[],[f247,f8496]) ).
fof(f8496,plain,
( spl0_478
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f247,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
fof(f8494,plain,
spl0_477,
inference(avatar_split_clause,[],[f246,f8492]) ).
fof(f8492,plain,
( spl0_477
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f246,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
fof(f8490,plain,
spl0_476,
inference(avatar_split_clause,[],[f245,f8488]) ).
fof(f8488,plain,
( spl0_476
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f245,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
fof(f8486,plain,
spl0_475,
inference(avatar_split_clause,[],[f186,f8484]) ).
fof(f8484,plain,
( spl0_475
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f186,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
fof(f8482,plain,
spl0_474,
inference(avatar_split_clause,[],[f185,f8480]) ).
fof(f8480,plain,
( spl0_474
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f185,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
fof(f8478,plain,
spl0_473,
inference(avatar_split_clause,[],[f184,f8476]) ).
fof(f8476,plain,
( spl0_473
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f184,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
fof(f8474,plain,
spl0_472,
inference(avatar_split_clause,[],[f183,f8472]) ).
fof(f8472,plain,
( spl0_472
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f183,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
fof(f8442,plain,
spl0_471,
inference(avatar_split_clause,[],[f128,f8440]) ).
fof(f8440,plain,
( spl0_471
<=> ! [X4,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X5,X3),c_HOL_Oone__class_Oone(X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,X5,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f128,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X5,X3),c_HOL_Oone__class_Oone(X3),X3) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,X5,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
fof(f8438,plain,
spl0_470,
inference(avatar_split_clause,[],[f127,f8436]) ).
fof(f8436,plain,
( spl0_470
<=> ! [X4,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X5,X4,X3),X5,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X5,X3),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f127,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X5,X4,X3),X5,X3) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X5,X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
fof(f8274,plain,
spl0_469,
inference(avatar_split_clause,[],[f410,f8272]) ).
fof(f8272,plain,
( spl0_469
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f410,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
fof(f8270,plain,
( ~ spl0_468
| ~ spl0_179
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3331,f3044,f1696,f8267]) ).
fof(f8267,plain,
( spl0_468
<=> c_lessequals(c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f1696,plain,
( spl0_179
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f3044,plain,
( spl0_271
<=> ! [X0] : ~ c_lessequals(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f3331,plain,
( ~ c_lessequals(c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_179
| ~ spl0_271 ),
inference(superposition,[],[f3045,f1698]) ).
fof(f1698,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1696]) ).
fof(f3045,plain,
( ! [X0] : ~ c_lessequals(c_Suc(X0),X0,tc_nat)
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f3044]) ).
fof(f8265,plain,
spl0_467,
inference(avatar_split_clause,[],[f409,f8263]) ).
fof(f8263,plain,
( spl0_467
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f409,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
fof(f8261,plain,
spl0_466,
inference(avatar_split_clause,[],[f359,f8259]) ).
fof(f8259,plain,
( spl0_466
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f359,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
fof(f8257,plain,
spl0_465,
inference(avatar_split_clause,[],[f355,f8255]) ).
fof(f8255,plain,
( spl0_465
<=> ! [X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X5,X4,X3)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X7,X3),c_HOL_Oinverse__class_Odivide(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f355,axiom,
! [X3,X7,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X5,X4,X3)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X7,X3),c_HOL_Oinverse__class_Odivide(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
fof(f8253,plain,
spl0_464,
inference(avatar_split_clause,[],[f354,f8251]) ).
fof(f8251,plain,
( spl0_464
<=> ! [X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X7,X3),c_HOL_Oinverse__class_Odivide(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f354,axiom,
! [X3,X7,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X7,X3),c_HOL_Oinverse__class_Odivide(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
fof(f8249,plain,
spl0_463,
inference(avatar_split_clause,[],[f142,f8247]) ).
fof(f8247,plain,
( spl0_463
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f142,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
fof(f8245,plain,
spl0_462,
inference(avatar_split_clause,[],[f96,f8243]) ).
fof(f8243,plain,
( spl0_462
<=> ! [X4,X5,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X4,X3),c_RealVector_Onorm__class_Onorm(X5,X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f96,axiom,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X4,X3),c_RealVector_Onorm__class_Onorm(X5,X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__norm__divide_0) ).
fof(f8144,plain,
( spl0_461
| ~ spl0_58
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f3309,f1696,f847,f8141]) ).
fof(f8141,plain,
( spl0_461
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f847,plain,
( spl0_58
<=> ! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f3309,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_nat)
| ~ spl0_58
| ~ spl0_179 ),
inference(superposition,[],[f848,f1698]) ).
fof(f848,plain,
( ! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f847]) ).
fof(f7329,plain,
( spl0_396
| ~ spl0_460
| ~ spl0_219
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3173,f3130,f2105,f7326,f6240]) ).
fof(f6240,plain,
( spl0_396
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f7326,plain,
( spl0_460
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2105,plain,
( spl0_219
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f3130,plain,
( spl0_292
<=> ! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f3173,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_nat)
| c_HOL_Oabs__class_Oabs(X0,tc_nat) = X0 )
| ~ spl0_219
| ~ spl0_292 ),
inference(resolution,[],[f3131,f2106]) ).
fof(f2106,plain,
( ! [X3,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2105]) ).
fof(f3131,plain,
( ! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3130]) ).
fof(f7262,plain,
spl0_459,
inference(avatar_split_clause,[],[f496,f7260]) ).
fof(f7260,plain,
( spl0_459
<=> ! [X24,X0,X9,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X9,X3),X24,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,X24,X3),c_HOL_Oinverse__class_Odivide(X9,X24,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f496,axiom,
! [X3,X0,X9,X24] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X9,X3),X24,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,X24,X3),c_HOL_Oinverse__class_Odivide(X9,X24,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
fof(f7258,plain,
spl0_458,
inference(avatar_split_clause,[],[f495,f7256]) ).
fof(f7256,plain,
( spl0_458
<=> ! [X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X7,X3),c_HOL_Oinverse__class_Odivide(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f495,axiom,
! [X3,X7,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X7,X3),c_HOL_Oinverse__class_Odivide(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
fof(f7254,plain,
spl0_457,
inference(avatar_split_clause,[],[f446,f7252]) ).
fof(f7252,plain,
( spl0_457
<=> ! [X17,X9,X0,X23,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X0,X17,X3) = X23
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X9,X17,X3),X3) != c_HOL_Oplus__class_Oplus(X9,X23,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f446,axiom,
! [X3,X0,X9,X17,X23] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X0,X17,X3) = X23
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X9,X17,X3),X3) != c_HOL_Oplus__class_Oplus(X9,X23,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f7250,plain,
spl0_456,
inference(avatar_split_clause,[],[f445,f7248]) ).
fof(f7248,plain,
( spl0_456
<=> ! [X18,X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X7,X18,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f445,axiom,
! [X3,X18,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X7,X18,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f7246,plain,
( spl0_455
| ~ spl0_100
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1287,f1247,f1046,f7244]) ).
fof(f7244,plain,
( spl0_455
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f1046,plain,
( spl0_100
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1247,plain,
( spl0_129
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1287,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
| ~ spl0_100
| ~ spl0_129 ),
inference(resolution,[],[f1248,f1047]) ).
fof(f1047,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f1248,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f7242,plain,
spl0_454,
inference(avatar_split_clause,[],[f429,f7240]) ).
fof(f7240,plain,
( spl0_454
<=> ! [X18,X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X7,X18,X3)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X7,X3),X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f429,axiom,
! [X3,X18,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X7,X18,X3)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X7,X3),X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f7238,plain,
spl0_453,
inference(avatar_split_clause,[],[f394,f7236]) ).
fof(f7236,plain,
( spl0_453
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X0,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f394,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X0,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
fof(f7234,plain,
spl0_452,
inference(avatar_split_clause,[],[f393,f7232]) ).
fof(f7232,plain,
( spl0_452
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X0,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f393,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X0,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
fof(f7230,plain,
spl0_451,
inference(avatar_split_clause,[],[f378,f7228]) ).
fof(f7228,plain,
( spl0_451
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f378,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f7226,plain,
spl0_450,
inference(avatar_split_clause,[],[f351,f7224]) ).
fof(f7224,plain,
( spl0_450
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f351,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
fof(f7222,plain,
spl0_449,
inference(avatar_split_clause,[],[f350,f7220]) ).
fof(f7220,plain,
( spl0_449
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f350,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
fof(f7218,plain,
spl0_448,
inference(avatar_split_clause,[],[f225,f7216]) ).
fof(f7216,plain,
( spl0_448
<=> ! [X18,X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X7,X18,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f225,axiom,
! [X3,X18,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X7,X18,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f7214,plain,
spl0_447,
inference(avatar_split_clause,[],[f224,f7212]) ).
fof(f7212,plain,
( spl0_447
<=> ! [X18,X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X7,X18,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f224,axiom,
! [X3,X18,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_lessequals(X7,X18,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f7210,plain,
spl0_446,
inference(avatar_split_clause,[],[f221,f7208]) ).
fof(f7208,plain,
( spl0_446
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f221,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f7206,plain,
spl0_445,
inference(avatar_split_clause,[],[f220,f7204]) ).
fof(f7204,plain,
( spl0_445
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X5,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f220,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X5,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X7,X3)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f7202,plain,
spl0_444,
inference(avatar_split_clause,[],[f216,f7200]) ).
fof(f7200,plain,
( spl0_444
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f216,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f7198,plain,
spl0_443,
inference(avatar_split_clause,[],[f211,f7196]) ).
fof(f7196,plain,
( spl0_443
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f211,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f7194,plain,
spl0_442,
inference(avatar_split_clause,[],[f190,f7192]) ).
fof(f7192,plain,
( spl0_442
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f190,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f7190,plain,
spl0_441,
inference(avatar_split_clause,[],[f154,f7188]) ).
fof(f7188,plain,
( spl0_441
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f154,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X5,X7,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f7186,plain,
spl0_440,
inference(avatar_split_clause,[],[f153,f7184]) ).
fof(f7184,plain,
( spl0_440
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f153,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f7182,plain,
spl0_439,
inference(avatar_split_clause,[],[f152,f7180]) ).
fof(f7180,plain,
( spl0_439
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f152,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f7178,plain,
spl0_438,
inference(avatar_split_clause,[],[f151,f7176]) ).
fof(f7176,plain,
( spl0_438
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f151,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f7174,plain,
spl0_437,
inference(avatar_split_clause,[],[f150,f7172]) ).
fof(f7172,plain,
( spl0_437
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f150,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f7170,plain,
spl0_436,
inference(avatar_split_clause,[],[f149,f7168]) ).
fof(f7168,plain,
( spl0_436
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f149,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f7166,plain,
spl0_435,
inference(avatar_split_clause,[],[f141,f7164]) ).
fof(f7164,plain,
( spl0_435
<=> ! [X18,X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X7,X18,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f141,axiom,
! [X3,X18,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(X7,X18,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X18,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f7162,plain,
( ~ spl0_433
| spl0_434
| ~ spl0_60
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3822,f3134,f856,f7160,f7156]) ).
fof(f7156,plain,
( spl0_433
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f7160,plain,
( spl0_434
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f856,plain,
( spl0_60
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f3134,plain,
( spl0_293
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3822,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_60
| ~ spl0_293 ),
inference(resolution,[],[f3135,f857]) ).
fof(f857,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f3135,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3134]) ).
fof(f7154,plain,
spl0_432,
inference(avatar_split_clause,[],[f123,f7152]) ).
fof(f7152,plain,
( spl0_432
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f123,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
fof(f7150,plain,
spl0_431,
inference(avatar_split_clause,[],[f122,f7148]) ).
fof(f7148,plain,
( spl0_431
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f122,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
fof(f7146,plain,
spl0_430,
inference(avatar_split_clause,[],[f120,f7144]) ).
fof(f7144,plain,
( spl0_430
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X0,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f120,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X9,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X0,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
fof(f7142,plain,
spl0_429,
inference(avatar_split_clause,[],[f119,f7140]) ).
fof(f7140,plain,
( spl0_429
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X0,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f119,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X0,X3)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X0,X9,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
fof(f7138,plain,
spl0_428,
inference(avatar_split_clause,[],[f13,f7136]) ).
fof(f7136,plain,
( spl0_428
<=> ! [X4,X7,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Omod(X5,X7,X3),X3),X7,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f13,axiom,
! [X3,X7,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,c_Divides_Odiv__class_Omod(X5,X7,X3),X3),X7,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
fof(f7134,plain,
spl0_427,
inference(avatar_split_clause,[],[f8,f7132]) ).
fof(f7132,plain,
( spl0_427
<=> ! [X4,X7,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X7,X3),X5,X3),X7,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f8,axiom,
! [X3,X7,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X4,X7,X3),X5,X3),X7,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
fof(f7120,plain,
spl0_426,
inference(avatar_split_clause,[],[f289,f7118]) ).
fof(f7118,plain,
( spl0_426
<=> ! [X4,X5,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X4,X3),c_RealVector_Onorm__class_Onorm(X5,X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f289,axiom,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X4,X3),c_RealVector_Onorm__class_Onorm(X5,X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__divide_0) ).
fof(f7116,plain,
spl0_425,
inference(avatar_split_clause,[],[f271,f7114]) ).
fof(f7114,plain,
( spl0_425
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f271,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
fof(f7112,plain,
spl0_424,
inference(avatar_split_clause,[],[f270,f7110]) ).
fof(f7110,plain,
( spl0_424
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f270,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
fof(f7108,plain,
spl0_423,
inference(avatar_split_clause,[],[f52,f7106]) ).
fof(f7106,plain,
( spl0_423
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f52,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__divide_0) ).
fof(f6805,plain,
( spl0_422
| ~ spl0_179
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f6376,f6371,f1696,f6803]) ).
fof(f6803,plain,
( spl0_422
<=> ! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X1
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f6371,plain,
( spl0_408
<=> ! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f6376,plain,
( ! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X1
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X2 )
| ~ spl0_179
| ~ spl0_408 ),
inference(forward_demodulation,[],[f6375,f1698]) ).
fof(f6375,plain,
( ! [X2,X1] :
( c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X1
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) )
| ~ spl0_179
| ~ spl0_408 ),
inference(forward_demodulation,[],[f6374,f1698]) ).
fof(f6374,plain,
( ! [X2,X1] :
( c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) )
| ~ spl0_179
| ~ spl0_408 ),
inference(forward_demodulation,[],[f6372,f1698]) ).
fof(f6372,plain,
( ! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) )
| ~ spl0_408 ),
inference(avatar_component_clause,[],[f6371]) ).
fof(f6438,plain,
spl0_421,
inference(avatar_split_clause,[],[f412,f6436]) ).
fof(f6436,plain,
( spl0_421
<=> ! [X9,X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X0,X9,X3),X3),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X0,X3),c_RealVector_Onorm__class_Onorm(X9,X3),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f412,axiom,
! [X3,X0,X9] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X0,X9,X3),X3),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X0,X3),c_RealVector_Onorm__class_Onorm(X9,X3),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__triangle__ineq_0) ).
fof(f6434,plain,
spl0_420,
inference(avatar_split_clause,[],[f408,f6432]) ).
fof(f6432,plain,
( spl0_420
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f408,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
fof(f6430,plain,
spl0_419,
inference(avatar_split_clause,[],[f407,f6428]) ).
fof(f6428,plain,
( spl0_419
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f407,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
fof(f6426,plain,
spl0_418,
inference(avatar_split_clause,[],[f406,f6424]) ).
fof(f6424,plain,
( spl0_418
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f406,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
fof(f6422,plain,
spl0_417,
inference(avatar_split_clause,[],[f335,f6420]) ).
fof(f6420,plain,
( spl0_417
<=> ! [X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f335,axiom,
! [X3,X7,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X5,X7,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f6418,plain,
spl0_416,
inference(avatar_split_clause,[],[f334,f6416]) ).
fof(f6416,plain,
( spl0_416
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f334,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
fof(f6414,plain,
spl0_415,
inference(avatar_split_clause,[],[f305,f6412]) ).
fof(f6412,plain,
( spl0_415
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f305,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
fof(f6410,plain,
spl0_414,
inference(avatar_split_clause,[],[f295,f6408]) ).
fof(f6408,plain,
( spl0_414
<=> ! [X9,X0] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f295,axiom,
! [X0,X9] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_0) ).
fof(f6406,plain,
spl0_413,
inference(avatar_split_clause,[],[f294,f6404]) ).
fof(f6404,plain,
( spl0_413
<=> ! [X9,X0] :
( c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f294,axiom,
! [X0,X9] :
( c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_1) ).
fof(f6402,plain,
spl0_412,
inference(avatar_split_clause,[],[f293,f6400]) ).
fof(f6400,plain,
( spl0_412
<=> ! [X9,X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f293,axiom,
! [X0,X9] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_2) ).
fof(f6388,plain,
spl0_411,
inference(avatar_split_clause,[],[f292,f6386]) ).
fof(f6386,plain,
( spl0_411
<=> ! [X9,X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f292,axiom,
! [X0,X9] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_3) ).
fof(f6384,plain,
spl0_410,
inference(avatar_split_clause,[],[f291,f6382]) ).
fof(f6382,plain,
( spl0_410
<=> ! [X9,X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f291,axiom,
! [X0,X9] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_4) ).
fof(f6380,plain,
spl0_409,
inference(avatar_split_clause,[],[f290,f6378]) ).
fof(f6378,plain,
( spl0_409
<=> ! [X9,X0] :
( ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f290,axiom,
! [X0,X9] :
( ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_5) ).
fof(f6373,plain,
spl0_408,
inference(avatar_split_clause,[],[f275,f6371]) ).
fof(f275,axiom,
! [X2,X1] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
fof(f6369,plain,
spl0_407,
inference(avatar_split_clause,[],[f240,f6367]) ).
fof(f6367,plain,
( spl0_407
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f240,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
fof(f6365,plain,
spl0_406,
inference(avatar_split_clause,[],[f223,f6363]) ).
fof(f6363,plain,
( spl0_406
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f223,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
fof(f6361,plain,
spl0_405,
inference(avatar_split_clause,[],[f217,f6359]) ).
fof(f6359,plain,
( spl0_405
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X7,c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f217,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X7,c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
fof(f6357,plain,
spl0_404,
inference(avatar_split_clause,[],[f194,f6355]) ).
fof(f6355,plain,
( spl0_404
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f194,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f6353,plain,
spl0_403,
inference(avatar_split_clause,[],[f109,f6351]) ).
fof(f6351,plain,
( spl0_403
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f109,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
fof(f6349,plain,
spl0_402,
inference(avatar_split_clause,[],[f108,f6347]) ).
fof(f6347,plain,
( spl0_402
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f108,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
fof(f6335,plain,
spl0_401,
inference(avatar_split_clause,[],[f107,f6333]) ).
fof(f6333,plain,
( spl0_401
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f107,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
fof(f6331,plain,
spl0_400,
inference(avatar_split_clause,[],[f106,f6329]) ).
fof(f6329,plain,
( spl0_400
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f106,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X3),X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
fof(f6327,plain,
spl0_399,
inference(avatar_split_clause,[],[f81,f6325]) ).
fof(f6325,plain,
( spl0_399
<=> ! [X13,X14,X16,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f81,axiom,
! [X16,X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f6323,plain,
spl0_398,
inference(avatar_split_clause,[],[f30,f6321]) ).
fof(f6321,plain,
( spl0_398
<=> ! [X4,X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_RComplete_Onatfloor(c_HOL_Oplus__class_Oplus(X0,c_RealDef_Oreal(X4,tc_nat),tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_RComplete_Onatfloor(X0),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_RComplete_Onatfloor(c_HOL_Oplus__class_Oplus(X0,c_RealDef_Oreal(X4,tc_nat),tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_RComplete_Onatfloor(X0),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__add_0) ).
fof(f6319,plain,
spl0_397,
inference(avatar_split_clause,[],[f4,f6317]) ).
fof(f6317,plain,
( spl0_397
<=> ! [X2,X1] :
( c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) = X1
| c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f4,axiom,
! [X2,X1] :
( c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) = X1
| c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
fof(f6242,plain,
( ~ spl0_395
| spl0_396
| ~ spl0_60
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2342,f2121,f856,f6240,f6236]) ).
fof(f6236,plain,
( spl0_395
<=> class_Ring__and__Field_Oabs__if(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f2121,plain,
( spl0_223
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2342,plain,
( ! [X0] :
( c_HOL_Oabs__class_Oabs(X0,tc_nat) = X0
| ~ class_Ring__and__Field_Oabs__if(tc_nat) )
| ~ spl0_60
| ~ spl0_223 ),
inference(resolution,[],[f2122,f857]) ).
fof(f2122,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| ~ class_Ring__and__Field_Oabs__if(X3) )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2121]) ).
fof(f6185,plain,
( spl0_394
| ~ spl0_179
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f6066,f6062,f1696,f6183]) ).
fof(f6183,plain,
( spl0_394
<=> ! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f6062,plain,
( spl0_377
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f6066,plain,
( ! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_179
| ~ spl0_377 ),
inference(forward_demodulation,[],[f6065,f1698]) ).
fof(f6065,plain,
( ! [X2,X1] :
( c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) )
| ~ spl0_179
| ~ spl0_377 ),
inference(forward_demodulation,[],[f6063,f1698]) ).
fof(f6063,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f6062]) ).
fof(f6181,plain,
( spl0_393
| ~ spl0_179
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f6060,f6056,f1696,f6179]) ).
fof(f6179,plain,
( spl0_393
<=> ! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f6056,plain,
( spl0_376
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f6060,plain,
( ! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
| ~ spl0_179
| ~ spl0_376 ),
inference(forward_demodulation,[],[f6059,f1698]) ).
fof(f6059,plain,
( ! [X2,X1] :
( c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) )
| ~ spl0_179
| ~ spl0_376 ),
inference(forward_demodulation,[],[f6057,f1698]) ).
fof(f6057,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) )
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f6056]) ).
fof(f6156,plain,
spl0_392,
inference(avatar_split_clause,[],[f565,f6154]) ).
fof(f6154,plain,
( spl0_392
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal)
| c_RComplete_Onatfloor(X0) = X1
| ~ c_lessequals(c_RealDef_Oreal(X1,tc_nat),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f565,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal)
| c_RComplete_Onatfloor(X0) = X1
| ~ c_lessequals(c_RealDef_Oreal(X1,tc_nat),X0,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f31,f457]) ).
fof(f457,axiom,
! [X1] : c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealDef_Oreal(c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__Suc_0) ).
fof(f31,axiom,
! [X0,X1] :
( c_RComplete_Onatfloor(X0) = X1
| ~ c_lessequals(c_RealDef_Oreal(X1,tc_nat),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__eq_0) ).
fof(f6152,plain,
spl0_391,
inference(avatar_split_clause,[],[f560,f6150]) ).
fof(f6150,plain,
( spl0_391
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f560,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(duplicate_literal_removal,[],[f222]) ).
fof(f222,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f6148,plain,
spl0_390,
inference(avatar_split_clause,[],[f492,f6146]) ).
fof(f6146,plain,
( spl0_390
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f492,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f6144,plain,
spl0_389,
inference(avatar_split_clause,[],[f489,f6142]) ).
fof(f6142,plain,
( spl0_389
<=> ! [X18,X4,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X7,X18,X3),X3) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X4,X18,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f489,axiom,
! [X3,X18,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X7,X18,X3),X3) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oplus__class_Oplus(X4,X18,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f6135,plain,
spl0_388,
inference(avatar_split_clause,[],[f488,f6133]) ).
fof(f6133,plain,
( spl0_388
<=> ! [X4,X7,X5,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X7,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f488,axiom,
! [X3,X7,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X7,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f6131,plain,
spl0_387,
inference(avatar_split_clause,[],[f487,f6129]) ).
fof(f6129,plain,
( spl0_387
<=> ! [X18,X4,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X7,X18,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X7,X3),X18,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f487,axiom,
! [X3,X18,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X7,X18,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X7,X3),X18,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(f6127,plain,
spl0_386,
inference(avatar_split_clause,[],[f486,f6125]) ).
fof(f6125,plain,
( spl0_386
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f486,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f6123,plain,
spl0_385,
inference(avatar_split_clause,[],[f485,f6121]) ).
fof(f6121,plain,
( spl0_385
<=> ! [X17,X0,X9,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X9,X17,X3),X3) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X0,X17,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f485,axiom,
! [X3,X0,X9,X17] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X9,X17,X3),X3) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X0,X17,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f6119,plain,
spl0_384,
inference(avatar_split_clause,[],[f481,f6117]) ).
fof(f6117,plain,
( spl0_384
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f481,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f6115,plain,
spl0_383,
inference(avatar_split_clause,[],[f480,f6113]) ).
fof(f6113,plain,
( spl0_383
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f480,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X4,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f6111,plain,
spl0_382,
inference(avatar_split_clause,[],[f460,f6108]) ).
fof(f6108,plain,
( spl0_382
<=> c_lessequals(c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f460,axiom,
c_lessequals(c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th00_0) ).
fof(f6106,plain,
spl0_381,
inference(avatar_split_clause,[],[f459,f6104]) ).
fof(f6104,plain,
( spl0_381
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f459,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f6102,plain,
spl0_380,
inference(avatar_split_clause,[],[f426,f6100]) ).
fof(f6100,plain,
( spl0_380
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f426,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f6098,plain,
spl0_379,
inference(avatar_split_clause,[],[f425,f6096]) ).
fof(f6096,plain,
( spl0_379
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f425,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f6070,plain,
spl0_378,
inference(avatar_split_clause,[],[f301,f6068]) ).
fof(f6068,plain,
( spl0_378
<=> ! [X9,X0] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X9,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f301,axiom,
! [X0,X9] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X9,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__add__cancel_0) ).
fof(f6064,plain,
spl0_377,
inference(avatar_split_clause,[],[f279,f6062]) ).
fof(f279,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
fof(f6058,plain,
spl0_376,
inference(avatar_split_clause,[],[f278,f6056]) ).
fof(f278,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
fof(f6054,plain,
spl0_375,
inference(avatar_split_clause,[],[f269,f6052]) ).
fof(f6052,plain,
( spl0_375
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X3) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f269,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X3) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
fof(f6050,plain,
spl0_374,
inference(avatar_split_clause,[],[f82,f6048]) ).
fof(f6048,plain,
( spl0_374
<=> ! [X14,X16,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(X14,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f82,axiom,
! [X2,X1,X16,X14] :
( ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(X14,X1,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f5424,plain,
( spl0_373
| ~ spl0_179
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f5040,f5037,f1696,f5422]) ).
fof(f5422,plain,
( spl0_373
<=> ! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f5037,plain,
( spl0_358
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f5040,plain,
( ! [X2,X1] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
| ~ spl0_179
| ~ spl0_358 ),
inference(forward_demodulation,[],[f5038,f1698]) ).
fof(f5038,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f5037]) ).
fof(f5420,plain,
( spl0_372
| ~ spl0_179
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f5031,f5027,f1696,f5418]) ).
fof(f5418,plain,
( spl0_372
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))),tc_nat)
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f5027,plain,
( spl0_356
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f5031,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))),tc_nat)
| c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_179
| ~ spl0_356 ),
inference(forward_demodulation,[],[f5030,f1698]) ).
fof(f5030,plain,
( ! [X0] :
( c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) )
| ~ spl0_179
| ~ spl0_356 ),
inference(forward_demodulation,[],[f5028,f1698]) ).
fof(f5028,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f5027]) ).
fof(f5111,plain,
spl0_371,
inference(avatar_split_clause,[],[f494,f5109]) ).
fof(f5109,plain,
( spl0_371
<=> ! [X17,X0,X9,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X17,X3) = X0
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X9,X17,X3),X3) != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f494,axiom,
! [X3,X0,X9,X17] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X17,X3) = X0
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X9,X17,X3),X3) != X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f5088,plain,
spl0_370,
inference(avatar_split_clause,[],[f469,f5086]) ).
fof(f5086,plain,
( spl0_370
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f469,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f5084,plain,
spl0_369,
inference(avatar_split_clause,[],[f468,f5082]) ).
fof(f5082,plain,
( spl0_369
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f468,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f5080,plain,
spl0_368,
inference(avatar_split_clause,[],[f467,f5078]) ).
fof(f5078,plain,
( spl0_368
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f467,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f5076,plain,
spl0_367,
inference(avatar_split_clause,[],[f466,f5074]) ).
fof(f5074,plain,
( spl0_367
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f466,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f5072,plain,
spl0_366,
inference(avatar_split_clause,[],[f465,f5070]) ).
fof(f5070,plain,
( spl0_366
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f465,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f5068,plain,
spl0_365,
inference(avatar_split_clause,[],[f464,f5066]) ).
fof(f5066,plain,
( spl0_365
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f464,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f5064,plain,
spl0_364,
inference(avatar_split_clause,[],[f451,f5062]) ).
fof(f5062,plain,
( spl0_364
<=> ! [X17,X0,X9,X3] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| X9 = X17
| c_HOL_Oplus__class_Oplus(X0,X9,X3) != c_HOL_Oplus__class_Oplus(X0,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f451,axiom,
! [X3,X0,X9,X17] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| X9 = X17
| c_HOL_Oplus__class_Oplus(X0,X9,X3) != c_HOL_Oplus__class_Oplus(X0,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f5060,plain,
spl0_363,
inference(avatar_split_clause,[],[f415,f5058]) ).
fof(f5058,plain,
( spl0_363
<=> ! [X0,X1] : c_lessequals(c_RealDef_Oreal(c_Divides_Odiv__class_Odiv(X1,X0,tc_nat),tc_nat),c_HOL_Oinverse__class_Odivide(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f415,axiom,
! [X0,X1] : c_lessequals(c_RealDef_Oreal(c_Divides_Odiv__class_Odiv(X1,X0,tc_nat),tc_nat),c_HOL_Oinverse__class_Odivide(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__div4_0) ).
fof(f5056,plain,
spl0_362,
inference(avatar_split_clause,[],[f312,f5054]) ).
fof(f5054,plain,
( spl0_362
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f312,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
fof(f5052,plain,
spl0_361,
inference(avatar_split_clause,[],[f304,f5050]) ).
fof(f5050,plain,
( spl0_361
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f304,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f5048,plain,
spl0_360,
inference(avatar_split_clause,[],[f303,f5046]) ).
fof(f5046,plain,
( spl0_360
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f303,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f5044,plain,
spl0_359,
inference(avatar_split_clause,[],[f297,f5042]) ).
fof(f5042,plain,
( spl0_359
<=> ! [X0,X10] :
( ~ c_lessequals(X0,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X10,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X10,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f297,axiom,
! [X10,X0] :
( ~ c_lessequals(X0,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X10,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X10,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_2) ).
fof(f5039,plain,
spl0_358,
inference(avatar_split_clause,[],[f276,f5037]) ).
fof(f276,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
fof(f5035,plain,
spl0_357,
inference(avatar_split_clause,[],[f265,f5033]) ).
fof(f5033,plain,
( spl0_357
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| X4 = X5
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oone__class_Oone(X3) != c_HOL_Oinverse__class_Odivide(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f265,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| X4 = X5
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oone__class_Oone(X3) != c_HOL_Oinverse__class_Odivide(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f5029,plain,
spl0_356,
inference(avatar_split_clause,[],[f193,f5027]) ).
fof(f193,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X0
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
fof(f5025,plain,
spl0_355,
inference(avatar_split_clause,[],[f148,f5023]) ).
fof(f5023,plain,
( spl0_355
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f148,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f5021,plain,
spl0_354,
inference(avatar_split_clause,[],[f147,f5019]) ).
fof(f5019,plain,
( spl0_354
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f147,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f5017,plain,
spl0_353,
inference(avatar_split_clause,[],[f146,f5015]) ).
fof(f5015,plain,
( spl0_353
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f146,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X7,X3),c_HOL_Oplus__class_Oplus(X5,X7,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f5013,plain,
spl0_352,
inference(avatar_split_clause,[],[f145,f5011]) ).
fof(f5011,plain,
( spl0_352
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f145,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f5009,plain,
spl0_351,
inference(avatar_split_clause,[],[f144,f5007]) ).
fof(f5007,plain,
( spl0_351
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f144,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f4996,plain,
spl0_350,
inference(avatar_split_clause,[],[f143,f4994]) ).
fof(f4994,plain,
( spl0_350
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f143,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X4,X3),c_HOL_Oplus__class_Oplus(X7,X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f4644,plain,
( spl0_349
| ~ spl0_89
| spl0_335 ),
inference(avatar_split_clause,[],[f4511,f4467,f983,f4641]) ).
fof(f983,plain,
( spl0_89
<=> ! [X17,X19] :
( c_lessequals(X17,X19,tc_RealDef_Oreal)
| c_lessequals(X19,X17,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f4511,plain,
( c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_89
| spl0_335 ),
inference(resolution,[],[f4469,f984]) ).
fof(f984,plain,
( ! [X19,X17] :
( c_lessequals(X17,X19,tc_RealDef_Oreal)
| c_lessequals(X19,X17,tc_RealDef_Oreal) )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f983]) ).
fof(f4469,plain,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_335 ),
inference(avatar_component_clause,[],[f4467]) ).
fof(f4526,plain,
spl0_348,
inference(avatar_split_clause,[],[f493,f4524]) ).
fof(f4524,plain,
( spl0_348
<=> ! [X9,X0,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f493,axiom,
! [X3,X0,X9] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,X3),X9,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X9,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f4522,plain,
spl0_347,
inference(avatar_split_clause,[],[f491,f4520]) ).
fof(f4520,plain,
( spl0_347
<=> ! [X2,X1] : c_RealDef_Oreal(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X2,tc_nat),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f491,axiom,
! [X2,X1] : c_RealDef_Oreal(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X2,tc_nat),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__add_0) ).
fof(f4518,plain,
spl0_346,
inference(avatar_split_clause,[],[f484,f4516]) ).
fof(f4516,plain,
( spl0_346
<=> ! [X9,X0,X17] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X9,X17,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X0,X17,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f484,axiom,
! [X0,X9,X17] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X9,X17,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X0,X17,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f4510,plain,
spl0_345,
inference(avatar_split_clause,[],[f483,f4508]) ).
fof(f4508,plain,
( spl0_345
<=> ! [X2,X1,X14] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X14,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f483,axiom,
! [X2,X1,X14] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X14,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f4506,plain,
spl0_344,
inference(avatar_split_clause,[],[f458,f4504]) ).
fof(f4504,plain,
( spl0_344
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f458,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f4502,plain,
spl0_343,
inference(avatar_split_clause,[],[f343,f4500]) ).
fof(f4500,plain,
( spl0_343
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f343,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f4498,plain,
spl0_342,
inference(avatar_split_clause,[],[f342,f4496]) ).
fof(f4496,plain,
( spl0_342
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f342,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f4494,plain,
spl0_341,
inference(avatar_split_clause,[],[f320,f4492]) ).
fof(f4492,plain,
( spl0_341
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f320,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f4490,plain,
spl0_340,
inference(avatar_split_clause,[],[f319,f4488]) ).
fof(f4488,plain,
( spl0_340
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f319,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f4486,plain,
spl0_339,
inference(avatar_split_clause,[],[f318,f4484]) ).
fof(f4484,plain,
( spl0_339
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f318,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f4482,plain,
spl0_338,
inference(avatar_split_clause,[],[f317,f4480]) ).
fof(f4480,plain,
( spl0_338
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f317,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f4478,plain,
spl0_337,
inference(avatar_split_clause,[],[f215,f4476]) ).
fof(f4476,plain,
( spl0_337
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f215,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f4474,plain,
spl0_336,
inference(avatar_split_clause,[],[f214,f4472]) ).
fof(f4472,plain,
( spl0_336
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f214,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f4470,plain,
( ~ spl0_335
| spl0_91
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f4365,f3277,f1005,f4467]) ).
fof(f1005,plain,
( spl0_91
<=> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f3277,plain,
( spl0_326
<=> ! [X9,X0,X17] :
( ~ c_lessequals(X0,X9,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X17,X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X17,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f4365,plain,
( ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_91
| ~ spl0_326 ),
inference(resolution,[],[f3278,f1007]) ).
fof(f1007,plain,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_91 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f3278,plain,
( ! [X0,X9,X17] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X17,X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X17,X9,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,X9,tc_RealDef_Oreal) )
| ~ spl0_326 ),
inference(avatar_component_clause,[],[f3277]) ).
fof(f4465,plain,
spl0_334,
inference(avatar_split_clause,[],[f213,f4463]) ).
fof(f4463,plain,
( spl0_334
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f213,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f4461,plain,
spl0_333,
inference(avatar_split_clause,[],[f212,f4459]) ).
fof(f4459,plain,
( spl0_333
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f212,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f4457,plain,
spl0_332,
inference(avatar_split_clause,[],[f25,f4455]) ).
fof(f4455,plain,
( spl0_332
<=> ! [X2,X1] :
( c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) != X1
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f25,axiom,
! [X2,X1] :
( c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)) != X1
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
fof(f3519,plain,
( ~ spl0_331
| ~ spl0_56
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f3307,f1696,f839,f3516]) ).
fof(f3516,plain,
( spl0_331
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f839,plain,
( spl0_56
<=> ! [X1] : c_Suc(X1) != X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f3307,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_56
| ~ spl0_179 ),
inference(superposition,[],[f840,f1698]) ).
fof(f840,plain,
( ! [X1] : c_Suc(X1) != X1
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f839]) ).
fof(f3295,plain,
spl0_330,
inference(avatar_split_clause,[],[f504,f3293]) ).
fof(f3293,plain,
( spl0_330
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X4,X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f504,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X4,X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
fof(f3291,plain,
spl0_329,
inference(avatar_split_clause,[],[f503,f3289]) ).
fof(f3289,plain,
( spl0_329
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f503,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
fof(f3287,plain,
spl0_328,
inference(avatar_split_clause,[],[f479,f3285]) ).
fof(f3285,plain,
( spl0_328
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f479,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f3283,plain,
spl0_327,
inference(avatar_split_clause,[],[f478,f3281]) ).
fof(f3281,plain,
( spl0_327
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f478,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f3279,plain,
spl0_326,
inference(avatar_split_clause,[],[f470,f3277]) ).
fof(f470,axiom,
! [X0,X9,X17] :
( ~ c_lessequals(X0,X9,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X17,X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X17,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
fof(f3275,plain,
spl0_325,
inference(avatar_split_clause,[],[f450,f3273]) ).
fof(f3273,plain,
( spl0_325
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| X5 = X7
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Oplus__class_Oplus(X4,X7,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f450,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| X5 = X7
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Oplus__class_Oplus(X4,X7,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f3271,plain,
spl0_324,
inference(avatar_split_clause,[],[f449,f3269]) ).
fof(f3269,plain,
( spl0_324
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X7
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Oplus__class_Oplus(X4,X7,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f449,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X7
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Oplus__class_Oplus(X4,X7,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f3262,plain,
spl0_323,
inference(avatar_split_clause,[],[f448,f3260]) ).
fof(f3260,plain,
( spl0_323
<=> ! [X4,X7,X5,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X7
| c_HOL_Oplus__class_Oplus(X5,X4,X3) != c_HOL_Oplus__class_Oplus(X7,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f448,axiom,
! [X3,X7,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X7
| c_HOL_Oplus__class_Oplus(X5,X4,X3) != c_HOL_Oplus__class_Oplus(X7,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f3258,plain,
spl0_322,
inference(avatar_split_clause,[],[f428,f3256]) ).
fof(f3256,plain,
( spl0_322
<=> ! [X17,X0,X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X0,X9,X3)
| ~ c_lessequals(X9,X17,X3)
| c_lessequals(X0,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f428,axiom,
! [X3,X0,X9,X17] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X0,X9,X3)
| ~ c_lessequals(X9,X17,X3)
| c_lessequals(X0,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3254,plain,
spl0_321,
inference(avatar_split_clause,[],[f427,f3252]) ).
fof(f3252,plain,
( spl0_321
<=> ! [X17,X0,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X9,X0,X3)
| ~ c_lessequals(X17,X9,X3)
| c_lessequals(X17,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f427,axiom,
! [X3,X0,X9,X17] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X9,X0,X3)
| ~ c_lessequals(X17,X9,X3)
| c_lessequals(X17,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3250,plain,
spl0_320,
inference(avatar_split_clause,[],[f420,f3248]) ).
fof(f3248,plain,
( spl0_320
<=> ! [X9,X0] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f420,axiom,
! [X0,X9] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__add__iff_1) ).
fof(f3246,plain,
spl0_319,
inference(avatar_split_clause,[],[f419,f3244]) ).
fof(f3244,plain,
( spl0_319
<=> ! [X9,X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f419,axiom,
! [X0,X9] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__add__iff_0) ).
fof(f3242,plain,
spl0_318,
inference(avatar_split_clause,[],[f417,f3240]) ).
fof(f3240,plain,
( spl0_318
<=> ! [X9,X0] :
( ~ c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f417,axiom,
! [X0,X9] :
( ~ c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_1) ).
fof(f3238,plain,
spl0_317,
inference(avatar_split_clause,[],[f416,f3236]) ).
fof(f3236,plain,
( spl0_317
<=> ! [X9,X0] :
( c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f416,axiom,
! [X0,X9] :
( c_lessequals(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_0) ).
fof(f3234,plain,
spl0_316,
inference(avatar_split_clause,[],[f411,f3232]) ).
fof(f3232,plain,
( spl0_316
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f411,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X2),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
fof(f3230,plain,
spl0_315,
inference(avatar_split_clause,[],[f398,f3228]) ).
fof(f3228,plain,
( spl0_315
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f398,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f3226,plain,
spl0_314,
inference(avatar_split_clause,[],[f397,f3224]) ).
fof(f3224,plain,
( spl0_314
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f397,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f3222,plain,
( spl0_313
| ~ spl0_18
| ~ spl0_58
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1493,f1309,f847,f652,f3220]) ).
fof(f3220,plain,
( spl0_313
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f652,plain,
( spl0_18
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1309,plain,
( spl0_144
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| c_lessequals(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1493,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_lessequals(X0,c_Suc(X0),tc_nat) )
| ~ spl0_58
| ~ spl0_144 ),
inference(resolution,[],[f1310,f848]) ).
fof(f1310,plain,
( ! [X3,X0,X9] :
( ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| ~ class_Orderings_Oorder(X3)
| c_lessequals(X0,X9,X3) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1309]) ).
fof(f3218,plain,
spl0_312,
inference(avatar_split_clause,[],[f388,f3216]) ).
fof(f3216,plain,
( spl0_312
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ class_Orderings_Olinorder(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f388,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ class_Orderings_Olinorder(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
fof(f3214,plain,
spl0_311,
inference(avatar_split_clause,[],[f384,f3212]) ).
fof(f3212,plain,
( spl0_311
<=> ! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f384,axiom,
! [X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f3210,plain,
spl0_310,
inference(avatar_split_clause,[],[f383,f3208]) ).
fof(f3208,plain,
( spl0_310
<=> ! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f383,axiom,
! [X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f3206,plain,
spl0_309,
inference(avatar_split_clause,[],[f381,f3204]) ).
fof(f3204,plain,
( spl0_309
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f381,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f3202,plain,
spl0_308,
inference(avatar_split_clause,[],[f380,f3200]) ).
fof(f3200,plain,
( spl0_308
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f380,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f3198,plain,
spl0_307,
inference(avatar_split_clause,[],[f321,f3196]) ).
fof(f3196,plain,
( spl0_307
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f321,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
fof(f3194,plain,
spl0_306,
inference(avatar_split_clause,[],[f314,f3192]) ).
fof(f3192,plain,
( spl0_306
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f314,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
fof(f3190,plain,
spl0_305,
inference(avatar_split_clause,[],[f313,f3188]) ).
fof(f3188,plain,
( spl0_305
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f313,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_0) ).
fof(f3186,plain,
spl0_304,
inference(avatar_split_clause,[],[f260,f3184]) ).
fof(f3184,plain,
( spl0_304
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = X5
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Ozero__class_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f260,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = X5
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f3182,plain,
spl0_303,
inference(avatar_split_clause,[],[f259,f3180]) ).
fof(f3180,plain,
( spl0_303
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X5,X3) = X4
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Ozero__class_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f259,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X5,X3) = X4
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f3172,plain,
spl0_302,
inference(avatar_split_clause,[],[f244,f3170]) ).
fof(f3170,plain,
( spl0_302
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f244,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f3168,plain,
spl0_301,
inference(avatar_split_clause,[],[f243,f3166]) ).
fof(f3166,plain,
( spl0_301
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f243,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f3164,plain,
spl0_300,
inference(avatar_split_clause,[],[f242,f3162]) ).
fof(f3162,plain,
( spl0_300
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f242,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
fof(f3160,plain,
spl0_299,
inference(avatar_split_clause,[],[f239,f3158]) ).
fof(f3158,plain,
( spl0_299
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f239,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f3156,plain,
spl0_298,
inference(avatar_split_clause,[],[f238,f3154]) ).
fof(f3154,plain,
( spl0_298
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f238,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f3152,plain,
spl0_297,
inference(avatar_split_clause,[],[f209,f3150]) ).
fof(f3150,plain,
( spl0_297
<=> ! [X9,X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f209,axiom,
! [X0,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_0) ).
fof(f3148,plain,
spl0_296,
inference(avatar_split_clause,[],[f208,f3146]) ).
fof(f3146,plain,
( spl0_296
<=> ! [X9,X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f208,axiom,
! [X0,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X9,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).
fof(f3144,plain,
spl0_295,
inference(avatar_split_clause,[],[f207,f3142]) ).
fof(f3142,plain,
( spl0_295
<=> ! [X20,X21] :
( ~ c_HOL_Oord__class_Oless(X20,X21,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X21,c_HOL_Ouminus__class_Ouminus(X20,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f207,axiom,
! [X21,X20] :
( ~ c_HOL_Oord__class_Oless(X20,X21,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X21,c_HOL_Ouminus__class_Ouminus(X20,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__sum__gt__zero_0) ).
fof(f3140,plain,
spl0_294,
inference(avatar_split_clause,[],[f206,f3138]) ).
fof(f3138,plain,
( spl0_294
<=> ! [X20,X21] :
( c_HOL_Oord__class_Oless(X20,X21,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X21,c_HOL_Ouminus__class_Ouminus(X20,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f206,axiom,
! [X21,X20] :
( c_HOL_Oord__class_Oless(X20,X21,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X21,c_HOL_Ouminus__class_Ouminus(X20,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__gt__zero__less_0) ).
fof(f3136,plain,
spl0_293,
inference(avatar_split_clause,[],[f202,f3134]) ).
fof(f202,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f3132,plain,
( ~ spl0_17
| spl0_292
| ~ spl0_60
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1460,f1301,f856,f3130,f647]) ).
fof(f647,plain,
( spl0_17
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1301,plain,
( spl0_142
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X0,X3)
| c_HOL_Oord__class_Oless(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1460,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_60
| ~ spl0_142 ),
inference(resolution,[],[f1302,f857]) ).
fof(f1302,plain,
( ! [X3,X0,X9] :
( c_HOL_Oord__class_Oless(X0,X9,X3)
| c_lessequals(X9,X0,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f3128,plain,
spl0_291,
inference(avatar_split_clause,[],[f201,f3126]) ).
fof(f3126,plain,
( spl0_291
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f201,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f3124,plain,
spl0_290,
inference(avatar_split_clause,[],[f197,f3122]) ).
fof(f3122,plain,
( spl0_290
<=> ! [X17,X0,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| c_HOL_Oord__class_Oless(X17,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f197,axiom,
! [X3,X0,X9,X17] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| c_HOL_Oord__class_Oless(X17,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3120,plain,
spl0_289,
inference(avatar_split_clause,[],[f196,f3118]) ).
fof(f3118,plain,
( spl0_289
<=> ! [X17,X0,X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X0,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f196,axiom,
! [X3,X0,X9,X17] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X0,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f3116,plain,
spl0_288,
inference(avatar_split_clause,[],[f179,f3114]) ).
fof(f3114,plain,
( spl0_288
<=> ! [X17,X0,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3)
| c_HOL_Oord__class_Oless(X17,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f179,axiom,
! [X3,X0,X9,X17] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X17,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3)
| c_HOL_Oord__class_Oless(X17,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f3112,plain,
spl0_287,
inference(avatar_split_clause,[],[f178,f3110]) ).
fof(f3110,plain,
( spl0_287
<=> ! [X17,X0,X9,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X9,X0,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| c_HOL_Oord__class_Oless(X17,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f178,axiom,
! [X3,X0,X9,X17] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X9,X0,X3)
| ~ c_HOL_Oord__class_Oless(X17,X9,X3)
| c_HOL_Oord__class_Oless(X17,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f3108,plain,
spl0_286,
inference(avatar_split_clause,[],[f177,f3106]) ).
fof(f3106,plain,
( spl0_286
<=> ! [X17,X0,X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| c_HOL_Oord__class_Oless(X0,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f177,axiom,
! [X3,X0,X9,X17] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X17,X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| c_HOL_Oord__class_Oless(X0,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f3104,plain,
spl0_285,
inference(avatar_split_clause,[],[f176,f3102]) ).
fof(f3102,plain,
( spl0_285
<=> ! [X17,X0,X9,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X0,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X0,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f176,axiom,
! [X3,X0,X9,X17] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X0,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X17,X3)
| c_HOL_Oord__class_Oless(X0,X17,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f3100,plain,
spl0_284,
inference(avatar_split_clause,[],[f173,f3098]) ).
fof(f3098,plain,
( spl0_284
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X0,X9,X3)
| c_lessequals(X9,X0,X3)
| c_HOL_Oord__class_Oless(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f173,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X0,X9,X3)
| c_lessequals(X9,X0,X3)
| c_HOL_Oord__class_Oless(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3096,plain,
spl0_283,
inference(avatar_split_clause,[],[f139,f3094]) ).
fof(f3094,plain,
( spl0_283
<=> ! [X4,X0,X3] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oplus__class_Oplus(X0,X4,X3) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f139,axiom,
! [X3,X0,X4] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oplus__class_Oplus(X0,X4,X3) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f3092,plain,
spl0_282,
inference(avatar_split_clause,[],[f125,f3090]) ).
fof(f3090,plain,
( spl0_282
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f125,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
fof(f3086,plain,
spl0_281,
inference(avatar_split_clause,[],[f103,f3084]) ).
fof(f3084,plain,
( spl0_281
<=> ! [X9,X0] :
( c_HOL_Oord__class_Oless(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f103,axiom,
! [X0,X9] :
( c_HOL_Oord__class_Oless(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__less__0__iff_0) ).
fof(f3082,plain,
spl0_280,
inference(avatar_split_clause,[],[f102,f3080]) ).
fof(f3080,plain,
( spl0_280
<=> ! [X9,X0] :
( ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f102,axiom,
! [X0,X9] :
( ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__less__0__iff_1) ).
fof(f3078,plain,
spl0_279,
inference(avatar_split_clause,[],[f78,f3076]) ).
fof(f3076,plain,
( spl0_279
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f78,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f3074,plain,
spl0_278,
inference(avatar_split_clause,[],[f77,f3072]) ).
fof(f3072,plain,
( spl0_278
<=> ! [X2,X1,X14] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X2,tc_nat),c_HOL_Oplus__class_Oplus(X14,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f77,axiom,
! [X2,X1,X14] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X2,tc_nat),c_HOL_Oplus__class_Oplus(X14,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f3070,plain,
spl0_277,
inference(avatar_split_clause,[],[f76,f3068]) ).
fof(f3068,plain,
( spl0_277
<=> ! [X2,X1,X14] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X2,tc_nat),c_HOL_Oplus__class_Oplus(X14,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f76,axiom,
! [X2,X1,X14] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X2,tc_nat),c_HOL_Oplus__class_Oplus(X14,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f3066,plain,
spl0_276,
inference(avatar_split_clause,[],[f44,f3064]) ).
fof(f3064,plain,
( spl0_276
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f44,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ouminus__class_Ouminus(X4,X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
fof(f3062,plain,
spl0_275,
inference(avatar_split_clause,[],[f43,f3060]) ).
fof(f3060,plain,
( spl0_275
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f43,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
fof(f3058,plain,
spl0_274,
inference(avatar_split_clause,[],[f40,f3056]) ).
fof(f3056,plain,
( spl0_274
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f40,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f3054,plain,
spl0_273,
inference(avatar_split_clause,[],[f39,f3052]) ).
fof(f3052,plain,
( spl0_273
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f39,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f3050,plain,
spl0_272,
inference(avatar_split_clause,[],[f18,f3048]) ).
fof(f3048,plain,
( spl0_272
<=> ! [X4,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X5,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f18,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X4,X5,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f3046,plain,
( ~ spl0_17
| spl0_271
| ~ spl0_58
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1442,f1297,f847,f3044,f647]) ).
fof(f1297,plain,
( spl0_141
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X0,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1442,plain,
( ! [X0] :
( ~ c_lessequals(c_Suc(X0),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_58
| ~ spl0_141 ),
inference(resolution,[],[f1298,f848]) ).
fof(f1298,plain,
( ! [X3,X0,X9] :
( ~ c_HOL_Oord__class_Oless(X9,X0,X3)
| ~ c_lessequals(X0,X9,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1297]) ).
fof(f3042,plain,
spl0_270,
inference(avatar_split_clause,[],[f12,f3040]) ).
fof(f3040,plain,
( spl0_270
<=> ! [X4,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f12,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X5,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
fof(f3038,plain,
spl0_269,
inference(avatar_split_clause,[],[f11,f3036]) ).
fof(f3036,plain,
( spl0_269
<=> ! [X4,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f11,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,X5,X3) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X4,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
fof(f3034,plain,
spl0_268,
inference(avatar_split_clause,[],[f5,f3032]) ).
fof(f3032,plain,
( spl0_268
<=> ! [X2,X1] : c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f5,axiom,
! [X2,X1] : c_Divides_Odiv__class_Omod(c_Suc(X2),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X2,X1,tc_nat)),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
fof(f2960,plain,
( spl0_267
| ~ spl0_58
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1394,f1259,f847,f2958]) ).
fof(f2958,plain,
( spl0_267
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1259,plain,
( spl0_132
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1394,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0
| ~ spl0_58
| ~ spl0_132 ),
inference(resolution,[],[f1260,f848]) ).
fof(f1260,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = X2 )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f2713,plain,
( spl0_266
| ~ spl0_44
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1245,f1152,f782,f2711]) ).
fof(f2711,plain,
( spl0_266
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f782,plain,
( spl0_44
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1152,plain,
( spl0_126
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1245,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_44
| ~ spl0_126 ),
inference(resolution,[],[f1153,f784]) ).
fof(f784,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f1153,plain,
( ! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = X4 )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f2609,plain,
( spl0_265
| ~ spl0_46
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1244,f1148,f792,f2607]) ).
fof(f2607,plain,
( spl0_265
<=> ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f792,plain,
( spl0_46
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1148,plain,
( spl0_125
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1244,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_46
| ~ spl0_125 ),
inference(resolution,[],[f1149,f794]) ).
fof(f794,plain,
( class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f1149,plain,
( ! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1148]) ).
fof(f2564,plain,
spl0_264,
inference(avatar_split_clause,[],[f564,f2562]) ).
fof(f2562,plain,
( spl0_264
<=> ! [X2,X1] :
( ~ c_lessequals(c_RealDef_Oreal(c_Suc(X1),tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f564,plain,
! [X2,X1] :
( ~ c_lessequals(c_RealDef_Oreal(c_Suc(X1),tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(forward_demodulation,[],[f422,f457]) ).
fof(f422,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__real__le_1) ).
fof(f2560,plain,
spl0_263,
inference(avatar_split_clause,[],[f563,f2558]) ).
fof(f2558,plain,
( spl0_263
<=> ! [X2,X1] :
( c_lessequals(c_RealDef_Oreal(c_Suc(X1),tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f563,plain,
! [X2,X1] :
( c_lessequals(c_RealDef_Oreal(c_Suc(X1),tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
inference(forward_demodulation,[],[f421,f457]) ).
fof(f421,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__real__le_0) ).
fof(f2556,plain,
spl0_262,
inference(avatar_split_clause,[],[f471,f2554]) ).
fof(f2554,plain,
( spl0_262
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Oorder(X3)
| X0 = X9
| ~ c_lessequals(X9,X0,X3)
| ~ c_lessequals(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f471,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Oorder(X3)
| X0 = X9
| ~ c_lessequals(X9,X0,X3)
| ~ c_lessequals(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f2552,plain,
spl0_261,
inference(avatar_split_clause,[],[f463,f2550]) ).
fof(f2550,plain,
( spl0_261
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3),X3) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f463,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3),X3) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f2548,plain,
spl0_260,
inference(avatar_split_clause,[],[f436,f2546]) ).
fof(f2546,plain,
( spl0_260
<=> ! [X9,X17,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X17,X3),c_HOL_Oplus__class_Oplus(X9,X17,X3),X3) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f436,axiom,
! [X3,X9,X17] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X17,X3),c_HOL_Oplus__class_Oplus(X9,X17,X3),X3) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f2544,plain,
spl0_259,
inference(avatar_split_clause,[],[f435,f2542]) ).
fof(f2542,plain,
( spl0_259
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f435,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f2540,plain,
spl0_258,
inference(avatar_split_clause,[],[f400,f2538]) ).
fof(f2538,plain,
( spl0_258
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f400,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f2536,plain,
spl0_257,
inference(avatar_split_clause,[],[f399,f2534]) ).
fof(f2534,plain,
( spl0_257
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f399,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f2532,plain,
( spl0_256
| ~ spl0_34
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1219,f1128,f732,f2529]) ).
fof(f2529,plain,
( spl0_256
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f732,plain,
( spl0_34
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1128,plain,
( spl0_120
<=> ! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1219,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_34
| ~ spl0_120 ),
inference(resolution,[],[f1129,f734]) ).
fof(f734,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f1129,plain,
( ! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f2527,plain,
spl0_255,
inference(avatar_split_clause,[],[f365,f2525]) ).
fof(f2525,plain,
( spl0_255
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f365,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f2523,plain,
spl0_254,
inference(avatar_split_clause,[],[f363,f2521]) ).
fof(f2521,plain,
( spl0_254
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oone__class_Oone(X3) = c_Divides_Odiv__class_Odiv(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f363,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oone__class_Oone(X3) = c_Divides_Odiv__class_Odiv(X4,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
fof(f2519,plain,
spl0_253,
inference(avatar_split_clause,[],[f333,f2517]) ).
fof(f2517,plain,
( spl0_253
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f333,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).
fof(f2515,plain,
spl0_252,
inference(avatar_split_clause,[],[f331,f2513]) ).
fof(f2513,plain,
( spl0_252
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X0 = X9
| c_HOL_Oord__class_Oless(X0,X9,X3)
| c_HOL_Oord__class_Oless(X9,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f331,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X0 = X9
| c_HOL_Oord__class_Oless(X0,X9,X3)
| c_HOL_Oord__class_Oless(X9,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f2511,plain,
spl0_251,
inference(avatar_split_clause,[],[f330,f2509]) ).
fof(f2509,plain,
( spl0_251
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Olinorder(X3)
| X0 = X9
| c_HOL_Oord__class_Oless(X0,X9,X3)
| c_HOL_Oord__class_Oless(X9,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f330,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Olinorder(X3)
| X0 = X9
| c_HOL_Oord__class_Oless(X0,X9,X3)
| c_HOL_Oord__class_Oless(X9,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
fof(f2507,plain,
spl0_250,
inference(avatar_split_clause,[],[f324,f2505]) ).
fof(f2505,plain,
( spl0_250
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f324,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f2503,plain,
spl0_249,
inference(avatar_split_clause,[],[f266,f2501]) ).
fof(f2501,plain,
( spl0_249
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oinverse__class_Odivide(X0,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f266,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oinverse__class_Odivide(X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
fof(f2499,plain,
spl0_248,
inference(avatar_split_clause,[],[f237,f2497]) ).
fof(f2497,plain,
( spl0_248
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f237,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f2495,plain,
spl0_247,
inference(avatar_split_clause,[],[f236,f2493]) ).
fof(f2493,plain,
( spl0_247
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f236,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f2491,plain,
spl0_246,
inference(avatar_split_clause,[],[f235,f2489]) ).
fof(f2489,plain,
( spl0_246
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f235,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f2487,plain,
( spl0_245
| ~ spl0_41
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1218,f1123,f767,f2484]) ).
fof(f2484,plain,
( spl0_245
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f767,plain,
( spl0_41
<=> class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1123,plain,
( spl0_119
<=> ! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1218,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal)
| ~ spl0_41
| ~ spl0_119 ),
inference(resolution,[],[f1124,f769]) ).
fof(f769,plain,
( class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f1124,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f2482,plain,
spl0_244,
inference(avatar_split_clause,[],[f234,f2480]) ).
fof(f2480,plain,
( spl0_244
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f234,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f2478,plain,
spl0_243,
inference(avatar_split_clause,[],[f233,f2476]) ).
fof(f2476,plain,
( spl0_243
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f233,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f2474,plain,
spl0_242,
inference(avatar_split_clause,[],[f232,f2472]) ).
fof(f2472,plain,
( spl0_242
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f232,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f2470,plain,
spl0_241,
inference(avatar_split_clause,[],[f231,f2468]) ).
fof(f2468,plain,
( spl0_241
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f231,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f2466,plain,
spl0_240,
inference(avatar_split_clause,[],[f230,f2464]) ).
fof(f2464,plain,
( spl0_240
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f230,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f2462,plain,
spl0_239,
inference(avatar_split_clause,[],[f205,f2460]) ).
fof(f2460,plain,
( spl0_239
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f205,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
fof(f2458,plain,
spl0_238,
inference(avatar_split_clause,[],[f169,f2456]) ).
fof(f2456,plain,
( spl0_238
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Olinorder(X3)
| X0 = X9
| ~ c_lessequals(X0,X9,X3)
| c_HOL_Oord__class_Oless(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f169,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Olinorder(X3)
| X0 = X9
| ~ c_lessequals(X0,X9,X3)
| c_HOL_Oord__class_Oless(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f2454,plain,
spl0_237,
inference(avatar_split_clause,[],[f167,f2452]) ).
fof(f2452,plain,
( spl0_237
<=> ! [X4,X5,X3] :
( ~ class_Orderings_Oorder(X3)
| X4 = X5
| ~ c_lessequals(X4,X5,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f167,axiom,
! [X3,X4,X5] :
( ~ class_Orderings_Oorder(X3)
| X4 = X5
| ~ c_lessequals(X4,X5,X3)
| c_HOL_Oord__class_Oless(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
fof(f2450,plain,
spl0_236,
inference(avatar_split_clause,[],[f140,f2448]) ).
fof(f2448,plain,
( spl0_236
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f140,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X4,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f2446,plain,
spl0_235,
inference(avatar_split_clause,[],[f72,f2444]) ).
fof(f2444,plain,
( spl0_235
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_Suc(X2) = X1
| c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f72,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_Suc(X2) = X1
| c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f2442,plain,
( spl0_234
| ~ spl0_12
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1217,f1123,f622,f2439]) ).
fof(f2439,plain,
( spl0_234
<=> 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_234])]) ).
fof(f622,plain,
( spl0_12
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1217,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_12
| ~ spl0_119 ),
inference(resolution,[],[f1124,f624]) ).
fof(f624,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f2437,plain,
spl0_233,
inference(avatar_split_clause,[],[f69,f2435]) ).
fof(f2435,plain,
( spl0_233
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X13),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f69,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X13),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f2314,plain,
( spl0_232
| ~ spl0_30
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1214,f1111,f712,f2311]) ).
fof(f2311,plain,
( spl0_232
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f712,plain,
( spl0_30
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1111,plain,
( spl0_116
<=> ! [X3] :
( ~ class_RealVector_Oreal__normed__algebra__1(X3)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1214,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_30
| ~ spl0_116 ),
inference(resolution,[],[f1112,f714]) ).
fof(f714,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f1112,plain,
( ! [X3] :
( ~ class_RealVector_Oreal__normed__algebra__1(X3)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X3),X3) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f2238,plain,
( spl0_231
| ~ spl0_22
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f1210,f1099,f672,f2235]) ).
fof(f2235,plain,
( spl0_231
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f672,plain,
( spl0_22
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1099,plain,
( spl0_113
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1210,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_22
| ~ spl0_113 ),
inference(resolution,[],[f1100,f674]) ).
fof(f674,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f1100,plain,
( ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f2151,plain,
spl0_230,
inference(avatar_split_clause,[],[f476,f2149]) ).
fof(f2149,plain,
( spl0_230
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X5
| c_HOL_Ouminus__class_Ouminus(X4,X3) != c_HOL_Ouminus__class_Ouminus(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f476,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X5
| c_HOL_Ouminus__class_Ouminus(X4,X3) != c_HOL_Ouminus__class_Ouminus(X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2147,plain,
( spl0_229
| ~ spl0_33
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1197,f1066,f727,f2145]) ).
fof(f2145,plain,
( spl0_229
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f727,plain,
( spl0_33
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1066,plain,
( spl0_105
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1197,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_33
| ~ spl0_105 ),
inference(resolution,[],[f1067,f729]) ).
fof(f729,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f1067,plain,
( ! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f2143,plain,
spl0_228,
inference(avatar_split_clause,[],[f457,f2141]) ).
fof(f2141,plain,
( spl0_228
<=> ! [X1] : c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X1,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealDef_Oreal(c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2139,plain,
spl0_227,
inference(avatar_split_clause,[],[f454,f2137]) ).
fof(f2137,plain,
( spl0_227
<=> ! [X2,X1,X14] :
( X1 = X2
| c_HOL_Oplus__class_Oplus(X2,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f454,axiom,
! [X2,X1,X14] :
( X1 = X2
| c_HOL_Oplus__class_Oplus(X2,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X1,X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f2135,plain,
spl0_226,
inference(avatar_split_clause,[],[f453,f2133]) ).
fof(f2133,plain,
( spl0_226
<=> ! [X2,X1,X14] :
( X1 = X2
| c_HOL_Oplus__class_Oplus(X14,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f453,axiom,
! [X2,X1,X14] :
( X1 = X2
| c_HOL_Oplus__class_Oplus(X14,X2,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
fof(f2131,plain,
spl0_225,
inference(avatar_split_clause,[],[f431,f2129]) ).
fof(f431,axiom,
! [X14,X15,X13] :
( ~ c_lessequals(X13,X15,tc_RealDef_Oreal)
| ~ c_lessequals(X15,X14,tc_RealDef_Oreal)
| c_lessequals(X13,X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f2127,plain,
spl0_224,
inference(avatar_split_clause,[],[f391,f2125]) ).
fof(f2125,plain,
( spl0_224
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f391,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f2123,plain,
spl0_223,
inference(avatar_split_clause,[],[f389,f2121]) ).
fof(f389,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oabs__if(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f2119,plain,
spl0_222,
inference(avatar_split_clause,[],[f371,f2117]) ).
fof(f2117,plain,
( spl0_222
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f371,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oord__class_Oless(X4,X5,X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f2115,plain,
spl0_221,
inference(avatar_split_clause,[],[f368,f2113]) ).
fof(f2113,plain,
( spl0_221
<=> ! [X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f368,axiom,
! [X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__gt__zero__cancel__iff_1) ).
fof(f2111,plain,
spl0_220,
inference(avatar_split_clause,[],[f367,f2109]) ).
fof(f2109,plain,
( spl0_220
<=> ! [X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f367,axiom,
! [X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__gt__zero__cancel__iff_0) ).
fof(f2107,plain,
spl0_219,
inference(avatar_split_clause,[],[f332,f2105]) ).
fof(f332,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f2103,plain,
( spl0_218
| ~ spl0_33
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1195,f1062,f727,f2101]) ).
fof(f2101,plain,
( spl0_218
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1062,plain,
( spl0_104
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1195,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_33
| ~ spl0_104 ),
inference(resolution,[],[f1063,f729]) ).
fof(f1063,plain,
( ! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 )
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f2099,plain,
spl0_217,
inference(avatar_split_clause,[],[f311,f2097]) ).
fof(f2097,plain,
( spl0_217
<=> ! [X10] :
( ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(X10,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X10,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f311,axiom,
! [X10] :
( ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(X10,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X10,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_0) ).
fof(f2095,plain,
spl0_216,
inference(avatar_split_clause,[],[f309,f2093]) ).
fof(f2093,plain,
( spl0_216
<=> ! [X2,X1,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f309,axiom,
! [X2,X3,X1] :
( ~ class_Nat_Osemiring__char__0(X3)
| X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) != c_Nat_Osemiring__1__class_Oof__nat(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f2091,plain,
spl0_215,
inference(avatar_split_clause,[],[f307,f2089]) ).
fof(f2089,plain,
( spl0_215
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f307,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X0
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
fof(f2087,plain,
spl0_214,
inference(avatar_split_clause,[],[f300,f2085]) ).
fof(f2085,plain,
( spl0_214
<=> ! [X4,X0] :
( X0 = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f300,axiom,
! [X0,X4] :
( X0 = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__minus__iff_0) ).
fof(f2083,plain,
spl0_213,
inference(avatar_split_clause,[],[f299,f2081]) ).
fof(f2081,plain,
( spl0_213
<=> ! [X9,X0] :
( c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = X9
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f299,axiom,
! [X0,X9] :
( c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = X9
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X0,X9,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_0) ).
fof(f2079,plain,
spl0_212,
inference(avatar_split_clause,[],[f298,f2077]) ).
fof(f2077,plain,
( spl0_212
<=> ! [X0,X10] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X10,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f298,axiom,
! [X10,X0] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X10,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).
fof(f2075,plain,
spl0_211,
inference(avatar_split_clause,[],[f199,f2073]) ).
fof(f2073,plain,
( spl0_211
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f199,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__less__iff_1) ).
fof(f2071,plain,
spl0_210,
inference(avatar_split_clause,[],[f198,f2069]) ).
fof(f2069,plain,
( spl0_210
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f198,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_RealDef_Oreal(X2,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__less__iff_0) ).
fof(f2067,plain,
spl0_209,
inference(avatar_split_clause,[],[f189,f2065]) ).
fof(f2065,plain,
( spl0_209
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f189,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f2063,plain,
spl0_208,
inference(avatar_split_clause,[],[f163,f2061]) ).
fof(f2061,plain,
( spl0_208
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f163,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f2059,plain,
( spl0_207
| ~ spl0_40
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1193,f1058,f762,f2056]) ).
fof(f2056,plain,
( spl0_207
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f762,plain,
( spl0_40
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1058,plain,
( spl0_103
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1193,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_40
| ~ spl0_103 ),
inference(resolution,[],[f1059,f764]) ).
fof(f764,plain,
( class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f1059,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X3),X3) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f2054,plain,
spl0_206,
inference(avatar_split_clause,[],[f129,f2052]) ).
fof(f2052,plain,
( spl0_206
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f129,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X3),c_HOL_Oone__class_Oone(X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f2050,plain,
spl0_205,
inference(avatar_split_clause,[],[f60,f2048]) ).
fof(f2048,plain,
( spl0_205
<=> ! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f60,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
fof(f2046,plain,
spl0_204,
inference(avatar_split_clause,[],[f49,f2044]) ).
fof(f2044,plain,
( spl0_204
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f49,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
fof(f2042,plain,
spl0_203,
inference(avatar_split_clause,[],[f38,f2040]) ).
fof(f2040,plain,
( spl0_203
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X3) != c_HOL_Ozero__class_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f38,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
fof(f2038,plain,
spl0_202,
inference(avatar_split_clause,[],[f24,f2036]) ).
fof(f2036,plain,
( spl0_202
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f24,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f2034,plain,
spl0_201,
inference(avatar_split_clause,[],[f22,f2032]) ).
fof(f2032,plain,
( spl0_201
<=> ! [X4,X5,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X4,X5,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f22,axiom,
! [X3,X4,X5] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X4,X5,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
fof(f2030,plain,
spl0_200,
inference(avatar_split_clause,[],[f1,f2028]) ).
fof(f2028,plain,
( spl0_200
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_RealDef_Oreal(c_RComplete_Onatfloor(X0),tc_nat),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1,axiom,
! [X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_RealDef_Oreal(c_RComplete_Onatfloor(X0),tc_nat),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__natfloor__le_0) ).
fof(f1969,plain,
( spl0_199
| ~ spl0_14
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1192,f1054,f632,f1967]) ).
fof(f1967,plain,
( spl0_199
<=> ! [X0] : c_Divides_Odiv__class_Odiv(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f632,plain,
( spl0_14
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1054,plain,
( spl0_102
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1192,plain,
( ! [X0] : c_Divides_Odiv__class_Odiv(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_14
| ~ spl0_102 ),
inference(resolution,[],[f1055,f634]) ).
fof(f634,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f1055,plain,
( ! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1054]) ).
fof(f1891,plain,
( spl0_198
| ~ spl0_28
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1161,f1025,f702,f1888]) ).
fof(f1888,plain,
( spl0_198
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f702,plain,
( spl0_28
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1025,plain,
( spl0_95
<=> ! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1161,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_28
| ~ spl0_95 ),
inference(resolution,[],[f1026,f704]) ).
fof(f704,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f1026,plain,
( ! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f1792,plain,
( spl0_197
| ~ spl0_14
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f1156,f1016,f632,f1790]) ).
fof(f1790,plain,
( spl0_197
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1016,plain,
( spl0_93
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1156,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_14
| ~ spl0_93 ),
inference(resolution,[],[f1017,f634]) ).
fof(f1017,plain,
( ! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,X4,X3) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f1767,plain,
spl0_196,
inference(avatar_split_clause,[],[f474,f1765]) ).
fof(f1765,plain,
( spl0_196
<=> ! [X17,X19] :
( X17 = X19
| ~ c_lessequals(X17,X19,tc_RealDef_Oreal)
| ~ c_lessequals(X19,X17,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f474,axiom,
! [X19,X17] :
( X17 = X19
| ~ c_lessequals(X17,X19,tc_RealDef_Oreal)
| ~ c_lessequals(X19,X17,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f1763,plain,
spl0_195,
inference(avatar_split_clause,[],[f444,f1761]) ).
fof(f1761,plain,
( spl0_195
<=> ! [X2,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X2),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f444,axiom,
! [X2,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X2),X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
fof(f1759,plain,
spl0_194,
inference(avatar_split_clause,[],[f443,f1757]) ).
fof(f1757,plain,
( spl0_194
<=> ! [X2,X1] : c_HOL_Oplus__class_Oplus(X2,c_Suc(X1),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f443,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(X2,c_Suc(X1),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
fof(f1755,plain,
spl0_193,
inference(avatar_split_clause,[],[f442,f1753]) ).
fof(f1753,plain,
( spl0_193
<=> ! [X4,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,X7,X3) = c_HOL_Oplus__class_Oplus(X7,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f442,axiom,
! [X3,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,X7,X3) = c_HOL_Oplus__class_Oplus(X7,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f1751,plain,
spl0_192,
inference(avatar_split_clause,[],[f439,f1749]) ).
fof(f1749,plain,
( spl0_192
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,X5,X3) = c_HOL_Oplus__class_Oplus(X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f439,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,X5,X3) = c_HOL_Oplus__class_Oplus(X5,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f1747,plain,
spl0_191,
inference(avatar_split_clause,[],[f364,f1745]) ).
fof(f1745,plain,
( spl0_191
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f364,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f1743,plain,
( spl0_190
| ~ spl0_14
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1155,f1012,f632,f1741]) ).
fof(f1741,plain,
( spl0_190
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1012,plain,
( spl0_92
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1155,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_14
| ~ spl0_92 ),
inference(resolution,[],[f1013,f634]) ).
fof(f1013,plain,
( ! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1739,plain,
spl0_189,
inference(avatar_split_clause,[],[f362,f1737]) ).
fof(f1737,plain,
( spl0_189
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f362,axiom,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__gt__zero_0) ).
fof(f1735,plain,
spl0_188,
inference(avatar_split_clause,[],[f356,f1733]) ).
fof(f1733,plain,
( spl0_188
<=> ! [X1,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f356,axiom,
! [X3,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X1,X3) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X1,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
fof(f1731,plain,
spl0_187,
inference(avatar_split_clause,[],[f326,f1729]) ).
fof(f1729,plain,
( spl0_187
<=> ! [X9,X0] :
( X0 = X9
| c_HOL_Oord__class_Oless(X0,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f326,axiom,
! [X0,X9] :
( X0 = X9
| c_HOL_Oord__class_Oless(X0,X9,tc_nat)
| c_HOL_Oord__class_Oless(X9,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f1727,plain,
spl0_186,
inference(avatar_split_clause,[],[f308,f1725]) ).
fof(f1725,plain,
( spl0_186
<=> ! [X4,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(X4,X3) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X4,X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f308,axiom,
! [X3,X4] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(X4,X3) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X4,X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
fof(f1723,plain,
spl0_185,
inference(avatar_split_clause,[],[f263,f1721]) ).
fof(f1721,plain,
( spl0_185
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f263,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f1719,plain,
spl0_184,
inference(avatar_split_clause,[],[f262,f1717]) ).
fof(f1717,plain,
( spl0_184
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f262,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f1715,plain,
spl0_183,
inference(avatar_split_clause,[],[f261,f1713]) ).
fof(f1713,plain,
( spl0_183
<=> ! [X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f261,axiom,
! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X3),X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
fof(f1711,plain,
spl0_182,
inference(avatar_split_clause,[],[f188,f1709]) ).
fof(f1709,plain,
( spl0_182
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f188,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__less_0) ).
fof(f1707,plain,
spl0_181,
inference(avatar_split_clause,[],[f138,f1705]) ).
fof(f1705,plain,
( spl0_181
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f138,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f1703,plain,
spl0_180,
inference(avatar_split_clause,[],[f134,f1701]) ).
fof(f1701,plain,
( spl0_180
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(X3),X3) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f134,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(X3),X3) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f1699,plain,
( spl0_179
| ~ spl0_61
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f999,f978,f860,f1696]) ).
fof(f860,plain,
( spl0_61
<=> ! [X1] : c_RComplete_Onatfloor(c_RealDef_Oreal(X1,tc_nat)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f978,plain,
( spl0_88
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f999,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_61
| ~ spl0_88 ),
inference(superposition,[],[f861,f980]) ).
fof(f980,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f978]) ).
fof(f861,plain,
( ! [X1] : c_RComplete_Onatfloor(c_RealDef_Oreal(X1,tc_nat)) = X1
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f1694,plain,
spl0_178,
inference(avatar_split_clause,[],[f126,f1692]) ).
fof(f1692,plain,
( spl0_178
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f126,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f1690,plain,
spl0_177,
inference(avatar_split_clause,[],[f98,f1688]) ).
fof(f1688,plain,
( spl0_177
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_lessequals(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f98,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_lessequals(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__le__zero__cancel__iff_0) ).
fof(f1686,plain,
spl0_176,
inference(avatar_split_clause,[],[f91,f1684]) ).
fof(f1684,plain,
( spl0_176
<=> ! [X13,X2,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_HOL_Oord__class_Oless(X13,c_HOL_Oplus__class_Oplus(X2,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f91,axiom,
! [X2,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_HOL_Oord__class_Oless(X13,c_HOL_Oplus__class_Oplus(X2,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f1682,plain,
spl0_175,
inference(avatar_split_clause,[],[f89,f1680]) ).
fof(f1680,plain,
( spl0_175
<=> ! [X13,X14,X15] :
( c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X15,tc_nat),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f89,axiom,
! [X14,X15,X13] :
( c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X15,tc_nat),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f1678,plain,
spl0_174,
inference(avatar_split_clause,[],[f87,f1676]) ).
fof(f1676,plain,
( spl0_174
<=> ! [X9,X0,X17] :
( ~ c_HOL_Oord__class_Oless(X0,X9,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X9,X17,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f87,axiom,
! [X0,X9,X17] :
( ~ c_HOL_Oord__class_Oless(X0,X9,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X9,X17,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f1674,plain,
spl0_173,
inference(avatar_split_clause,[],[f84,f1672]) ).
fof(f1672,plain,
( spl0_173
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f84,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1670,plain,
spl0_172,
inference(avatar_split_clause,[],[f83,f1668]) ).
fof(f1668,plain,
( spl0_172
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f83,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f1666,plain,
spl0_171,
inference(avatar_split_clause,[],[f54,f1664]) ).
fof(f1664,plain,
( spl0_171
<=> ! [X9,X0] :
( X0 = X9
| ~ c_lessequals(X0,X9,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X9,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f54,axiom,
! [X0,X9] :
( X0 = X9
| ~ c_lessequals(X0,X9,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X9,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f1662,plain,
spl0_170,
inference(avatar_split_clause,[],[f37,f1660]) ).
fof(f1660,plain,
( spl0_170
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X3) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f37,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X3) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f1658,plain,
spl0_169,
inference(avatar_split_clause,[],[f36,f1656]) ).
fof(f1656,plain,
( spl0_169
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = c_HOL_Oabs__class_Oabs(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f36,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = c_HOL_Oabs__class_Oabs(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f1652,plain,
spl0_168,
inference(avatar_split_clause,[],[f35,f1650]) ).
fof(f1650,plain,
( spl0_168
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X0,X3),X3) = c_RealVector_Onorm__class_Onorm(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f35,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X0,X3),X3) = c_RealVector_Onorm__class_Onorm(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
fof(f1638,plain,
( spl0_167
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1634,f1631,f1636]) ).
fof(f1636,plain,
( spl0_167
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_RealDef_Oreal(c_Suc(c_RComplete_Onatfloor(X0)),tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1631,plain,
( spl0_166
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(c_RComplete_Onatfloor(X0),tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1634,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_RealDef_Oreal(c_Suc(c_RComplete_Onatfloor(X0)),tc_nat),tc_RealDef_Oreal)
| ~ spl0_166 ),
inference(forward_demodulation,[],[f1632,f457]) ).
fof(f1632,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(c_RComplete_Onatfloor(X0),tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1631]) ).
fof(f1633,plain,
spl0_166,
inference(avatar_split_clause,[],[f29,f1631]) ).
fof(f29,axiom,
! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(c_RComplete_Onatfloor(X0),tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__natfloor__add__one__gt_0) ).
fof(f1567,plain,
( spl0_165
| ~ spl0_65
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1476,f1301,f878,f1565]) ).
fof(f1565,plain,
( spl0_165
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f878,plain,
( spl0_65
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1476,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_65
| ~ spl0_142 ),
inference(duplicate_literal_removal,[],[f1456]) ).
fof(f1456,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_65
| ~ spl0_142 ),
inference(resolution,[],[f1302,f879]) ).
fof(f879,plain,
( ! [X3,X0] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f1523,plain,
( spl0_164
| ~ spl0_61
| ~ spl0_88
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1324,f1321,f978,f860,f1521]) ).
fof(f1521,plain,
( spl0_164
<=> ! [X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1321,plain,
( spl0_147
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1324,plain,
( ! [X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_61
| ~ spl0_88
| ~ spl0_147 ),
inference(forward_demodulation,[],[f1322,f999]) ).
fof(f1322,plain,
( ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f1415,plain,
( spl0_163
| ~ spl0_55
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1405,f1275,f835,f1413]) ).
fof(f1413,plain,
( spl0_163
<=> ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f835,plain,
( spl0_55
<=> ! [X19] : c_lessequals(X19,X19,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1275,plain,
( spl0_136
<=> ! [X0,X10] :
( c_lessequals(X0,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X10,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1405,plain,
( ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_136 ),
inference(resolution,[],[f1276,f836]) ).
fof(f836,plain,
( ! [X19] : c_lessequals(X19,X19,tc_RealDef_Oreal)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f1276,plain,
( ! [X10,X0] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(X0,X10,tc_RealDef_Oreal) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f1386,plain,
spl0_162,
inference(avatar_split_clause,[],[f477,f1384]) ).
fof(f1384,plain,
( spl0_162
<=> ! [X2,X1] :
( X1 = X2
| c_RealDef_Oreal(X1,tc_nat) != c_RealDef_Oreal(X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f477,axiom,
! [X2,X1] :
( X1 = X2
| c_RealDef_Oreal(X1,tc_nat) != c_RealDef_Oreal(X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__inject_0) ).
fof(f1382,plain,
spl0_161,
inference(avatar_split_clause,[],[f424,f1380]) ).
fof(f1380,plain,
( spl0_161
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X0,X9,X3)
| c_lessequals(X9,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f424,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X0,X9,X3)
| c_lessequals(X9,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1378,plain,
spl0_160,
inference(avatar_split_clause,[],[f405,f1376]) ).
fof(f1376,plain,
( spl0_160
<=> ! [X4,X5,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X5,X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f405,axiom,
! [X3,X4,X5] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X5,X4,X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1372,plain,
spl0_159,
inference(avatar_split_clause,[],[f404,f1370]) ).
fof(f1370,plain,
( spl0_159
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f404,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1368,plain,
spl0_158,
inference(avatar_split_clause,[],[f403,f1366]) ).
fof(f1366,plain,
( spl0_158
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f403,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1364,plain,
spl0_157,
inference(avatar_split_clause,[],[f392,f1362]) ).
fof(f1362,plain,
( spl0_157
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f392,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f1360,plain,
spl0_156,
inference(avatar_split_clause,[],[f387,f1358]) ).
fof(f1358,plain,
( spl0_156
<=> ! [X10] :
( c_HOL_Oabs__class_Oabs(X10,tc_RealDef_Oreal) = X10
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f387,axiom,
! [X10] :
( c_HOL_Oabs__class_Oabs(X10,tc_RealDef_Oreal) = X10
| c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
fof(f1356,plain,
spl0_155,
inference(avatar_split_clause,[],[f357,f1354]) ).
fof(f1354,plain,
( spl0_155
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f357,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f1352,plain,
spl0_154,
inference(avatar_split_clause,[],[f323,f1350]) ).
fof(f1350,plain,
( spl0_154
<=> ! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f323,axiom,
! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
fof(f1348,plain,
spl0_153,
inference(avatar_split_clause,[],[f316,f1346]) ).
fof(f1346,plain,
( spl0_153
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f316,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f1344,plain,
spl0_152,
inference(avatar_split_clause,[],[f315,f1342]) ).
fof(f1342,plain,
( spl0_152
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f315,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f1340,plain,
spl0_151,
inference(avatar_split_clause,[],[f306,f1338]) ).
fof(f1338,plain,
( spl0_151
<=> ! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f306,axiom,
! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f1336,plain,
spl0_150,
inference(avatar_split_clause,[],[f229,f1334]) ).
fof(f1334,plain,
( spl0_150
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f229,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f1332,plain,
( spl0_149
| ~ spl0_101
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1215,f1199,f1050,f1330]) ).
fof(f1199,plain,
( spl0_128
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1215,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_101
| ~ spl0_128 ),
inference(resolution,[],[f1200,f1051]) ).
fof(f1200,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f1328,plain,
spl0_148,
inference(avatar_split_clause,[],[f228,f1326]) ).
fof(f1326,plain,
( spl0_148
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f228,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X3),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f1323,plain,
spl0_147,
inference(avatar_split_clause,[],[f200,f1321]) ).
fof(f200,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f1319,plain,
spl0_146,
inference(avatar_split_clause,[],[f180,f1317]) ).
fof(f1317,plain,
( spl0_146
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealDef_Oreal(X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f180,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealDef_Oreal(X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__zero__iff_0) ).
fof(f1315,plain,
spl0_145,
inference(avatar_split_clause,[],[f175,f1313]) ).
fof(f1313,plain,
( spl0_145
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| c_lessequals(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f175,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| c_lessequals(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1311,plain,
spl0_144,
inference(avatar_split_clause,[],[f174,f1309]) ).
fof(f174,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3)
| c_lessequals(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1307,plain,
spl0_143,
inference(avatar_split_clause,[],[f162,f1305]) ).
fof(f1305,plain,
( spl0_143
<=> ! [X9,X0,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X0,X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f162,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X9,X0,X3)
| ~ c_HOL_Oord__class_Oless(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1303,plain,
spl0_142,
inference(avatar_split_clause,[],[f161,f1301]) ).
fof(f161,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X9,X0,X3)
| c_HOL_Oord__class_Oless(X0,X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1299,plain,
spl0_141,
inference(avatar_split_clause,[],[f155,f1297]) ).
fof(f155,axiom,
! [X3,X0,X9] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X0,X9,X3)
| ~ c_HOL_Oord__class_Oless(X9,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1295,plain,
spl0_140,
inference(avatar_split_clause,[],[f101,f1293]) ).
fof(f1293,plain,
( spl0_140
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f101,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__not__less__self_0) ).
fof(f1291,plain,
spl0_139,
inference(avatar_split_clause,[],[f85,f1289]) ).
fof(f1289,plain,
( spl0_139
<=> ! [X4,X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X0,X4,tc_nat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f85,axiom,
! [X0,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X0,X4,tc_nat) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
fof(f1285,plain,
spl0_138,
inference(avatar_split_clause,[],[f75,f1283]) ).
fof(f1283,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f75,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
fof(f1281,plain,
spl0_137,
inference(avatar_split_clause,[],[f74,f1279]) ).
fof(f1279,plain,
( spl0_137
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X2),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f74,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X2),c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f1277,plain,
spl0_136,
inference(avatar_split_clause,[],[f55,f1275]) ).
fof(f55,axiom,
! [X10,X0] :
( c_lessequals(X0,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X10,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
fof(f1273,plain,
spl0_135,
inference(avatar_split_clause,[],[f51,f1271]) ).
fof(f1271,plain,
( spl0_135
<=> ! [X9,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f51,axiom,
! [X3,X9] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X9,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f1269,plain,
spl0_134,
inference(avatar_split_clause,[],[f48,f1267]) ).
fof(f1267,plain,
( spl0_134
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f48,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f1265,plain,
spl0_133,
inference(avatar_split_clause,[],[f21,f1263]) ).
fof(f1263,plain,
( spl0_133
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f21,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
fof(f1261,plain,
spl0_132,
inference(avatar_split_clause,[],[f17,f1259]) ).
fof(f17,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X2,X1,tc_nat) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f1257,plain,
spl0_131,
inference(avatar_split_clause,[],[f16,f1255]) ).
fof(f1255,plain,
( spl0_131
<=> ! [X4,X3] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f16,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f1253,plain,
spl0_130,
inference(avatar_split_clause,[],[f2,f1251]) ).
fof(f1251,plain,
( spl0_130
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_RComplete_Onatfloor(X0) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f2,axiom,
! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_RComplete_Onatfloor(X0) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__neg_0) ).
fof(f1249,plain,
( spl0_129
| ~ spl0_58
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1176,f1046,f847,f1247]) ).
fof(f1176,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_58
| ~ spl0_100 ),
inference(resolution,[],[f1047,f848]) ).
fof(f1201,plain,
( spl0_128
| ~ spl0_54
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1183,f1050,f831,f1199]) ).
fof(f831,plain,
( spl0_54
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1183,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_54
| ~ spl0_101 ),
inference(resolution,[],[f1051,f832]) ).
fof(f832,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f1160,plain,
( spl0_127
| ~ spl0_61
| ~ spl0_88
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1023,f1020,f978,f860,f1158]) ).
fof(f1158,plain,
( spl0_127
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X2,c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1020,plain,
( spl0_94
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1023,plain,
( ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X2,c_RComplete_Onatfloor(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_nat)
| ~ spl0_61
| ~ spl0_88
| ~ spl0_94 ),
inference(forward_demodulation,[],[f1021,f999]) ).
fof(f1021,plain,
( ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1154,plain,
spl0_126,
inference(avatar_split_clause,[],[f498,f1152]) ).
fof(f498,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
fof(f1150,plain,
spl0_125,
inference(avatar_split_clause,[],[f455,f1148]) ).
fof(f455,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f1146,plain,
spl0_124,
inference(avatar_split_clause,[],[f441,f1144]) ).
fof(f1144,plain,
( spl0_124
<=> ! [X2,X1] : c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f441,axiom,
! [X2,X1] : c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f1142,plain,
spl0_123,
inference(avatar_split_clause,[],[f401,f1140]) ).
fof(f1140,plain,
( spl0_123
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f401,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1138,plain,
spl0_122,
inference(avatar_split_clause,[],[f385,f1136]) ).
fof(f1136,plain,
( spl0_122
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f385,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1134,plain,
spl0_121,
inference(avatar_split_clause,[],[f379,f1132]) ).
fof(f1132,plain,
( spl0_121
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f379,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f1130,plain,
spl0_120,
inference(avatar_split_clause,[],[f366,f1128]) ).
fof(f366,axiom,
! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f1125,plain,
spl0_119,
inference(avatar_split_clause,[],[f358,f1123]) ).
fof(f358,axiom,
! [X3] :
( ~ class_Ring__and__Field_Osemiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f1121,plain,
spl0_118,
inference(avatar_split_clause,[],[f345,f1119]) ).
fof(f1119,plain,
( spl0_118
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f345,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f1117,plain,
spl0_117,
inference(avatar_split_clause,[],[f302,f1115]) ).
fof(f1115,plain,
( spl0_117
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f302,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_1) ).
fof(f1113,plain,
spl0_116,
inference(avatar_split_clause,[],[f272,f1111]) ).
fof(f272,axiom,
! [X3] :
( ~ class_RealVector_Oreal__normed__algebra__1(X3)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__one_0) ).
fof(f1109,plain,
spl0_115,
inference(avatar_split_clause,[],[f210,f1107]) ).
fof(f1107,plain,
( spl0_115
<=> ! [X0] : c_RealDef_Oreal(X0,tc_nat) = c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f210,axiom,
! [X0] : c_RealDef_Oreal(X0,tc_nat) = c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__real__of__nat__cancel_0) ).
fof(f1105,plain,
spl0_114,
inference(avatar_split_clause,[],[f203,f1103]) ).
fof(f1103,plain,
( spl0_114
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f203,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f1101,plain,
spl0_113,
inference(avatar_split_clause,[],[f195,f1099]) ).
fof(f195,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1097,plain,
spl0_112,
inference(avatar_split_clause,[],[f187,f1095]) ).
fof(f1095,plain,
( spl0_112
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f187,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X2,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1093,plain,
spl0_111,
inference(avatar_split_clause,[],[f182,f1091]) ).
fof(f1091,plain,
( spl0_111
<=> ! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f182,axiom,
! [X2,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
fof(f1089,plain,
spl0_110,
inference(avatar_split_clause,[],[f137,f1087]) ).
fof(f1087,plain,
( spl0_110
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f137,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1085,plain,
( ~ spl0_109
| ~ spl0_75
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f998,f978,f918,f1082]) ).
fof(f1082,plain,
( spl0_109
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f918,plain,
( spl0_75
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f998,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_75
| ~ spl0_88 ),
inference(superposition,[],[f919,f980]) ).
fof(f919,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f1080,plain,
spl0_108,
inference(avatar_split_clause,[],[f136,f1078]) ).
fof(f1078,plain,
( spl0_108
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f136,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1076,plain,
spl0_107,
inference(avatar_split_clause,[],[f135,f1074]) ).
fof(f1074,plain,
( spl0_107
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f135,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1072,plain,
spl0_106,
inference(avatar_split_clause,[],[f132,f1070]) ).
fof(f1070,plain,
( spl0_106
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f132,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1068,plain,
spl0_105,
inference(avatar_split_clause,[],[f131,f1066]) ).
fof(f131,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1064,plain,
spl0_104,
inference(avatar_split_clause,[],[f130,f1062]) ).
fof(f130,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1060,plain,
spl0_103,
inference(avatar_split_clause,[],[f112,f1058]) ).
fof(f112,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oone__class_Oone(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f1056,plain,
spl0_102,
inference(avatar_split_clause,[],[f110,f1054]) ).
fof(f110,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
fof(f1052,plain,
spl0_101,
inference(avatar_split_clause,[],[f66,f1050]) ).
fof(f66,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1048,plain,
spl0_100,
inference(avatar_split_clause,[],[f65,f1046]) ).
fof(f65,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X2),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1044,plain,
spl0_99,
inference(avatar_split_clause,[],[f63,f1042]) ).
fof(f1042,plain,
( spl0_99
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f63,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1040,plain,
( spl0_98
| ~ spl0_79
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f996,f978,f942,f1037]) ).
fof(f1037,plain,
( spl0_98
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f942,plain,
( spl0_79
<=> ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f996,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_79
| ~ spl0_88 ),
inference(superposition,[],[f943,f980]) ).
fof(f943,plain,
( ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f1035,plain,
spl0_97,
inference(avatar_split_clause,[],[f62,f1033]) ).
fof(f1033,plain,
( spl0_97
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f62,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1031,plain,
spl0_96,
inference(avatar_split_clause,[],[f34,f1029]) ).
fof(f1029,plain,
( spl0_96
<=> ! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f34,axiom,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
fof(f1027,plain,
spl0_95,
inference(avatar_split_clause,[],[f32,f1025]) ).
fof(f32,axiom,
! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1022,plain,
spl0_94,
inference(avatar_split_clause,[],[f26,f1020]) ).
fof(f26,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f1018,plain,
spl0_93,
inference(avatar_split_clause,[],[f20,f1016]) ).
fof(f20,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Divides_Odiv__class_Omod(X4,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1014,plain,
spl0_92,
inference(avatar_split_clause,[],[f19,f1012]) ).
fof(f19,axiom,
! [X3,X4] :
( ~ class_Divides_Osemiring__div(X3)
| c_Divides_Odiv__class_Omod(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1008,plain,
~ spl0_91,
inference(avatar_split_clause,[],[f507,f1005]) ).
fof(f507,axiom,
~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f989,plain,
spl0_90,
inference(avatar_split_clause,[],[f437,f987]) ).
fof(f987,plain,
( spl0_90
<=> ! [X9,X0] :
( X0 = X9
| c_Suc(X0) != c_Suc(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f437,axiom,
! [X0,X9] :
( X0 = X9
| c_Suc(X0) != c_Suc(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
fof(f985,plain,
spl0_89,
inference(avatar_split_clause,[],[f423,f983]) ).
fof(f423,axiom,
! [X19,X17] :
( c_lessequals(X17,X19,tc_RealDef_Oreal)
| c_lessequals(X19,X17,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f981,plain,
spl0_88,
inference(avatar_split_clause,[],[f414,f978]) ).
fof(f414,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__one_0) ).
fof(f976,plain,
spl0_87,
inference(avatar_split_clause,[],[f382,f974]) ).
fof(f974,plain,
( spl0_87
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f382,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f972,plain,
spl0_86,
inference(avatar_split_clause,[],[f370,f970]) ).
fof(f970,plain,
( spl0_86
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f370,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f968,plain,
spl0_85,
inference(avatar_split_clause,[],[f344,f966]) ).
fof(f966,plain,
( spl0_85
<=> ! [X2] : c_Divides_Odiv__class_Odiv(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f344,axiom,
! [X2] : c_Divides_Odiv__class_Odiv(X2,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__1_0) ).
fof(f964,plain,
spl0_84,
inference(avatar_split_clause,[],[f284,f962]) ).
fof(f962,plain,
( spl0_84
<=> ! [X2,X0] : c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f284,axiom,
! [X2,X0] : c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f960,plain,
spl0_83,
inference(avatar_split_clause,[],[f283,f958]) ).
fof(f958,plain,
( spl0_83
<=> ! [X13,X2] : c_HOL_Oord__class_Oless(X13,c_Suc(c_HOL_Oplus__class_Oplus(X2,X13,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f283,axiom,
! [X2,X13] : c_HOL_Oord__class_Oless(X13,c_Suc(c_HOL_Oplus__class_Oplus(X2,X13,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f956,plain,
spl0_82,
inference(avatar_split_clause,[],[f227,f954]) ).
fof(f954,plain,
( spl0_82
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f227,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oone__class_Oone(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f952,plain,
spl0_81,
inference(avatar_split_clause,[],[f226,f950]) ).
fof(f950,plain,
( spl0_81
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f226,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f948,plain,
spl0_80,
inference(avatar_split_clause,[],[f172,f946]) ).
fof(f946,plain,
( spl0_80
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f172,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f944,plain,
spl0_79,
inference(avatar_split_clause,[],[f99,f942]) ).
fof(f99,axiom,
! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__Suc__gt__zero_0) ).
fof(f940,plain,
spl0_78,
inference(avatar_split_clause,[],[f53,f938]) ).
fof(f938,plain,
( spl0_78
<=> ! [X9,X0] :
( ~ c_HOL_Oord__class_Oless(X0,X9,tc_RealDef_Oreal)
| c_lessequals(X0,X9,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f53,axiom,
! [X0,X9] :
( ~ c_HOL_Oord__class_Oless(X0,X9,tc_RealDef_Oreal)
| c_lessequals(X0,X9,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f929,plain,
spl0_77,
inference(avatar_split_clause,[],[f390,f926]) ).
fof(f926,plain,
( spl0_77
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f390,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__zero_0) ).
fof(f924,plain,
spl0_76,
inference(avatar_split_clause,[],[f296,f922]) ).
fof(f922,plain,
( spl0_76
<=> ! [X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f296,axiom,
! [X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X1,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__ge__zero_0) ).
fof(f920,plain,
spl0_75,
inference(avatar_split_clause,[],[f204,f918]) ).
fof(f204,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).
fof(f916,plain,
spl0_74,
inference(avatar_split_clause,[],[f111,f914]) ).
fof(f914,plain,
( spl0_74
<=> ! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f111,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f912,plain,
spl0_73,
inference(avatar_split_clause,[],[f95,f910]) ).
fof(f910,plain,
( spl0_73
<=> ! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f95,axiom,
! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f908,plain,
spl0_72,
inference(avatar_split_clause,[],[f94,f906]) ).
fof(f906,plain,
( spl0_72
<=> ! [X2] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f94,axiom,
! [X2] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f904,plain,
spl0_71,
inference(avatar_split_clause,[],[f80,f902]) ).
fof(f902,plain,
( spl0_71
<=> ! [X13,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X13,tc_nat),X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f80,axiom,
! [X15,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X13,tc_nat),X13,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f900,plain,
spl0_70,
inference(avatar_split_clause,[],[f79,f898]) ).
fof(f898,plain,
( spl0_70
<=> ! [X13,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X15,tc_nat),X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f79,axiom,
! [X15,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X15,tc_nat),X13,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f896,plain,
spl0_69,
inference(avatar_split_clause,[],[f433,f894]) ).
fof(f894,plain,
( spl0_69
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f433,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f892,plain,
spl0_68,
inference(avatar_split_clause,[],[f432,f890]) ).
fof(f890,plain,
( spl0_68
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X0,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f432,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f888,plain,
spl0_67,
inference(avatar_split_clause,[],[f377,f886]) ).
fof(f886,plain,
( spl0_67
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f377,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f884,plain,
spl0_66,
inference(avatar_split_clause,[],[f373,f882]) ).
fof(f882,plain,
( spl0_66
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f373,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f880,plain,
spl0_65,
inference(avatar_split_clause,[],[f372,f878]) ).
fof(f372,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f876,plain,
spl0_64,
inference(avatar_split_clause,[],[f288,f873]) ).
fof(f873,plain,
( spl0_64
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f288,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th000_I1_J_0) ).
fof(f871,plain,
spl0_63,
inference(avatar_split_clause,[],[f192,f869]) ).
fof(f869,plain,
( spl0_63
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f192,axiom,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f867,plain,
spl0_62,
inference(avatar_split_clause,[],[f23,f864]) ).
fof(f864,plain,
( spl0_62
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_RComplete_Onatfloor(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f23,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_RComplete_Onatfloor(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__zero_0) ).
fof(f862,plain,
spl0_61,
inference(avatar_split_clause,[],[f3,f860]) ).
fof(f3,axiom,
! [X1] : c_RComplete_Onatfloor(c_RealDef_Oreal(X1,tc_nat)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natfloor__real__of__nat_0) ).
fof(f858,plain,
spl0_60,
inference(avatar_split_clause,[],[f361,f856]) ).
fof(f361,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f854,plain,
~ spl0_59,
inference(avatar_split_clause,[],[f100,f851]) ).
fof(f851,plain,
( spl0_59
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f100,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f849,plain,
spl0_58,
inference(avatar_split_clause,[],[f67,f847]) ).
fof(f67,axiom,
! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
fof(f845,plain,
spl0_57,
inference(avatar_split_clause,[],[f58,f843]) ).
fof(f843,plain,
( spl0_57
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f58,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
fof(f841,plain,
spl0_56,
inference(avatar_split_clause,[],[f461,f839]) ).
fof(f461,axiom,
! [X1] : c_Suc(X1) != X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f837,plain,
spl0_55,
inference(avatar_split_clause,[],[f430,f835]) ).
fof(f430,axiom,
! [X19] : c_lessequals(X19,X19,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f833,plain,
spl0_54,
inference(avatar_split_clause,[],[f376,f831]) ).
fof(f376,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f829,plain,
spl0_53,
inference(avatar_split_clause,[],[f374,f827]) ).
fof(f827,plain,
( spl0_53
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f374,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f825,plain,
spl0_52,
inference(avatar_split_clause,[],[f559,f822]) ).
fof(f822,plain,
( spl0_52
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f559,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f820,plain,
spl0_51,
inference(avatar_split_clause,[],[f558,f817]) ).
fof(f817,plain,
( spl0_51
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f558,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f815,plain,
spl0_50,
inference(avatar_split_clause,[],[f557,f812]) ).
fof(f812,plain,
( spl0_50
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f557,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f810,plain,
spl0_49,
inference(avatar_split_clause,[],[f556,f807]) ).
fof(f807,plain,
( spl0_49
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f556,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f805,plain,
spl0_48,
inference(avatar_split_clause,[],[f555,f802]) ).
fof(f802,plain,
( spl0_48
<=> class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f555,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Nat_Osemiring__char__0) ).
fof(f800,plain,
spl0_47,
inference(avatar_split_clause,[],[f554,f797]) ).
fof(f797,plain,
( spl0_47
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f554,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f795,plain,
spl0_46,
inference(avatar_split_clause,[],[f553,f792]) ).
fof(f553,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f790,plain,
spl0_45,
inference(avatar_split_clause,[],[f552,f787]) ).
fof(f787,plain,
( spl0_45
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f552,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
fof(f785,plain,
spl0_44,
inference(avatar_split_clause,[],[f551,f782]) ).
fof(f551,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f780,plain,
spl0_43,
inference(avatar_split_clause,[],[f550,f777]) ).
fof(f777,plain,
( spl0_43
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f550,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f775,plain,
spl0_42,
inference(avatar_split_clause,[],[f549,f772]) ).
fof(f772,plain,
( spl0_42
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f549,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f770,plain,
spl0_41,
inference(avatar_split_clause,[],[f548,f767]) ).
fof(f548,axiom,
class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) ).
fof(f765,plain,
spl0_40,
inference(avatar_split_clause,[],[f547,f762]) ).
fof(f547,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f760,plain,
spl0_39,
inference(avatar_split_clause,[],[f546,f757]) ).
fof(f757,plain,
( spl0_39
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f546,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
fof(f755,plain,
spl0_38,
inference(avatar_split_clause,[],[f545,f752]) ).
fof(f752,plain,
( spl0_38
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f545,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f750,plain,
spl0_37,
inference(avatar_split_clause,[],[f544,f747]) ).
fof(f747,plain,
( spl0_37
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f544,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f745,plain,
spl0_36,
inference(avatar_split_clause,[],[f543,f742]) ).
fof(f742,plain,
( spl0_36
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f543,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f740,plain,
spl0_35,
inference(avatar_split_clause,[],[f542,f737]) ).
fof(f737,plain,
( spl0_35
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f542,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f735,plain,
spl0_34,
inference(avatar_split_clause,[],[f541,f732]) ).
fof(f541,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f730,plain,
spl0_33,
inference(avatar_split_clause,[],[f540,f727]) ).
fof(f540,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f725,plain,
spl0_32,
inference(avatar_split_clause,[],[f539,f722]) ).
fof(f722,plain,
( spl0_32
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f539,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f720,plain,
spl0_31,
inference(avatar_split_clause,[],[f538,f717]) ).
fof(f717,plain,
( spl0_31
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f538,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f715,plain,
spl0_30,
inference(avatar_split_clause,[],[f537,f712]) ).
fof(f537,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f710,plain,
spl0_29,
inference(avatar_split_clause,[],[f536,f707]) ).
fof(f707,plain,
( spl0_29
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f536,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f705,plain,
spl0_28,
inference(avatar_split_clause,[],[f535,f702]) ).
fof(f535,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f700,plain,
spl0_27,
inference(avatar_split_clause,[],[f534,f697]) ).
fof(f697,plain,
( spl0_27
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f534,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f695,plain,
spl0_26,
inference(avatar_split_clause,[],[f533,f692]) ).
fof(f692,plain,
( spl0_26
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f533,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f690,plain,
spl0_25,
inference(avatar_split_clause,[],[f532,f687]) ).
fof(f687,plain,
( spl0_25
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f532,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f685,plain,
spl0_24,
inference(avatar_split_clause,[],[f531,f682]) ).
fof(f682,plain,
( spl0_24
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f531,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f680,plain,
spl0_23,
inference(avatar_split_clause,[],[f530,f677]) ).
fof(f677,plain,
( spl0_23
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f530,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
fof(f675,plain,
spl0_22,
inference(avatar_split_clause,[],[f529,f672]) ).
fof(f529,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f670,plain,
spl0_21,
inference(avatar_split_clause,[],[f528,f667]) ).
fof(f667,plain,
( spl0_21
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f528,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f665,plain,
spl0_20,
inference(avatar_split_clause,[],[f527,f662]) ).
fof(f662,plain,
( spl0_20
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f527,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f660,plain,
spl0_19,
inference(avatar_split_clause,[],[f526,f657]) ).
fof(f657,plain,
( spl0_19
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f526,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f655,plain,
spl0_18,
inference(avatar_split_clause,[],[f525,f652]) ).
fof(f525,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f650,plain,
spl0_17,
inference(avatar_split_clause,[],[f524,f647]) ).
fof(f524,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f645,plain,
spl0_16,
inference(avatar_split_clause,[],[f523,f642]) ).
fof(f642,plain,
( spl0_16
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f523,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f640,plain,
spl0_15,
inference(avatar_split_clause,[],[f522,f637]) ).
fof(f637,plain,
( spl0_15
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f522,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f635,plain,
spl0_14,
inference(avatar_split_clause,[],[f521,f632]) ).
fof(f521,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f630,plain,
spl0_13,
inference(avatar_split_clause,[],[f520,f627]) ).
fof(f627,plain,
( spl0_13
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f520,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f625,plain,
spl0_12,
inference(avatar_split_clause,[],[f519,f622]) ).
fof(f519,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f620,plain,
spl0_11,
inference(avatar_split_clause,[],[f518,f617]) ).
fof(f617,plain,
( spl0_11
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f518,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f615,plain,
spl0_10,
inference(avatar_split_clause,[],[f517,f612]) ).
fof(f612,plain,
( spl0_10
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f517,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f610,plain,
spl0_9,
inference(avatar_split_clause,[],[f516,f607]) ).
fof(f607,plain,
( spl0_9
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f516,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f605,plain,
spl0_8,
inference(avatar_split_clause,[],[f515,f602]) ).
fof(f602,plain,
( spl0_8
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f515,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f600,plain,
spl0_7,
inference(avatar_split_clause,[],[f514,f597]) ).
fof(f597,plain,
( spl0_7
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f514,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f595,plain,
spl0_6,
inference(avatar_split_clause,[],[f513,f592]) ).
fof(f592,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f513,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f590,plain,
spl0_5,
inference(avatar_split_clause,[],[f512,f587]) ).
fof(f587,plain,
( spl0_5
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f512,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f585,plain,
spl0_4,
inference(avatar_split_clause,[],[f511,f582]) ).
fof(f582,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f511,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f580,plain,
spl0_3,
inference(avatar_split_clause,[],[f510,f577]) ).
fof(f577,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f510,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f575,plain,
spl0_2,
inference(avatar_split_clause,[],[f509,f572]) ).
fof(f572,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f509,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f570,plain,
spl0_1,
inference(avatar_split_clause,[],[f508,f567]) ).
fof(f567,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f508,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG377-1 : TPTP v8.2.0. Released v4.1.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat May 18 22:51:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (9068)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (9071)WARNING: value z3 for option sas not known
% 0.22/0.43 % (9072)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.43 % (9069)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.43 % (9070)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.43 % (9074)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.43 % (9075)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.43 % (9073)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.43 % (9071)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.48 TRYING [1]
% 0.22/0.49 TRYING [2]
% 1.23/0.61 TRYING [3]
% 2.09/0.70 TRYING [1]
% 2.54/0.74 TRYING [2]
% 3.32/0.85 % (9073)First to succeed.
% 3.32/0.88 % (9073)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9068"
% 3.32/0.88 % (9073)Refutation found. Thanks to Tanya!
% 3.32/0.88 % SZS status Unsatisfiable for theBenchmark
% 3.32/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 3.32/0.89 % (9073)------------------------------
% 3.32/0.89 % (9073)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.32/0.89 % (9073)Termination reason: Refutation
% 3.32/0.89
% 3.32/0.89 % (9073)Memory used [KB]: 5408
% 3.32/0.89 % (9073)Time elapsed: 0.446 s
% 3.32/0.89 % (9073)Instructions burned: 708 (million)
% 3.32/0.89 % (9068)Success in time 0.512 s
%------------------------------------------------------------------------------