TSTP Solution File: SWW230+1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SWW230+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n026.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 : Wed Aug 31 19:18:45 EDT 2022
% Result : Theorem 26.07s 3.79s
% Output : Refutation 27.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 902
% Syntax : Number of formulae : 3680 (1176 unt; 0 def)
% Number of atoms : 8180 (1500 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 7750 (3250 ~;3372 |; 320 &)
% ( 649 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 557 ( 555 usr; 491 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 20 con; 0-3 aty)
% Number of variables : 2854 (2806 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16453,plain,
$false,
inference(avatar_smt_refutation,[],[f6254,f6259,f6264,f6273,f6278,f6284,f6289,f6294,f6299,f6314,f6319,f6324,f6329,f6334,f6339,f6344,f6349,f6354,f6365,f6370,f6375,f6376,f6390,f6397,f6402,f6407,f6416,f6421,f6426,f6432,f6437,f6442,f6452,f6457,f6462,f6467,f6474,f6479,f6485,f6490,f6511,f6520,f6525,f6530,f6539,f6544,f6549,f6554,f6559,f6569,f6574,f6579,f6586,f6595,f6600,f6605,f6610,f6615,f6617,f6630,f6635,f6640,f6645,f6650,f6655,f6660,f6665,f6674,f6679,f6684,f6691,f6706,f6712,f6722,f6728,f6737,f6742,f6750,f6761,f6766,f6771,f6782,f6787,f6793,f6802,f6807,f6820,f6825,f6830,f6842,f6850,f6855,f6860,f6867,f6873,f6878,f6888,f6891,f6900,f6905,f6911,f6921,f6931,f6936,f6941,f6946,f6951,f6956,f6961,f6966,f6971,f6976,f6981,f6987,f6992,f6998,f7003,f7011,f7016,f7021,f7028,f7034,f7039,f7044,f7056,f7063,f7068,f7073,f7078,f7082,f7087,f7092,f7105,f7110,f7120,f7128,f7133,f7144,f7149,f7160,f7166,f7173,f7189,f7196,f7205,f7210,f7217,f7224,f7229,f7234,f7248,f7253,f7258,f7267,f7272,f7277,f7290,f7295,f7300,f7306,f7311,f7319,f7324,f7340,f7345,f7351,f7356,f7361,f7377,f7382,f7387,f7392,f7397,f7511,f7516,f7521,f7534,f7545,f7548,f7553,f7559,f7575,f7580,f7585,f7590,f7595,f7600,f7605,f7633,f7638,f7643,f7648,f7655,f7660,f7665,f7686,f7691,f7840,f7899,f7904,f7913,f7918,f7923,f7928,f7933,f7938,f7943,f7968,f7973,f7985,f7990,f7996,f8008,f8013,f8018,f8038,f8043,f8048,f8053,f8058,f8063,f8068,f8074,f8085,f8091,f8096,f8101,f8107,f8113,f8115,f8132,f8137,f8149,f8172,f8177,f8182,f8187,f8192,f8197,f8203,f8208,f8226,f8231,f8236,f8237,f8243,f8249,f8270,f8287,f8294,f8305,f8320,f8373,f8385,f8391,f8398,f8412,f8419,f8428,f8434,f8447,f8466,f8480,f8494,f8504,f8520,f8539,f8545,f8552,f8578,f8594,f8601,f8618,f8623,f8684,f8689,f8695,f8716,f8717,f8771,f8789,f8814,f8891,f8921,f8926,f9052,f9057,f9066,f9071,f9076,f9081,f9100,f9188,f9203,f9208,f9241,f9532,f9606,f10189,f10205,f10228,f10231,f10246,f10258,f10309,f10328,f10336,f10382,f10383,f10463,f10687,f10691,f10708,f10718,f10958,f10962,f10966,f10968,f10974,f10995,f10996,f11005,f11010,f11015,f11016,f11020,f11022,f11024,f11028,f11030,f11035,f11043,f11045,f11051,f11054,f11061,f11066,f11071,f11073,f11078,f11085,f11090,f11093,f11098,f11102,f11107,f11108,f11110,f11111,f11115,f11120,f11123,f11133,f11135,f11143,f11145,f11146,f11152,f11158,f11165,f11169,f11178,f11179,f11183,f11190,f11191,f11192,f11196,f11198,f11204,f11210,f11212,f11216,f11218,f11223,f11230,f11232,f11236,f11241,f11244,f11249,f11250,f11251,f11254,f11262,f11265,f11266,f11267,f11276,f11277,f11282,f11287,f11290,f11291,f11299,f11306,f11311,f11312,f11317,f11320,f11324,f11326,f11328,f11331,f11332,f11336,f11343,f11347,f11348,f11354,f11357,f11362,f11370,f11372,f11383,f11385,f11389,f11391,f11394,f11395,f11401,f11403,f11407,f11413,f11422,f11428,f11437,f11447,f11450,f11457,f11460,f11466,f11476,f11485,f11486,f11600,f11606,f11631,f11676,f11705,f11793,f11842,f11849,f11871,f11877,f11984,f12012,f12048,f12049,f12052,f12056,f12058,f12201,f12238,f12413,f12661,f12666,f12817,f12818,f12822,f12823,f12838,f12839,f12846,f12853,f12864,f12869,f12876,f12890,f12898,f12915,f12923,f12930,f12933,f12939,f12948,f12957,f12972,f12977,f12984,f12991,f12998,f13047,f13055,f13066,f13082,f13087,f13096,f13101,f13135,f13140,f13145,f13150,f13155,f13160,f13165,f13170,f13175,f13181,f13186,f13191,f13196,f13201,f13206,f13211,f13216,f13221,f13250,f13274,f13275,f13376,f13387,f13394,f13396,f13401,f13484,f13485,f13850,f13878,f13883,f13930,f13935,f13940,f13942,f13947,f14057,f14061,f14066,f14088,f14089,f14189,f14255,f14425,f14599,f14902,f14917,f14922,f14927,f14932,f14937,f15085,f15118,f15124,f15227,f15233,f15235,f15237,f15442,f15462,f15471,f15482,f15498,f15512,f15716,f15717,f15924,f15935,f15945,f15955,f16070,f16194,f16199,f16204,f16213,f16218,f16223,f16253,f16262,f16267,f16272,f16277,f16282,f16288,f16294,f16383,f16388,f16401,f16406,f16416,f16434,f16442,f16447,f16452]) ).
fof(f16452,plain,
( ~ spl35_264
| ~ spl35_188
| ~ spl35_289
| ~ spl35_292
| ~ spl35_401
| spl35_490 ),
inference(avatar_split_clause,[],[f16451,f16444,f13098,f9529,f9201,f7640,f8591]) ).
fof(f8591,plain,
( spl35_264
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_264])]) ).
fof(f7640,plain,
( spl35_188
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_188])]) ).
fof(f9201,plain,
( spl35_289
<=> ! [X0] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_289])]) ).
fof(f9529,plain,
( spl35_292
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_292])]) ).
fof(f13098,plain,
( spl35_401
<=> c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_401])]) ).
fof(f16444,plain,
( spl35_490
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_490])]) ).
fof(f16451,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_188
| ~ spl35_289
| ~ spl35_292
| ~ spl35_401
| spl35_490 ),
inference(forward_demodulation,[],[f16446,f16449]) ).
fof(f16449,plain,
( ! [X0] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = X0
| ~ spl35_188
| ~ spl35_289
| ~ spl35_292
| ~ spl35_401 ),
inference(backward_demodulation,[],[f16421,f16448]) ).
fof(f16448,plain,
( ! [X7] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X7,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) = X7
| ~ spl35_188
| ~ spl35_289
| ~ spl35_292
| ~ spl35_401 ),
inference(forward_demodulation,[],[f16420,f9202]) ).
fof(f9202,plain,
( ! [X0] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X0
| ~ spl35_289 ),
inference(avatar_component_clause,[],[f9201]) ).
fof(f16420,plain,
( ! [X7] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X7,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_188
| ~ spl35_292
| ~ spl35_401 ),
inference(superposition,[],[f13110,f9534]) ).
fof(f9534,plain,
( ! [X1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X1
| ~ spl35_188
| ~ spl35_292 ),
inference(backward_demodulation,[],[f9526,f9531]) ).
fof(f9531,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_292 ),
inference(avatar_component_clause,[],[f9529]) ).
fof(f9526,plain,
( ! [X1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint))) = X1
| ~ spl35_188 ),
inference(resolution,[],[f7642,f7762]) ).
fof(f7762,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) = X1 ),
inference(forward_demodulation,[],[f7700,f4335]) ).
fof(f4335,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f1883]) ).
fof(f1883,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X20) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f7700,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) = X1 ),
inference(backward_demodulation,[],[f6701,f4335]) ).
fof(f6701,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))) = X1 ),
inference(forward_demodulation,[],[f6700,f5637]) ).
fof(f5637,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
inference(cnf_transformation,[],[f1512]) ).
fof(f1512,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X14,X22] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f6700,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))) = X1 ),
inference(forward_demodulation,[],[f5829,f5637]) ).
fof(f5829,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = X1 ),
inference(definition_unfolding,[],[f4336,f5442]) ).
fof(f5442,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0) = c_Int_OBit1(X0),
inference(cnf_transformation,[],[f2036]) ).
fof(f2036,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0) = c_Int_OBit1(X0),
inference(rectify,[],[f299]) ).
fof(f299,axiom,
! [X20] : c_Int_OBit1(X20) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X20),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f4336,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))) = X1 ),
inference(cnf_transformation,[],[f3215]) ).
fof(f3215,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Otimes__class_Otimes(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))) = X1 ),
inference(rectify,[],[f2127]) ).
fof(f2127,plain,
! [X1,X0] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Otimes__class_Otimes(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X0 ),
inference(ennf_transformation,[],[f1553]) ).
fof(f1553,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Otimes__class_Otimes(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X0 ),
inference(rectify,[],[f70]) ).
fof(f70,axiom,
! [X3,X15] :
( class_Int_Onumber__ring(X15)
=> c_Groups_Otimes__class_Otimes(X15,X3,c_Int_Onumber__class_Onumber__of(X15,c_Int_OBit1(c_Int_OPls))) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
fof(f7642,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ spl35_188 ),
inference(avatar_component_clause,[],[f7640]) ).
fof(f13110,plain,
( ! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)))
| ~ spl35_401 ),
inference(backward_demodulation,[],[f7798,f13100]) ).
fof(f13100,plain,
( c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_401 ),
inference(avatar_component_clause,[],[f13098]) ).
fof(f7798,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1))),
inference(forward_demodulation,[],[f7797,f4335]) ).
fof(f7797,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X1))),
inference(forward_demodulation,[],[f7796,f4335]) ).
fof(f7796,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X1))),
inference(forward_demodulation,[],[f7707,f4335]) ).
fof(f7707,plain,
! [X0,X1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),X1))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1),
inference(backward_demodulation,[],[f7431,f4335]) ).
fof(f7431,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),X1))),
inference(forward_demodulation,[],[f7430,f5723]) ).
fof(f5723,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(cnf_transformation,[],[f1368]) ).
fof(f1368,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X10,X36,X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,X14)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f7430,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),X1))),
inference(forward_demodulation,[],[f7429,f5723]) ).
fof(f7429,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),X1))),
inference(forward_demodulation,[],[f7412,f5723]) ).
fof(f7412,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),X1))),
inference(backward_demodulation,[],[f6563,f5723]) ).
fof(f6563,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),X1))),
inference(forward_demodulation,[],[f6562,f5637]) ).
fof(f6562,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),X1))),
inference(forward_demodulation,[],[f6561,f5637]) ).
fof(f6561,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),X1))),
inference(forward_demodulation,[],[f6560,f5537]) ).
fof(f5537,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)),
inference(cnf_transformation,[],[f1930]) ).
fof(f1930,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X2),X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X41,X42,X40] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X41,X40),X42) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X41,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X40,X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f6560,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X1))),
inference(forward_demodulation,[],[f6113,f5537]) ).
fof(f6113,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1))),
inference(equality_resolution,[],[f5895]) ).
fof(f5895,plain,
! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2)
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)) != X2 ),
inference(definition_unfolding,[],[f4734,f4431,f5442,f4431,f5442]) ).
fof(f4431,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f1267]) ).
fof(f1267,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X20] : c_Int_OBit0(X20) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f4734,plain,
! [X2,X0,X1] :
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) != X2 ),
inference(cnf_transformation,[],[f3434]) ).
fof(f3434,plain,
! [X0,X1,X2] :
( ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) != X2 )
& ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) = X2
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ) ),
inference(rectify,[],[f3433]) ).
fof(f3433,plain,
! [X1,X0,X2] :
( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0)
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)) != X2 )
& ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)) = X2
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f2062]) ).
fof(f2062,plain,
! [X1,X0,X2] :
( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0)
<=> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)) = X2 ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X11,X12,X13] :
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X12,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X11)) = X13
<=> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X13) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X12,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__2__times__iff) ).
fof(f16421,plain,
( ! [X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_401 ),
inference(superposition,[],[f13110,f4894]) ).
fof(f4894,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)),
inference(cnf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0,X1] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X0) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)),
inference(rectify,[],[f625]) ).
fof(f625,axiom,
! [X51,X3] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X51,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X51,X51)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3,X51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).
fof(f16446,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| spl35_490 ),
inference(avatar_component_clause,[],[f16444]) ).
fof(f16447,plain,
( ~ spl35_490
| ~ spl35_401
| spl35_415 ),
inference(avatar_split_clause,[],[f16437,f13198,f13098,f16444]) ).
fof(f13198,plain,
( spl35_415
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_415])]) ).
fof(f16437,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_401
| spl35_415 ),
inference(backward_demodulation,[],[f13200,f16421]) ).
fof(f13200,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| spl35_415 ),
inference(avatar_component_clause,[],[f13198]) ).
fof(f16442,plain,
( ~ spl35_489
| ~ spl35_401
| spl35_405 ),
inference(avatar_split_clause,[],[f16436,f13147,f13098,f16439]) ).
fof(f16439,plain,
( spl35_489
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_489])]) ).
fof(f13147,plain,
( spl35_405
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_405])]) ).
fof(f16436,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_401
| spl35_405 ),
inference(backward_demodulation,[],[f13149,f16421]) ).
fof(f13149,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| spl35_405 ),
inference(avatar_component_clause,[],[f13147]) ).
fof(f16434,plain,
( ~ spl35_389
| spl35_488
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f16430,f13098,f16432,f12969]) ).
fof(f12969,plain,
( spl35_389
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_389])]) ).
fof(f16432,plain,
( spl35_488
<=> ! [X27,X28] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X27,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X28)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X27,X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_488])]) ).
fof(f16430,plain,
( ! [X28,X27] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X27,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X28)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X27,X28))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
| ~ spl35_401 ),
inference(superposition,[],[f5682,f13110]) ).
fof(f5682,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(cnf_transformation,[],[f2542]) ).
fof(f2542,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0)) ),
inference(flattening,[],[f2541]) ).
fof(f2541,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(ennf_transformation,[],[f1409]) ).
fof(f1409,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0)) ) ),
inference(rectify,[],[f149]) ).
fof(f149,axiom,
! [X36,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X36)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(f16416,plain,
( ~ spl35_486
| spl35_487
| spl35_340 ),
inference(avatar_split_clause,[],[f16407,f11201,f16413,f16409]) ).
fof(f16409,plain,
( spl35_486
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_486])]) ).
fof(f16413,plain,
( spl35_487
<=> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_487])]) ).
fof(f11201,plain,
( spl35_340
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_340])]) ).
fof(f16407,plain,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| spl35_340 ),
inference(resolution,[],[f11202,f4559]) ).
fof(f4559,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f3339]) ).
fof(f3339,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
& X0 != X1 ) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ) ),
inference(rectify,[],[f3338]) ).
fof(f3338,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
& X0 != X1 ) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f3337]) ).
fof(f3337,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
& X0 != X1 ) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f1800]) ).
fof(f1800,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 = X1 ) ),
inference(rectify,[],[f211]) ).
fof(f211,axiom,
! [X12,X13] :
( ( X12 = X13
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X12) )
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(f11202,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| spl35_340 ),
inference(avatar_component_clause,[],[f11201]) ).
fof(f16406,plain,
( spl35_485
| ~ spl35_268 ),
inference(avatar_split_clause,[],[f16395,f8681,f16403]) ).
fof(f16403,plain,
( spl35_485
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_485])]) ).
fof(f8681,plain,
( spl35_268
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_268])]) ).
fof(f16395,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_268 ),
inference(superposition,[],[f9432,f8683]) ).
fof(f8683,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_268 ),
inference(avatar_component_clause,[],[f8681]) ).
fof(f9432,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),
inference(resolution,[],[f5009,f4108]) ).
fof(f4108,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(cnf_transformation,[],[f1560]) ).
fof(f1560,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(rectify,[],[f274]) ).
fof(f274,axiom,
! [X10] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(f5009,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
inference(cnf_transformation,[],[f3596]) ).
fof(f3596,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ) ),
inference(rectify,[],[f3595]) ).
fof(f3595,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1) ) ),
inference(nnf_transformation,[],[f1603]) ).
fof(f1603,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)) ),
inference(rectify,[],[f177]) ).
fof(f177,axiom,
! [X13,X12] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13),X12)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(f16401,plain,
( spl35_484
| ~ spl35_377 ),
inference(avatar_split_clause,[],[f16396,f12850,f16398]) ).
fof(f16398,plain,
( spl35_484
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_484])]) ).
fof(f12850,plain,
( spl35_377
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_377])]) ).
fof(f16396,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_377 ),
inference(superposition,[],[f9432,f12852]) ).
fof(f12852,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_377 ),
inference(avatar_component_clause,[],[f12850]) ).
fof(f16388,plain,
( spl35_483
| ~ spl35_35 ),
inference(avatar_split_clause,[],[f16376,f6464,f16385]) ).
fof(f16385,plain,
( spl35_483
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_483])]) ).
fof(f6464,plain,
( spl35_35
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_35])]) ).
fof(f16376,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))
| ~ spl35_35 ),
inference(superposition,[],[f8211,f6466]) ).
fof(f6466,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_35 ),
inference(avatar_component_clause,[],[f6464]) ).
fof(f8211,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(X0))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),
inference(backward_demodulation,[],[f5873,f5992]) ).
fof(f5992,plain,
! [X0] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f5244,f4497]) ).
fof(f4497,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1515]) ).
fof(f1515,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(rectify,[],[f391]) ).
fof(f391,axiom,
! [X37] : c_Nat_OSuc(X37) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f5244,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1649]) ).
fof(f1649,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0)),
inference(rectify,[],[f268]) ).
fof(f268,axiom,
! [X37] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X37)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X37),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
fof(f5873,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(X0))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))))),
inference(definition_unfolding,[],[f4555,f4497]) ).
fof(f4555,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(X0))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0))))),
inference(cnf_transformation,[],[f1722]) ).
fof(f1722,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(X0))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0))))),
inference(rectify,[],[f90]) ).
fof(f90,axiom,
! [X5] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(X5))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X5))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_g_I2_J) ).
fof(f16383,plain,
( spl35_482
| ~ spl35_64 ),
inference(avatar_split_clause,[],[f16377,f6657,f16380]) ).
fof(f16380,plain,
( spl35_482
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_482])]) ).
fof(f6657,plain,
( spl35_64
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_64])]) ).
fof(f16377,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))
| ~ spl35_64 ),
inference(superposition,[],[f8211,f6659]) ).
fof(f6659,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl35_64 ),
inference(avatar_component_clause,[],[f6657]) ).
fof(f16294,plain,
( ~ spl35_188
| spl35_481
| ~ spl35_20
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f16290,f13098,f6367,f16292,f7640]) ).
fof(f16292,plain,
( spl35_481
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_481])]) ).
fof(f6367,plain,
( spl35_20
<=> class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_20])]) ).
fof(f16290,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
| ~ spl35_20
| ~ spl35_401 ),
inference(forward_demodulation,[],[f16289,f13100]) ).
fof(f16289,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) )
| ~ spl35_20 ),
inference(resolution,[],[f7811,f6369]) ).
fof(f6369,plain,
( class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal)
| ~ spl35_20 ),
inference(avatar_component_clause,[],[f6367]) ).
fof(f7811,plain,
! [X0,X1] :
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f7810,f4335]) ).
fof(f7810,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(forward_demodulation,[],[f7809,f4335]) ).
fof(f7809,plain,
! [X0,X1] :
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
inference(forward_demodulation,[],[f7710,f4335]) ).
fof(f7710,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ class_Int_Onumber__ring(X1) ),
inference(backward_demodulation,[],[f7440,f4335]) ).
fof(f7440,plain,
! [X0,X1] :
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(forward_demodulation,[],[f7439,f5723]) ).
fof(f7439,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(forward_demodulation,[],[f7438,f5723]) ).
fof(f7438,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(forward_demodulation,[],[f7413,f5723]) ).
fof(f7413,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ class_Int_Onumber__ring(X1) ),
inference(backward_demodulation,[],[f6697,f5723]) ).
fof(f6697,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(forward_demodulation,[],[f6696,f5637]) ).
fof(f6696,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))))) ),
inference(forward_demodulation,[],[f6695,f5637]) ).
fof(f6695,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(forward_demodulation,[],[f6694,f5537]) ).
fof(f6694,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5871,f5537]) ).
fof(f5871,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(definition_unfolding,[],[f4551,f4431,f5442]) ).
fof(f4551,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f3332]) ).
fof(f3332,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ),
inference(nnf_transformation,[],[f2164]) ).
fof(f2164,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(flattening,[],[f2163]) ).
fof(f2163,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) )
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f2028]) ).
fof(f2028,plain,
! [X1,X0] :
( ( class_Fields_Olinordered__field__inverse__zero(X1)
& class_Int_Onumber__ring(X1) )
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ) ),
inference(rectify,[],[f208]) ).
fof(f208,axiom,
! [X25,X15] :
( ( class_Fields_Olinordered__field__inverse__zero(X15)
& class_Int_Onumber__ring(X15) )
=> ( c_Orderings_Oord__class_Oless(X15,c_Groups_Ozero__class_Ozero(X15),c_Rings_Oinverse__class_Odivide(X15,X25,c_Int_Onumber__class_Onumber__of(X15,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless(X15,c_Groups_Ozero__class_Ozero(X15),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).
fof(f16288,plain,
( ~ spl35_188
| spl35_480
| ~ spl35_20
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f16284,f13098,f6367,f16286,f7640]) ).
fof(f16286,plain,
( spl35_480
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_480])]) ).
fof(f16284,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) )
| ~ spl35_20
| ~ spl35_401 ),
inference(forward_demodulation,[],[f16283,f13100]) ).
fof(f16283,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) )
| ~ spl35_20 ),
inference(resolution,[],[f7794,f6369]) ).
fof(f7794,plain,
! [X0,X1] :
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(forward_demodulation,[],[f7793,f4335]) ).
fof(f7793,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(forward_demodulation,[],[f7792,f4335]) ).
fof(f7792,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f7718,f4335]) ).
fof(f7718,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(backward_demodulation,[],[f7489,f4335]) ).
fof(f7489,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(forward_demodulation,[],[f7404,f5723]) ).
fof(f7404,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ class_Int_Onumber__ring(X1) ),
inference(backward_demodulation,[],[f6384,f5723]) ).
fof(f6384,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(forward_demodulation,[],[f6377,f5537]) ).
fof(f6377,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(backward_demodulation,[],[f6360,f5537]) ).
fof(f6360,plain,
! [X0,X1] :
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
inference(forward_demodulation,[],[f6359,f5637]) ).
fof(f6359,plain,
! [X0,X1] :
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))) ),
inference(forward_demodulation,[],[f5872,f5637]) ).
fof(f5872,plain,
! [X0,X1] :
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(definition_unfolding,[],[f4550,f4431,f5442]) ).
fof(f4550,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(cnf_transformation,[],[f3332]) ).
fof(f16282,plain,
( spl35_479
| ~ spl35_286 ),
inference(avatar_split_clause,[],[f16227,f9078,f16279]) ).
fof(f16279,plain,
( spl35_479
<=> v_N2____ = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N2____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_479])]) ).
fof(f9078,plain,
( spl35_286
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_286])]) ).
fof(f16227,plain,
( v_N2____ = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N2____))
| ~ spl35_286 ),
inference(resolution,[],[f9080,f4159]) ).
fof(f4159,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2217]) ).
fof(f2217,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X0 ),
inference(ennf_transformation,[],[f2010]) ).
fof(f2010,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X0 ),
inference(rectify,[],[f456]) ).
fof(f456,axiom,
! [X44,X37] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X37)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X37,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X37,X44)) = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(f9080,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_286 ),
inference(avatar_component_clause,[],[f9078]) ).
fof(f16277,plain,
( spl35_478
| ~ spl35_286 ),
inference(avatar_split_clause,[],[f16243,f9078,f16274]) ).
fof(f16274,plain,
( spl35_478
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,sK30(v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_478])]) ).
fof(f16243,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,sK30(v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_286 ),
inference(resolution,[],[f9080,f5515]) ).
fof(f5515,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK30(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f3889]) ).
fof(f3889,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK30(X0,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ! [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f3887,f3888]) ).
fof(f3888,plain,
! [X0,X1] :
( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK30(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f3887,plain,
! [X0,X1] :
( ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ! [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X1 ) ),
inference(rectify,[],[f3886]) ).
fof(f3886,plain,
! [X0,X1] :
( ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) != X1 ) ),
inference(nnf_transformation,[],[f2056]) ).
fof(f2056,plain,
! [X0,X1] :
( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f311]) ).
fof(f311,axiom,
! [X27,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X26)
<=> ? [X5] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X5) = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(f16272,plain,
( spl35_477
| ~ spl35_286 ),
inference(avatar_split_clause,[],[f16241,f9078,f16269]) ).
fof(f16269,plain,
( spl35_477
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_477])]) ).
fof(f16241,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_286 ),
inference(resolution,[],[f9080,f5346]) ).
fof(f5346,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3792]) ).
fof(f3792,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f3011]) ).
fof(f3011,plain,
! [X1,X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f2060]) ).
fof(f2060,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f498]) ).
fof(f498,axiom,
! [X37,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X37)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X37) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(f16267,plain,
( spl35_476
| ~ spl35_286 ),
inference(avatar_split_clause,[],[f16240,f9078,f16264]) ).
fof(f16264,plain,
( spl35_476
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,sK24(v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_476])]) ).
fof(f16240,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,sK24(v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_286 ),
inference(resolution,[],[f9080,f5301]) ).
fof(f5301,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK24(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f3771]) ).
fof(f3771,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) != X1 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK24(X0,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f3769,f3770]) ).
fof(f3770,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK24(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f3769,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) != X1 )
& ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
inference(rectify,[],[f3768]) ).
fof(f3768,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) != X1 )
& ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ),
inference(nnf_transformation,[],[f1605]) ).
fof(f1605,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
<=> ? [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = X1 ),
inference(rectify,[],[f432]) ).
fof(f432,axiom,
! [X6,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X50)
<=> ? [X70] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X70) = X50 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(f16262,plain,
( ~ spl35_474
| spl35_475
| ~ spl35_286 ),
inference(avatar_split_clause,[],[f16237,f9078,f16259,f16255]) ).
fof(f16255,plain,
( spl35_474
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N2____) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_474])]) ).
fof(f16259,plain,
( spl35_475
<=> v_N2____ = hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_475])]) ).
fof(f16237,plain,
( v_N2____ = hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N2____)
| ~ spl35_286 ),
inference(resolution,[],[f9080,f5011]) ).
fof(f5011,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f2534]) ).
fof(f2534,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(flattening,[],[f2533]) ).
fof(f2533,plain,
! [X1,X0] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1672]) ).
fof(f1672,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> X0 = X1 ) ),
inference(rectify,[],[f346]) ).
fof(f346,axiom,
! [X37,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X37)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X0)
=> X0 = X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(f16253,plain,
( spl35_473
| ~ spl35_286 ),
inference(avatar_split_clause,[],[f16248,f9078,f16250]) ).
fof(f16250,plain,
( spl35_473
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N2____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_473])]) ).
fof(f16248,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N2____))
| ~ spl35_286 ),
inference(resolution,[],[f9080,f6620]) ).
fof(f6620,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
inference(backward_demodulation,[],[f4476,f5023]) ).
fof(f5023,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f3604]) ).
fof(f3604,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(rectify,[],[f1309]) ).
fof(f1309,plain,
! [X1,X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(rectify,[],[f345]) ).
fof(f345,axiom,
! [X37,X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X37) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f4476,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X0) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3010]) ).
fof(f3010,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X0) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f1246]) ).
fof(f1246,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X0) = X1 ),
inference(rectify,[],[f510]) ).
fof(f510,axiom,
! [X37,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X0)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X37),X37) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(f16223,plain,
( spl35_472
| ~ spl35_280 ),
inference(avatar_split_clause,[],[f16168,f9049,f16220]) ).
fof(f16220,plain,
( spl35_472
<=> v_N1____ = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N1____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_472])]) ).
fof(f9049,plain,
( spl35_280
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_280])]) ).
fof(f16168,plain,
( v_N1____ = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N1____))
| ~ spl35_280 ),
inference(resolution,[],[f9051,f4159]) ).
fof(f9051,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_280 ),
inference(avatar_component_clause,[],[f9049]) ).
fof(f16218,plain,
( spl35_471
| ~ spl35_280 ),
inference(avatar_split_clause,[],[f16189,f9049,f16215]) ).
fof(f16215,plain,
( spl35_471
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N1____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_471])]) ).
fof(f16189,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N1____))
| ~ spl35_280 ),
inference(resolution,[],[f9051,f6620]) ).
fof(f16213,plain,
( spl35_469
| ~ spl35_470
| ~ spl35_280 ),
inference(avatar_split_clause,[],[f16178,f9049,f16210,f16206]) ).
fof(f16206,plain,
( spl35_469
<=> v_N1____ = hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_469])]) ).
fof(f16210,plain,
( spl35_470
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N1____) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_470])]) ).
fof(f16178,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),v_N1____)
| v_N1____ = hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
| ~ spl35_280 ),
inference(resolution,[],[f9051,f5011]) ).
fof(f16204,plain,
( spl35_468
| ~ spl35_280 ),
inference(avatar_split_clause,[],[f16182,f9049,f16201]) ).
fof(f16201,plain,
( spl35_468
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_468])]) ).
fof(f16182,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_280 ),
inference(resolution,[],[f9051,f5346]) ).
fof(f16199,plain,
( spl35_467
| ~ spl35_280 ),
inference(avatar_split_clause,[],[f16181,f9049,f16196]) ).
fof(f16196,plain,
( spl35_467
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,sK24(v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_467])]) ).
fof(f16181,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,sK24(v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_280 ),
inference(resolution,[],[f9051,f5301]) ).
fof(f16194,plain,
( spl35_466
| ~ spl35_280 ),
inference(avatar_split_clause,[],[f16184,f9049,f16191]) ).
fof(f16191,plain,
( spl35_466
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,sK30(v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_466])]) ).
fof(f16184,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,sK30(v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_280 ),
inference(resolution,[],[f9051,f5515]) ).
fof(f16070,plain,
( spl35_464
| spl35_465
| ~ spl35_259 ),
inference(avatar_split_clause,[],[f16059,f8517,f16067,f16064]) ).
fof(f16064,plain,
( spl35_464
<=> ! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_464])]) ).
fof(f16067,plain,
( spl35_465
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_465])]) ).
fof(f8517,plain,
( spl35_259
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_259])]) ).
fof(f16059,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1) )
| ~ spl35_259 ),
inference(superposition,[],[f4574,f8519]) ).
fof(f8519,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_259 ),
inference(avatar_component_clause,[],[f8517]) ).
fof(f4574,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f3349]) ).
fof(f3349,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ) ),
inference(rectify,[],[f3348]) ).
fof(f3348,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(flattening,[],[f3347]) ).
fof(f3347,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(nnf_transformation,[],[f2269]) ).
fof(f2269,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(ennf_transformation,[],[f1658]) ).
fof(f1658,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) )
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(rectify,[],[f538]) ).
fof(f538,axiom,
! [X74,X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X24),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X74))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X74)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,c_Int_OPls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
fof(f15955,plain,
( spl35_463
| ~ spl35_230
| spl35_296 ),
inference(avatar_split_clause,[],[f15954,f10225,f8146,f15943]) ).
fof(f15943,plain,
( spl35_463
<=> ! [X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_463])]) ).
fof(f8146,plain,
( spl35_230
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_230])]) ).
fof(f10225,plain,
( spl35_296
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_296])]) ).
fof(f15954,plain,
( ! [X47] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls) )
| ~ spl35_230
| spl35_296 ),
inference(forward_demodulation,[],[f15953,f5023]) ).
fof(f15953,plain,
( ! [X47] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls) )
| ~ spl35_230
| spl35_296 ),
inference(forward_demodulation,[],[f15911,f8148]) ).
fof(f8148,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_230 ),
inference(avatar_component_clause,[],[f8146]) ).
fof(f15911,plain,
( ! [X47] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls) )
| spl35_296 ),
inference(resolution,[],[f4813,f10227]) ).
fof(f10227,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)
| spl35_296 ),
inference(avatar_component_clause,[],[f10225]) ).
fof(f4813,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ),
inference(cnf_transformation,[],[f2547]) ).
fof(f2547,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ) ),
inference(ennf_transformation,[],[f2068]) ).
fof(f2068,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1)) ) ) ) ),
inference(rectify,[],[f550]) ).
fof(f550,axiom,
! [X28,X63] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,c_Int_OPls)
=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Int_OPls)
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X28) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X28),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X28),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,X63)) ) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X28,c_Int_OPls)
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X28),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
fof(f15945,plain,
( spl35_462
| spl35_463
| ~ spl35_230 ),
inference(avatar_split_clause,[],[f15941,f8146,f15943,f15922]) ).
fof(f15922,plain,
( spl35_462
<=> ! [X49] :
( c_Orderings_Oord__class_Oless(X49,c_Groups_Oone__class_Oone(X49),c_Groups_Ozero__class_Ozero(X49))
| ~ class_Int_Onumber__ring(X49)
| ~ class_Rings_Olinordered__idom(X49) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_462])]) ).
fof(f15941,plain,
( ! [X48,X49] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
| c_Orderings_Oord__class_Oless(X49,c_Groups_Oone__class_Oone(X49),c_Groups_Ozero__class_Ozero(X49))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48))
| ~ class_Int_Onumber__ring(X49)
| ~ class_Rings_Olinordered__idom(X49) )
| ~ spl35_230 ),
inference(forward_subsumption_demodulation,[],[f15940,f5704]) ).
fof(f5704,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X0) ),
inference(cnf_transformation,[],[f2180]) ).
fof(f2180,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X0) ),
inference(ennf_transformation,[],[f2067]) ).
fof(f2067,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Int_Onumber__class_Onumber__of(X0,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X0) ),
inference(rectify,[],[f463]) ).
fof(f463,axiom,
! [X15] :
( class_Int_Onumber__ring(X15)
=> c_Int_Onumber__class_Onumber__of(X15,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(f15940,plain,
( ! [X48,X49] :
( ~ class_Rings_Olinordered__idom(X49)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48))
| c_Orderings_Oord__class_Oless(X49,c_Groups_Oone__class_Oone(X49),c_Int_Onumber__class_Onumber__of(X49,c_Int_OPls))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
| ~ class_Int_Onumber__ring(X49) )
| ~ spl35_230 ),
inference(forward_demodulation,[],[f15939,f5023]) ).
fof(f15939,plain,
( ! [X48,X49] :
( c_Orderings_Oord__class_Oless(X49,c_Groups_Oone__class_Oone(X49),c_Int_Onumber__class_Onumber__of(X49,c_Int_OPls))
| ~ class_Rings_Olinordered__idom(X49)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
| ~ class_Int_Onumber__ring(X49) )
| ~ spl35_230 ),
inference(forward_demodulation,[],[f15912,f8148]) ).
fof(f15912,plain,
! [X48,X49] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(X49)
| c_Orderings_Oord__class_Oless(X49,c_Groups_Oone__class_Oone(X49),c_Int_Onumber__class_Onumber__of(X49,c_Int_OPls))
| ~ class_Int_Onumber__ring(X49) ),
inference(resolution,[],[f4813,f7738]) ).
fof(f7738,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f7698,f4335]) ).
fof(f7698,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) ),
inference(backward_demodulation,[],[f6686,f4335]) ).
fof(f6686,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(forward_demodulation,[],[f6685,f5637]) ).
fof(f6685,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),X0)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) ),
inference(forward_demodulation,[],[f5981,f5637]) ).
fof(f5981,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X0) ),
inference(definition_unfolding,[],[f5175,f5442]) ).
fof(f5175,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0) ),
inference(cnf_transformation,[],[f3704]) ).
fof(f3704,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) )
& ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0) ) ) ),
inference(rectify,[],[f3703]) ).
fof(f3703,plain,
! [X1,X0] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0)
| ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1)
| ~ c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) )
& ( c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1) ) ) ),
inference(nnf_transformation,[],[f2333]) ).
fof(f2333,plain,
! [X1,X0] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0)
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1)
<=> c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) ) ),
inference(flattening,[],[f2332]) ).
fof(f2332,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1)
<=> c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) )
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f1751]) ).
fof(f1751,plain,
! [X0,X1] :
( ( class_Rings_Olinordered__idom(X0)
& class_Int_Onumber__ring(X0) )
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1)
<=> c_Orderings_Oord__class_Oless(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,X1)) ) ),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X15,X12] :
( ( class_Rings_Olinordered__idom(X15)
& class_Int_Onumber__ring(X15) )
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X12)
<=> c_Orderings_Oord__class_Oless(X15,c_Groups_Oone__class_Oone(X15),c_Int_Onumber__class_Onumber__of(X15,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I2_J) ).
fof(f15935,plain,
( spl35_461
| ~ spl35_230
| spl35_296 ),
inference(avatar_split_clause,[],[f15934,f10225,f8146,f15919]) ).
fof(f15919,plain,
( spl35_461
<=> ! [X48] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X48)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_461])]) ).
fof(f15934,plain,
( ! [X47] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X47)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls) )
| ~ spl35_230
| spl35_296 ),
inference(forward_demodulation,[],[f15887,f8148]) ).
fof(f15887,plain,
( ! [X47] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X47)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) )
| spl35_296 ),
inference(resolution,[],[f4813,f10227]) ).
fof(f15924,plain,
( spl35_461
| spl35_462
| ~ spl35_230 ),
inference(avatar_split_clause,[],[f15917,f8146,f15922,f15919]) ).
fof(f15917,plain,
( ! [X48,X49] :
( c_Orderings_Oord__class_Oless(X49,c_Groups_Oone__class_Oone(X49),c_Groups_Ozero__class_Ozero(X49))
| ~ class_Rings_Olinordered__idom(X49)
| ~ class_Int_Onumber__ring(X49)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X48)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls) )
| ~ spl35_230 ),
inference(forward_subsumption_demodulation,[],[f15916,f5704]) ).
fof(f15916,plain,
( ! [X48,X49] :
( c_Orderings_Oord__class_Oless(X49,c_Groups_Oone__class_Oone(X49),c_Int_Onumber__class_Onumber__of(X49,c_Int_OPls))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X48)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
| ~ class_Int_Onumber__ring(X49)
| ~ class_Rings_Olinordered__idom(X49) )
| ~ spl35_230 ),
inference(forward_demodulation,[],[f15888,f8148]) ).
fof(f15888,plain,
! [X48,X49] :
( c_Orderings_Oord__class_Oless(X49,c_Groups_Oone__class_Oone(X49),c_Int_Onumber__class_Onumber__of(X49,c_Int_OPls))
| ~ class_Rings_Olinordered__idom(X49)
| ~ class_Int_Onumber__ring(X49)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X48)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) ),
inference(resolution,[],[f4813,f7738]) ).
fof(f15717,plain,
( ~ spl35_460
| spl35_271 ),
inference(avatar_split_clause,[],[f15662,f8713,f15713]) ).
fof(f15713,plain,
( spl35_460
<=> c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_460])]) ).
fof(f8713,plain,
( spl35_271
<=> c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_271])]) ).
fof(f15662,plain,
( c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))
| spl35_271 ),
inference(superposition,[],[f8715,f5637]) ).
fof(f8715,plain,
( c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)
| spl35_271 ),
inference(avatar_component_clause,[],[f8713]) ).
fof(f15716,plain,
( ~ spl35_460
| spl35_271 ),
inference(avatar_split_clause,[],[f15693,f8713,f15713]) ).
fof(f15693,plain,
( c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))
| spl35_271 ),
inference(superposition,[],[f8715,f5637]) ).
fof(f15512,plain,
( spl35_459
| ~ spl35_248 ),
inference(avatar_split_clause,[],[f15507,f8370,f15509]) ).
fof(f15509,plain,
( spl35_459
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_459])]) ).
fof(f8370,plain,
( spl35_248
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_248])]) ).
fof(f15507,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_248 ),
inference(forward_demodulation,[],[f15506,f4335]) ).
fof(f15506,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_248 ),
inference(forward_demodulation,[],[f15505,f5637]) ).
fof(f15505,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_248 ),
inference(forward_demodulation,[],[f15486,f4335]) ).
fof(f15486,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_248 ),
inference(resolution,[],[f7168,f8372]) ).
fof(f8372,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_248 ),
inference(avatar_component_clause,[],[f8370]) ).
fof(f7168,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f7167,f5637]) ).
fof(f7167,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f6043,f5637]) ).
fof(f6043,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(definition_unfolding,[],[f5658,f5442,f5442]) ).
fof(f5658,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3971]) ).
fof(f3971,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X0)) ) ),
inference(rectify,[],[f3970]) ).
fof(f3970,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OBit1(X1)) ) ),
inference(nnf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OBit1(X1))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X49,X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X49),c_Int_OBit1(X48))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X49,X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).
fof(f15498,plain,
( spl35_458
| ~ spl35_352 ),
inference(avatar_split_clause,[],[f15493,f11597,f15495]) ).
fof(f15495,plain,
( spl35_458
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_458])]) ).
fof(f11597,plain,
( spl35_352
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_352])]) ).
fof(f15493,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_352 ),
inference(forward_demodulation,[],[f15492,f9212]) ).
fof(f9212,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)),
inference(superposition,[],[f4702,f7834]) ).
fof(f7834,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
inference(backward_demodulation,[],[f5945,f4702]) ).
fof(f5945,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)),
inference(definition_unfolding,[],[f4992,f4431,f4431]) ).
fof(f4992,plain,
! [X0] : c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X0)),
inference(cnf_transformation,[],[f1735]) ).
fof(f1735,plain,
! [X0] : c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X0)),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X20] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(X20)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit0) ).
fof(f4702,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),
inference(cnf_transformation,[],[f1823]) ).
fof(f1823,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),
inference(rectify,[],[f101]) ).
fof(f101,axiom,
! [X14,X22] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(f15492,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_352 ),
inference(forward_demodulation,[],[f15491,f4702]) ).
fof(f15491,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_352 ),
inference(forward_demodulation,[],[f15490,f5723]) ).
fof(f15490,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_352 ),
inference(forward_demodulation,[],[f15489,f4335]) ).
fof(f15489,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_352 ),
inference(forward_demodulation,[],[f15488,f5637]) ).
fof(f15488,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))
| ~ spl35_352 ),
inference(forward_demodulation,[],[f15487,f4335]) ).
fof(f15487,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))
| ~ spl35_352 ),
inference(resolution,[],[f7168,f11599]) ).
fof(f11599,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_352 ),
inference(avatar_component_clause,[],[f11597]) ).
fof(f15482,plain,
( spl35_457
| ~ spl35_422 ),
inference(avatar_split_clause,[],[f15477,f13373,f15479]) ).
fof(f15479,plain,
( spl35_457
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_457])]) ).
fof(f13373,plain,
( spl35_422
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_422])]) ).
fof(f15477,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f15476,f9212]) ).
fof(f15476,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f15475,f4702]) ).
fof(f15475,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f15474,f5723]) ).
fof(f15474,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f15473,f4335]) ).
fof(f15473,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f15472,f5637]) ).
fof(f15472,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f15430,f4335]) ).
fof(f15430,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))
| ~ spl35_422 ),
inference(resolution,[],[f6744,f13375]) ).
fof(f13375,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_422 ),
inference(avatar_component_clause,[],[f13373]) ).
fof(f6744,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f6743,f5637]) ).
fof(f6743,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f5807,f5637]) ).
fof(f5807,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(definition_unfolding,[],[f4216,f5442,f5442]) ).
fof(f4216,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3147]) ).
fof(f3147,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X0)) ) ),
inference(rectify,[],[f3146]) ).
fof(f3146,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OBit1(X1)) ) ),
inference(nnf_transformation,[],[f1724]) ).
fof(f1724,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OBit1(X1))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,X48)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X49),c_Int_OBit1(X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).
fof(f15471,plain,
( spl35_456
| ~ spl35_265 ),
inference(avatar_split_clause,[],[f15466,f8598,f15468]) ).
fof(f15468,plain,
( spl35_456
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_456])]) ).
fof(f8598,plain,
( spl35_265
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_265])]) ).
fof(f15466,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_265 ),
inference(forward_demodulation,[],[f15465,f4335]) ).
fof(f15465,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_265 ),
inference(forward_demodulation,[],[f15464,f5637]) ).
fof(f15464,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_265 ),
inference(forward_demodulation,[],[f15431,f4335]) ).
fof(f15431,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_265 ),
inference(resolution,[],[f6744,f8600]) ).
fof(f8600,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_265 ),
inference(avatar_component_clause,[],[f8598]) ).
fof(f15462,plain,
( spl35_455
| ~ spl35_263 ),
inference(avatar_split_clause,[],[f15457,f8575,f15459]) ).
fof(f15459,plain,
( spl35_455
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_455])]) ).
fof(f8575,plain,
( spl35_263
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_263])]) ).
fof(f15457,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15456,f4335]) ).
fof(f15456,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15455,f5637]) ).
fof(f15455,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15454,f4335]) ).
fof(f15454,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15453,f5637]) ).
fof(f15453,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15452,f5723]) ).
fof(f15452,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15451,f5723]) ).
fof(f15451,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15450,f5637]) ).
fof(f15450,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15449,f5723]) ).
fof(f15449,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f15427,f5723]) ).
fof(f15427,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(resolution,[],[f6744,f8577]) ).
fof(f8577,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_263 ),
inference(avatar_component_clause,[],[f8575]) ).
fof(f15442,plain,
( spl35_454
| ~ spl35_256 ),
inference(avatar_split_clause,[],[f15437,f8477,f15439]) ).
fof(f15439,plain,
( spl35_454
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_454])]) ).
fof(f8477,plain,
( spl35_256
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_256])]) ).
fof(f15437,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f15436,f4335]) ).
fof(f15436,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f15435,f5637]) ).
fof(f15435,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f15434,f4335]) ).
fof(f15434,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f15433,f5637]) ).
fof(f15433,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f15432,f5723]) ).
fof(f15432,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f15426,f5723]) ).
fof(f15426,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(resolution,[],[f6744,f8479]) ).
fof(f8479,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_256 ),
inference(avatar_component_clause,[],[f8477]) ).
fof(f15237,plain,
( spl35_316
| ~ spl35_131 ),
inference(avatar_split_clause,[],[f15236,f7102,f10992]) ).
fof(f10992,plain,
( spl35_316
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_316])]) ).
fof(f7102,plain,
( spl35_131
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_131])]) ).
fof(f15236,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_131 ),
inference(forward_demodulation,[],[f15222,f6129]) ).
fof(f6129,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(equality_resolution,[],[f4850]) ).
fof(f4850,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)
| c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) != X1 ),
inference(cnf_transformation,[],[f3502]) ).
fof(f3502,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)
| c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) != X1 )
& ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) = X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1) ) ),
inference(rectify,[],[f3501]) ).
fof(f3501,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
| c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) != X0 )
& ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f1601]) ).
fof(f1601,plain,
! [X1,X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)
<=> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) = X0 ),
inference(rectify,[],[f155]) ).
fof(f155,axiom,
! [X12,X13] :
( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13) = X12
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(f15222,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))
| ~ spl35_131 ),
inference(resolution,[],[f7104,f5008]) ).
fof(f5008,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ),
inference(cnf_transformation,[],[f3596]) ).
fof(f7104,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ spl35_131 ),
inference(avatar_component_clause,[],[f7102]) ).
fof(f15235,plain,
( spl35_316
| ~ spl35_131 ),
inference(avatar_split_clause,[],[f15234,f7102,f10992]) ).
fof(f15234,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_131 ),
inference(forward_demodulation,[],[f15223,f6129]) ).
fof(f15223,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_131 ),
inference(resolution,[],[f7104,f5220]) ).
fof(f5220,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3725]) ).
fof(f3725,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(rectify,[],[f3724]) ).
fof(f3724,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(nnf_transformation,[],[f1920]) ).
fof(f1920,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)) ),
inference(rectify,[],[f178]) ).
fof(f178,axiom,
! [X13,X12] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
fof(f15233,plain,
( spl35_453
| ~ spl35_131
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f15228,f13098,f7102,f15230]) ).
fof(f15230,plain,
( spl35_453
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),v_s____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_453])]) ).
fof(f15228,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),v_s____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_131
| ~ spl35_401 ),
inference(forward_demodulation,[],[f15225,f4750]) ).
fof(f4750,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(cnf_transformation,[],[f3450]) ).
fof(f3450,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0)),
inference(rectify,[],[f1693]) ).
fof(f1693,plain,
! [X1,X0] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(rectify,[],[f220]) ).
fof(f220,axiom,
! [X51,X53] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X51,X53) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X51,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X53)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(f15225,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_131
| ~ spl35_401 ),
inference(resolution,[],[f7104,f13103]) ).
fof(f13103,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) )
| ~ spl35_401 ),
inference(backward_demodulation,[],[f7747,f13100]) ).
fof(f7747,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(forward_demodulation,[],[f7746,f4335]) ).
fof(f7746,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f7745,f4335]) ).
fof(f7745,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(forward_demodulation,[],[f7725,f4335]) ).
fof(f7725,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(backward_demodulation,[],[f7614,f4335]) ).
fof(f7614,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
inference(forward_demodulation,[],[f7613,f5723]) ).
fof(f7613,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(forward_demodulation,[],[f7612,f5637]) ).
fof(f7612,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))))) ),
inference(forward_demodulation,[],[f7611,f5723]) ).
fof(f7611,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))))) ),
inference(forward_demodulation,[],[f7610,f5637]) ).
fof(f7610,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))) ),
inference(forward_demodulation,[],[f7609,f5723]) ).
fof(f7609,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(forward_demodulation,[],[f7608,f5637]) ).
fof(f7608,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))) ),
inference(forward_demodulation,[],[f7607,f5723]) ).
fof(f7607,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))) ),
inference(forward_demodulation,[],[f7606,f5537]) ).
fof(f7606,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))))) ),
inference(forward_demodulation,[],[f5959,f5723]) ).
fof(f5959,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(definition_unfolding,[],[f5054,f4431,f5442]) ).
fof(f5054,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(cnf_transformation,[],[f2749]) ).
fof(f2749,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(ennf_transformation,[],[f1538]) ).
fof(f1538,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(rectify,[],[f224]) ).
fof(f224,axiom,
! [X10,X36] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,X36)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X10,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X36),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__half__sum) ).
fof(f15227,plain,
~ spl35_131,
inference(avatar_contradiction_clause,[],[f15224]) ).
fof(f15224,plain,
( $false
| ~ spl35_131 ),
inference(resolution,[],[f7104,f6122]) ).
fof(f6122,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_resolution,[],[f4807]) ).
fof(f4807,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f3483]) ).
fof(f3483,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ) ),
inference(flattening,[],[f3482]) ).
fof(f3482,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ) ),
inference(nnf_transformation,[],[f1970]) ).
fof(f1970,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ) ),
inference(rectify,[],[f210]) ).
fof(f210,axiom,
! [X13,X12] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X12)
& X12 != X13 )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(f15124,plain,
( spl35_452
| ~ spl35_188 ),
inference(avatar_split_clause,[],[f15113,f7640,f15121]) ).
fof(f15121,plain,
( spl35_452
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_452])]) ).
fof(f15113,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls)
| ~ spl35_188 ),
inference(resolution,[],[f5704,f7642]) ).
fof(f15118,plain,
( spl35_451
| ~ spl35_92 ),
inference(avatar_split_clause,[],[f15112,f6857,f15115]) ).
fof(f15115,plain,
( spl35_451
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_451])]) ).
fof(f6857,plain,
( spl35_92
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_92])]) ).
fof(f15112,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls)
| ~ spl35_92 ),
inference(resolution,[],[f5704,f6859]) ).
fof(f6859,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ spl35_92 ),
inference(avatar_component_clause,[],[f6857]) ).
fof(f15085,plain,
( spl35_450
| ~ spl35_188
| ~ spl35_20
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f15080,f13098,f6367,f7640,f15082]) ).
fof(f15082,plain,
( spl35_450
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_450])]) ).
fof(f15080,plain,
( ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_20
| ~ spl35_401 ),
inference(forward_demodulation,[],[f15079,f13100]) ).
fof(f15079,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ spl35_20 ),
inference(resolution,[],[f7787,f6369]) ).
fof(f7787,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(forward_demodulation,[],[f7786,f4335]) ).
fof(f7786,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X0) ),
inference(forward_demodulation,[],[f7785,f4335]) ).
fof(f7785,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7712,f4335]) ).
fof(f7712,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f7449,f4335]) ).
fof(f7449,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
inference(forward_demodulation,[],[f7448,f5723]) ).
fof(f7448,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
inference(forward_demodulation,[],[f7447,f5723]) ).
fof(f7447,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7407,f5723]) ).
fof(f7407,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
inference(backward_demodulation,[],[f6447,f5723]) ).
fof(f6447,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
inference(forward_demodulation,[],[f6446,f5637]) ).
fof(f6446,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f6445,f5637]) ).
fof(f6445,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))))
| ~ class_Fields_Olinordered__field__inverse__zero(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f6444,f5537]) ).
fof(f6444,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) ),
inference(forward_demodulation,[],[f5830,f5537]) ).
fof(f5830,plain,
! [X0] :
( ~ class_Fields_Olinordered__field__inverse__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(definition_unfolding,[],[f4347,f4431,f5442]) ).
fof(f4347,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X0) ),
inference(cnf_transformation,[],[f2413]) ).
fof(f2413,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X0) ),
inference(flattening,[],[f2412]) ).
fof(f2412,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X0) ),
inference(ennf_transformation,[],[f1866]) ).
fof(f1866,plain,
! [X0] :
( ( class_Int_Onumber__ring(X0)
& class_Fields_Olinordered__field__inverse__zero(X0) )
=> c_Orderings_Oord__class_Oless(X0,c_Groups_Ozero__class_Ozero(X0),c_Rings_Oinverse__class_Odivide(X0,c_Groups_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(rectify,[],[f288]) ).
fof(f288,axiom,
! [X15] :
( ( class_Int_Onumber__ring(X15)
& class_Fields_Olinordered__field__inverse__zero(X15) )
=> c_Orderings_Oord__class_Oless(X15,c_Groups_Ozero__class_Ozero(X15),c_Rings_Oinverse__class_Odivide(X15,c_Groups_Oone__class_Oone(X15),c_Int_Onumber__class_Onumber__of(X15,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half) ).
fof(f14937,plain,
( spl35_449
| ~ spl35_249
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f14903,f13098,f8388,f14934]) ).
fof(f14934,plain,
( spl35_449
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_449])]) ).
fof(f8388,plain,
( spl35_249
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_249])]) ).
fof(f14903,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_249
| ~ spl35_401 ),
inference(resolution,[],[f13103,f8390]) ).
fof(f8390,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_249 ),
inference(avatar_component_clause,[],[f8388]) ).
fof(f14932,plain,
( spl35_448
| ~ spl35_145
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f14907,f13098,f7207,f14929]) ).
fof(f14929,plain,
( spl35_448
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_448])]) ).
fof(f7207,plain,
( spl35_145
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_145])]) ).
fof(f14907,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_145
| ~ spl35_401 ),
inference(resolution,[],[f13103,f7209]) ).
fof(f7209,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____)
| ~ spl35_145 ),
inference(avatar_component_clause,[],[f7207]) ).
fof(f14927,plain,
( spl35_447
| ~ spl35_371
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f14908,f13098,f12410,f14924]) ).
fof(f14924,plain,
( spl35_447
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_447])]) ).
fof(f12410,plain,
( spl35_371
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_371])]) ).
fof(f14908,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_371
| ~ spl35_401 ),
inference(resolution,[],[f13103,f12412]) ).
fof(f12412,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_371 ),
inference(avatar_component_clause,[],[f12410]) ).
fof(f14922,plain,
( spl35_446
| ~ spl35_187
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f14910,f13098,f7635,f14919]) ).
fof(f14919,plain,
( spl35_446
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_446])]) ).
fof(f7635,plain,
( spl35_187
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_187])]) ).
fof(f14910,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_187
| ~ spl35_401 ),
inference(resolution,[],[f13103,f7637]) ).
fof(f7637,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18)
| ~ spl35_187 ),
inference(avatar_component_clause,[],[f7635]) ).
fof(f14917,plain,
( spl35_445
| ~ spl35_183
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f14909,f13098,f7592,f14914]) ).
fof(f14914,plain,
( spl35_445
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_445])]) ).
fof(f7592,plain,
( spl35_183
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_183])]) ).
fof(f14909,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_183
| ~ spl35_401 ),
inference(resolution,[],[f13103,f7594]) ).
fof(f7594,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14)
| ~ spl35_183 ),
inference(avatar_component_clause,[],[f7592]) ).
fof(f14902,plain,
( spl35_444
| spl35_305
| ~ spl35_244 ),
inference(avatar_split_clause,[],[f14850,f8267,f10376,f14900]) ).
fof(f14900,plain,
( spl35_444
<=> ! [X43] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X43)) != X43 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_444])]) ).
fof(f10376,plain,
( spl35_305
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_305])]) ).
fof(f8267,plain,
( spl35_244
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_244])]) ).
fof(f14850,plain,
( ! [X43] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X43)) != X43 )
| ~ spl35_244 ),
inference(superposition,[],[f5271,f8583]) ).
fof(f8583,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ spl35_244 ),
inference(backward_demodulation,[],[f7750,f8269]) ).
fof(f8269,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_244 ),
inference(avatar_component_clause,[],[f8267]) ).
fof(f7750,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f7749,f4335]) ).
fof(f7749,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f7748,f4335]) ).
fof(f7748,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),
inference(forward_demodulation,[],[f7720,f4335]) ).
fof(f7720,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(backward_demodulation,[],[f7495,f4335]) ).
fof(f7495,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f7494,f5723]) ).
fof(f7494,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f7493,f5723]) ).
fof(f7493,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f7410,f5723]) ).
fof(f7410,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(backward_demodulation,[],[f6515,f5723]) ).
fof(f6515,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f6514,f5637]) ).
fof(f6514,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))))),
inference(forward_demodulation,[],[f6513,f5637]) ).
fof(f6513,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f6512,f5537]) ).
fof(f6512,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(forward_demodulation,[],[f6052,f5537]) ).
fof(f6052,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(definition_unfolding,[],[f5686,f4497,f4497,f4431,f5442]) ).
fof(f5686,plain,
! [X0] : c_Nat_OSuc(c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1662]) ).
fof(f1662,plain,
! [X0] : c_Nat_OSuc(c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(rectify,[],[f554]) ).
fof(f554,axiom,
! [X37] : c_Nat_OSuc(c_Nat_OSuc(X37)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
fof(f5271,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f3751]) ).
fof(f3751,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f2827]) ).
fof(f2827,plain,
! [X1,X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(ennf_transformation,[],[f1318]) ).
fof(f1318,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X0
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(rectify,[],[f370]) ).
fof(f370,axiom,
! [X0,X37] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X37) = X0
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X37 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(f14599,plain,
( spl35_442
| ~ spl35_443
| ~ spl35_429 ),
inference(avatar_split_clause,[],[f14589,f13880,f14596,f14592]) ).
fof(f14592,plain,
( spl35_442
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_442])]) ).
fof(f14596,plain,
( spl35_443
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_443])]) ).
fof(f13880,plain,
( spl35_429
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_429])]) ).
fof(f14589,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_429 ),
inference(resolution,[],[f13882,f4624]) ).
fof(f4624,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f3375]) ).
fof(f3375,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(rectify,[],[f2566]) ).
fof(f2566,plain,
! [X1,X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(flattening,[],[f2565]) ).
fof(f2565,plain,
! [X1,X0] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(ennf_transformation,[],[f1986]) ).
fof(f1986,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> X0 = X1 ) ),
inference(rectify,[],[f195]) ).
fof(f195,axiom,
! [X14,X22] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X14)
=> X14 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(f13882,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_429 ),
inference(avatar_component_clause,[],[f13880]) ).
fof(f14425,plain,
( spl35_441
| ~ spl35_422 ),
inference(avatar_split_clause,[],[f14420,f13373,f14422]) ).
fof(f14422,plain,
( spl35_441
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_441])]) ).
fof(f14420,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f14419,f4702]) ).
fof(f14419,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f14418,f4335]) ).
fof(f14418,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f14417,f5637]) ).
fof(f14417,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f14407,f4335]) ).
fof(f14407,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))
| ~ spl35_422 ),
inference(resolution,[],[f7241,f13375]) ).
fof(f7241,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) ),
inference(forward_demodulation,[],[f5968,f5637]) ).
fof(f5968,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) ),
inference(definition_unfolding,[],[f5086,f4431,f5442]) ).
fof(f5086,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3648]) ).
fof(f3648,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit1(X1)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ) ),
inference(nnf_transformation,[],[f1646]) ).
fof(f1646,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit1(X1)) ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X49,X48] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X49,X48)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X49),c_Int_OBit1(X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).
fof(f14255,plain,
( spl35_440
| ~ spl35_422 ),
inference(avatar_split_clause,[],[f14250,f13373,f14252]) ).
fof(f14252,plain,
( spl35_440
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_440])]) ).
fof(f14250,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f14249,f4702]) ).
fof(f14249,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f14248,f4335]) ).
fof(f14248,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f14247,f5637]) ).
fof(f14247,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))
| ~ spl35_422 ),
inference(forward_demodulation,[],[f14241,f4335]) ).
fof(f14241,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))
| ~ spl35_422 ),
inference(resolution,[],[f6301,f13375]) ).
fof(f6301,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))) ),
inference(backward_demodulation,[],[f5923,f5637]) ).
fof(f5923,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(definition_unfolding,[],[f4855,f4431,f5442]) ).
fof(f4855,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3505]) ).
fof(f3505,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X0)) ) ),
inference(rectify,[],[f3504]) ).
fof(f3504,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit1(X1)) ) ),
inference(nnf_transformation,[],[f2074]) ).
fof(f2074,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit1(X1))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(rectify,[],[f167]) ).
fof(f167,axiom,
! [X27,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,X26)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X27),c_Int_OBit1(X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).
fof(f14189,plain,
( ~ spl35_439
| spl35_342 ),
inference(avatar_split_clause,[],[f14182,f11220,f14186]) ).
fof(f14186,plain,
( spl35_439
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_439])]) ).
fof(f11220,plain,
( spl35_342
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_342])]) ).
fof(f14182,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl35_342 ),
inference(resolution,[],[f11222,f4943]) ).
fof(f4943,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3558]) ).
fof(f3558,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f3557]) ).
fof(f3557,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) ) ),
inference(nnf_transformation,[],[f1282]) ).
fof(f1282,plain,
! [X1,X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f499]) ).
fof(f499,axiom,
! [X6,X50] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X50)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(f11222,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl35_342 ),
inference(avatar_component_clause,[],[f11220]) ).
fof(f14089,plain,
( ~ spl35_75
| spl35_438 ),
inference(avatar_split_clause,[],[f14080,f14086,f6734]) ).
fof(f6734,plain,
( spl35_75
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_75])]) ).
fof(f14086,plain,
( spl35_438
<=> ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_438])]) ).
fof(f14080,plain,
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(resolution,[],[f5574,f5282]) ).
fof(f5282,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[],[f2061]) ).
fof(f2061,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(rectify,[],[f192]) ).
fof(f192,axiom,
! [X22] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X22,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(f5574,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1)) ),
inference(cnf_transformation,[],[f3918]) ).
fof(f3918,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1)) ) ),
inference(flattening,[],[f3917]) ).
fof(f3917,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1)) ) ),
inference(nnf_transformation,[],[f1949]) ).
fof(f1949,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ) ),
inference(rectify,[],[f151]) ).
fof(f151,axiom,
! [X13,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X13,X12))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).
fof(f14088,plain,
( spl35_438
| spl35_437 ),
inference(avatar_split_clause,[],[f14084,f14064,f14086]) ).
fof(f14064,plain,
( spl35_437
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_437])]) ).
fof(f14084,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(forward_subsumption_demodulation,[],[f14079,f8957]) ).
fof(f8957,plain,
! [X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X4)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X4) ),
inference(resolution,[],[f4731,f4624]) ).
fof(f4731,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3432]) ).
fof(f3432,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f2086]) ).
fof(f2086,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rectify,[],[f153]) ).
fof(f153,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X12)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X13,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
fof(f14079,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(resolution,[],[f5574,f4731]) ).
fof(f14066,plain,
( spl35_437
| spl35_436 ),
inference(avatar_split_clause,[],[f14062,f14059,f14064]) ).
fof(f14059,plain,
( spl35_436
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_436])]) ).
fof(f14062,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(forward_subsumption_demodulation,[],[f14043,f8957]) ).
fof(f14043,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) ),
inference(resolution,[],[f5571,f4731]) ).
fof(f5571,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3918]) ).
fof(f14061,plain,
( ~ spl35_75
| spl35_436 ),
inference(avatar_split_clause,[],[f14044,f14059,f6734]) ).
fof(f14044,plain,
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(resolution,[],[f5571,f5282]) ).
fof(f14057,plain,
( spl35_434
| ~ spl35_435
| ~ spl35_268 ),
inference(avatar_split_clause,[],[f14049,f8681,f14054,f14051]) ).
fof(f14051,plain,
( spl35_434
<=> ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_434])]) ).
fof(f14054,plain,
( spl35_435
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_435])]) ).
fof(f14049,plain,
( ! [X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X4)) )
| ~ spl35_268 ),
inference(forward_demodulation,[],[f14048,f8683]) ).
fof(f14048,plain,
( ! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) )
| ~ spl35_268 ),
inference(forward_demodulation,[],[f14045,f8683]) ).
fof(f14045,plain,
! [X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),X4)) ),
inference(resolution,[],[f5571,f8953]) ).
fof(f8953,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)),X0),
inference(resolution,[],[f4682,f5282]) ).
fof(f4682,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) ),
inference(cnf_transformation,[],[f3406]) ).
fof(f3406,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),X1) ) ),
inference(rectify,[],[f3405]) ).
fof(f3405,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X0) ) ),
inference(flattening,[],[f3404]) ).
fof(f3404,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X0) ) ),
inference(nnf_transformation,[],[f1941]) ).
fof(f1941,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X0)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0),X1) ) ),
inference(rectify,[],[f219]) ).
fof(f219,axiom,
! [X25,X13] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13,X25)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X25),X13) )
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X13),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).
fof(f13947,plain,
~ spl35_433,
inference(avatar_split_clause,[],[f13923,f13944]) ).
fof(f13944,plain,
( spl35_433
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK24(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_433])]) ).
fof(f13923,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK24(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[],[f5818,f8981]) ).
fof(f8981,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK24(X0,X0)) = X0,
inference(resolution,[],[f5301,f6078]) ).
fof(f6078,plain,
! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_resolution,[],[f4295]) ).
fof(f4295,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f3184]) ).
fof(f3184,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| X0 != X1 ),
inference(rectify,[],[f2729]) ).
fof(f2729,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 != X1 ),
inference(ennf_transformation,[],[f1846]) ).
fof(f1846,plain,
! [X1,X0] :
( X0 = X1
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f348]) ).
fof(f348,axiom,
! [X37,X0] :
( X0 = X37
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(f5818,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X0),
inference(definition_unfolding,[],[f4306,f4497]) ).
fof(f4306,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(cnf_transformation,[],[f1247]) ).
fof(f1247,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(rectify,[],[f392]) ).
fof(f392,axiom,
! [X37] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X37),X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f13942,plain,
spl35_432,
inference(avatar_split_clause,[],[f13885,f13937]) ).
fof(f13937,plain,
( spl35_432
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK24(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_432])]) ).
fof(f13885,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK24(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[],[f8981,f6110]) ).
fof(f6110,plain,
! [X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(equality_resolution,[],[f4636]) ).
fof(f4636,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f2726]) ).
fof(f2726,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(ennf_transformation,[],[f1773]) ).
fof(f1773,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = X1 ) ),
inference(rectify,[],[f532]) ).
fof(f532,axiom,
! [X0,X37] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X37) = X37 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X37) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(f13940,plain,
spl35_432,
inference(avatar_split_clause,[],[f13920,f13937]) ).
fof(f13920,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = sK24(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(superposition,[],[f6110,f8981]) ).
fof(f13935,plain,
~ spl35_431,
inference(avatar_split_clause,[],[f13924,f13932]) ).
fof(f13932,plain,
( spl35_431
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = sK24(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_431])]) ).
fof(f13924,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) != sK24(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[],[f5814,f8981]) ).
fof(f5814,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != X0,
inference(definition_unfolding,[],[f4292,f4497]) ).
fof(f4292,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(cnf_transformation,[],[f1262]) ).
fof(f1262,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(rectify,[],[f331]) ).
fof(f331,axiom,
! [X37] : c_Nat_OSuc(X37) != X37,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(f13930,plain,
spl35_430,
inference(avatar_split_clause,[],[f13921,f13927]) ).
fof(f13927,plain,
( spl35_430
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_430])]) ).
fof(f13921,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[],[f5882,f8981]) ).
fof(f5882,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(definition_unfolding,[],[f4625,f4497]) ).
fof(f4625,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1795]) ).
fof(f1795,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X37] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,c_Nat_OSuc(X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(f13883,plain,
( spl35_429
| ~ spl35_377 ),
inference(avatar_split_clause,[],[f13872,f12850,f13880]) ).
fof(f13872,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_377 ),
inference(superposition,[],[f8953,f12852]) ).
fof(f13878,plain,
( spl35_428
| ~ spl35_268 ),
inference(avatar_split_clause,[],[f13871,f8681,f13875]) ).
fof(f13875,plain,
( spl35_428
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_428])]) ).
fof(f13871,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_268 ),
inference(superposition,[],[f8953,f8683]) ).
fof(f13850,plain,
( ~ spl35_427
| ~ spl35_48 ),
inference(avatar_split_clause,[],[f13839,f6556,f13847]) ).
fof(f13847,plain,
( spl35_427
<=> c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_427])]) ).
fof(f6556,plain,
( spl35_48
<=> c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_48])]) ).
fof(f13839,plain,
( c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_48 ),
inference(superposition,[],[f5826,f8631]) ).
fof(f8631,plain,
( ! [X0] : c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0))
| ~ spl35_48 ),
inference(superposition,[],[f8333,f4084]) ).
fof(f4084,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(cnf_transformation,[],[f1772]) ).
fof(f1772,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)) = X0,
inference(rectify,[],[f92]) ).
fof(f92,axiom,
! [X14] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14)) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(f8333,plain,
( ! [X0] : c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0)
| ~ spl35_48 ),
inference(backward_demodulation,[],[f4935,f6558]) ).
fof(f6558,plain,
( c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ spl35_48 ),
inference(avatar_component_clause,[],[f6556]) ).
fof(f4935,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
inference(cnf_transformation,[],[f1732]) ).
fof(f1732,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0),X0),
inference(rectify,[],[f261]) ).
fof(f261,axiom,
! [X14] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X14),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(f5826,plain,
! [X0] : c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(definition_unfolding,[],[f4329,f5442]) ).
fof(f4329,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(cnf_transformation,[],[f1611]) ).
fof(f1611,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X21] : c_Int_OPls != c_Int_OBit1(X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
fof(f13485,plain,
( spl35_426
| ~ spl35_169 ),
inference(avatar_split_clause,[],[f13471,f7384,f13481]) ).
fof(f13481,plain,
( spl35_426
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_426])]) ).
fof(f7384,plain,
( spl35_169
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_169])]) ).
fof(f13471,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_169 ),
inference(superposition,[],[f7386,f4211]) ).
fof(f4211,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X1)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0),X1),
inference(cnf_transformation,[],[f3145]) ).
fof(f3145,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X1)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X0),X1),
inference(rectify,[],[f1430]) ).
fof(f1430,plain,
! [X2,X1,X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X2),X1) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1)),
inference(rectify,[],[f213]) ).
fof(f213,axiom,
! [X41,X22,X40] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X41,X40),X22) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X41,X22),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X40,X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(f7386,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl35_169 ),
inference(avatar_component_clause,[],[f7384]) ).
fof(f13484,plain,
( spl35_426
| ~ spl35_169 ),
inference(avatar_split_clause,[],[f13468,f7384,f13481]) ).
fof(f13468,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_169 ),
inference(superposition,[],[f4211,f7386]) ).
fof(f13401,plain,
( spl35_425
| ~ spl35_422 ),
inference(avatar_split_clause,[],[f13379,f13373,f13398]) ).
fof(f13398,plain,
( spl35_425
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_425])]) ).
fof(f13379,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_422 ),
inference(resolution,[],[f13375,f5627]) ).
fof(f5627,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f3954]) ).
fof(f3954,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f1468]) ).
fof(f1468,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ),
inference(rectify,[],[f522]) ).
fof(f522,axiom,
! [X24] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,c_Int_OPls)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
fof(f13396,plain,
( spl35_424
| ~ spl35_422 ),
inference(avatar_split_clause,[],[f13395,f13373,f13391]) ).
fof(f13391,plain,
( spl35_424
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_424])]) ).
fof(f13395,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_422 ),
inference(forward_demodulation,[],[f13378,f4702]) ).
fof(f13378,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl35_422 ),
inference(resolution,[],[f13375,f5812]) ).
fof(f5812,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),c_Int_OPls) ),
inference(definition_unfolding,[],[f4271,f4431]) ).
fof(f4271,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f3175]) ).
fof(f3175,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OPls) ) ),
inference(nnf_transformation,[],[f1981]) ).
fof(f1981,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ),
inference(rectify,[],[f170]) ).
fof(f170,axiom,
! [X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,c_Int_OPls)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X27),c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).
fof(f13394,plain,
( spl35_424
| ~ spl35_422 ),
inference(avatar_split_clause,[],[f13389,f13373,f13391]) ).
fof(f13389,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_422 ),
inference(forward_demodulation,[],[f13388,f4702]) ).
fof(f13388,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl35_422 ),
inference(forward_demodulation,[],[f13380,f4931]) ).
fof(f4931,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f1741]) ).
fof(f1741,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,c_Int_OPls) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f13380,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls))
| ~ spl35_422 ),
inference(resolution,[],[f13375,f5786]) ).
fof(f5786,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) ),
inference(definition_unfolding,[],[f4081,f4431,f4431]) ).
fof(f4081,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit0(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ),
inference(cnf_transformation,[],[f3074]) ).
fof(f3074,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit0(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit0(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1) ) ),
inference(nnf_transformation,[],[f1879]) ).
fof(f1879,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit0(X1)) ),
inference(rectify,[],[f142]) ).
fof(f142,axiom,
! [X27,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X27),c_Int_OBit0(X26))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X27,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).
fof(f13387,plain,
( spl35_423
| ~ spl35_49
| ~ spl35_422 ),
inference(avatar_split_clause,[],[f13382,f13373,f6566,f13384]) ).
fof(f13384,plain,
( spl35_423
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_423])]) ).
fof(f6566,plain,
( spl35_49
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_49])]) ).
fof(f13382,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_49
| ~ spl35_422 ),
inference(forward_demodulation,[],[f13381,f6568]) ).
fof(f6568,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)
| ~ spl35_49 ),
inference(avatar_component_clause,[],[f6566]) ).
fof(f13381,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls))
| ~ spl35_422 ),
inference(resolution,[],[f13375,f4575]) ).
fof(f4575,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
inference(cnf_transformation,[],[f3349]) ).
fof(f13376,plain,
( spl35_422
| ~ spl35_352 ),
inference(avatar_split_clause,[],[f13371,f11597,f13373]) ).
fof(f13371,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_352 ),
inference(resolution,[],[f4615,f11599]) ).
fof(f4615,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3370]) ).
fof(f3370,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(flattening,[],[f3369]) ).
fof(f3369,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f2033]) ).
fof(f2033,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X23,X11] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X23)
& X11 != X23 )
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(f13275,plain,
( spl35_421
| spl35_208
| ~ spl35_188
| ~ spl35_292 ),
inference(avatar_split_clause,[],[f13255,f9529,f7640,f7982,f13272]) ).
fof(f13272,plain,
( spl35_421
<=> ! [X4,X5] :
( X4 = X5
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X5,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_421])]) ).
fof(f7982,plain,
( spl35_208
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_208])]) ).
fof(f13255,plain,
( ! [X2,X3] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X2 = X3
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) != X2 )
| ~ spl35_188
| ~ spl35_292 ),
inference(superposition,[],[f4662,f9534]) ).
fof(f4662,plain,
! [X2,X0,X1] :
( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X2)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f3389]) ).
fof(f3389,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X2) )
& ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X2)
| X0 != X1 ) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
inference(rectify,[],[f3388]) ).
fof(f3388,plain,
! [X2,X1,X0] :
( ( ( X1 = X2
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0) )
& ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0)
| X1 != X2 ) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(nnf_transformation,[],[f2634]) ).
fof(f2634,plain,
! [X2,X1,X0] :
( ( X1 = X2
<=> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(ennf_transformation,[],[f1207]) ).
fof(f1207,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0
=> ( X1 = X2
<=> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X0) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0) ) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X47,X7,X9] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X47
=> ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X9,X47) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X7,X47)
<=> X7 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(f13274,plain,
( spl35_208
| spl35_421
| ~ spl35_188
| ~ spl35_292 ),
inference(avatar_split_clause,[],[f13256,f9529,f7640,f13272,f7982]) ).
fof(f13256,plain,
( ! [X4,X5] :
( X4 = X5
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X5,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) != X4
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| ~ spl35_188
| ~ spl35_292 ),
inference(superposition,[],[f4662,f9534]) ).
fof(f13250,plain,
( spl35_420
| ~ spl35_249 ),
inference(avatar_split_clause,[],[f13245,f8388,f13247]) ).
fof(f13247,plain,
( spl35_420
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_420])]) ).
fof(f13245,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_249 ),
inference(resolution,[],[f8390,f4806]) ).
fof(f4806,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f3483]) ).
fof(f13221,plain,
( spl35_419
| ~ spl35_255
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13121,f13098,f8463,f13218]) ).
fof(f13218,plain,
( spl35_419
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_419])]) ).
fof(f8463,plain,
( spl35_255
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_255])]) ).
fof(f13121,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_255
| ~ spl35_401 ),
inference(backward_demodulation,[],[f8465,f13100]) ).
fof(f8465,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_255 ),
inference(avatar_component_clause,[],[f8463]) ).
fof(f13216,plain,
( ~ spl35_418
| spl35_197
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13115,f13098,f7896,f13213]) ).
fof(f13213,plain,
( spl35_418
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_418])]) ).
fof(f7896,plain,
( spl35_197
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_197])]) ).
fof(f13115,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| spl35_197
| ~ spl35_401 ),
inference(backward_demodulation,[],[f7897,f13100]) ).
fof(f7897,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| spl35_197 ),
inference(avatar_component_clause,[],[f7896]) ).
fof(f13211,plain,
( spl35_417
| ~ spl35_245
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13118,f13098,f8284,f13208]) ).
fof(f13208,plain,
( spl35_417
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_417])]) ).
fof(f8284,plain,
( spl35_245
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_245])]) ).
fof(f13118,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_245
| ~ spl35_401 ),
inference(backward_demodulation,[],[f8286,f13100]) ).
fof(f8286,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_245 ),
inference(avatar_component_clause,[],[f8284]) ).
fof(f13206,plain,
( ~ spl35_416
| spl35_195
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13113,f13098,f7888,f13203]) ).
fof(f13203,plain,
( spl35_416
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_416])]) ).
fof(f7888,plain,
( spl35_195
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_195])]) ).
fof(f13113,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| spl35_195
| ~ spl35_401 ),
inference(backward_demodulation,[],[f7890,f13100]) ).
fof(f7890,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| spl35_195 ),
inference(avatar_component_clause,[],[f7888]) ).
fof(f13201,plain,
( ~ spl35_415
| spl35_214
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13117,f13098,f8035,f13198]) ).
fof(f8035,plain,
( spl35_214
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_214])]) ).
fof(f13117,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| spl35_214
| ~ spl35_401 ),
inference(backward_demodulation,[],[f8037,f13100]) ).
fof(f8037,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| spl35_214 ),
inference(avatar_component_clause,[],[f8035]) ).
fof(f13196,plain,
( ~ spl35_414
| spl35_320
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13125,f13098,f11012,f13193]) ).
fof(f13193,plain,
( spl35_414
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_414])]) ).
fof(f11012,plain,
( spl35_320
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_320])]) ).
fof(f13125,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| spl35_320
| ~ spl35_401 ),
inference(backward_demodulation,[],[f11013,f13100]) ).
fof(f11013,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| spl35_320 ),
inference(avatar_component_clause,[],[f11012]) ).
fof(f13191,plain,
( spl35_413
| ~ spl35_257
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13122,f13098,f8491,f13188]) ).
fof(f13188,plain,
( spl35_413
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_413])]) ).
fof(f8491,plain,
( spl35_257
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_257])]) ).
fof(f13122,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_257
| ~ spl35_401 ),
inference(backward_demodulation,[],[f8493,f13100]) ).
fof(f8493,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_257 ),
inference(avatar_component_clause,[],[f8491]) ).
fof(f13186,plain,
( ~ spl35_412
| spl35_326
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13128,f13098,f11082,f13183]) ).
fof(f13183,plain,
( spl35_412
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_412])]) ).
fof(f11082,plain,
( spl35_326
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_326])]) ).
fof(f13128,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| spl35_326
| ~ spl35_401 ),
inference(backward_demodulation,[],[f11083,f13100]) ).
fof(f11083,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| spl35_326 ),
inference(avatar_component_clause,[],[f11082]) ).
fof(f13181,plain,
( ~ spl35_411
| spl35_336
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13129,f13098,f11162,f13178]) ).
fof(f13178,plain,
( spl35_411
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_411])]) ).
fof(f11162,plain,
( spl35_336
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_336])]) ).
fof(f13129,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| spl35_336
| ~ spl35_401 ),
inference(backward_demodulation,[],[f11164,f13100]) ).
fof(f11164,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| spl35_336 ),
inference(avatar_component_clause,[],[f11162]) ).
fof(f13175,plain,
( spl35_410
| ~ spl35_260
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13124,f13098,f8536,f13172]) ).
fof(f13172,plain,
( spl35_410
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_410])]) ).
fof(f8536,plain,
( spl35_260
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_260])]) ).
fof(f13124,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_260
| ~ spl35_401 ),
inference(backward_demodulation,[],[f8538,f13100]) ).
fof(f8538,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_260 ),
inference(avatar_component_clause,[],[f8536]) ).
fof(f13170,plain,
( ~ spl35_409
| spl35_322
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13126,f13098,f11048,f13167]) ).
fof(f13167,plain,
( spl35_409
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_409])]) ).
fof(f11048,plain,
( spl35_322
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_322])]) ).
fof(f13126,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| spl35_322
| ~ spl35_401 ),
inference(backward_demodulation,[],[f11050,f13100]) ).
fof(f11050,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| spl35_322 ),
inference(avatar_component_clause,[],[f11048]) ).
fof(f13165,plain,
( spl35_408
| ~ spl35_258
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13123,f13098,f8501,f13162]) ).
fof(f13162,plain,
( spl35_408
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_408])]) ).
fof(f8501,plain,
( spl35_258
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_258])]) ).
fof(f13123,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_258
| ~ spl35_401 ),
inference(backward_demodulation,[],[f8503,f13100]) ).
fof(f8503,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_258 ),
inference(avatar_component_clause,[],[f8501]) ).
fof(f13160,plain,
( spl35_407
| ~ spl35_247
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13119,f13098,f8317,f13157]) ).
fof(f13157,plain,
( spl35_407
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_407])]) ).
fof(f8317,plain,
( spl35_247
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_247])]) ).
fof(f13119,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_247
| ~ spl35_401 ),
inference(backward_demodulation,[],[f8319,f13100]) ).
fof(f8319,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_247 ),
inference(avatar_component_clause,[],[f8317]) ).
fof(f13155,plain,
( spl35_406
| ~ spl35_251
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13120,f13098,f8409,f13152]) ).
fof(f13152,plain,
( spl35_406
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_406])]) ).
fof(f8409,plain,
( spl35_251
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_251])]) ).
fof(f13120,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_251
| ~ spl35_401 ),
inference(backward_demodulation,[],[f8411,f13100]) ).
fof(f8411,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_251 ),
inference(avatar_component_clause,[],[f8409]) ).
fof(f13150,plain,
( ~ spl35_405
| spl35_325
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13127,f13098,f11075,f13147]) ).
fof(f11075,plain,
( spl35_325
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_325])]) ).
fof(f13127,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| spl35_325
| ~ spl35_401 ),
inference(backward_demodulation,[],[f11077,f13100]) ).
fof(f11077,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| spl35_325 ),
inference(avatar_component_clause,[],[f11075]) ).
fof(f13145,plain,
( ~ spl35_404
| spl35_196
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13114,f13098,f7892,f13142]) ).
fof(f13142,plain,
( spl35_404
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_404])]) ).
fof(f7892,plain,
( spl35_196
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_196])]) ).
fof(f13114,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| spl35_196
| ~ spl35_401 ),
inference(backward_demodulation,[],[f7894,f13100]) ).
fof(f7894,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| spl35_196 ),
inference(avatar_component_clause,[],[f7892]) ).
fof(f13140,plain,
( ~ spl35_403
| spl35_344
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13130,f13098,f11259,f13137]) ).
fof(f13137,plain,
( spl35_403
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_403])]) ).
fof(f11259,plain,
( spl35_344
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_344])]) ).
fof(f13130,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| spl35_344
| ~ spl35_401 ),
inference(backward_demodulation,[],[f11260,f13100]) ).
fof(f11260,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| spl35_344 ),
inference(avatar_component_clause,[],[f11259]) ).
fof(f13135,plain,
( spl35_402
| ~ spl35_206
| ~ spl35_401 ),
inference(avatar_split_clause,[],[f13116,f13098,f7965,f13132]) ).
fof(f13132,plain,
( spl35_402
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_402])]) ).
fof(f7965,plain,
( spl35_206
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_206])]) ).
fof(f13116,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____))
| ~ spl35_206
| ~ spl35_401 ),
inference(backward_demodulation,[],[f7967,f13100]) ).
fof(f7967,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____))
| ~ spl35_206 ),
inference(avatar_component_clause,[],[f7965]) ).
fof(f13101,plain,
( spl35_401
| ~ spl35_188 ),
inference(avatar_split_clause,[],[f13091,f7640,f13098]) ).
fof(f13091,plain,
( c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_188 ),
inference(resolution,[],[f7737,f7642]) ).
fof(f7737,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(forward_demodulation,[],[f7736,f4335]) ).
fof(f7736,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(forward_demodulation,[],[f7735,f4335]) ).
fof(f7735,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7711,f4335]) ).
fof(f7711,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f7446,f4335]) ).
fof(f7446,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(forward_demodulation,[],[f7445,f5723]) ).
fof(f7445,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7444,f5723]) ).
fof(f7444,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7418,f5723]) ).
fof(f7418,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f7262,f5723]) ).
fof(f7262,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(forward_demodulation,[],[f7261,f5637]) ).
fof(f7261,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(forward_demodulation,[],[f7260,f5637]) ).
fof(f7260,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(forward_demodulation,[],[f7259,f5537]) ).
fof(f7259,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f5839,f5537]) ).
fof(f5839,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(definition_unfolding,[],[f4416,f4431,f5442]) ).
fof(f4416,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f2476]) ).
fof(f2476,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f1924]) ).
fof(f1924,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f278]) ).
fof(f278,axiom,
! [X15] :
( class_Int_Onumber__ring(X15)
=> c_Int_Onumber__class_Onumber__of(X15,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(X15,c_Groups_Oone__class_Oone(X15),c_Groups_Oone__class_Oone(X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).
fof(f13096,plain,
( spl35_400
| ~ spl35_92 ),
inference(avatar_split_clause,[],[f13090,f6857,f13093]) ).
fof(f13093,plain,
( spl35_400
<=> c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_400])]) ).
fof(f13090,plain,
( c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ spl35_92 ),
inference(resolution,[],[f7737,f6859]) ).
fof(f13087,plain,
( spl35_399
| ~ spl35_169 ),
inference(avatar_split_clause,[],[f13077,f7384,f13084]) ).
fof(f13084,plain,
( spl35_399
<=> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_399])]) ).
fof(f13077,plain,
( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl35_169 ),
inference(trivial_inequality_removal,[],[f13069]) ).
fof(f13069,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl35_169 ),
inference(superposition,[],[f4849,f7386]) ).
fof(f4849,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X1)
| c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) = X1 ),
inference(cnf_transformation,[],[f3502]) ).
fof(f13082,plain,
( spl35_398
| ~ spl35_75
| ~ spl35_169 ),
inference(avatar_split_clause,[],[f13071,f7384,f6734,f13079]) ).
fof(f13079,plain,
( spl35_398
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_398])]) ).
fof(f13071,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))
| ~ spl35_169 ),
inference(superposition,[],[f5135,f7386]) ).
fof(f5135,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(cnf_transformation,[],[f3675]) ).
fof(f3675,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ) ),
inference(nnf_transformation,[],[f1445]) ).
fof(f1445,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rectify,[],[f176]) ).
fof(f176,axiom,
! [X12,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X13))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
fof(f13066,plain,
( ~ spl35_396
| spl35_397
| ~ spl35_151 ),
inference(avatar_split_clause,[],[f13057,f7250,f13063,f13059]) ).
fof(f13059,plain,
( spl35_396
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_396])]) ).
fof(f13063,plain,
( spl35_397
<=> v_r = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_397])]) ).
fof(f7250,plain,
( spl35_151
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_151])]) ).
fof(f13057,plain,
( v_r = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))
| ~ spl35_151 ),
inference(resolution,[],[f7252,f4624]) ).
fof(f7252,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r)
| ~ spl35_151 ),
inference(avatar_component_clause,[],[f7250]) ).
fof(f13055,plain,
( spl35_395
| spl35_208 ),
inference(avatar_split_clause,[],[f13051,f7982,f13053]) ).
fof(f13053,plain,
( spl35_395
<=> ! [X7] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X7,X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_395])]) ).
fof(f13051,plain,
! [X7] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X7,X7),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(superposition,[],[f5678,f5089]) ).
fof(f5089,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) = X0,
inference(cnf_transformation,[],[f1896]) ).
fof(f1896,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) = X0,
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X14] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14) = X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(f5678,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1 ),
inference(cnf_transformation,[],[f3988]) ).
fof(f3988,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
& c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) ) ),
inference(rectify,[],[f3987]) ).
fof(f3987,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
& c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1 )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) ) ),
inference(flattening,[],[f3986]) ).
fof(f3986,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
& c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1 )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) ) ),
inference(nnf_transformation,[],[f1771]) ).
fof(f1771,plain,
! [X1,X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0))
<=> ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
& c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X1 ) ),
inference(rectify,[],[f154]) ).
fof(f154,axiom,
! [X12,X13] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X13),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X12))
<=> ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X12
& c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(f13047,plain,
( spl35_394
| spl35_208 ),
inference(avatar_split_clause,[],[f13041,f7982,f13045]) ).
fof(f13045,plain,
( spl35_394
<=> ! [X7] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X7,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_394])]) ).
fof(f13041,plain,
! [X7] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X7,X7)) ),
inference(superposition,[],[f5677,f5089]) ).
fof(f5677,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(cnf_transformation,[],[f3988]) ).
fof(f12998,plain,
( spl35_393
| ~ spl35_188
| ~ spl35_201 ),
inference(avatar_split_clause,[],[f12993,f7920,f7640,f12996]) ).
fof(f12996,plain,
( spl35_393
<=> ! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_393])]) ).
fof(f7920,plain,
( spl35_201
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_201])]) ).
fof(f12993,plain,
( ! [X1] :
( ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) )
| ~ spl35_201 ),
inference(resolution,[],[f7977,f7922]) ).
fof(f7922,plain,
( class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ~ spl35_201 ),
inference(avatar_component_clause,[],[f7920]) ).
fof(f7977,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f7976,f4335]) ).
fof(f7976,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f7975,f5637]) ).
fof(f7975,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),X0)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(forward_demodulation,[],[f7974,f4335]) ).
fof(f7974,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5788,f5637]) ).
fof(f5788,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X0) ),
inference(definition_unfolding,[],[f4090,f5442]) ).
fof(f4090,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f3077]) ).
fof(f3077,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0) ) )
| ~ class_Int_Onumber__ring(X1) ),
inference(nnf_transformation,[],[f2835]) ).
fof(f2835,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) )
| ~ class_Int_Onumber__ring(X1) ),
inference(flattening,[],[f2834]) ).
fof(f2834,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) )
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f1457]) ).
fof(f1457,plain,
! [X0,X1] :
( ( class_Int_Onumber__ring(X1)
& class_Rings_Olinordered__idom(X1) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) ) ),
inference(rectify,[],[f277]) ).
fof(f277,axiom,
! [X12,X15] :
( ( class_Rings_Olinordered__idom(X15)
& class_Int_Onumber__ring(X15) )
=> ( c_Orderings_Oord__class_Oless__eq(X15,c_Groups_Oone__class_Oone(X15),c_Int_Onumber__class_Onumber__of(X15,X12))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I2_J) ).
fof(f12991,plain,
( ~ spl35_188
| spl35_392
| ~ spl35_201 ),
inference(avatar_split_clause,[],[f12986,f7920,f12989,f7640]) ).
fof(f12989,plain,
( spl35_392
<=> ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_392])]) ).
fof(f12986,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) )
| ~ spl35_201 ),
inference(resolution,[],[f7908,f7922]) ).
fof(f7908,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) ),
inference(forward_demodulation,[],[f7907,f4335]) ).
fof(f7907,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) ),
inference(forward_demodulation,[],[f7906,f5637]) ).
fof(f7906,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),X0)
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f7905,f4335]) ).
fof(f7905,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5789,f5637]) ).
fof(f5789,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X0) ),
inference(definition_unfolding,[],[f4089,f5442]) ).
fof(f4089,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f3077]) ).
fof(f12984,plain,
( ~ spl35_188
| spl35_391
| ~ spl35_201 ),
inference(avatar_split_clause,[],[f12979,f7920,f12982,f7640]) ).
fof(f12982,plain,
( spl35_391
<=> ! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_391])]) ).
fof(f12979,plain,
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) )
| ~ spl35_201 ),
inference(resolution,[],[f7829,f7922]) ).
fof(f7829,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7693,f4335]) ).
fof(f7693,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f6309,f4335]) ).
fof(f6309,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(forward_demodulation,[],[f6304,f5637]) ).
fof(f6304,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f5950,f5637]) ).
fof(f5950,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(definition_unfolding,[],[f5020,f5442]) ).
fof(f5020,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) ),
inference(cnf_transformation,[],[f3602]) ).
fof(f3602,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0)
| ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) )
& ( c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls)) ) ) ),
inference(rectify,[],[f3601]) ).
fof(f3601,plain,
! [X1,X0] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) )
& ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OBit1(c_Int_OPls)) ) ) ),
inference(nnf_transformation,[],[f2504]) ).
fof(f2504,plain,
! [X1,X0] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OBit1(c_Int_OPls))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) ) ),
inference(flattening,[],[f2503]) ).
fof(f2503,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OBit1(c_Int_OPls))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) )
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f1828]) ).
fof(f1828,plain,
! [X0,X1] :
( ( class_Rings_Olinordered__idom(X1)
& class_Int_Onumber__ring(X1) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OBit1(c_Int_OPls))
<=> c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X0),c_Groups_Oone__class_Oone(X1)) ) ),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X13,X15] :
( ( class_Rings_Olinordered__idom(X15)
& class_Int_Onumber__ring(X15) )
=> ( c_Orderings_Oord__class_Oless__eq(X15,c_Int_Onumber__class_Onumber__of(X15,X13),c_Groups_Oone__class_Oone(X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X13,c_Int_OBit1(c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I4_J) ).
fof(f12977,plain,
( ~ spl35_390
| ~ spl35_377 ),
inference(avatar_split_clause,[],[f12967,f12850,f12974]) ).
fof(f12974,plain,
( spl35_390
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_390])]) ).
fof(f12967,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_377 ),
inference(superposition,[],[f4343,f12852]) ).
fof(f4343,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(cnf_transformation,[],[f1427]) ).
fof(f1427,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(rectify,[],[f269]) ).
fof(f269,axiom,
! [X10] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X10),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
fof(f12972,plain,
( spl35_389
| ~ spl35_377 ),
inference(avatar_split_clause,[],[f12965,f12850,f12969]) ).
fof(f12965,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_377 ),
inference(superposition,[],[f4108,f12852]) ).
fof(f12957,plain,
( ~ spl35_188
| spl35_388
| ~ spl35_201 ),
inference(avatar_split_clause,[],[f12953,f7920,f12955,f7640]) ).
fof(f12955,plain,
( spl35_388
<=> ! [X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_388])]) ).
fof(f12953,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) )
| ~ spl35_201 ),
inference(resolution,[],[f7815,f7922]) ).
fof(f7815,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7701,f4335]) ).
fof(f7701,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f6717,f4335]) ).
fof(f6717,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0)
| ~ class_Rings_Olinordered__idom(X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(forward_demodulation,[],[f6716,f5637]) ).
fof(f6716,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))
| ~ class_Int_Onumber__ring(X0)
| ~ c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(forward_demodulation,[],[f5846,f5637]) ).
fof(f5846,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(definition_unfolding,[],[f4460,f5442]) ).
fof(f4460,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Rings_Olinordered__idom(X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) ),
inference(cnf_transformation,[],[f3285]) ).
fof(f3285,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) )
& ( c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls)) ) ) ),
inference(nnf_transformation,[],[f2888]) ).
fof(f2888,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Rings_Olinordered__idom(X0)
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
<=> c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) ) ),
inference(flattening,[],[f2887]) ).
fof(f2887,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
<=> c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) )
| ~ class_Int_Onumber__ring(X0)
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1382]) ).
fof(f1382,plain,
! [X1,X0] :
( ( class_Int_Onumber__ring(X0)
& class_Rings_Olinordered__idom(X0) )
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
<=> c_Orderings_Oord__class_Oless(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) ) ),
inference(rectify,[],[f279]) ).
fof(f279,axiom,
! [X15,X13] :
( ( class_Int_Onumber__ring(X15)
& class_Rings_Olinordered__idom(X15) )
=> ( c_Orderings_Oord__class_Oless(X15,c_Int_Onumber__class_Onumber__of(X15,X13),c_Groups_Oone__class_Oone(X15))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X13,c_Int_OBit1(c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I4_J) ).
fof(f12948,plain,
( ~ spl35_188
| spl35_387
| ~ spl35_201 ),
inference(avatar_split_clause,[],[f12943,f7920,f12946,f7640]) ).
fof(f12946,plain,
( spl35_387
<=> ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_387])]) ).
fof(f12943,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) )
| ~ spl35_201 ),
inference(resolution,[],[f7778,f7922]) ).
fof(f7778,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) ),
inference(forward_demodulation,[],[f7694,f4335]) ).
fof(f7694,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(backward_demodulation,[],[f6469,f4335]) ).
fof(f6469,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(forward_demodulation,[],[f6468,f5637]) ).
fof(f6468,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))) ),
inference(forward_demodulation,[],[f5951,f5637]) ).
fof(f5951,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0)
| ~ class_Rings_Olinordered__idom(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0)) ),
inference(definition_unfolding,[],[f5019,f5442]) ).
fof(f5019,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Int_Onumber__class_Onumber__of(X0,X1),c_Groups_Oone__class_Oone(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls)) ),
inference(cnf_transformation,[],[f3602]) ).
fof(f12939,plain,
( spl35_386
| ~ spl35_48
| ~ spl35_352 ),
inference(avatar_split_clause,[],[f12934,f11597,f6556,f12936]) ).
fof(f12936,plain,
( spl35_386
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_386])]) ).
fof(f12934,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_48
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12903,f4084]) ).
fof(f12903,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_48
| ~ spl35_352 ),
inference(resolution,[],[f11599,f8328]) ).
fof(f8328,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) )
| ~ spl35_48 ),
inference(backward_demodulation,[],[f4569,f6558]) ).
fof(f4569,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) ),
inference(cnf_transformation,[],[f2954]) ).
fof(f2954,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = X0 )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(ennf_transformation,[],[f1492]) ).
fof(f1492,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = X0 ) ),
inference(rectify,[],[f259]) ).
fof(f259,axiom,
! [X44] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X44,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X44) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X44) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X44,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X44) = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__def) ).
fof(f12933,plain,
( spl35_385
| ~ spl35_352 ),
inference(avatar_split_clause,[],[f12932,f11597,f12927]) ).
fof(f12927,plain,
( spl35_385
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_385])]) ).
fof(f12932,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12904,f4702]) ).
fof(f12904,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl35_352 ),
inference(resolution,[],[f11599,f5844]) ).
fof(f5844,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),c_Int_OPls) ),
inference(definition_unfolding,[],[f4441,f4431]) ).
fof(f4441,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f3271]) ).
fof(f3271,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OPls) ) ),
inference(nnf_transformation,[],[f2002]) ).
fof(f2002,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(rectify,[],[f165]) ).
fof(f165,axiom,
! [X27] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X27),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).
fof(f12930,plain,
( spl35_385
| ~ spl35_352 ),
inference(avatar_split_clause,[],[f12925,f11597,f12927]) ).
fof(f12925,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12924,f4702]) ).
fof(f12924,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12906,f4931]) ).
fof(f12906,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls))
| ~ spl35_352 ),
inference(resolution,[],[f11599,f5988]) ).
fof(f5988,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) ),
inference(definition_unfolding,[],[f5237,f4431,f4431]) ).
fof(f5237,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3735]) ).
fof(f3735,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X0)) ) ),
inference(rectify,[],[f3734]) ).
fof(f3734,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit0(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit0(X1)) ) ),
inference(nnf_transformation,[],[f1499]) ).
fof(f1499,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X0),c_Int_OBit0(X1))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(rectify,[],[f137]) ).
fof(f137,axiom,
! [X27,X26] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X27),c_Int_OBit0(X26))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).
fof(f12923,plain,
( spl35_384
| ~ spl35_352 ),
inference(avatar_split_clause,[],[f12918,f11597,f12920]) ).
fof(f12920,plain,
( spl35_384
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_384])]) ).
fof(f12918,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12917,f9212]) ).
fof(f12917,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12916,f4702]) ).
fof(f12916,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12901,f5723]) ).
fof(f12901,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OPls)
| ~ spl35_352 ),
inference(resolution,[],[f11599,f6723]) ).
fof(f6723,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Int_OPls) ),
inference(forward_demodulation,[],[f5926,f5637]) ).
fof(f5926,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(definition_unfolding,[],[f4863,f5442]) ).
fof(f4863,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f3511]) ).
fof(f3511,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ) ),
inference(nnf_transformation,[],[f1194]) ).
fof(f1194,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls) ),
inference(rectify,[],[f161]) ).
fof(f161,axiom,
! [X27] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X27),c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).
fof(f12915,plain,
( spl35_383
| ~ spl35_352 ),
inference(avatar_split_clause,[],[f12910,f11597,f12912]) ).
fof(f12912,plain,
( spl35_383
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_383])]) ).
fof(f12910,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12909,f9212]) ).
fof(f12909,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12908,f4702]) ).
fof(f12908,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OPls)
| ~ spl35_352 ),
inference(forward_demodulation,[],[f12900,f5723]) ).
fof(f12900,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OPls)
| ~ spl35_352 ),
inference(resolution,[],[f11599,f7301]) ).
fof(f7301,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Int_OPls) ),
inference(forward_demodulation,[],[f5878,f5637]) ).
fof(f5878,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Int_OPls) ),
inference(definition_unfolding,[],[f4581,f5442]) ).
fof(f4581,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f3351]) ).
fof(f3351,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ) ),
inference(nnf_transformation,[],[f1254]) ).
fof(f1254,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls) ),
inference(rectify,[],[f125]) ).
fof(f125,axiom,
! [X27] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Int_OPls)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X27),c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).
fof(f12898,plain,
( ~ spl35_382
| spl35_337 ),
inference(avatar_split_clause,[],[f12891,f11175,f12895]) ).
fof(f12895,plain,
( spl35_382
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_382])]) ).
fof(f11175,plain,
( spl35_337
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_337])]) ).
fof(f12891,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| spl35_337 ),
inference(resolution,[],[f11176,f4943]) ).
fof(f11176,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| spl35_337 ),
inference(avatar_component_clause,[],[f11175]) ).
fof(f12890,plain,
( ~ spl35_381
| spl35_328 ),
inference(avatar_split_clause,[],[f12883,f11095,f12887]) ).
fof(f12887,plain,
( spl35_381
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_381])]) ).
fof(f11095,plain,
( spl35_328
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_328])]) ).
fof(f12883,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| spl35_328 ),
inference(resolution,[],[f11096,f4943]) ).
fof(f11096,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| spl35_328 ),
inference(avatar_component_clause,[],[f11095]) ).
fof(f12876,plain,
( ~ spl35_188
| spl35_380
| ~ spl35_201 ),
inference(avatar_split_clause,[],[f12872,f7920,f12874,f7640]) ).
fof(f12874,plain,
( spl35_380
<=> ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_380])]) ).
fof(f12872,plain,
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1))
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) )
| ~ spl35_201 ),
inference(resolution,[],[f7757,f7922]) ).
fof(f7757,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f7702,f4335]) ).
fof(f7702,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(backward_demodulation,[],[f7094,f4335]) ).
fof(f7094,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) ),
inference(forward_demodulation,[],[f7093,f5637]) ).
fof(f7093,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),X0)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(forward_demodulation,[],[f5980,f5637]) ).
fof(f5980,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X0)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(definition_unfolding,[],[f5176,f5442]) ).
fof(f5176,plain,
! [X0,X1] :
( ~ class_Rings_Olinordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X0)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) ),
inference(cnf_transformation,[],[f3704]) ).
fof(f12869,plain,
( spl35_379
| ~ spl35_268 ),
inference(avatar_split_clause,[],[f12857,f8681,f12866]) ).
fof(f12866,plain,
( spl35_379
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_379])]) ).
fof(f12857,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl35_268 ),
inference(superposition,[],[f4108,f8683]) ).
fof(f12864,plain,
( ~ spl35_378
| ~ spl35_268 ),
inference(avatar_split_clause,[],[f12859,f8681,f12861]) ).
fof(f12861,plain,
( spl35_378
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_378])]) ).
fof(f12859,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_268 ),
inference(superposition,[],[f4343,f8683]) ).
fof(f12853,plain,
( spl35_377
| spl35_376 ),
inference(avatar_split_clause,[],[f12847,f12843,f12850]) ).
fof(f12843,plain,
( spl35_376
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_376])]) ).
fof(f12847,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| spl35_376 ),
inference(resolution,[],[f12845,f4631]) ).
fof(f4631,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ),
inference(cnf_transformation,[],[f2649]) ).
fof(f2649,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 )
& ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(ennf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = X0 ) ),
inference(rectify,[],[f179]) ).
fof(f179,axiom,
! [X3] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__def) ).
fof(f12845,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| spl35_376 ),
inference(avatar_component_clause,[],[f12843]) ).
fof(f12846,plain,
( ~ spl35_376
| ~ spl35_64 ),
inference(avatar_split_clause,[],[f12841,f6657,f12843]) ).
fof(f12841,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_64 ),
inference(superposition,[],[f4654,f6659]) ).
fof(f4654,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1626]) ).
fof(f1626,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X37] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X37),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(f12839,plain,
( spl35_208
| spl35_375 ),
inference(avatar_split_clause,[],[f12833,f12836,f7982]) ).
fof(f12836,plain,
( spl35_375
<=> ! [X11,X10] :
( X10 = X11
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) != X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_375])]) ).
fof(f12833,plain,
! [X10,X11] :
( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) != X10
| X10 = X11
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(superposition,[],[f5597,f5089]) ).
fof(f5597,plain,
! [X2,X0,X1] :
( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0)
| X0 = X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
inference(cnf_transformation,[],[f3935]) ).
fof(f3935,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0) )
& ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0)
| X0 != X1 ) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
inference(nnf_transformation,[],[f2662]) ).
fof(f2662,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0) )
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 ),
inference(ennf_transformation,[],[f1865]) ).
fof(f1865,plain,
! [X1,X2,X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X2
=> ( X0 = X1
<=> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X0) ) ),
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X7,X9,X47] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X47
=> ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X47,X9) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X47,X7)
<=> X7 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(f12838,plain,
( spl35_208
| spl35_375 ),
inference(avatar_split_clause,[],[f12829,f12836,f7982]) ).
fof(f12829,plain,
! [X10,X11] :
( X10 = X11
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) != X10 ),
inference(superposition,[],[f5597,f5089]) ).
fof(f12823,plain,
( spl35_332
| spl35_374 ),
inference(avatar_split_clause,[],[f12812,f12820,f11137]) ).
fof(f11137,plain,
( spl35_332
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_332])]) ).
fof(f12820,plain,
( spl35_374
<=> ! [X20,X21] :
( X20 = X21
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X21) != X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_374])]) ).
fof(f12812,plain,
! [X21,X20] :
( X20 = X21
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X21) != X20
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(superposition,[],[f5312,f5439]) ).
fof(f5439,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f1291]) ).
fof(f1291,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f356]) ).
fof(f356,axiom,
! [X37] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X37) = X37,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(f5312,plain,
! [X2,X0,X1] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| X1 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f3776]) ).
fof(f3776,plain,
! [X0,X1,X2] :
( ( X1 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) )
& ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| ( X1 != X2
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(rectify,[],[f3775]) ).
fof(f3775,plain,
! [X1,X2,X0] :
( ( X0 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) )
& ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)
| ( X0 != X2
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ),
inference(flattening,[],[f3774]) ).
fof(f3774,plain,
! [X1,X2,X0] :
( ( X0 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) )
& ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)
| ( X0 != X2
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ),
inference(nnf_transformation,[],[f1464]) ).
fof(f1464,plain,
! [X1,X2,X0] :
( ( X0 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
<=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) ),
inference(rectify,[],[f411]) ).
fof(f411,axiom,
! [X50,X27,X6] :
( ( X6 = X50
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X27 )
<=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X27,X6) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X27,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(f12822,plain,
( spl35_332
| spl35_374 ),
inference(avatar_split_clause,[],[f12803,f12820,f11137]) ).
fof(f12803,plain,
! [X21,X20] :
( X20 = X21
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X21) != X20 ),
inference(superposition,[],[f5312,f5439]) ).
fof(f12818,plain,
( spl35_373
| spl35_305
| ~ spl35_244 ),
inference(avatar_split_clause,[],[f12809,f8267,f10376,f12815]) ).
fof(f12815,plain,
( spl35_373
<=> ! [X13,X12] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X13) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X12)
| X12 = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_373])]) ).
fof(f12809,plain,
( ! [X12,X13] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X12 = X13
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X13) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X12) )
| ~ spl35_244 ),
inference(superposition,[],[f5312,f8581]) ).
fof(f8581,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ spl35_244 ),
inference(backward_demodulation,[],[f7814,f8269]) ).
fof(f7814,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0),
inference(forward_demodulation,[],[f7813,f4335]) ).
fof(f7813,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),X0),
inference(forward_demodulation,[],[f7812,f4335]) ).
fof(f7812,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),X0),
inference(forward_demodulation,[],[f7726,f4335]) ).
fof(f7726,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),X0),
inference(backward_demodulation,[],[f7628,f4335]) ).
fof(f7628,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0),
inference(forward_demodulation,[],[f7627,f5723]) ).
fof(f7627,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),X0),
inference(forward_demodulation,[],[f7626,f5637]) ).
fof(f7626,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),X0),
inference(forward_demodulation,[],[f7625,f5723]) ).
fof(f7625,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),X0),
inference(forward_demodulation,[],[f7624,f5637]) ).
fof(f7624,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),X0),
inference(forward_demodulation,[],[f7623,f5723]) ).
fof(f7623,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),X0),
inference(forward_demodulation,[],[f7622,f5637]) ).
fof(f7622,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),X0),
inference(forward_demodulation,[],[f7621,f5723]) ).
fof(f7621,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),X0),
inference(forward_demodulation,[],[f7620,f5537]) ).
fof(f7620,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),X0),
inference(forward_demodulation,[],[f5888,f5723]) ).
fof(f5888,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0),
inference(definition_unfolding,[],[f4687,f4431,f5442]) ).
fof(f4687,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0),
inference(cnf_transformation,[],[f1850]) ).
fof(f1850,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0),
inference(rectify,[],[f556]) ).
fof(f556,axiom,
! [X14] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2) ).
fof(f12817,plain,
( spl35_373
| spl35_305
| ~ spl35_244 ),
inference(avatar_split_clause,[],[f12800,f8267,f10376,f12815]) ).
fof(f12800,plain,
( ! [X12,X13] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X13) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X12)
| X12 = X13 )
| ~ spl35_244 ),
inference(superposition,[],[f5312,f8581]) ).
fof(f12666,plain,
( spl35_332
| spl35_372 ),
inference(avatar_split_clause,[],[f12646,f12659,f11137]) ).
fof(f12659,plain,
( spl35_372
<=> ! [X14,X15] :
( X14 = X15
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_372])]) ).
fof(f12646,plain,
! [X16,X17] :
( X16 = X17
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X16
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(superposition,[],[f5149,f5611]) ).
fof(f5611,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1543]) ).
fof(f1543,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f354]) ).
fof(f354,axiom,
! [X37] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X37,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X37,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(f5149,plain,
! [X2,X0,X1] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| X1 = X2 ),
inference(cnf_transformation,[],[f3685]) ).
fof(f3685,plain,
! [X0,X1,X2] :
( ( X1 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X0) )
& ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X0)
| ( X1 != X2
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(rectify,[],[f3684]) ).
fof(f3684,plain,
! [X0,X2,X1] :
( ( X1 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X0) )
& ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X0)
| ( X1 != X2
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(flattening,[],[f3683]) ).
fof(f3683,plain,
! [X0,X2,X1] :
( ( X1 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X0) )
& ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X0)
| ( X1 != X2
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(nnf_transformation,[],[f2099]) ).
fof(f2099,plain,
! [X0,X2,X1] :
( ( X1 = X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
<=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X0) ),
inference(rectify,[],[f412]) ).
fof(f412,axiom,
! [X27,X6,X50] :
( ( X6 = X50
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X27 )
<=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X6,X27) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X50,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(f12661,plain,
( spl35_332
| spl35_372 ),
inference(avatar_split_clause,[],[f12645,f12659,f11137]) ).
fof(f12645,plain,
! [X14,X15] :
( X14 = X15
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X14
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(superposition,[],[f5149,f5611]) ).
fof(f12413,plain,
( spl35_371
| spl35_208 ),
inference(avatar_split_clause,[],[f12408,f7982,f12410]) ).
fof(f12408,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(superposition,[],[f5016,f5089]) ).
fof(f5016,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ),
inference(cnf_transformation,[],[f3600]) ).
fof(f3600,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ) ),
inference(nnf_transformation,[],[f2065]) ).
fof(f2065,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0)) ),
inference(rectify,[],[f693]) ).
fof(f693,axiom,
! [X13] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X13
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(f12238,plain,
( ~ spl35_369
| spl35_370
| ~ spl35_139 ),
inference(avatar_split_clause,[],[f12229,f7157,f12235,f12231]) ).
fof(f12231,plain,
( spl35_369
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_369])]) ).
fof(f12235,plain,
( spl35_370
<=> v_r = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_370])]) ).
fof(f7157,plain,
( spl35_139
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_139])]) ).
fof(f12229,plain,
( v_r = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ spl35_139 ),
inference(resolution,[],[f7159,f4624]) ).
fof(f7159,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r)
| ~ spl35_139 ),
inference(avatar_component_clause,[],[f7157]) ).
fof(f12201,plain,
( ~ spl35_368
| spl35_361 ),
inference(avatar_split_clause,[],[f12194,f11846,f12198]) ).
fof(f12198,plain,
( spl35_368
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_368])]) ).
fof(f11846,plain,
( spl35_361
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_361])]) ).
fof(f12194,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl35_361 ),
inference(resolution,[],[f11847,f4943]) ).
fof(f11847,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl35_361 ),
inference(avatar_component_clause,[],[f11846]) ).
fof(f12058,plain,
( spl35_348
| ~ spl35_274 ),
inference(avatar_split_clause,[],[f12057,f8782,f11341]) ).
fof(f11341,plain,
( spl35_348
<=> ! [X4] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_348])]) ).
fof(f8782,plain,
( spl35_274
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_274])]) ).
fof(f12057,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ spl35_274 ),
inference(forward_demodulation,[],[f12039,f6110]) ).
fof(f12039,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0))
| ~ spl35_274 ),
inference(resolution,[],[f8784,f4209]) ).
fof(f4209,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f3144]) ).
fof(f3144,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ) ),
inference(rectify,[],[f3143]) ).
fof(f3143,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
inference(flattening,[],[f3142]) ).
fof(f3142,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
inference(nnf_transformation,[],[f1531]) ).
fof(f1531,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(rectify,[],[f472]) ).
fof(f472,axiom,
! [X50,X6] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X50)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) )
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(f8784,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_274 ),
inference(avatar_component_clause,[],[f8782]) ).
fof(f12056,plain,
( spl35_348
| ~ spl35_274 ),
inference(avatar_split_clause,[],[f12055,f8782,f11341]) ).
fof(f12055,plain,
( ! [X2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ spl35_274 ),
inference(forward_demodulation,[],[f12044,f6110]) ).
fof(f12044,plain,
( ! [X2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))
| ~ spl35_274 ),
inference(resolution,[],[f8784,f4396]) ).
fof(f4396,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(cnf_transformation,[],[f2743]) ).
fof(f2743,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2) ),
inference(ennf_transformation,[],[f2009]) ).
fof(f2009,plain,
! [X1,X0,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(rectify,[],[f404]) ).
fof(f404,axiom,
! [X44,X0,X43] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X44,X43)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X44,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(f12052,plain,
( spl35_348
| ~ spl35_274 ),
inference(avatar_split_clause,[],[f12051,f8782,f11341]) ).
fof(f12051,plain,
( ! [X3] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
| ~ spl35_274 ),
inference(forward_demodulation,[],[f12045,f5392]) ).
fof(f5392,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f372]) ).
fof(f372,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f12045,plain,
( ! [X3] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_274 ),
inference(resolution,[],[f8784,f4983]) ).
fof(f4983,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(cnf_transformation,[],[f2978]) ).
fof(f2978,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(ennf_transformation,[],[f1964]) ).
fof(f1964,plain,
! [X1,X2,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ),
inference(rectify,[],[f403]) ).
fof(f403,axiom,
! [X0,X44,X43] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X44,X43)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X44,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(f12049,plain,
~ spl35_274,
inference(avatar_contradiction_clause,[],[f12040]) ).
fof(f12040,plain,
( $false
| ~ spl35_274 ),
inference(resolution,[],[f8784,f5382]) ).
fof(f5382,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1989]) ).
fof(f1989,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f365]) ).
fof(f365,axiom,
! [X37] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(f12048,plain,
~ spl35_274,
inference(avatar_contradiction_clause,[],[f12041]) ).
fof(f12041,plain,
( $false
| ~ spl35_274 ),
inference(resolution,[],[f8784,f4608]) ).
fof(f4608,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1903]) ).
fof(f1903,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f337]) ).
fof(f337,axiom,
! [X37] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(f12012,plain,
( ~ spl35_367
| spl35_208
| ~ spl35_168 ),
inference(avatar_split_clause,[],[f12007,f7379,f7982,f12009]) ).
fof(f12009,plain,
( spl35_367
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_367])]) ).
fof(f7379,plain,
( spl35_168
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_168])]) ).
fof(f12007,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_168 ),
inference(resolution,[],[f7381,f4624]) ).
fof(f7381,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_168 ),
inference(avatar_component_clause,[],[f7379]) ).
fof(f11984,plain,
( ~ spl35_365
| spl35_366
| ~ spl35_364 ),
inference(avatar_split_clause,[],[f11975,f11874,f11981,f11977]) ).
fof(f11977,plain,
( spl35_365
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_365])]) ).
fof(f11981,plain,
( spl35_366
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d____ ),
introduced(avatar_definition,[new_symbols(naming,[spl35_366])]) ).
fof(f11874,plain,
( spl35_364
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_364])]) ).
fof(f11975,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_d____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_d____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_364 ),
inference(resolution,[],[f11876,f4624]) ).
fof(f11876,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____)
| ~ spl35_364 ),
inference(avatar_component_clause,[],[f11874]) ).
fof(f11877,plain,
( spl35_364
| ~ spl35_145 ),
inference(avatar_split_clause,[],[f11872,f7207,f11874]) ).
fof(f11872,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____)
| ~ spl35_145 ),
inference(resolution,[],[f7209,f4806]) ).
fof(f11871,plain,
( spl35_362
| ~ spl35_363
| ~ spl35_135 ),
inference(avatar_split_clause,[],[f11862,f7125,f11868,f11864]) ).
fof(f11864,plain,
( spl35_362
<=> v_r = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_362])]) ).
fof(f11868,plain,
( spl35_363
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_363])]) ).
fof(f7125,plain,
( spl35_135
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_135])]) ).
fof(f11862,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| v_r = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ spl35_135 ),
inference(resolution,[],[f7127,f4624]) ).
fof(f7127,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
| ~ spl35_135 ),
inference(avatar_component_clause,[],[f7125]) ).
fof(f11849,plain,
( spl35_361
| ~ spl35_49
| ~ spl35_230
| ~ spl35_302 ),
inference(avatar_split_clause,[],[f11844,f10325,f8146,f6566,f11846]) ).
fof(f10325,plain,
( spl35_302
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_302])]) ).
fof(f11844,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_49
| ~ spl35_230
| ~ spl35_302 ),
inference(forward_demodulation,[],[f11843,f8148]) ).
fof(f11843,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_49
| ~ spl35_302 ),
inference(forward_demodulation,[],[f11837,f6568]) ).
fof(f11837,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls))
| ~ spl35_302 ),
inference(resolution,[],[f10327,f4575]) ).
fof(f10327,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)
| ~ spl35_302 ),
inference(avatar_component_clause,[],[f10325]) ).
fof(f11842,plain,
( spl35_360
| ~ spl35_302 ),
inference(avatar_split_clause,[],[f11835,f10325,f11839]) ).
fof(f11839,plain,
( spl35_360
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_360])]) ).
fof(f11835,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_302 ),
inference(resolution,[],[f10327,f5627]) ).
fof(f11793,plain,
( spl35_359
| ~ spl35_48
| spl35_296 ),
inference(avatar_split_clause,[],[f11788,f10225,f6556,f11790]) ).
fof(f11790,plain,
( spl35_359
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_359])]) ).
fof(f11788,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_48
| spl35_296 ),
inference(resolution,[],[f10227,f8329]) ).
fof(f8329,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = X0 )
| ~ spl35_48 ),
inference(backward_demodulation,[],[f4570,f6558]) ).
fof(f4570,plain,
! [X0] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0) = X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f2954]) ).
fof(f11705,plain,
( spl35_357
| ~ spl35_358
| ~ spl35_267 ),
inference(avatar_split_clause,[],[f11696,f8620,f11702,f11698]) ).
fof(f11698,plain,
( spl35_357
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_357])]) ).
fof(f11702,plain,
( spl35_358
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_358])]) ).
fof(f8620,plain,
( spl35_267
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_267])]) ).
fof(f11696,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = sK18
| ~ spl35_267 ),
inference(resolution,[],[f8622,f4624]) ).
fof(f8622,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18)
| ~ spl35_267 ),
inference(avatar_component_clause,[],[f8620]) ).
fof(f11676,plain,
( spl35_355
| ~ spl35_356
| ~ spl35_266 ),
inference(avatar_split_clause,[],[f11667,f8615,f11673,f11669]) ).
fof(f11669,plain,
( spl35_355
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = sK14 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_355])]) ).
fof(f11673,plain,
( spl35_356
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK14,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_356])]) ).
fof(f8615,plain,
( spl35_266
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_266])]) ).
fof(f11667,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK14,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = sK14
| ~ spl35_266 ),
inference(resolution,[],[f8617,f4624]) ).
fof(f8617,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14)
| ~ spl35_266 ),
inference(avatar_component_clause,[],[f8615]) ).
fof(f11631,plain,
( spl35_354
| ~ spl35_265 ),
inference(avatar_split_clause,[],[f11620,f8598,f11628]) ).
fof(f11628,plain,
( spl35_354
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_354])]) ).
fof(f11620,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_265 ),
inference(resolution,[],[f8600,f7329]) ).
fof(f7329,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f5866,f5637]) ).
fof(f5866,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) ),
inference(definition_unfolding,[],[f4536,f5442]) ).
fof(f4536,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) ),
inference(cnf_transformation,[],[f3322]) ).
fof(f3322,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X0)) ) ),
inference(nnf_transformation,[],[f1489]) ).
fof(f1489,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) ),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X27)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).
fof(f11606,plain,
( spl35_353
| ~ spl35_230
| ~ spl35_248 ),
inference(avatar_split_clause,[],[f11601,f8370,f8146,f11603]) ).
fof(f11603,plain,
( spl35_353
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_353])]) ).
fof(f11601,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl35_230
| ~ spl35_248 ),
inference(forward_demodulation,[],[f11591,f8148]) ).
fof(f11591,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_248 ),
inference(resolution,[],[f8372,f4679]) ).
fof(f4679,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(cnf_transformation,[],[f3402]) ).
fof(f3402,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(nnf_transformation,[],[f1755]) ).
fof(f1755,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0) ),
inference(rectify,[],[f547]) ).
fof(f547,axiom,
! [X24] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X24))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__0__number__of) ).
fof(f11600,plain,
( spl35_352
| ~ spl35_48
| ~ spl35_248 ),
inference(avatar_split_clause,[],[f11595,f8370,f6556,f11597]) ).
fof(f11595,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_48
| ~ spl35_248 ),
inference(forward_demodulation,[],[f11594,f8798]) ).
fof(f8798,plain,
! [X3] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X3) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X3),
inference(superposition,[],[f4335,f4702]) ).
fof(f11594,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ spl35_48
| ~ spl35_248 ),
inference(resolution,[],[f8372,f8343]) ).
fof(f8343,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Int_OPls) )
| ~ spl35_48 ),
inference(backward_demodulation,[],[f5478,f6558]) ).
fof(f5478,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3866]) ).
fof(f3866,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(nnf_transformation,[],[f1829]) ).
fof(f1829,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(rectify,[],[f260]) ).
fof(f260,axiom,
! [X26,X27] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,X26)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X27,X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(f11486,plain,
spl35_313,
inference(avatar_contradiction_clause,[],[f11481]) ).
fof(f11481,plain,
( $false
| spl35_313 ),
inference(resolution,[],[f10957,f4578]) ).
fof(f4578,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1689]) ).
fof(f1689,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X37] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(f10957,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl35_313 ),
inference(avatar_component_clause,[],[f10955]) ).
fof(f10955,plain,
( spl35_313
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_313])]) ).
fof(f11485,plain,
spl35_313,
inference(avatar_contradiction_clause,[],[f11482]) ).
fof(f11482,plain,
( $false
| spl35_313 ),
inference(resolution,[],[f10957,f6078]) ).
fof(f11476,plain,
( ~ spl35_313
| spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11475,f10376,f8267,f10689,f10955]) ).
fof(f10689,plain,
( spl35_310
<=> ! [X14,X15] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_310])]) ).
fof(f11475,plain,
( ! [X31,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11474,f4221]) ).
fof(f4221,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f409]) ).
fof(f409,axiom,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(f11474,plain,
( ! [X31,X32] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10425,f10653]) ).
fof(f10653,plain,
( ! [X56,X55] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X56)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9977,f10467]) ).
fof(f10467,plain,
( ! [X10,X11] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X11)
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10466,f5245]) ).
fof(f5245,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1855]) ).
fof(f1855,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f422]) ).
fof(f422,axiom,
! [X37] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(f10466,plain,
( ! [X10,X11] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X11) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X11))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10438,f5420]) ).
fof(f5420,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1654]) ).
fof(f1654,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f408]) ).
fof(f408,axiom,
! [X37] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
fof(f10438,plain,
( ! [X10,X11] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X11) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X10),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X11))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9932,f10378]) ).
fof(f10378,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl35_305 ),
inference(avatar_component_clause,[],[f10376]) ).
fof(f9932,plain,
( ! [X10,X11] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X11) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X10),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X11))
| ~ spl35_244 ),
inference(superposition,[],[f5544,f8581]) ).
fof(f5544,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),
inference(cnf_transformation,[],[f3907]) ).
fof(f3907,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0),
inference(rectify,[],[f1383]) ).
fof(f1383,plain,
! [X1,X2,X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(rectify,[],[f449]) ).
fof(f449,axiom,
! [X0,X37,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X37) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(f9977,plain,
! [X56,X57,X55] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X57)),X57) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X56),
inference(superposition,[],[f4809,f5609]) ).
fof(f5609,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1),
inference(cnf_transformation,[],[f3943]) ).
fof(f3943,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1),
inference(rectify,[],[f1475]) ).
fof(f1475,plain,
! [X1,X0,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(rectify,[],[f343]) ).
fof(f343,axiom,
! [X20,X0,X37] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X37),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(f4809,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) = X0,
inference(cnf_transformation,[],[f3484]) ).
fof(f3484,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) = X0,
inference(rectify,[],[f1579]) ).
fof(f1579,plain,
! [X1,X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(rectify,[],[f452]) ).
fof(f452,axiom,
! [X37,X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X37),X37) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(f10425,plain,
( ! [X31,X32] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X31,X32))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9630,f10378]) ).
fof(f9630,plain,
( ! [X31,X32] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X31,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X31,X32))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32) )
| ~ spl35_244 ),
inference(superposition,[],[f4919,f8584]) ).
fof(f8584,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl35_244 ),
inference(backward_demodulation,[],[f7734,f8269]) ).
fof(f7734,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f7733,f4335]) ).
fof(f7733,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f7732,f4335]) ).
fof(f7732,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),
inference(forward_demodulation,[],[f7714,f4335]) ).
fof(f7714,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0),
inference(backward_demodulation,[],[f7473,f4335]) ).
fof(f7473,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f7472,f5723]) ).
fof(f7472,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f7471,f5723]) ).
fof(f7471,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f7420,f5723]) ).
fof(f7420,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(backward_demodulation,[],[f7355,f5723]) ).
fof(f7355,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f7354,f5637]) ).
fof(f7354,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))))),
inference(forward_demodulation,[],[f7353,f5637]) ).
fof(f7353,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f7352,f5537]) ).
fof(f7352,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f6008,f5537]) ).
fof(f6008,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(definition_unfolding,[],[f5350,f4431,f5442]) ).
fof(f5350,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1976]) ).
fof(f1976,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(rectify,[],[f557]) ).
fof(f557,axiom,
! [X14] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X14) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
fof(f4919,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3544]) ).
fof(f3544,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f3543]) ).
fof(f3543,plain,
! [X0,X2,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ) ),
inference(nnf_transformation,[],[f1231]) ).
fof(f1231,plain,
! [X0,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f431]) ).
fof(f431,axiom,
! [X50,X27,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X50)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X6),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(f11466,plain,
( spl35_351
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10385,f10376,f8267,f11463]) ).
fof(f11463,plain,
( spl35_351
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_351])]) ).
fof(f10385,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8269,f10378]) ).
fof(f11460,plain,
( ~ spl35_313
| spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11459,f10376,f8267,f10689,f10955]) ).
fof(f11459,plain,
( ! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11458,f10653]) ).
fof(f11458,plain,
( ! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10426,f4221]) ).
fof(f10426,plain,
( ! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X33,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9631,f10378]) ).
fof(f9631,plain,
( ! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
| ~ spl35_244 ),
inference(superposition,[],[f4919,f8584]) ).
fof(f11457,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11456,f10376,f8267,f10685]) ).
fof(f10685,plain,
( spl35_309
<=> ! [X26] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_309])]) ).
fof(f11456,plain,
( ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10416,f4221]) ).
fof(f10416,plain,
( ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9616,f10378]) ).
fof(f9616,plain,
( ! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ spl35_244 ),
inference(superposition,[],[f4331,f8584]) ).
fof(f4331,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(cnf_transformation,[],[f1927]) ).
fof(f1927,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(rectify,[],[f433]) ).
fof(f433,axiom,
! [X37,X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(f11450,plain,
( spl35_315
| spl35_314
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11449,f10376,f8267,f10964,f10972]) ).
fof(f10972,plain,
( spl35_315
<=> ! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_315])]) ).
fof(f10964,plain,
( spl35_314
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_314])]) ).
fof(f11449,plain,
( ! [X24,X23] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11448,f10467]) ).
fof(f11448,plain,
( ! [X24,X23] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X23)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10422,f4221]) ).
fof(f10422,plain,
( ! [X24,X23] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X23)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9625,f10378]) ).
fof(f9625,plain,
( ! [X24,X23] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X23))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X24) )
| ~ spl35_244 ),
inference(superposition,[],[f4704,f8584]) ).
fof(f4704,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f3418]) ).
fof(f3418,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ) ),
inference(rectify,[],[f3417]) ).
fof(f3417,plain,
! [X2,X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0)) ) ),
inference(nnf_transformation,[],[f1875]) ).
fof(f1875,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) ),
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X27,X73,X72] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X73,X27),X72)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X73,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(f11447,plain,
( spl35_310
| ~ spl35_313
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11446,f10376,f8267,f10955,f10689]) ).
fof(f11446,plain,
( ! [X34,X33] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11445,f10653]) ).
fof(f11445,plain,
( ! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10403,f5420]) ).
fof(f10403,plain,
( ! [X34,X33] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X33))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9585,f10378]) ).
fof(f9585,plain,
( ! [X34,X33] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X33)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X34),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33)) )
| ~ spl35_244 ),
inference(superposition,[],[f4919,f8581]) ).
fof(f11437,plain,
( spl35_315
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11436,f10376,f8267,f10972]) ).
fof(f11436,plain,
( ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10420,f4221]) ).
fof(f10420,plain,
( ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9622,f10378]) ).
fof(f9622,plain,
( ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X20)
| ~ spl35_244 ),
inference(superposition,[],[f4540,f8584]) ).
fof(f4540,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),
inference(cnf_transformation,[],[f1843]) ).
fof(f1843,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1),
inference(rectify,[],[f406]) ).
fof(f406,axiom,
! [X43,X44] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X44),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(f11428,plain,
( spl35_315
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11427,f10376,f8267,f10972]) ).
fof(f11427,plain,
( ! [X39] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10405,f5420]) ).
fof(f10405,plain,
( ! [X39] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39),X39)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9587,f10378]) ).
fof(f9587,plain,
( ! [X39] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X39),X39)
| ~ spl35_244 ),
inference(superposition,[],[f5249,f8581]) ).
fof(f5249,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
inference(cnf_transformation,[],[f1504]) ).
fof(f1504,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f407]) ).
fof(f407,axiom,
! [X43,X44] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X43),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(f11422,plain,
( spl35_314
| spl35_315
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11421,f10376,f8267,f10972,f10964]) ).
fof(f11421,plain,
( ! [X24,X23] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11420,f10467]) ).
fof(f11420,plain,
( ! [X24,X23] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X23))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10399,f5420]) ).
fof(f10399,plain,
( ! [X24,X23] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23),X24)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X23)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9579,f10378]) ).
fof(f9579,plain,
( ! [X24,X23] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X23),X24)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X23)) )
| ~ spl35_244 ),
inference(superposition,[],[f4704,f8581]) ).
fof(f11413,plain,
( spl35_312
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11412,f10376,f8267,f10716]) ).
fof(f10716,plain,
( spl35_312
<=> ! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_312])]) ).
fof(f11412,plain,
( ! [X21] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21
| ~ spl35_244
| ~ spl35_305 ),
inference(subsumption_resolution,[],[f10421,f11272]) ).
fof(f11272,plain,
( ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10635,f10653]) ).
fof(f10635,plain,
( ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5465,f10467]) ).
fof(f5465,plain,
! [X0,X1] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f3859]) ).
fof(f3859,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f2174]) ).
fof(f2174,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(ennf_transformation,[],[f1206]) ).
fof(f1206,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ) ),
inference(rectify,[],[f542]) ).
fof(f542,axiom,
! [X0,X37] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X37) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X37) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(f10421,plain,
( ! [X21] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9623,f10378]) ).
fof(f9623,plain,
( ! [X21] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
| ~ spl35_244 ),
inference(superposition,[],[f4542,f8584]) ).
fof(f4542,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f3327]) ).
fof(f3327,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(rectify,[],[f3326]) ).
fof(f3326,plain,
! [X1,X0] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(flattening,[],[f3325]) ).
fof(f3325,plain,
! [X1,X0] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(nnf_transformation,[],[f2024]) ).
fof(f2024,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f371]) ).
fof(f371,axiom,
! [X6,X50] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X50)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X50 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(f11407,plain,
( ~ spl35_313
| spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11406,f10376,f8267,f10689,f10955]) ).
fof(f11406,plain,
( ! [X31,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11405,f5420]) ).
fof(f11405,plain,
( ! [X31,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10402,f10653]) ).
fof(f10402,plain,
( ! [X31,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X31,X32)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9584,f10378]) ).
fof(f9584,plain,
( ! [X31,X32] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,X32)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X31),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X31,X32)) )
| ~ spl35_244 ),
inference(superposition,[],[f4919,f8581]) ).
fof(f11403,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11402,f10376,f8267,f10685]) ).
fof(f11402,plain,
( ! [X15] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10396,f5420]) ).
fof(f10396,plain,
( ! [X15] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9573,f10378]) ).
fof(f9573,plain,
( ! [X15] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X15))
| ~ spl35_244 ),
inference(superposition,[],[f4462,f8581]) ).
fof(f4462,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(cnf_transformation,[],[f1249]) ).
fof(f1249,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(rectify,[],[f434]) ).
fof(f434,axiom,
! [X0,X37] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(f11401,plain,
( spl35_315
| spl35_314
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11400,f10376,f8267,f10964,f10972]) ).
fof(f11400,plain,
( ! [X2,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10588,f10653]) ).
fof(f10588,plain,
( ! [X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9399,f10467]) ).
fof(f9399,plain,
! [X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X3)) ),
inference(superposition,[],[f4704,f5023]) ).
fof(f11395,plain,
( spl35_274
| spl35_319
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10536,f10376,f8267,f11008,f8782]) ).
fof(f11008,plain,
( spl35_319
<=> ! [X6,X7] :
( X6 = X7
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_319])]) ).
fof(f10536,plain,
( ! [X3,X4] :
( X3 = X4
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9031,f10467]) ).
fof(f9031,plain,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| X3 = X4
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)) ),
inference(resolution,[],[f5710,f5211]) ).
fof(f5211,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f3720]) ).
fof(f3720,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| X0 = X1 )
& ( X0 != X1
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ) ),
inference(flattening,[],[f3719]) ).
fof(f3719,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| X0 = X1 )
& ( X0 != X1
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ) ),
inference(nnf_transformation,[],[f2000]) ).
fof(f2000,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
<=> X0 != X1 ),
inference(rectify,[],[f335]) ).
fof(f335,axiom,
! [X6,X50] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X50)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X50,X6) )
<=> X6 != X50 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(f5710,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f3998]) ).
fof(f3998,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
inference(nnf_transformation,[],[f1581]) ).
fof(f1581,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f491]) ).
fof(f491,axiom,
! [X6,X50] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X50)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(f11394,plain,
( spl35_349
| spl35_350
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11393,f10376,f8267,f11368,f11365]) ).
fof(f11365,plain,
( spl35_349
<=> ! [X1] : hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_349])]) ).
fof(f11368,plain,
( spl35_350
<=> ! [X2,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_350])]) ).
fof(f11393,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10474,f10653]) ).
fof(f10474,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK1(X0,X1,X2)) = X0
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4122,f10467]) ).
fof(f4122,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK1(X0,X1,X2)) = X0
| hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3098]) ).
fof(f3098,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ( ~ hBOOL(hAPP(X2,sK1(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK1(X0,X1,X2)) = X0 ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X4) != X0 ) )
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f3096,f3097]) ).
fof(f3097,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0 )
=> ( ~ hBOOL(hAPP(X2,sK1(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK1(X0,X1,X2)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f3096,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0 ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X4] :
( hBOOL(hAPP(X2,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X4) != X0 ) )
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) ) ),
inference(rectify,[],[f3095]) ).
fof(f3095,plain,
! [X2,X0,X1] :
( ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0)))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X2 ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X3] :
( hBOOL(hAPP(X1,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X2 ) )
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))) ) ),
inference(flattening,[],[f3094]) ).
fof(f3094,plain,
! [X2,X0,X1] :
( ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0)))
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X2 ) )
& ( ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X3] :
( hBOOL(hAPP(X1,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X2 ) )
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))) ) ),
inference(nnf_transformation,[],[f2814]) ).
fof(f2814,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0)))
<=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X3] :
( hBOOL(hAPP(X1,X3))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) != X2 ) ) ),
inference(ennf_transformation,[],[f1415]) ).
fof(f1415,plain,
! [X0,X2,X1] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
=> hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X3) = X2
=> hBOOL(hAPP(X1,X3)) ) )
<=> hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))) ),
inference(rectify,[],[f536]) ).
fof(f536,axiom,
! [X7,X67,X9] :
( ( ! [X54] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X54) = X9
=> hBOOL(hAPP(X67,X54)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X7)
=> hBOOL(hAPP(X67,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
<=> hBOOL(hAPP(X67,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(f11391,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11390,f10376,f8267,f10685]) ).
fof(f11390,plain,
( ! [X29] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10557,f10653]) ).
fof(f10557,plain,
( ! [X29,X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9318,f10467]) ).
fof(f9318,plain,
! [X29,X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X30,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X30),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X30))))),
inference(forward_demodulation,[],[f9310,f5023]) ).
fof(f9310,plain,
! [X29,X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X30),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X30),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X29,X30))),X30)),
inference(resolution,[],[f4399,f5564]) ).
fof(f5564,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X0))),
inference(cnf_transformation,[],[f444]) ).
fof(f444,axiom,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
fof(f4399,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f3245]) ).
fof(f3245,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ) ),
inference(rectify,[],[f3244]) ).
fof(f3244,plain,
! [X0,X2,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) ) ),
inference(nnf_transformation,[],[f1373]) ).
fof(f1373,plain,
! [X0,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0) ),
inference(rectify,[],[f515]) ).
fof(f515,axiom,
! [X73,X72,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X72,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X73,X27))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X27),X73) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(f11389,plain,
( spl35_309
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11388,f10376,f8267,f10685,f10685]) ).
fof(f11388,plain,
( ! [X10,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10555,f10653]) ).
fof(f10555,plain,
( ! [X10,X11,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X12)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9304,f10467]) ).
fof(f9304,plain,
! [X10,X11,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X12))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X10,X12)) ),
inference(resolution,[],[f4399,f4994]) ).
fof(f4994,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3589]) ).
fof(f3589,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f1193]) ).
fof(f1193,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f349]) ).
fof(f349,axiom,
! [X0,X37] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X37)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(f11385,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11384,f10376,f8267,f10685]) ).
fof(f11384,plain,
( ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10667,f10653]) ).
fof(f10667,plain,
( ! [X6,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6))
| ~ spl35_244
| ~ spl35_305 ),
inference(trivial_inequality_removal,[],[f10622]) ).
fof(f10622,plain,
( ! [X6,X4,X5] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9321,f10467]) ).
fof(f9321,plain,
! [X6,X4,X5] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6)) ),
inference(forward_demodulation,[],[f9302,f5077]) ).
fof(f5077,plain,
! [X2,X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2),
inference(cnf_transformation,[],[f3644]) ).
fof(f3644,plain,
! [X0,X1,X2] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X2),
inference(rectify,[],[f1895]) ).
fof(f1895,plain,
! [X2,X1,X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X0),
inference(rectify,[],[f450]) ).
fof(f450,axiom,
! [X20,X43,X44] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X44,X43),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X44,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(f9302,plain,
! [X6,X4,X5] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X6),X5)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6)) ),
inference(resolution,[],[f4399,f4943]) ).
fof(f11383,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11382,f10376,f8267,f10685]) ).
fof(f11382,plain,
( ! [X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10608,f10653]) ).
fof(f10608,plain,
( ! [X14,X15,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9994,f10467]) ).
fof(f9994,plain,
! [X14,X15,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X13,X14),X15))),
inference(backward_demodulation,[],[f9322,f9985]) ).
fof(f9985,plain,
! [X86,X84,X85] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X86,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X84,X85)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X84,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X85,X86)),
inference(superposition,[],[f5023,f5609]) ).
fof(f9322,plain,
! [X14,X15,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X13,X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14))),
inference(forward_demodulation,[],[f9305,f5609]) ).
fof(f9305,plain,
! [X14,X15,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X13,X14),X15),X14)),
inference(resolution,[],[f4399,f4331]) ).
fof(f11372,plain,
( spl35_274
| spl35_312
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11371,f10376,f8267,f10716,f8782]) ).
fof(f11371,plain,
( ! [X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10541,f10653]) ).
fof(f10541,plain,
( ! [X2,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9125,f10467]) ).
fof(f9125,plain,
! [X2,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(resolution,[],[f5274,f5710]) ).
fof(f5274,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
inference(cnf_transformation,[],[f3753]) ).
fof(f3753,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f2556]) ).
fof(f2556,plain,
! [X1,X0] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f1263]) ).
fof(f1263,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) = X0 ),
inference(rectify,[],[f502]) ).
fof(f502,axiom,
! [X0,X37] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X37)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X37)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(f11370,plain,
( spl35_349
| spl35_350
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11363,f10376,f8267,f11368,f11365]) ).
fof(f11363,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10504,f10653]) ).
fof(f10504,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK23(X0,X1,X2)) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5071,f10467]) ).
fof(f5071,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK23(X0,X1,X2)) = X0
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))) ),
inference(cnf_transformation,[],[f3638]) ).
fof(f3638,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)))
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK23(X0,X1,X2)) = X0
& ~ hBOOL(hAPP(X1,sK23(X0,X1,X2))) )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
& ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
& ( ( ! [X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X0
| hBOOL(hAPP(X1,X4)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f3636,f3637]) ).
fof(f3637,plain,
! [X0,X1,X2] :
( ? [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X0
& ~ hBOOL(hAPP(X1,X3)) )
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK23(X0,X1,X2)) = X0
& ~ hBOOL(hAPP(X1,sK23(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f3636,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)))
| ? [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X0
& ~ hBOOL(hAPP(X1,X3)) )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
& ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
& ( ( ! [X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X0
| hBOOL(hAPP(X1,X4)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))) ) ),
inference(rectify,[],[f3635]) ).
fof(f3635,plain,
! [X0,X2,X1] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)))
| ? [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
& ~ hBOOL(hAPP(X2,X3)) )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
& ( ( ! [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != X0
| hBOOL(hAPP(X2,X3)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) ) ),
inference(flattening,[],[f3634]) ).
fof(f3634,plain,
! [X0,X2,X1] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)))
| ? [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
& ~ hBOOL(hAPP(X2,X3)) )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
& ( ( ! [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != X0
| hBOOL(hAPP(X2,X3)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) )
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) ) ),
inference(nnf_transformation,[],[f2259]) ).
fof(f2259,plain,
! [X0,X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)))
<=> ( ! [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != X0
| hBOOL(hAPP(X2,X3)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
inference(ennf_transformation,[],[f2088]) ).
fof(f2088,plain,
! [X2,X1,X0] :
( ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
& ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X3] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
& ~ hBOOL(hAPP(X2,X3)) ) )
<=> hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))) ),
inference(rectify,[],[f537]) ).
fof(f537,axiom,
! [X9,X7,X67] :
( hBOOL(hAPP(X67,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X7)))
<=> ~ ( ? [X54] :
( ~ hBOOL(hAPP(X67,X54))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X54) = X9 )
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X7)
& ~ hBOOL(hAPP(X67,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(f11362,plain,
( spl35_321
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11361,f10376,f8267,f10685,f11033]) ).
fof(f11033,plain,
( spl35_321
<=> ! [X6] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_321])]) ).
fof(f11361,plain,
( ! [X24,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10558,f10653]) ).
fof(f10558,plain,
( ! [X26,X24,X25,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9319,f10467]) ).
fof(f9319,plain,
! [X26,X24,X25,X23] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X26),X24)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X26))) ),
inference(forward_demodulation,[],[f9308,f5609]) ).
fof(f9308,plain,
! [X26,X24,X25,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X25),X26))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X26),X24) ),
inference(resolution,[],[f4399,f4220]) ).
fof(f4220,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f3150]) ).
fof(f3150,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rectify,[],[f2605]) ).
fof(f2605,plain,
! [X0,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(ennf_transformation,[],[f1399]) ).
fof(f1399,plain,
! [X1,X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(rectify,[],[f430]) ).
fof(f430,axiom,
! [X0,X44,X43] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X43)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(f11357,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11356,f10376,f8267,f10685]) ).
fof(f11356,plain,
( ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11355,f5392]) ).
fof(f11355,plain,
( ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10589,f10653]) ).
fof(f10589,plain,
( ! [X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X5))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9404,f10467]) ).
fof(f9404,plain,
! [X6,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X6)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X5)),
inference(resolution,[],[f4918,f5291]) ).
fof(f5291,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0),
inference(cnf_transformation,[],[f3762]) ).
fof(f3762,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),X0),
inference(rectify,[],[f1453]) ).
fof(f1453,plain,
! [X1,X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f459]) ).
fof(f459,axiom,
! [X37,X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X37),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(f4918,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(cnf_transformation,[],[f3544]) ).
fof(f11354,plain,
( spl35_309
| spl35_308
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10642,f10376,f8267,f10682,f10685]) ).
fof(f10682,plain,
( spl35_308
<=> ! [X29,X27] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X27) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_308])]) ).
fof(f10642,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4699,f10467]) ).
fof(f4699,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)) ),
inference(cnf_transformation,[],[f2105]) ).
fof(f2105,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2) ),
inference(ennf_transformation,[],[f1786]) ).
fof(f1786,plain,
! [X2,X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)) ),
inference(rectify,[],[f514]) ).
fof(f514,axiom,
! [X20,X0,X37] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X37)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X0),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(f11348,plain,
( spl35_274
| spl35_324
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10537,f10376,f8267,f11064,f8782]) ).
fof(f11064,plain,
( spl35_324
<=> ! [X13,X12] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X13)
| X12 = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_324])]) ).
fof(f10537,plain,
( ! [X6,X5] :
( X5 = X6
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9032,f10467]) ).
fof(f9032,plain,
! [X6,X5] :
( X5 = X6
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X6)) ),
inference(resolution,[],[f5710,f5104]) ).
fof(f5104,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3659]) ).
fof(f3659,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f2307]) ).
fof(f2307,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(flattening,[],[f2306]) ).
fof(f2306,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f2016]) ).
fof(f2016,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> ( X0 != X1
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ) ),
inference(rectify,[],[f417]) ).
fof(f417,axiom,
! [X0,X37] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X37)
=> ( X0 != X37
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X37) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(f11347,plain,
( spl35_324
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10669,f10376,f8267,f11064]) ).
fof(f10669,plain,
( ! [X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
| X4 = X5 )
| ~ spl35_244
| ~ spl35_305 ),
inference(trivial_inequality_removal,[],[f10526]) ).
fof(f10526,plain,
( ! [X4,X5] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
| X4 = X5 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8825,f10467]) ).
fof(f8825,plain,
! [X4,X5] :
( X4 = X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X4) ),
inference(resolution,[],[f5011,f4943]) ).
fof(f11343,plain,
( spl35_348
| spl35_312
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11339,f10376,f8267,f10716,f11341]) ).
fof(f11339,plain,
( ! [X2,X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11338,f10653]) ).
fof(f11338,plain,
( ! [X2,X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10582,f10653]) ).
fof(f10582,plain,
( ! [X2,X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X4)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X2 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9382,f10467]) ).
fof(f9382,plain,
! [X2,X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X4)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X3))) = X2 ),
inference(resolution,[],[f4703,f5274]) ).
fof(f4703,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) ),
inference(cnf_transformation,[],[f3418]) ).
fof(f11336,plain,
( spl35_309
| spl35_321
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11335,f10376,f8267,f11033,f10685]) ).
fof(f11335,plain,
( ! [X21,X19] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10559,f10653]) ).
fof(f10559,plain,
( ! [X21,X19,X22,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X22)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9320,f10467]) ).
fof(f9320,plain,
! [X21,X19,X22,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X22)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X22),X21) ),
inference(forward_demodulation,[],[f9307,f5609]) ).
fof(f9307,plain,
! [X21,X19,X22,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X21),X22))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X22),X21) ),
inference(resolution,[],[f4399,f4438]) ).
fof(f4438,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(cnf_transformation,[],[f3270]) ).
fof(f3270,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f2152]) ).
fof(f2152,plain,
! [X0,X2,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(ennf_transformation,[],[f1398]) ).
fof(f1398,plain,
! [X2,X1,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(rectify,[],[f429]) ).
fof(f429,axiom,
! [X43,X44,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,X43)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(f11332,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10639,f10376,f8267,f10685]) ).
fof(f10639,plain,
( ! [X33] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9373,f10467]) ).
fof(f9373,plain,
! [X34,X33] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X34,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X34,X34)),X33),X34)),
inference(resolution,[],[f4699,f5564]) ).
fof(f11331,plain,
( spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10670,f10376,f8267,f10689]) ).
fof(f10670,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ spl35_244
| ~ spl35_305 ),
inference(trivial_inequality_removal,[],[f10496]) ).
fof(f10496,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4943,f10467]) ).
fof(f11328,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11327,f10376,f8267,f10685]) ).
fof(f11327,plain,
( ! [X27] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10561,f10653]) ).
fof(f10561,plain,
( ! [X28,X27] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9325,f10467]) ).
fof(f9325,plain,
! [X28,X27] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X28),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X28)))),
inference(forward_demodulation,[],[f9309,f5023]) ).
fof(f9309,plain,
! [X28,X27] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X28),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X27,X28)),X28)),
inference(resolution,[],[f4399,f4773]) ).
fof(f4773,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X0)),
inference(cnf_transformation,[],[f443]) ).
fof(f443,axiom,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
fof(f11326,plain,
( spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11325,f10376,f8267,f10689]) ).
fof(f11325,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10556,f5392]) ).
fof(f10556,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9317,f10467]) ).
fof(f9317,plain,
! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))),
inference(forward_demodulation,[],[f9301,f5023]) ).
fof(f9301,plain,
! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),X3)),
inference(resolution,[],[f4399,f6078]) ).
fof(f11324,plain,
( spl35_321
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11323,f10376,f8267,f10685,f11033]) ).
fof(f11323,plain,
( ! [X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10482,f10653]) ).
fof(f10482,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4399,f10467]) ).
fof(f11320,plain,
( spl35_274
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11319,f10376,f8267,f8782]) ).
fof(f11319,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10522,f10653]) ).
fof(f10522,plain,
( ! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5983,f10467]) ).
fof(f5983,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),
inference(definition_unfolding,[],[f5206,f4497]) ).
fof(f5206,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
inference(cnf_transformation,[],[f1885]) ).
fof(f1885,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)),
inference(rectify,[],[f495]) ).
fof(f495,axiom,
! [X37,X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X37),c_Nat_OSuc(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(f11317,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11316,f10376,f8267,f10685]) ).
fof(f11316,plain,
( ! [X16] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10560,f10653]) ).
fof(f10560,plain,
( ! [X18,X16,X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9324,f10467]) ).
fof(f9324,plain,
! [X18,X16,X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X18)))),
inference(forward_demodulation,[],[f9323,f5023]) ).
fof(f9323,plain,
! [X18,X16,X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X18),X18))),
inference(forward_demodulation,[],[f9306,f5609]) ).
fof(f9306,plain,
! [X18,X16,X17] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X16,X18)),X18)),
inference(resolution,[],[f4399,f4462]) ).
fof(f11312,plain,
( spl35_308
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10655,f10376,f8267,f10685,f10682]) ).
fof(f10655,plain,
( ! [X24,X22,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9374,f10467]) ).
fof(f9374,plain,
! [X24,X22,X25,X23] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X22)),X25)) ),
inference(forward_demodulation,[],[f9369,f5609]) ).
fof(f9369,plain,
! [X24,X22,X25,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X24),X22),X25))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24) ),
inference(resolution,[],[f4699,f4438]) ).
fof(f11311,plain,
( spl35_274
| spl35_347
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11307,f10376,f8267,f11309,f8782]) ).
fof(f11309,plain,
( spl35_347
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_347])]) ).
fof(f11307,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10506,f10467]) ).
fof(f10506,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5223,f10467]) ).
fof(f5223,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f2349]) ).
fof(f2349,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(flattening,[],[f2348]) ).
fof(f2348,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(ennf_transformation,[],[f1477]) ).
fof(f1477,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ) ),
inference(rectify,[],[f440]) ).
fof(f440,axiom,
! [X21,X0,X37] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X37)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X37),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(f11306,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11305,f10376,f8267,f10685]) ).
fof(f11305,plain,
( ! [X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10672,f10467]) ).
fof(f10672,plain,
( ! [X8,X9,X7] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X7),X9))
| ~ spl35_244
| ~ spl35_305 ),
inference(trivial_inequality_removal,[],[f10581]) ).
fof(f10581,plain,
( ! [X8,X9,X7] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X7),X9)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9364,f10467]) ).
fof(f9364,plain,
! [X8,X9,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X7),X9))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X8) ),
inference(resolution,[],[f4699,f4943]) ).
fof(f11299,plain,
( spl35_274
| spl35_346
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11295,f10376,f8267,f11297,f8782]) ).
fof(f11297,plain,
( spl35_346
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_346])]) ).
fof(f11295,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10478,f10467]) ).
fof(f10478,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4380,f10467]) ).
fof(f4380,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3234]) ).
fof(f3234,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X2) ),
inference(rectify,[],[f3233]) ).
fof(f3233,plain,
! [X2,X1,X0] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(nnf_transformation,[],[f2927]) ).
fof(f2927,plain,
! [X2,X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(flattening,[],[f2926]) ).
fof(f2926,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1635]) ).
fof(f1635,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2)) ) ) ),
inference(rectify,[],[f505]) ).
fof(f505,axiom,
! [X50,X6,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X50)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X27),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X50,X27))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X50) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(f11291,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10640,f10376,f8267,f10685]) ).
fof(f10640,plain,
( ! [X31] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9372,f10467]) ).
fof(f9372,plain,
! [X31,X32] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X32,X32),X31),X32)),
inference(resolution,[],[f4699,f4773]) ).
fof(f11290,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11289,f10376,f8267,f10685]) ).
fof(f11289,plain,
( ! [X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11288,f10653]) ).
fof(f11288,plain,
( ! [X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X4))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10580,f5025]) ).
fof(f5025,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f421]) ).
fof(f421,axiom,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(f10580,plain,
( ! [X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9363,f10467]) ).
fof(f9363,plain,
! [X6,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X6))),
inference(resolution,[],[f4699,f5291]) ).
fof(f11287,plain,
( spl35_274
| spl35_345
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11283,f10376,f8267,f11285,f8782]) ).
fof(f11285,plain,
( spl35_345
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_345])]) ).
fof(f11283,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10477,f10467]) ).
fof(f10477,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4258,f10467]) ).
fof(f4258,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3167]) ).
fof(f3167,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(rectify,[],[f2290]) ).
fof(f2290,plain,
! [X2,X1,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ),
inference(flattening,[],[f2289]) ).
fof(f2289,plain,
! [X0,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(ennf_transformation,[],[f1614]) ).
fof(f1614,plain,
! [X0,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X1)) ) ),
inference(rectify,[],[f504]) ).
fof(f504,axiom,
! [X2,X1,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(f11282,plain,
( spl35_309
| ~ spl35_31
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10656,f10376,f8267,f6439,f10685]) ).
fof(f6439,plain,
( spl35_31
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_31])]) ).
fof(f10656,plain,
( ! [X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_31
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9371,f10467]) ).
fof(f9371,plain,
( ! [X30] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X30,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),X30),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_31 ),
inference(resolution,[],[f4699,f6441]) ).
fof(f6441,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_31 ),
inference(avatar_component_clause,[],[f6439]) ).
fof(f11277,plain,
( spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10674,f10376,f8267,f10689]) ).
fof(f10674,plain,
( ! [X6,X4] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X6)
| ~ spl35_244
| ~ spl35_305 ),
inference(trivial_inequality_removal,[],[f10644]) ).
fof(f10644,plain,
( ! [X6,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X6)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8817,f10467]) ).
fof(f8817,plain,
! [X6,X4,X5] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X5),X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X6) ),
inference(resolution,[],[f4943,f4078]) ).
fof(f4078,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f3073]) ).
fof(f3073,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1) ),
inference(rectify,[],[f2872]) ).
fof(f2872,plain,
! [X2,X1,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1) ),
inference(ennf_transformation,[],[f1673]) ).
fof(f1673,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),X1)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ) ),
inference(rectify,[],[f424]) ).
fof(f424,axiom,
! [X0,X37,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X20),X37)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X37)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X37) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(f11276,plain,
( spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10675,f10376,f8267,f10689]) ).
fof(f10675,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ spl35_244
| ~ spl35_305 ),
inference(trivial_inequality_removal,[],[f10643]) ).
fof(f10643,plain,
( ! [X2,X3] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8816,f10467]) ).
fof(f8816,plain,
! [X2,X3,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(resolution,[],[f4943,f4079]) ).
fof(f4079,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3073]) ).
fof(f11267,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10733,f10376,f8267,f10685]) ).
fof(f10733,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4331,f10653]) ).
fof(f11266,plain,
( spl35_312
| spl35_274
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10779,f10376,f8267,f8782,f10716]) ).
fof(f10779,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8821,f10653]) ).
fof(f8821,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(resolution,[],[f4983,f4623]) ).
fof(f4623,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f2305]) ).
fof(f2305,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(ennf_transformation,[],[f1321]) ).
fof(f1321,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(rectify,[],[f369]) ).
fof(f369,axiom,
! [X37] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X37
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(f11265,plain,
( spl35_311
| spl35_274
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11264,f10376,f8267,f8782,f10706]) ).
fof(f10706,plain,
( spl35_311
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_311])]) ).
fof(f11264,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10926,f10653]) ).
fof(f10926,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5853,f10653]) ).
fof(f5853,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(definition_unfolding,[],[f4510,f4497,f4497]) ).
fof(f4510,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X0),c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f2108]) ).
fof(f2108,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X0),c_Nat_OSuc(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(ennf_transformation,[],[f1527]) ).
fof(f1527,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X0),c_Nat_OSuc(X1)) ),
inference(rectify,[],[f327]) ).
fof(f327,axiom,
! [X0,X37] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X37)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X0),c_Nat_OSuc(X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(f11262,plain,
( spl35_344
| ~ spl35_35
| ~ spl35_244
| ~ spl35_245
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11257,f10376,f8284,f8267,f6464,f11259]) ).
fof(f11257,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_35
| ~ spl35_244
| ~ spl35_245
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10895,f10975]) ).
fof(f10975,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_35
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10941,f6466]) ).
fof(f10941,plain,
( ! [X0] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5992,f10653]) ).
fof(f10895,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_244
| ~ spl35_245
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8286,f10653]) ).
fof(f11254,plain,
( spl35_274
| spl35_311
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11253,f10376,f8267,f10706,f8782]) ).
fof(f11253,plain,
( ! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10739,f10653]) ).
fof(f10739,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4665,f10653]) ).
fof(f4665,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(cnf_transformation,[],[f3391]) ).
fof(f3391,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(rectify,[],[f2804]) ).
fof(f2804,plain,
! [X1,X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(ennf_transformation,[],[f1962]) ).
fof(f1962,plain,
! [X1,X0,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(rectify,[],[f402]) ).
fof(f402,axiom,
! [X44,X43,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X44,X43)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(f11251,plain,
( spl35_312
| spl35_314
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10819,f10376,f8267,f10964,f10716]) ).
fof(f10819,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9360,f10653]) ).
fof(f9360,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(forward_demodulation,[],[f9355,f6110]) ).
fof(f9355,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(resolution,[],[f4665,f4623]) ).
fof(f11250,plain,
( spl35_341
| ~ spl35_332
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10765,f10376,f8267,f11137,f11214]) ).
fof(f11214,plain,
( spl35_341
<=> ! [X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_341])]) ).
fof(f10765,plain,
( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f7949,f10653]) ).
fof(f7949,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(forward_demodulation,[],[f7948,f5392]) ).
fof(f7948,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
inference(forward_demodulation,[],[f6028,f5392]) ).
fof(f6028,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f5490,f4497,f4497]) ).
fof(f5490,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3874]) ).
fof(f3874,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ) ),
inference(flattening,[],[f3873]) ).
fof(f3873,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ) ),
inference(nnf_transformation,[],[f1315]) ).
fof(f1315,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) )
<=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f468]) ).
fof(f468,axiom,
! [X50,X6] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X50)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X50
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X50
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(f11249,plain,
( spl35_274
| spl35_311
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11248,f10376,f8267,f10706,f8782]) ).
fof(f11248,plain,
( ! [X14,X13] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X13)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10820,f10653]) ).
fof(f10820,plain,
( ! [X14,X12,X13] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X13)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X13)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9391,f10653]) ).
fof(f9391,plain,
! [X14,X12,X13] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X13)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X12),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,X13)) ),
inference(superposition,[],[f4703,f4859]) ).
fof(f4859,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) = X1,
inference(cnf_transformation,[],[f2030]) ).
fof(f2030,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) = X1,
inference(rectify,[],[f451]) ).
fof(f451,axiom,
! [X37,X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X0),X37) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(f11244,plain,
( spl35_312
| ~ spl35_332
| spl35_312
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10761,f10376,f8267,f10716,f11137,f10716]) ).
fof(f10761,plain,
( ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f7235,f10653]) ).
fof(f7235,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(backward_demodulation,[],[f6026,f5392]) ).
fof(f6026,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(definition_unfolding,[],[f5492,f4497]) ).
fof(f5492,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3874]) ).
fof(f11241,plain,
( spl35_322
| ~ spl35_35
| ~ spl35_244
| ~ spl35_247
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11240,f10376,f8317,f8267,f6464,f11048]) ).
fof(f11240,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_35
| ~ spl35_244
| ~ spl35_247
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10897,f10975]) ).
fof(f10897,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_244
| ~ spl35_247
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8319,f10653]) ).
fof(f11236,plain,
( spl35_309
| spl35_321
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11235,f10376,f8267,f11033,f10685]) ).
fof(f11235,plain,
( ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10773,f10653]) ).
fof(f10773,plain,
( ! [X2,X3,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8742,f10653]) ).
fof(f8742,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(resolution,[],[f4220,f4079]) ).
fof(f11232,plain,
( spl35_309
| spl35_321
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11231,f10376,f8267,f11033,f10685]) ).
fof(f11231,plain,
( ! [X6,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10777,f10653]) ).
fof(f10777,plain,
( ! [X6,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X5),X6) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8749,f10653]) ).
fof(f8749,plain,
! [X6,X7,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X5),X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6)) ),
inference(resolution,[],[f4438,f4078]) ).
fof(f11230,plain,
( spl35_310
| spl35_343
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11226,f10376,f8267,f11228,f10689]) ).
fof(f11228,plain,
( spl35_343
<=> ! [X69] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_343])]) ).
fof(f11226,plain,
( ! [X72,X71,X69] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X72) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11225,f5392]) ).
fof(f11225,plain,
( ! [X72,X71,X69] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X72) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10854,f10653]) ).
fof(f10854,plain,
( ! [X72,X70,X71,X69] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,X72)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X72) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9995,f10653]) ).
fof(f9995,plain,
! [X72,X70,X71,X69] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X72)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,X71)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,X72))) ),
inference(forward_demodulation,[],[f9981,f5609]) ).
fof(f9981,plain,
! [X72,X70,X71,X69] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X71,X72)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,X71)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,X70),X72)) ),
inference(superposition,[],[f4919,f5609]) ).
fof(f11223,plain,
( ~ spl35_342
| ~ spl35_244
| spl35_282
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10906,f10376,f9059,f8267,f11220]) ).
fof(f9059,plain,
( spl35_282
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_282])]) ).
fof(f10906,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| spl35_282
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9061,f10653]) ).
fof(f9061,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
| spl35_282 ),
inference(avatar_component_clause,[],[f9059]) ).
fof(f11218,plain,
( spl35_310
| spl35_321
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10826,f10376,f8267,f11033,f10689]) ).
fof(f10826,plain,
( ! [X6,X7,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X6) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9418,f10653]) ).
fof(f9418,plain,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X5),X7) ),
inference(resolution,[],[f4919,f4220]) ).
fof(f11216,plain,
( ~ spl35_332
| spl35_341
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10762,f10376,f8267,f11214,f11137]) ).
fof(f10762,plain,
( ! [X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f7238,f10653]) ).
fof(f7238,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(forward_demodulation,[],[f7236,f5392]) ).
fof(f7236,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
inference(backward_demodulation,[],[f5863,f5392]) ).
fof(f5863,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(definition_unfolding,[],[f4529,f4497,f4497]) ).
fof(f4529,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3321]) ).
fof(f3321,plain,
! [X0,X1] :
( ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) ) ),
inference(rectify,[],[f3320]) ).
fof(f3320,plain,
! [X1,X0] :
( ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ) ) ) ),
inference(flattening,[],[f3319]) ).
fof(f3319,plain,
! [X1,X0] :
( ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ) ) ) ),
inference(nnf_transformation,[],[f1759]) ).
fof(f1759,plain,
! [X1,X0] :
( ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ) )
<=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f469]) ).
fof(f469,axiom,
! [X50,X6] :
( ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X50
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X50
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X6 ) )
<=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(f11212,plain,
( spl35_311
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11211,f10376,f8267,f10706]) ).
fof(f11211,plain,
( ! [X44,X42] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X42,X44)
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10844,f5392]) ).
fof(f10844,plain,
( ! [X44,X42] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9973,f10653]) ).
fof(f9973,plain,
! [X44,X42,X43] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X44)),X44),
inference(superposition,[],[f4540,f5609]) ).
fof(f11210,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11209,f10376,f8267,f10685]) ).
fof(f11209,plain,
( ! [X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10772,f5420]) ).
fof(f10772,plain,
( ! [X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8735,f10653]) ).
fof(f8735,plain,
! [X14,X15] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14))),
inference(resolution,[],[f4079,f4773]) ).
fof(f11204,plain,
( spl35_340
| ~ spl35_35
| ~ spl35_244
| ~ spl35_246
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11199,f10376,f8291,f8267,f6464,f11201]) ).
fof(f8291,plain,
( spl35_246
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_246])]) ).
fof(f11199,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ spl35_35
| ~ spl35_244
| ~ spl35_246
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10896,f10975]) ).
fof(f10896,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_244
| ~ spl35_246
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8293,f10653]) ).
fof(f8293,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_246 ),
inference(avatar_component_clause,[],[f8291]) ).
fof(f11198,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11197,f10376,f8267,f10685]) ).
fof(f11197,plain,
( ! [X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10769,f5420]) ).
fof(f10769,plain,
( ! [X14] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8724,f10653]) ).
fof(f8724,plain,
! [X14,X15] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X15),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X15))),
inference(resolution,[],[f4078,f4773]) ).
fof(f11196,plain,
( spl35_312
| spl35_318
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11195,f10376,f8267,f11003,f10716]) ).
fof(f11003,plain,
( spl35_318
<=> ! [X39] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_318])]) ).
fof(f11195,plain,
( ! [X90,X92] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X90,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X92 )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10852,f10653]) ).
fof(f10852,plain,
( ! [X90,X91,X92] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X92
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X90,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X91,X92)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9987,f10653]) ).
fof(f9987,plain,
! [X90,X91,X92] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X92
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X90,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X91,X92)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X90,X91) ),
inference(superposition,[],[f5271,f5609]) ).
fof(f11192,plain,
( spl35_330
| spl35_338
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10916,f10376,f8267,f11185,f11128]) ).
fof(f11128,plain,
( spl35_330
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_330])]) ).
fof(f11185,plain,
( spl35_338
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_338])]) ).
fof(f10916,plain,
( ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4815,f10653]) ).
fof(f4815,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
inference(cnf_transformation,[],[f2547]) ).
fof(f11191,plain,
( spl35_321
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10923,f10376,f8267,f11033]) ).
fof(f10923,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5818,f10653]) ).
fof(f11190,plain,
( spl35_338
| spl35_339
| ~ spl35_48
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10915,f10376,f8267,f6556,f11188,f11185]) ).
fof(f11188,plain,
( spl35_339
<=> ! [X1] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_339])]) ).
fof(f10915,plain,
( ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) )
| ~ spl35_48
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10350,f10653]) ).
fof(f10350,plain,
( ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = X1
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) )
| ~ spl35_48 ),
inference(resolution,[],[f4815,f8329]) ).
fof(f11183,plain,
( spl35_310
| ~ spl35_313
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11182,f10376,f8267,f10955,f10689]) ).
fof(f11182,plain,
( ! [X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10829,f10653]) ).
fof(f10829,plain,
( ! [X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9427,f10653]) ).
fof(f9427,plain,
! [X2,X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
inference(superposition,[],[f4919,f5023]) ).
fof(f11179,plain,
( spl35_312
| spl35_274
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10775,f10376,f8267,f8782,f10716]) ).
fof(f10775,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8747,f10653]) ).
fof(f8747,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(resolution,[],[f4396,f4623]) ).
fof(f11178,plain,
( spl35_337
| ~ spl35_244
| ~ spl35_280
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10905,f10376,f9049,f8267,f11175]) ).
fof(f10905,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_280
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9051,f10653]) ).
fof(f11169,plain,
( spl35_321
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11168,f10376,f8267,f10685,f11033]) ).
fof(f11168,plain,
( ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10776,f10653]) ).
fof(f10776,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8748,f10653]) ).
fof(f8748,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(resolution,[],[f4438,f4079]) ).
fof(f11165,plain,
( ~ spl35_336
| ~ spl35_35
| spl35_197
| ~ spl35_198
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11160,f10376,f8267,f7901,f7896,f6464,f11162]) ).
fof(f7901,plain,
( spl35_198
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_198])]) ).
fof(f11160,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ spl35_35
| spl35_197
| ~ spl35_198
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11159,f7903]) ).
fof(f7903,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_198 ),
inference(avatar_component_clause,[],[f7901]) ).
fof(f11159,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ spl35_35
| spl35_197
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10914,f6466]) ).
fof(f10914,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| spl35_197
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f7897,f10653]) ).
fof(f11158,plain,
( spl35_311
| spl35_335
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11154,f10376,f8267,f11156,f10706]) ).
fof(f11156,plain,
( spl35_335
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_335])]) ).
fof(f11154,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(trivial_inequality_removal,[],[f11153]) ).
fof(f11153,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10745,f10653]) ).
fof(f10745,plain,
( ! [X2,X3,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4925,f10653]) ).
fof(f4925,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0) ),
inference(cnf_transformation,[],[f3548]) ).
fof(f3548,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rectify,[],[f2555]) ).
fof(f2555,plain,
! [X3,X1,X0,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(flattening,[],[f2554]) ).
fof(f2554,plain,
! [X1,X2,X0,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(ennf_transformation,[],[f1694]) ).
fof(f1694,plain,
! [X1,X2,X0,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ) ),
inference(rectify,[],[f400]) ).
fof(f400,axiom,
! [X21,X0,X20,X37] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X21)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X37)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X37) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(f11152,plain,
( spl35_334
| ~ spl35_244
| ~ spl35_261
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10901,f10376,f8542,f8267,f11149]) ).
fof(f11149,plain,
( spl35_334
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_334])]) ).
fof(f8542,plain,
( spl35_261
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_261])]) ).
fof(f10901,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))
| ~ spl35_244
| ~ spl35_261
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8544,f10653]) ).
fof(f8544,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))
| ~ spl35_261 ),
inference(avatar_component_clause,[],[f8542]) ).
fof(f11146,plain,
( spl35_314
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10930,f10376,f8267,f10964]) ).
fof(f10930,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5882,f10653]) ).
fof(f11145,plain,
( spl35_323
| ~ spl35_244
| ~ spl35_285
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11144,f10376,f9073,f8267,f11058]) ).
fof(f11058,plain,
( spl35_323
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_323])]) ).
fof(f9073,plain,
( spl35_285
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),sK24(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_285])]) ).
fof(f11144,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_285
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10890,f10653]) ).
fof(f10890,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ spl35_244
| ~ spl35_285
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9075,f10653]) ).
fof(f9075,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),sK24(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_285 ),
inference(avatar_component_clause,[],[f9073]) ).
fof(f11143,plain,
( ~ spl35_332
| spl35_333
| spl35_333
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10763,f10376,f8267,f11141,f11141,f11137]) ).
fof(f11141,plain,
( spl35_333
<=> ! [X1] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_333])]) ).
fof(f10763,plain,
( ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f7240,f10653]) ).
fof(f7240,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(forward_demodulation,[],[f7239,f5392]) ).
fof(f7239,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ),
inference(forward_demodulation,[],[f7237,f5392]) ).
fof(f7237,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(backward_demodulation,[],[f6027,f5392]) ).
fof(f6027,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ),
inference(definition_unfolding,[],[f5491,f4497,f4497,f4497]) ).
fof(f5491,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3874]) ).
fof(f11135,plain,
( ~ spl35_323
| ~ spl35_244
| spl35_283
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10907,f10376,f9063,f8267,f11058]) ).
fof(f9063,plain,
( spl35_283
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) = hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_283])]) ).
fof(f10907,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| spl35_283
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9064,f10653]) ).
fof(f9064,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) != hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
| spl35_283 ),
inference(avatar_component_clause,[],[f9063]) ).
fof(f11133,plain,
( spl35_330
| spl35_331
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10918,f10376,f8267,f11131,f11128]) ).
fof(f11131,plain,
( spl35_331
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_331])]) ).
fof(f10918,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4814,f10653]) ).
fof(f4814,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f2547]) ).
fof(f11123,plain,
( spl35_274
| spl35_319
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11122,f10376,f8267,f11008,f8782]) ).
fof(f11122,plain,
( ! [X10,X8] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X8)
| X8 = X10
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10817,f10653]) ).
fof(f10817,plain,
( ! [X10,X8,X9] :
( X8 = X10
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X8)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X9),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9358,f10653]) ).
fof(f9358,plain,
! [X10,X8,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X8)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X9),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X9))
| X8 = X10 ),
inference(resolution,[],[f4665,f5211]) ).
fof(f11120,plain,
( spl35_311
| spl35_274
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11119,f10376,f8267,f8782,f10706]) ).
fof(f11119,plain,
( ! [X2,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11118,f5420]) ).
fof(f11118,plain,
( ! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10924,f5420]) ).
fof(f10924,plain,
( ! [X2,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5823,f10653]) ).
fof(f5823,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)) ),
inference(definition_unfolding,[],[f4315,f4497,f4497]) ).
fof(f4315,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) ),
inference(cnf_transformation,[],[f3202]) ).
fof(f3202,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X0)) ) ),
inference(rectify,[],[f3201]) ).
fof(f3201,plain,
! [X1,X2,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2),X0),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2),X0),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2),X1)) ) ),
inference(nnf_transformation,[],[f1416]) ).
fof(f1416,plain,
! [X1,X2,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2),X0),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2),X1))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f493]) ).
fof(f493,axiom,
! [X6,X50,X27] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X50)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X27),X6),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X27),X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(f11115,plain,
( spl35_309
| spl35_329
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10878,f10376,f8267,f11113,f10685]) ).
fof(f11113,plain,
( spl35_329
<=> ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_329])]) ).
fof(f10878,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10515,f10653]) ).
fof(f10515,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5601,f10467]) ).
fof(f5601,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ),
inference(cnf_transformation,[],[f3938]) ).
fof(f3938,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(nnf_transformation,[],[f2679]) ).
fof(f2679,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(ennf_transformation,[],[f1621]) ).
fof(f1621,plain,
! [X1,X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ) ),
inference(rectify,[],[f511]) ).
fof(f511,axiom,
! [X73,X27,X72] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X72)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X27))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X73,X27),X72) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(f11111,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10736,f10376,f8267,f10685]) ).
fof(f10736,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4462,f10653]) ).
fof(f11110,plain,
( spl35_324
| spl35_274
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11109,f10376,f8267,f8782,f11064]) ).
fof(f11109,plain,
( ! [X11,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X11 = X13
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X13) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10818,f10653]) ).
fof(f10818,plain,
( ! [X11,X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X13)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X12))
| X11 = X13 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9359,f10653]) ).
fof(f9359,plain,
! [X11,X12,X13] :
( X11 = X13
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X13)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X12),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X12)) ),
inference(resolution,[],[f4665,f5104]) ).
fof(f11108,plain,
( spl35_314
| spl35_315
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10802,f10376,f8267,f10972,f10964]) ).
fof(f10802,plain,
( ! [X8,X7] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9028,f10653]) ).
fof(f9028,plain,
! [X8,X7] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X8)) ),
inference(superposition,[],[f5709,f4859]) ).
fof(f5709,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3998]) ).
fof(f11107,plain,
( spl35_315
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10749,f10376,f8267,f10972]) ).
fof(f10749,plain,
( ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5249,f10653]) ).
fof(f11102,plain,
( spl35_315
| spl35_314
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10877,f10376,f8267,f10964,f10972]) ).
fof(f10877,plain,
( ! [X2,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10490,f10653]) ).
fof(f10490,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4704,f10467]) ).
fof(f11098,plain,
( spl35_328
| ~ spl35_244
| ~ spl35_286
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10909,f10376,f9078,f8267,f11095]) ).
fof(f10909,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_286
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9080,f10653]) ).
fof(f11093,plain,
( spl35_312
| spl35_318
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11092,f10376,f8267,f11003,f10716]) ).
fof(f11092,plain,
( ! [X69,X67] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X69 )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11091,f10653]) ).
fof(f11091,plain,
( ! [X68,X69,X66,X67] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X68))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X69 )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10871,f10653]) ).
fof(f10871,plain,
( ! [X68,X69,X66,X67] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X68)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X69)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X69 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10081,f10653]) ).
fof(f10081,plain,
! [X68,X69,X66,X67] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,X68) = X69
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X68)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X69) ),
inference(superposition,[],[f4838,f5615]) ).
fof(f5615,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(cnf_transformation,[],[f3945]) ).
fof(f3945,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(rectify,[],[f1476]) ).
fof(f1476,plain,
! [X1,X2,X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rectify,[],[f344]) ).
fof(f344,axiom,
! [X10,X36,X14] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X14)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(f4838,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| X1 = X2 ),
inference(cnf_transformation,[],[f3495]) ).
fof(f3495,plain,
! [X0,X1,X2] :
( ( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| X1 != X2 ) ),
inference(rectify,[],[f3494]) ).
fof(f3494,plain,
! [X1,X2,X0] :
( ( X0 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| X0 != X2 ) ),
inference(nnf_transformation,[],[f1737]) ).
fof(f1737,plain,
! [X1,X2,X0] :
( X0 = X2
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X6,X27,X50] :
( X6 = X50
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(f11090,plain,
( spl35_327
| ~ spl35_244
| ~ spl35_264
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10903,f10376,f8591,f8267,f11087]) ).
fof(f11087,plain,
( spl35_327
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_327])]) ).
fof(f10903,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_244
| ~ spl35_264
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8593,f10653]) ).
fof(f8593,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_264 ),
inference(avatar_component_clause,[],[f8591]) ).
fof(f11085,plain,
( spl35_326
| ~ spl35_244
| ~ spl35_251
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10899,f10376,f8409,f8267,f11082]) ).
fof(f10899,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_244
| ~ spl35_251
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8411,f10653]) ).
fof(f11078,plain,
( ~ spl35_325
| spl35_214
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10893,f10376,f8267,f8035,f11075]) ).
fof(f10893,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| spl35_214
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8037,f10653]) ).
fof(f11073,plain,
( ~ spl35_313
| spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11072,f10376,f8267,f10689,f10955]) ).
fof(f11072,plain,
( ! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10827,f10653]) ).
fof(f10827,plain,
( ! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X7)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9425,f10653]) ).
fof(f9425,plain,
! [X6,X7,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X7))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7) ),
inference(superposition,[],[f4919,f5023]) ).
fof(f11071,plain,
( ~ spl35_313
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11070,f10376,f8267,f10685,f10955]) ).
fof(f11070,plain,
( ! [X80] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f11069,f10653]) ).
fof(f11069,plain,
( ! [X80,X77] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X77,X80),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10861,f10653]) ).
fof(f10861,plain,
( ! [X80,X78,X79,X77] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X77,X80),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X78,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X77,X79))) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10051,f10653]) ).
fof(f10051,plain,
! [X80,X78,X79,X77] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X80,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X78,X79))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X77,X80),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X78,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X77,X79))) ),
inference(superposition,[],[f4919,f5615]) ).
fof(f11066,plain,
( spl35_274
| spl35_324
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11062,f10376,f8267,f11064,f8782]) ).
fof(f11062,plain,
( ! [X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X13)
| X12 = X13
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10814,f10653]) ).
fof(f10814,plain,
( ! [X11,X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X13)
| X12 = X13
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9279,f10653]) ).
fof(f9279,plain,
! [X11,X12,X13] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12,X13)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X12),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X13))
| X12 = X13 ),
inference(resolution,[],[f4218,f5104]) ).
fof(f4218,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(cnf_transformation,[],[f3149]) ).
fof(f3149,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ) ),
inference(rectify,[],[f3148]) ).
fof(f3148,plain,
! [X0,X2,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
inference(nnf_transformation,[],[f1236]) ).
fof(f1236,plain,
! [X0,X2,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f405]) ).
fof(f405,axiom,
! [X50,X6,X27] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X50)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X6),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(f11061,plain,
( spl35_323
| ~ spl35_244
| ~ spl35_281
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11056,f10376,f9054,f8267,f11058]) ).
fof(f9054,plain,
( spl35_281
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),sK30(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_281])]) ).
fof(f11056,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_281
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10891,f10653]) ).
fof(f10891,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ spl35_244
| ~ spl35_281
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9056,f10653]) ).
fof(f9056,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),sK30(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_281 ),
inference(avatar_component_clause,[],[f9054]) ).
fof(f11054,plain,
( spl35_311
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11053,f10376,f8267,f10706]) ).
fof(f11053,plain,
( ! [X91,X92] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X92,X91)
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10863,f5392]) ).
fof(f10863,plain,
( ! [X91,X92] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X92,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X91)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10055,f10653]) ).
fof(f10055,plain,
! [X91,X92,X93] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X92,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X91,X93)),X91),
inference(superposition,[],[f5249,f5615]) ).
fof(f11051,plain,
( ~ spl35_322
| ~ spl35_35
| spl35_196
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11046,f10376,f8267,f7892,f6464,f11048]) ).
fof(f11046,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_35
| spl35_196
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10913,f6466]) ).
fof(f10913,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| spl35_196
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f7894,f10653]) ).
fof(f11045,plain,
( spl35_321
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10828,f10376,f8267,f10685,f11033]) ).
fof(f10828,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9426,f10653]) ).
fof(f9426,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[],[f4919,f5392]) ).
fof(f11043,plain,
( spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11036,f10376,f8267,f10685]) ).
fof(f11036,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4773,f10889]) ).
fof(f10889,plain,
( ! [X20] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X20)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9005,f10653]) ).
fof(f9005,plain,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,sK30(X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X20))) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X20),
inference(resolution,[],[f5515,f4773]) ).
fof(f11035,plain,
( spl35_309
| spl35_321
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11031,f10376,f8267,f11033,f10685]) ).
fof(f11031,plain,
( ! [X6,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10774,f10653]) ).
fof(f10774,plain,
( ! [X6,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X5),X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8743,f10653]) ).
fof(f8743,plain,
! [X6,X7,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X5),X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X7)) ),
inference(resolution,[],[f4220,f4078]) ).
fof(f11030,plain,
( spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11029,f10376,f8267,f10689]) ).
fof(f11029,plain,
( ! [X11,X12] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X12)
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10771,f5392]) ).
fof(f10771,plain,
( ! [X11,X12] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8734,f10653]) ).
fof(f8734,plain,
! [X11,X12,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X11))),
inference(resolution,[],[f4079,f4462]) ).
fof(f11028,plain,
( spl35_310
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11027,f10376,f8267,f10689]) ).
fof(f11027,plain,
( ! [X11,X12] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X12)
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10768,f5392]) ).
fof(f10768,plain,
( ! [X11,X12] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8723,f10653]) ).
fof(f8723,plain,
! [X11,X12,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X12,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X13))),
inference(resolution,[],[f4078,f4462]) ).
fof(f11024,plain,
( spl35_315
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10738,f10376,f8267,f10972]) ).
fof(f10738,plain,
( ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4540,f10653]) ).
fof(f11022,plain,
( spl35_311
| spl35_314
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11021,f10376,f8267,f10964,f10706]) ).
fof(f11021,plain,
( ! [X58,X56,X55] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X58) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10880,f5392]) ).
fof(f10880,plain,
( ! [X58,X56,X55] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X58) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10624,f10653]) ).
fof(f10624,plain,
( ! [X58,X56,X57,X55] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X57)),X58) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10078,f10467]) ).
fof(f10078,plain,
! [X58,X56,X57,X55] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X58,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X57)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X57)),X58) ),
inference(superposition,[],[f4704,f5615]) ).
fof(f11020,plain,
( spl35_274
| spl35_311
| spl35_311
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11019,f10376,f8267,f10706,f10706,f8782]) ).
fof(f11019,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10754,f10653]) ).
fof(f10754,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5513,f10653]) ).
fof(f5513,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(cnf_transformation,[],[f3885]) ).
fof(f3885,plain,
! [X0,X1,X2,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(rectify,[],[f2618]) ).
fof(f2618,plain,
! [X3,X1,X0,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(flattening,[],[f2617]) ).
fof(f2617,plain,
! [X2,X1,X3,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(ennf_transformation,[],[f1501]) ).
fof(f1501,plain,
! [X2,X1,X3,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ) ),
inference(rectify,[],[f401]) ).
fof(f401,axiom,
! [X21,X20,X43,X44] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X44,X43)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X21)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X44,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(f11016,plain,
( spl35_318
| spl35_312
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10845,f10376,f8267,f10716,f11003]) ).
fof(f10845,plain,
( ! [X47,X45] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9974,f10653]) ).
fof(f9974,plain,
! [X46,X47,X45] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X45,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X46,X47))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 ),
inference(superposition,[],[f4542,f5609]) ).
fof(f11015,plain,
( spl35_320
| ~ spl35_244
| ~ spl35_258
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10900,f10376,f8501,f8267,f11012]) ).
fof(f10900,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_244
| ~ spl35_258
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8503,f10653]) ).
fof(f11010,plain,
( spl35_274
| spl35_319
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f11006,f10376,f8267,f11008,f8782]) ).
fof(f11006,plain,
( ! [X6,X7] :
( X6 = X7
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10813,f10653]) ).
fof(f10813,plain,
( ! [X6,X7,X5] :
( X6 = X7
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X7)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9277,f10653]) ).
fof(f9277,plain,
! [X6,X7,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
| X6 = X7
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X7)) ),
inference(resolution,[],[f4218,f5211]) ).
fof(f11005,plain,
( spl35_317
| spl35_318
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10998,f10376,f8267,f11003,f11000]) ).
fof(f11000,plain,
( spl35_317
<=> ! [X38,X41] : X38 = X41 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_317])]) ).
fof(f10998,plain,
( ! [X38,X41,X39] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X38 = X41 )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10997,f10653]) ).
fof(f10997,plain,
( ! [X40,X38,X41,X39] :
( X38 = X41
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X40)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10869,f10653]) ).
fof(f10869,plain,
( ! [X40,X38,X41,X39] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X40)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X38 = X41 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f10073,f10653]) ).
fof(f10073,plain,
! [X40,X38,X41,X39] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X40)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X40))
| X38 = X41 ),
inference(superposition,[],[f4509,f5615]) ).
fof(f4509,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f3310]) ).
fof(f3310,plain,
! [X0,X1,X2] :
( ( X0 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| X0 != X2 ) ),
inference(rectify,[],[f3309]) ).
fof(f3309,plain,
! [X0,X2,X1] :
( ( X0 = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)
| X0 != X1 ) ),
inference(nnf_transformation,[],[f1219]) ).
fof(f1219,plain,
! [X0,X2,X1] :
( X0 = X1
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2) ),
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X6,X50,X27] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X27) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X50,X27)
<=> X6 = X50 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(f10996,plain,
( spl35_274
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10949,f10376,f8267,f8782]) ).
fof(f10949,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f6114,f10653]) ).
fof(f6114,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(equality_resolution,[],[f5897]) ).
fof(f5897,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(definition_unfolding,[],[f4738,f4497]) ).
fof(f4738,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3439]) ).
fof(f3439,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK11(X0,X1),X0)
& c_Nat_OSuc(sK11(X0,X1)) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f3437,f3438]) ).
fof(f3438,plain,
! [X0,X1] :
( ? [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
& c_Nat_OSuc(X3) = X1 )
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK11(X0,X1),X0)
& c_Nat_OSuc(sK11(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3437,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ? [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
& c_Nat_OSuc(X3) = X1 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(rectify,[],[f3436]) ).
fof(f3436,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Nat_OSuc(X2) != X0 ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
& c_Nat_OSuc(X2) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) ),
inference(flattening,[],[f3435]) ).
fof(f3435,plain,
! [X1,X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| c_Nat_OSuc(X2) != X0 ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
& c_Nat_OSuc(X2) = X0 )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ) ),
inference(nnf_transformation,[],[f1893]) ).
fof(f1893,plain,
! [X1,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
& c_Nat_OSuc(X2) = X0 ) ) ),
inference(rectify,[],[f465]) ).
fof(f465,axiom,
! [X6,X50] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6
| ? [X71] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X71,X50)
& c_Nat_OSuc(X71) = X6 ) )
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(f10995,plain,
( spl35_316
| ~ spl35_35
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10981,f10376,f8267,f6464,f10992]) ).
fof(f10981,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl35_35
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8210,f10975]) ).
fof(f8210,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(backward_demodulation,[],[f5827,f5992]) ).
fof(f5827,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))),
inference(definition_unfolding,[],[f4330,f4497]) ).
fof(f4330,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0))),
inference(cnf_transformation,[],[f1521]) ).
fof(f1521,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0))),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X37] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X37))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
fof(f10974,plain,
( spl35_314
| spl35_315
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10801,f10376,f8267,f10972,f10964]) ).
fof(f10801,plain,
( ! [X6,X5] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9027,f10653]) ).
fof(f9027,plain,
! [X6,X5] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6)) ),
inference(superposition,[],[f5709,f4809]) ).
fof(f10968,plain,
( spl35_274
| spl35_311
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10967,f10376,f8267,f10706,f8782]) ).
fof(f10967,plain,
( ! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10731,f10653]) ).
fof(f10731,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4218,f10653]) ).
fof(f10966,plain,
( spl35_312
| spl35_314
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10815,f10376,f8267,f10964,f10716]) ).
fof(f10815,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9280,f10653]) ).
fof(f9280,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(forward_demodulation,[],[f9275,f5392]) ).
fof(f9275,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)) ),
inference(resolution,[],[f4218,f4623]) ).
fof(f10962,plain,
( spl35_310
| ~ spl35_313
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10961,f10376,f8267,f10955,f10689]) ).
fof(f10961,plain,
( ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10960,f5420]) ).
fof(f10960,plain,
( ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10944,f5420]) ).
fof(f10944,plain,
( ! [X2,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f6006,f10653]) ).
fof(f6006,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(definition_unfolding,[],[f5322,f4497,f4497]) ).
fof(f5322,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X0),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X0),X2)) ),
inference(cnf_transformation,[],[f3783]) ).
fof(f3783,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X0),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X0),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X0),X2)) ) ),
inference(rectify,[],[f3782]) ).
fof(f3782,plain,
! [X1,X2,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X0)) ) ),
inference(nnf_transformation,[],[f2001]) ).
fof(f2001,plain,
! [X1,X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(rectify,[],[f500]) ).
fof(f500,axiom,
! [X50,X27,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X50)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X27),X6),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X27),X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(f10958,plain,
( spl35_310
| ~ spl35_313
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10953,f10376,f8267,f10955,f10689]) ).
fof(f10953,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10744,f10653]) ).
fof(f10744,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f4919,f10653]) ).
fof(f10718,plain,
( spl35_308
| spl35_312
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10714,f10376,f8267,f10716,f10682]) ).
fof(f10714,plain,
( ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10713,f10467]) ).
fof(f10713,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = X1 )
| ~ spl35_244
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10510,f6110]) ).
fof(f10510,plain,
( ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5285,f10467]) ).
fof(f5285,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1) ),
inference(cnf_transformation,[],[f3758]) ).
fof(f3758,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X0) ),
inference(rectify,[],[f2205]) ).
fof(f2205,plain,
! [X1,X0,X2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1441]) ).
fof(f1441,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X0) ),
inference(rectify,[],[f506]) ).
fof(f506,axiom,
! [X44,X43,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X43)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X43,X44),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X43,X20),X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(f10708,plain,
( spl35_311
| spl35_274
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10518,f10376,f8267,f8782,f10706]) ).
fof(f10518,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f5710,f10467]) ).
fof(f10691,plain,
( spl35_310
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10650,f10376,f8267,f10685,f10689]) ).
fof(f10650,plain,
( ! [X14,X15,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X15) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9366,f10467]) ).
fof(f9366,plain,
! [X14,X15,X13] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X15)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X13),X15)) ),
inference(resolution,[],[f4699,f4994]) ).
fof(f10687,plain,
( spl35_308
| spl35_309
| ~ spl35_244
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10654,f10376,f8267,f10685,f10682]) ).
fof(f10654,plain,
( ! [X29,X26,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X27) )
| ~ spl35_244
| ~ spl35_305 ),
inference(backward_demodulation,[],[f9380,f10467]) ).
fof(f9380,plain,
! [X28,X29,X26,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X26)),X29))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X27) ),
inference(forward_demodulation,[],[f9370,f5609]) ).
fof(f9370,plain,
! [X28,X29,X26,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X28),X26),X29))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29,X27) ),
inference(resolution,[],[f4699,f4220]) ).
fof(f10463,plain,
( spl35_307
| ~ spl35_259
| ~ spl35_305 ),
inference(avatar_split_clause,[],[f10458,f10376,f8517,f10460]) ).
fof(f10460,plain,
( spl35_307
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_307])]) ).
fof(f10458,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_259
| ~ spl35_305 ),
inference(forward_demodulation,[],[f10386,f5392]) ).
fof(f10386,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_259
| ~ spl35_305 ),
inference(backward_demodulation,[],[f8519,f10378]) ).
fof(f10383,plain,
( spl35_305
| spl35_306
| ~ spl35_244 ),
inference(avatar_split_clause,[],[f10370,f8267,f10380,f10376]) ).
fof(f10380,plain,
( spl35_306
<=> ! [X9,X8] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X8) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X8 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_306])]) ).
fof(f10370,plain,
( ! [X8,X9] :
( X8 = X9
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X8) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
| ~ spl35_244 ),
inference(superposition,[],[f5149,f8584]) ).
fof(f10382,plain,
( spl35_305
| spl35_306
| ~ spl35_244 ),
inference(avatar_split_clause,[],[f10363,f8267,f10380,f10376]) ).
fof(f10363,plain,
( ! [X8,X9] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X8) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X8 = X9 )
| ~ spl35_244 ),
inference(superposition,[],[f5149,f8584]) ).
fof(f10336,plain,
( spl35_303
| spl35_304
| ~ spl35_244 ),
inference(avatar_split_clause,[],[f10316,f8267,f10334,f10330]) ).
fof(f10330,plain,
( spl35_303
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_303])]) ).
fof(f10334,plain,
( spl35_304
<=> ! [X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_304])]) ).
fof(f10316,plain,
( ! [X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) )
| ~ spl35_244 ),
inference(superposition,[],[f4574,f8269]) ).
fof(f10328,plain,
( spl35_301
| spl35_302
| ~ spl35_230 ),
inference(avatar_split_clause,[],[f10315,f8146,f10325,f10322]) ).
fof(f10322,plain,
( spl35_301
<=> ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_301])]) ).
fof(f10315,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) )
| ~ spl35_230 ),
inference(superposition,[],[f4574,f8148]) ).
fof(f10309,plain,
( spl35_299
| ~ spl35_300
| ~ spl35_244 ),
inference(avatar_split_clause,[],[f10300,f8267,f10306,f10302]) ).
fof(f10302,plain,
( spl35_299
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_299])]) ).
fof(f10306,plain,
( spl35_300
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_300])]) ).
fof(f10300,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_244 ),
inference(superposition,[],[f4678,f8269]) ).
fof(f4678,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0) ),
inference(cnf_transformation,[],[f3402]) ).
fof(f10258,plain,
( spl35_298
| ~ spl35_256 ),
inference(avatar_split_clause,[],[f10253,f8477,f10255]) ).
fof(f10255,plain,
( spl35_298
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_298])]) ).
fof(f10253,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f10252,f5637]) ).
fof(f10252,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f10251,f5723]) ).
fof(f10251,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f10233,f5723]) ).
fof(f10233,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(resolution,[],[f7329,f8479]) ).
fof(f10246,plain,
( spl35_297
| ~ spl35_263 ),
inference(avatar_split_clause,[],[f10241,f8575,f10243]) ).
fof(f10243,plain,
( spl35_297
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_297])]) ).
fof(f10241,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10240,f5637]) ).
fof(f10240,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10239,f5723]) ).
fof(f10239,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10238,f5723]) ).
fof(f10238,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10237,f5637]) ).
fof(f10237,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10236,f5723]) ).
fof(f10236,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10234,f5723]) ).
fof(f10234,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(resolution,[],[f7329,f8577]) ).
fof(f10231,plain,
( spl35_56
| ~ spl35_296 ),
inference(avatar_split_clause,[],[f10230,f10225,f6607]) ).
fof(f6607,plain,
( spl35_56
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_56])]) ).
fof(f10230,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ),
inference(forward_demodulation,[],[f10229,f4335]) ).
fof(f10229,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ),
inference(forward_demodulation,[],[f10222,f5637]) ).
fof(f10222,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls) ),
inference(superposition,[],[f7095,f4335]) ).
fof(f7095,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(forward_demodulation,[],[f5925,f5637]) ).
fof(f5925,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),c_Int_OPls) ),
inference(definition_unfolding,[],[f4864,f5442]) ).
fof(f4864,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X0),c_Int_OPls) ),
inference(cnf_transformation,[],[f3511]) ).
fof(f10228,plain,
( ~ spl35_296
| spl35_56 ),
inference(avatar_split_clause,[],[f10223,f6607,f10225]) ).
fof(f10223,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls) ),
inference(forward_demodulation,[],[f10220,f4335]) ).
fof(f10220,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls) ),
inference(superposition,[],[f7095,f4931]) ).
fof(f10205,plain,
( spl35_295
| ~ spl35_263 ),
inference(avatar_split_clause,[],[f10200,f8575,f10202]) ).
fof(f10202,plain,
( spl35_295
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_295])]) ).
fof(f10200,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10199,f5637]) ).
fof(f10199,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10198,f5723]) ).
fof(f10198,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10197,f5723]) ).
fof(f10197,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10196,f5637]) ).
fof(f10196,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10195,f5723]) ).
fof(f10195,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f10180,f5723]) ).
fof(f10180,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(resolution,[],[f6427,f8577]) ).
fof(f6427,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f5930,f5637]) ).
fof(f5930,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) ),
inference(definition_unfolding,[],[f4893,f5442]) ).
fof(f4893,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) ),
inference(cnf_transformation,[],[f3528]) ).
fof(f3528,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X0)) ) ),
inference(nnf_transformation,[],[f1675]) ).
fof(f1675,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) ),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X27))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X27) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).
fof(f10189,plain,
( spl35_294
| ~ spl35_256 ),
inference(avatar_split_clause,[],[f10184,f8477,f10186]) ).
fof(f10186,plain,
( spl35_294
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_294])]) ).
fof(f10184,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f10183,f5637]) ).
fof(f10183,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f10182,f5723]) ).
fof(f10182,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f10179,f5723]) ).
fof(f10179,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(resolution,[],[f6427,f8479]) ).
fof(f9606,plain,
( spl35_293
| ~ spl35_244 ),
inference(avatar_split_clause,[],[f9601,f8267,f9603]) ).
fof(f9603,plain,
( spl35_293
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_293])]) ).
fof(f9601,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))
| ~ spl35_244 ),
inference(forward_demodulation,[],[f9590,f5977]) ).
fof(f5977,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0),
inference(definition_unfolding,[],[f5161,f4497,f4497]) ).
fof(f5161,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f3694]) ).
fof(f3694,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(rectify,[],[f1223]) ).
fof(f1223,plain,
! [X1,X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X0),X1) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(rectify,[],[f388]) ).
fof(f388,axiom,
! [X0,X37] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X0),X37) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(f9590,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ spl35_244 ),
inference(superposition,[],[f5564,f8581]) ).
fof(f9532,plain,
( spl35_292
| ~ spl35_188 ),
inference(avatar_split_clause,[],[f9527,f7640,f9529]) ).
fof(f9527,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_188 ),
inference(resolution,[],[f7642,f7800]) ).
fof(f7800,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(forward_demodulation,[],[f7703,f4335]) ).
fof(f7703,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oone__class_Oone(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f7335,f4335]) ).
fof(f7335,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7334,f5637]) ).
fof(f7334,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))) = c_Groups_Oone__class_Oone(X0) ),
inference(forward_demodulation,[],[f5833,f5637]) ).
fof(f5833,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(definition_unfolding,[],[f4352,f5442]) ).
fof(f4352,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f3000]) ).
fof(f3000,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f1272]) ).
fof(f1272,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Groups_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) ),
inference(rectify,[],[f265]) ).
fof(f265,axiom,
! [X15] :
( class_Int_Onumber__ring(X15)
=> c_Int_Onumber__class_Onumber__of(X15,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
fof(f9241,plain,
( spl35_291
| ~ spl35_263 ),
inference(avatar_split_clause,[],[f9236,f8575,f9238]) ).
fof(f9238,plain,
( spl35_291
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_291])]) ).
fof(f9236,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f9235,f5637]) ).
fof(f9235,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f9234,f5723]) ).
fof(f9234,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f9233,f5723]) ).
fof(f9233,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f9232,f5637]) ).
fof(f9232,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_263 ),
inference(forward_demodulation,[],[f9230,f5723]) ).
fof(f9230,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_263 ),
inference(resolution,[],[f8577,f5784]) ).
fof(f5784,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)) ),
inference(definition_unfolding,[],[f4063,f4431]) ).
fof(f4063,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) ),
inference(cnf_transformation,[],[f3064]) ).
fof(f3064,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X0)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0) ) ),
inference(nnf_transformation,[],[f2048]) ).
fof(f2048,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X0)) ),
inference(rectify,[],[f169]) ).
fof(f169,axiom,
! [X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X27)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).
fof(f9208,plain,
( spl35_290
| ~ spl35_92
| ~ spl35_102
| ~ spl35_276 ),
inference(avatar_split_clause,[],[f9204,f8811,f6933,f6857,f9206]) ).
fof(f9206,plain,
( spl35_290
<=> ! [X1] : c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl35_290])]) ).
fof(f6933,plain,
( spl35_102
<=> class_Fields_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_102])]) ).
fof(f8811,plain,
( spl35_276
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_276])]) ).
fof(f9204,plain,
( ! [X1] :
( ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X1 )
| ~ spl35_102
| ~ spl35_276 ),
inference(forward_demodulation,[],[f9198,f8813]) ).
fof(f8813,plain,
( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_276 ),
inference(avatar_component_clause,[],[f8811]) ).
fof(f9198,plain,
( ! [X1] :
( c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Int_Oint))) = X1
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex) )
| ~ spl35_102 ),
inference(resolution,[],[f7771,f6935]) ).
fof(f6935,plain,
( class_Fields_Ofield(tc_Complex_Ocomplex)
| ~ spl35_102 ),
inference(avatar_component_clause,[],[f6933]) ).
fof(f7771,plain,
! [X0,X1] :
( ~ class_Fields_Ofield(X0)
| c_Rings_Oinverse__class_Odivide(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) = X1
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7699,f4335]) ).
fof(f7699,plain,
! [X0,X1] :
( ~ class_Fields_Ofield(X0)
| c_Rings_Oinverse__class_Odivide(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) = X1
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f6699,f4335]) ).
fof(f6699,plain,
! [X0,X1] :
( ~ class_Fields_Ofield(X0)
| c_Rings_Oinverse__class_Odivide(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))) = X1
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f6698,f5637]) ).
fof(f6698,plain,
! [X0,X1] :
( ~ class_Fields_Ofield(X0)
| c_Rings_Oinverse__class_Odivide(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))) = X1
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f6048,f5637]) ).
fof(f6048,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Fields_Ofield(X0)
| c_Rings_Oinverse__class_Odivide(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = X1 ),
inference(definition_unfolding,[],[f5674,f5442]) ).
fof(f5674,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Rings_Oinverse__class_Odivide(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))) = X1
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f3984]) ).
fof(f3984,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Rings_Oinverse__class_Odivide(X0,X1,c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))) = X1
| ~ class_Fields_Ofield(X0) ),
inference(rectify,[],[f2585]) ).
fof(f2585,plain,
! [X1,X0] :
( ~ class_Int_Onumber__ring(X1)
| c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X0
| ~ class_Fields_Ofield(X1) ),
inference(flattening,[],[f2584]) ).
fof(f2584,plain,
! [X1,X0] :
( c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X0
| ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Ofield(X1) ),
inference(ennf_transformation,[],[f1709]) ).
fof(f1709,plain,
! [X1,X0] :
( ( class_Int_Onumber__ring(X1)
& class_Fields_Ofield(X1) )
=> c_Rings_Oinverse__class_Odivide(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X0 ),
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X10,X15] :
( ( class_Fields_Ofield(X15)
& class_Int_Onumber__ring(X15) )
=> c_Rings_Oinverse__class_Odivide(X15,X10,c_Int_Onumber__class_Onumber__of(X15,c_Int_OBit1(c_Int_OPls))) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral1) ).
fof(f9203,plain,
( ~ spl35_188
| spl35_289
| ~ spl35_38 ),
inference(avatar_split_clause,[],[f9199,f6482,f9201,f7640]) ).
fof(f6482,plain,
( spl35_38
<=> class_Fields_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_38])]) ).
fof(f9199,plain,
( ! [X0] :
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X0
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal) )
| ~ spl35_38 ),
inference(forward_subsumption_demodulation,[],[f9197,f7800]) ).
fof(f9197,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint))) = X0 )
| ~ spl35_38 ),
inference(resolution,[],[f7771,f6484]) ).
fof(f6484,plain,
( class_Fields_Ofield(tc_RealDef_Oreal)
| ~ spl35_38 ),
inference(avatar_component_clause,[],[f6482]) ).
fof(f9188,plain,
( spl35_288
| ~ spl35_31 ),
inference(avatar_split_clause,[],[f9178,f6439,f9185]) ).
fof(f9185,plain,
( spl35_288
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_288])]) ).
fof(f9178,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_31 ),
inference(resolution,[],[f6620,f6441]) ).
fof(f9100,plain,
( spl35_287
| ~ spl35_31 ),
inference(avatar_split_clause,[],[f9092,f6439,f9097]) ).
fof(f9097,plain,
( spl35_287
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_287])]) ).
fof(f9092,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_31 ),
inference(resolution,[],[f4159,f6441]) ).
fof(f9081,plain,
( spl35_286
| ~ spl35_31 ),
inference(avatar_split_clause,[],[f9041,f6439,f9078]) ).
fof(f9041,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N2____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_31 ),
inference(resolution,[],[f6441,f4079]) ).
fof(f9076,plain,
( spl35_285
| ~ spl35_31 ),
inference(avatar_split_clause,[],[f9045,f6439,f9073]) ).
fof(f9045,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),sK24(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_31 ),
inference(resolution,[],[f6441,f5301]) ).
fof(f9071,plain,
( spl35_284
| ~ spl35_31 ),
inference(avatar_split_clause,[],[f9046,f6439,f9068]) ).
fof(f9068,plain,
( spl35_284
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_284])]) ).
fof(f9046,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_31 ),
inference(resolution,[],[f6441,f5346]) ).
fof(f9066,plain,
( ~ spl35_282
| spl35_283
| ~ spl35_31 ),
inference(avatar_split_clause,[],[f9047,f6439,f9063,f9059]) ).
fof(f9047,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) = hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
| ~ spl35_31 ),
inference(resolution,[],[f6441,f5011]) ).
fof(f9057,plain,
( spl35_281
| ~ spl35_31 ),
inference(avatar_split_clause,[],[f9044,f6439,f9054]) ).
fof(f9044,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),sK30(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_31 ),
inference(resolution,[],[f6441,f5515]) ).
fof(f9052,plain,
( spl35_280
| ~ spl35_31 ),
inference(avatar_split_clause,[],[f9042,f6439,f9049]) ).
fof(f9042,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl35_31 ),
inference(resolution,[],[f6441,f4078]) ).
fof(f8926,plain,
( spl35_279
| ~ spl35_188
| ~ spl35_38 ),
inference(avatar_split_clause,[],[f8915,f6482,f7640,f8923]) ).
fof(f8923,plain,
( spl35_279
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_279])]) ).
fof(f8915,plain,
( ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_38 ),
inference(resolution,[],[f7808,f6484]) ).
fof(f7808,plain,
! [X0] :
( ~ class_Fields_Ofield(X0)
| ~ class_Int_Onumber__ring(X0)
| c_Groups_Oone__class_Oone(X0) = c_Rings_Oinverse__class_Oinverse(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(forward_subsumption_demodulation,[],[f7807,f7800]) ).
fof(f7807,plain,
! [X0] :
( c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Fields_Ofield(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f7697,f4335]) ).
fof(f7697,plain,
! [X0] :
( c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Fields_Ofield(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(backward_demodulation,[],[f6669,f4335]) ).
fof(f6669,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ class_Int_Onumber__ring(X0)
| ~ class_Fields_Ofield(X0) ),
inference(forward_demodulation,[],[f6668,f5637]) ).
fof(f6668,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))) = c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))
| ~ class_Int_Onumber__ring(X0)
| ~ class_Fields_Ofield(X0) ),
inference(forward_demodulation,[],[f5804,f5637]) ).
fof(f5804,plain,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Fields_Ofield(X0)
| c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(X0,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ),
inference(definition_unfolding,[],[f4200,f5442,f5442]) ).
fof(f4200,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)))
| ~ class_Fields_Ofield(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f2908]) ).
fof(f2908,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)))
| ~ class_Fields_Ofield(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(flattening,[],[f2907]) ).
fof(f2907,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)))
| ~ class_Fields_Ofield(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f1566]) ).
fof(f1566,plain,
! [X0] :
( ( class_Fields_Ofield(X0)
& class_Int_Onumber__ring(X0) )
=> c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(X0,c_Int_Onumber__class_Onumber__of(X0,c_Int_OBit1(c_Int_OPls))) ),
inference(rectify,[],[f262]) ).
fof(f262,axiom,
! [X15] :
( ( class_Int_Onumber__ring(X15)
& class_Fields_Ofield(X15) )
=> c_Int_Onumber__class_Onumber__of(X15,c_Int_OBit1(c_Int_OPls)) = c_Rings_Oinverse__class_Oinverse(X15,c_Int_Onumber__class_Onumber__of(X15,c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inverse__numeral__1) ).
fof(f8921,plain,
( spl35_278
| ~ spl35_92
| ~ spl35_102 ),
inference(avatar_split_clause,[],[f8916,f6933,f6857,f8918]) ).
fof(f8918,plain,
( spl35_278
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_278])]) ).
fof(f8916,plain,
( ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ spl35_102 ),
inference(resolution,[],[f7808,f6935]) ).
fof(f8891,plain,
( spl35_277
| ~ spl35_256 ),
inference(avatar_split_clause,[],[f8886,f8477,f8888]) ).
fof(f8888,plain,
( spl35_277
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_277])]) ).
fof(f8886,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f8885,f5637]) ).
fof(f8885,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_256 ),
inference(forward_demodulation,[],[f8883,f5723]) ).
fof(f8883,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_256 ),
inference(resolution,[],[f5784,f8479]) ).
fof(f8814,plain,
( spl35_276
| ~ spl35_92 ),
inference(avatar_split_clause,[],[f8809,f6857,f8811]) ).
fof(f8809,plain,
( c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_92 ),
inference(resolution,[],[f6859,f7800]) ).
fof(f8789,plain,
( spl35_274
| spl35_275
| ~ spl35_48
| ~ spl35_49 ),
inference(avatar_split_clause,[],[f8780,f6566,f6556,f8786,f8782]) ).
fof(f8786,plain,
( spl35_275
<=> c_Int_OPls = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_275])]) ).
fof(f8780,plain,
( c_Int_OPls = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl35_48
| ~ spl35_49 ),
inference(forward_demodulation,[],[f8779,f6568]) ).
fof(f8779,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls))
| c_Int_OPls = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls)
| ~ spl35_48 ),
inference(resolution,[],[f4679,f8329]) ).
fof(f8771,plain,
( ~ spl35_272
| spl35_273
| spl35_42 ),
inference(avatar_split_clause,[],[f8762,f6522,f8768,f8764]) ).
fof(f8764,plain,
( spl35_272
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_272])]) ).
fof(f8768,plain,
( spl35_273
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_273])]) ).
fof(f6522,plain,
( spl35_42
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_42])]) ).
fof(f8762,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| spl35_42 ),
inference(resolution,[],[f4559,f6524]) ).
fof(f6524,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| spl35_42 ),
inference(avatar_component_clause,[],[f6522]) ).
fof(f8717,plain,
~ spl35_271,
inference(avatar_split_clause,[],[f8711,f8713]) ).
fof(f8711,plain,
c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),
inference(superposition,[],[f5826,f4931]) ).
fof(f8716,plain,
~ spl35_271,
inference(avatar_split_clause,[],[f8710,f8713]) ).
fof(f8710,plain,
c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),
inference(superposition,[],[f5826,f4931]) ).
fof(f8695,plain,
( spl35_270
| ~ spl35_268
| ~ spl35_269 ),
inference(avatar_split_clause,[],[f8690,f8686,f8681,f8692]) ).
fof(f8692,plain,
( spl35_270
<=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_270])]) ).
fof(f8686,plain,
( spl35_269
<=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_269])]) ).
fof(f8690,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl35_268
| ~ spl35_269 ),
inference(backward_demodulation,[],[f8688,f8683]) ).
fof(f8688,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_269 ),
inference(avatar_component_clause,[],[f8686]) ).
fof(f8689,plain,
spl35_269,
inference(avatar_split_clause,[],[f8679,f8686]) ).
fof(f8679,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(resolution,[],[f4631,f4343]) ).
fof(f8684,plain,
spl35_268,
inference(avatar_split_clause,[],[f8677,f8681]) ).
fof(f8677,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(resolution,[],[f4631,f6122]) ).
fof(f8623,plain,
( spl35_267
| ~ spl35_187 ),
inference(avatar_split_clause,[],[f8613,f7635,f8620]) ).
fof(f8613,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18)
| ~ spl35_187 ),
inference(resolution,[],[f4806,f7637]) ).
fof(f8618,plain,
( spl35_266
| ~ spl35_183 ),
inference(avatar_split_clause,[],[f8612,f7592,f8615]) ).
fof(f8612,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14)
| ~ spl35_183 ),
inference(resolution,[],[f4806,f7594]) ).
fof(f8601,plain,
( spl35_265
| ~ spl35_48
| ~ spl35_90 ),
inference(avatar_split_clause,[],[f8596,f6847,f6556,f8598]) ).
fof(f6847,plain,
( spl35_90
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_90])]) ).
fof(f8596,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_48
| ~ spl35_90 ),
inference(forward_demodulation,[],[f6849,f6558]) ).
fof(f6849,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_90 ),
inference(avatar_component_clause,[],[f6847]) ).
fof(f8594,plain,
( spl35_264
| ~ spl35_141 ),
inference(avatar_split_clause,[],[f8589,f7170,f8591]) ).
fof(f7170,plain,
( spl35_141
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_141])]) ).
fof(f8589,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_141 ),
inference(forward_demodulation,[],[f8588,f7524]) ).
fof(f7524,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)),
inference(forward_demodulation,[],[f7523,f4750]) ).
fof(f7523,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)),
inference(forward_demodulation,[],[f5385,f4750]) ).
fof(f5385,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(cnf_transformation,[],[f1540]) ).
fof(f1540,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X0))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(rectify,[],[f222]) ).
fof(f222,axiom,
! [X36,X10] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X36))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X36,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(f8588,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_141 ),
inference(forward_demodulation,[],[f7172,f7524]) ).
fof(f7172,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_141 ),
inference(avatar_component_clause,[],[f7170]) ).
fof(f8578,plain,
( spl35_263
| ~ spl35_6
| ~ spl35_48 ),
inference(avatar_split_clause,[],[f8573,f6556,f6281,f8575]) ).
fof(f6281,plain,
( spl35_6
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_6])]) ).
fof(f8573,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_6
| ~ spl35_48 ),
inference(forward_demodulation,[],[f8572,f6558]) ).
fof(f8572,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8571,f4335]) ).
fof(f8571,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8570,f5723]) ).
fof(f8570,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8569,f5723]) ).
fof(f8569,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8568,f5637]) ).
fof(f8568,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8567,f4335]) ).
fof(f8567,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8566,f5723]) ).
fof(f8566,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8565,f5723]) ).
fof(f8565,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8564,f5637]) ).
fof(f8564,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8563,f4335]) ).
fof(f8563,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8562,f5723]) ).
fof(f8562,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8561,f5723]) ).
fof(f8561,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8560,f5637]) ).
fof(f8560,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8559,f4335]) ).
fof(f8559,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8558,f5723]) ).
fof(f8558,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8557,f5723]) ).
fof(f8557,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8556,f5537]) ).
fof(f8556,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8555,f5723]) ).
fof(f8555,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f8554,f5723]) ).
fof(f8554,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ spl35_6 ),
inference(forward_demodulation,[],[f6283,f5637]) ).
fof(f6283,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
| ~ spl35_6 ),
inference(avatar_component_clause,[],[f6281]) ).
fof(f8552,plain,
( spl35_262
| ~ spl35_23 ),
inference(avatar_split_clause,[],[f8547,f6394,f8549]) ).
fof(f8549,plain,
( spl35_262
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_262])]) ).
fof(f6394,plain,
( spl35_23
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_23])]) ).
fof(f8547,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))
| ~ spl35_23 ),
inference(forward_demodulation,[],[f8546,f5992]) ).
fof(f8546,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))
| ~ spl35_23 ),
inference(forward_demodulation,[],[f6396,f5992]) ).
fof(f6396,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))
| ~ spl35_23 ),
inference(avatar_component_clause,[],[f6394]) ).
fof(f8545,plain,
( spl35_261
| ~ spl35_37 ),
inference(avatar_split_clause,[],[f8540,f6476,f8542]) ).
fof(f6476,plain,
( spl35_37
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_37])]) ).
fof(f8540,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))
| ~ spl35_37 ),
inference(forward_demodulation,[],[f6478,f7524]) ).
fof(f6478,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))
| ~ spl35_37 ),
inference(avatar_component_clause,[],[f6476]) ).
fof(f8539,plain,
( spl35_260
| ~ spl35_4 ),
inference(avatar_split_clause,[],[f8534,f6270,f8536]) ).
fof(f6270,plain,
( spl35_4
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_4])]) ).
fof(f8534,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8533,f4335]) ).
fof(f8533,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8532,f5723]) ).
fof(f8532,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8531,f5637]) ).
fof(f8531,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8530,f4335]) ).
fof(f8530,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8529,f5723]) ).
fof(f8529,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8528,f5637]) ).
fof(f8528,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8527,f4335]) ).
fof(f8527,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8526,f5723]) ).
fof(f8526,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8525,f5637]) ).
fof(f8525,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8524,f4335]) ).
fof(f8524,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8523,f5723]) ).
fof(f8523,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8522,f5537]) ).
fof(f8522,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f8521,f5723]) ).
fof(f8521,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(forward_demodulation,[],[f6272,f7524]) ).
fof(f6272,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK12))
| ~ spl35_4 ),
inference(avatar_component_clause,[],[f6270]) ).
fof(f8520,plain,
( spl35_259
| ~ spl35_89 ),
inference(avatar_split_clause,[],[f8515,f6839,f8517]) ).
fof(f6839,plain,
( spl35_89
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_89])]) ).
fof(f8515,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8514,f4335]) ).
fof(f8514,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8513,f5723]) ).
fof(f8513,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8512,f5723]) ).
fof(f8512,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8511,f4335]) ).
fof(f8511,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8510,f5723]) ).
fof(f8510,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8509,f5723]) ).
fof(f8509,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8508,f4335]) ).
fof(f8508,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8507,f5723]) ).
fof(f8507,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f8506,f4335]) ).
fof(f8506,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl35_89 ),
inference(forward_demodulation,[],[f6841,f5723]) ).
fof(f6841,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_89 ),
inference(avatar_component_clause,[],[f6839]) ).
fof(f8504,plain,
( spl35_258
| ~ spl35_179 ),
inference(avatar_split_clause,[],[f8499,f7572,f8501]) ).
fof(f7572,plain,
( spl35_179
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_179])]) ).
fof(f8499,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_179 ),
inference(forward_demodulation,[],[f8498,f4335]) ).
fof(f8498,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_179 ),
inference(forward_demodulation,[],[f8497,f4335]) ).
fof(f8497,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_179 ),
inference(forward_demodulation,[],[f8496,f4335]) ).
fof(f8496,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_179 ),
inference(forward_demodulation,[],[f7574,f4335]) ).
fof(f7574,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl35_179 ),
inference(avatar_component_clause,[],[f7572]) ).
fof(f8494,plain,
( spl35_257
| ~ spl35_97 ),
inference(avatar_split_clause,[],[f8489,f6897,f8491]) ).
fof(f6897,plain,
( spl35_97
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_97])]) ).
fof(f8489,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f8488,f4335]) ).
fof(f8488,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f8487,f5723]) ).
fof(f8487,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f8486,f4335]) ).
fof(f8486,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f8485,f5723]) ).
fof(f8485,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f8484,f4335]) ).
fof(f8484,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f8483,f5723]) ).
fof(f8483,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f8482,f4335]) ).
fof(f8482,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f8481,f5723]) ).
fof(f8481,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(forward_demodulation,[],[f6899,f7524]) ).
fof(f6899,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25))
| ~ spl35_97 ),
inference(avatar_component_clause,[],[f6897]) ).
fof(f8480,plain,
( spl35_256
| ~ spl35_40
| ~ spl35_48 ),
inference(avatar_split_clause,[],[f8475,f6556,f6508,f8477]) ).
fof(f6508,plain,
( spl35_40
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_40])]) ).
fof(f8475,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_40
| ~ spl35_48 ),
inference(forward_demodulation,[],[f8474,f6558]) ).
fof(f8474,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_40 ),
inference(forward_demodulation,[],[f8473,f4335]) ).
fof(f8473,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_40 ),
inference(forward_demodulation,[],[f8472,f5723]) ).
fof(f8472,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_40 ),
inference(forward_demodulation,[],[f8471,f4335]) ).
fof(f8471,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_40 ),
inference(forward_demodulation,[],[f8470,f5723]) ).
fof(f8470,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_40 ),
inference(forward_demodulation,[],[f8469,f4335]) ).
fof(f8469,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_40 ),
inference(forward_demodulation,[],[f8468,f5723]) ).
fof(f8468,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_40 ),
inference(forward_demodulation,[],[f8467,f4335]) ).
fof(f8467,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_40 ),
inference(forward_demodulation,[],[f6510,f5723]) ).
fof(f6510,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_40 ),
inference(avatar_component_clause,[],[f6508]) ).
fof(f8466,plain,
( spl35_255
| ~ spl35_3 ),
inference(avatar_split_clause,[],[f8461,f6261,f8463]) ).
fof(f6261,plain,
( spl35_3
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_3])]) ).
fof(f8461,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8460,f7524]) ).
fof(f8460,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8459,f4335]) ).
fof(f8459,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8458,f5723]) ).
fof(f8458,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8457,f5637]) ).
fof(f8457,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8456,f4335]) ).
fof(f8456,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8455,f5723]) ).
fof(f8455,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8454,f5637]) ).
fof(f8454,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8453,f4335]) ).
fof(f8453,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8452,f5723]) ).
fof(f8452,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8451,f5637]) ).
fof(f8451,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8450,f4335]) ).
fof(f8450,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8449,f5723]) ).
fof(f8449,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f8448,f5537]) ).
fof(f8448,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_3 ),
inference(forward_demodulation,[],[f6263,f5723]) ).
fof(f6263,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl35_3 ),
inference(avatar_component_clause,[],[f6261]) ).
fof(f8447,plain,
( spl35_254
| ~ spl35_53 ),
inference(avatar_split_clause,[],[f8442,f6592,f8444]) ).
fof(f8444,plain,
( spl35_254
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_254])]) ).
fof(f6592,plain,
( spl35_53
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_53])]) ).
fof(f8442,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_53 ),
inference(forward_demodulation,[],[f8441,f4335]) ).
fof(f8441,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_53 ),
inference(forward_demodulation,[],[f8440,f5723]) ).
fof(f8440,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_53 ),
inference(forward_demodulation,[],[f8439,f4335]) ).
fof(f8439,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_53 ),
inference(forward_demodulation,[],[f8438,f5723]) ).
fof(f8438,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_53 ),
inference(forward_demodulation,[],[f8437,f4335]) ).
fof(f8437,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_53 ),
inference(forward_demodulation,[],[f8436,f5723]) ).
fof(f8436,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_53 ),
inference(forward_demodulation,[],[f8435,f4335]) ).
fof(f8435,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_53 ),
inference(forward_demodulation,[],[f6594,f5723]) ).
fof(f6594,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_53 ),
inference(avatar_component_clause,[],[f6592]) ).
fof(f8434,plain,
( spl35_253
| ~ spl35_48
| ~ spl35_225 ),
inference(avatar_split_clause,[],[f8429,f8098,f6556,f8431]) ).
fof(f8431,plain,
( spl35_253
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_253])]) ).
fof(f8098,plain,
( spl35_225
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_225])]) ).
fof(f8429,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_48
| ~ spl35_225 ),
inference(forward_demodulation,[],[f8100,f6558]) ).
fof(f8100,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_225 ),
inference(avatar_component_clause,[],[f8098]) ).
fof(f8428,plain,
( spl35_244
| ~ spl35_96 ),
inference(avatar_split_clause,[],[f8427,f6885,f8267]) ).
fof(f6885,plain,
( spl35_96
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_96])]) ).
fof(f8427,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_96 ),
inference(forward_demodulation,[],[f8426,f4335]) ).
fof(f8426,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_96 ),
inference(forward_demodulation,[],[f8425,f5723]) ).
fof(f8425,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_96 ),
inference(forward_demodulation,[],[f8424,f4335]) ).
fof(f8424,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_96 ),
inference(forward_demodulation,[],[f8423,f5723]) ).
fof(f8423,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_96 ),
inference(forward_demodulation,[],[f8422,f4335]) ).
fof(f8422,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_96 ),
inference(forward_demodulation,[],[f8421,f5723]) ).
fof(f8421,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_96 ),
inference(forward_demodulation,[],[f8420,f4335]) ).
fof(f8420,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_96 ),
inference(forward_demodulation,[],[f6887,f5723]) ).
fof(f6887,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_96 ),
inference(avatar_component_clause,[],[f6885]) ).
fof(f8419,plain,
( ~ spl35_252
| ~ spl35_48
| spl35_228 ),
inference(avatar_split_clause,[],[f8414,f8129,f6556,f8416]) ).
fof(f8416,plain,
( spl35_252
<=> c_Int_OPls = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_252])]) ).
fof(f8129,plain,
( spl35_228
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_228])]) ).
fof(f8414,plain,
( c_Int_OPls != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ spl35_48
| spl35_228 ),
inference(forward_demodulation,[],[f8131,f6558]) ).
fof(f8131,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| spl35_228 ),
inference(avatar_component_clause,[],[f8129]) ).
fof(f8412,plain,
( spl35_251
| ~ spl35_84 ),
inference(avatar_split_clause,[],[f8407,f6799,f8409]) ).
fof(f6799,plain,
( spl35_84
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_84])]) ).
fof(f8407,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f8406,f7524]) ).
fof(f8406,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f8405,f4335]) ).
fof(f8405,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f8404,f5723]) ).
fof(f8404,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f8403,f4335]) ).
fof(f8403,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f8402,f5723]) ).
fof(f8402,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f8401,f4335]) ).
fof(f8401,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f8400,f5723]) ).
fof(f8400,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f8399,f4335]) ).
fof(f8399,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl35_84 ),
inference(forward_demodulation,[],[f6801,f5723]) ).
fof(f6801,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl35_84 ),
inference(avatar_component_clause,[],[f6799]) ).
fof(f8398,plain,
( spl35_250
| ~ spl35_47 ),
inference(avatar_split_clause,[],[f8393,f6551,f8395]) ).
fof(f8395,plain,
( spl35_250
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_250])]) ).
fof(f6551,plain,
( spl35_47
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_47])]) ).
fof(f8393,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_47 ),
inference(forward_demodulation,[],[f8392,f5992]) ).
fof(f8392,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_47 ),
inference(forward_demodulation,[],[f6553,f5992]) ).
fof(f6553,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
| ~ spl35_47 ),
inference(avatar_component_clause,[],[f6551]) ).
fof(f8391,plain,
( spl35_249
| ~ spl35_122 ),
inference(avatar_split_clause,[],[f8386,f7041,f8388]) ).
fof(f7041,plain,
( spl35_122
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_122])]) ).
fof(f8386,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))
| ~ spl35_122 ),
inference(forward_demodulation,[],[f7043,f7524]) ).
fof(f7043,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))
| ~ spl35_122 ),
inference(avatar_component_clause,[],[f7041]) ).
fof(f8385,plain,
( spl35_230
| ~ spl35_123 ),
inference(avatar_split_clause,[],[f8384,f7053,f8146]) ).
fof(f7053,plain,
( spl35_123
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_123])]) ).
fof(f8384,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_123 ),
inference(forward_demodulation,[],[f8383,f4335]) ).
fof(f8383,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_123 ),
inference(forward_demodulation,[],[f7055,f4335]) ).
fof(f7055,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_123 ),
inference(avatar_component_clause,[],[f7053]) ).
fof(f8373,plain,
( spl35_248
| ~ spl35_48
| ~ spl35_78 ),
inference(avatar_split_clause,[],[f8349,f6758,f6556,f8370]) ).
fof(f6758,plain,
( spl35_78
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_78])]) ).
fof(f8349,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_48
| ~ spl35_78 ),
inference(backward_demodulation,[],[f6760,f6558]) ).
fof(f6760,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl35_78 ),
inference(avatar_component_clause,[],[f6758]) ).
fof(f8320,plain,
( spl35_247
| ~ spl35_26 ),
inference(avatar_split_clause,[],[f8315,f6413,f8317]) ).
fof(f6413,plain,
( spl35_26
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_26])]) ).
fof(f8315,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8314,f4335]) ).
fof(f8314,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8313,f5723]) ).
fof(f8313,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8312,f4335]) ).
fof(f8312,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8311,f5723]) ).
fof(f8311,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8310,f4335]) ).
fof(f8310,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8309,f5723]) ).
fof(f8309,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8308,f4335]) ).
fof(f8308,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8307,f5723]) ).
fof(f8307,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f8306,f7524]) ).
fof(f8306,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl35_26 ),
inference(forward_demodulation,[],[f6415,f5992]) ).
fof(f6415,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl35_26 ),
inference(avatar_component_clause,[],[f6413]) ).
fof(f8305,plain,
( spl35_244
| ~ spl35_58 ),
inference(avatar_split_clause,[],[f8304,f6627,f8267]) ).
fof(f6627,plain,
( spl35_58
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_58])]) ).
fof(f8304,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8303,f4335]) ).
fof(f8303,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8302,f5723]) ).
fof(f8302,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8301,f4335]) ).
fof(f8301,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8300,f5723]) ).
fof(f8300,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8299,f4335]) ).
fof(f8299,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8298,f5723]) ).
fof(f8298,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8297,f6110]) ).
fof(f8297,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8296,f5615]) ).
fof(f8296,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f8295,f4335]) ).
fof(f8295,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_58 ),
inference(forward_demodulation,[],[f6629,f5723]) ).
fof(f6629,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_58 ),
inference(avatar_component_clause,[],[f6627]) ).
fof(f8294,plain,
( spl35_246
| ~ spl35_143 ),
inference(avatar_split_clause,[],[f8289,f7193,f8291]) ).
fof(f7193,plain,
( spl35_143
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_143])]) ).
fof(f8289,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_143 ),
inference(forward_demodulation,[],[f8288,f7524]) ).
fof(f8288,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ spl35_143 ),
inference(forward_demodulation,[],[f7195,f5992]) ).
fof(f7195,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
| ~ spl35_143 ),
inference(avatar_component_clause,[],[f7193]) ).
fof(f8287,plain,
( spl35_245
| ~ spl35_101 ),
inference(avatar_split_clause,[],[f8282,f6928,f8284]) ).
fof(f6928,plain,
( spl35_101
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_101])]) ).
fof(f8282,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8281,f5992]) ).
fof(f8281,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8280,f7524]) ).
fof(f8280,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8279,f4335]) ).
fof(f8279,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8278,f5723]) ).
fof(f8278,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8277,f4335]) ).
fof(f8277,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8276,f5723]) ).
fof(f8276,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8275,f4335]) ).
fof(f8275,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8274,f5723]) ).
fof(f8274,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f8273,f4335]) ).
fof(f8273,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl35_101 ),
inference(forward_demodulation,[],[f6930,f5723]) ).
fof(f6930,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl35_101 ),
inference(avatar_component_clause,[],[f6928]) ).
fof(f8270,plain,
spl35_244,
inference(avatar_split_clause,[],[f8265,f8267]) ).
fof(f8265,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f8264,f4335]) ).
fof(f8264,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f8263,f5723]) ).
fof(f8263,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f8262,f5637]) ).
fof(f8262,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),
inference(forward_demodulation,[],[f8261,f4335]) ).
fof(f8261,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),
inference(forward_demodulation,[],[f8260,f5723]) ).
fof(f8260,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),
inference(forward_demodulation,[],[f8259,f5637]) ).
fof(f8259,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f8258,f4335]) ).
fof(f8258,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f8257,f5723]) ).
fof(f8257,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f8256,f5637]) ).
fof(f8256,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f8255,f4335]) ).
fof(f8255,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f8254,f5723]) ).
fof(f8254,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f8253,f5537]) ).
fof(f8253,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f8252,f6110]) ).
fof(f8252,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f8251,f5615]) ).
fof(f8251,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f8250,f5023]) ).
fof(f8250,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(forward_demodulation,[],[f6035,f5723]) ).
fof(f6035,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(definition_unfolding,[],[f5600,f4431,f5442,f4497,f4497]) ).
fof(f5600,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f551]) ).
fof(f551,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
fof(f8249,plain,
spl35_243,
inference(avatar_split_clause,[],[f4241,f8246]) ).
fof(f8246,plain,
( spl35_243
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_243])]) ).
fof(f4241,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1058]) ).
fof(f1058,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f8243,plain,
spl35_242,
inference(avatar_split_clause,[],[f5389,f8240]) ).
fof(f8240,plain,
( spl35_242
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_242])]) ).
fof(f5389,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f8237,plain,
spl35_35,
inference(avatar_split_clause,[],[f6136,f6464]) ).
fof(f6136,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f4883]) ).
fof(f4883,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3522]) ).
fof(f3522,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealDef_Oreal(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f1369]) ).
fof(f1369,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X50] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,X50)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X50 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(f8236,plain,
spl35_241,
inference(avatar_split_clause,[],[f5231,f8233]) ).
fof(f8233,plain,
( spl35_241
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_241])]) ).
fof(f5231,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f999]) ).
fof(f999,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f8231,plain,
spl35_240,
inference(avatar_split_clause,[],[f4571,f8228]) ).
fof(f8228,plain,
( spl35_240
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_240])]) ).
fof(f4571,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1033]) ).
fof(f1033,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f8226,plain,
spl35_239,
inference(avatar_split_clause,[],[f8221,f8223]) ).
fof(f8223,plain,
( spl35_239
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_239])]) ).
fof(f8221,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),
inference(forward_demodulation,[],[f6009,f5992]) ).
fof(f6009,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
inference(definition_unfolding,[],[f5380,f4497]) ).
fof(f5380,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
inference(cnf_transformation,[],[f229]) ).
fof(f229,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th32) ).
fof(f8208,plain,
spl35_238,
inference(avatar_split_clause,[],[f5306,f8205]) ).
fof(f8205,plain,
( spl35_238
<=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_238])]) ).
fof(f5306,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1086]) ).
fof(f1086,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(f8203,plain,
spl35_237,
inference(avatar_split_clause,[],[f4239,f8200]) ).
fof(f8200,plain,
( spl35_237
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_237])]) ).
fof(f4239,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1017]) ).
fof(f1017,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f8197,plain,
spl35_236,
inference(avatar_split_clause,[],[f4726,f8194]) ).
fof(f8194,plain,
( spl35_236
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_236])]) ).
fof(f4726,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1152]) ).
fof(f1152,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f8192,plain,
spl35_235,
inference(avatar_split_clause,[],[f5388,f8189]) ).
fof(f8189,plain,
( spl35_235
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_235])]) ).
fof(f5388,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1050]) ).
fof(f1050,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f8187,plain,
spl35_234,
inference(avatar_split_clause,[],[f4085,f8184]) ).
fof(f8184,plain,
( spl35_234
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_234])]) ).
fof(f4085,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1032]) ).
fof(f1032,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f8182,plain,
spl35_233,
inference(avatar_split_clause,[],[f4418,f8179]) ).
fof(f8179,plain,
( spl35_233
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_233])]) ).
fof(f4418,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1138]) ).
fof(f1138,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f8177,plain,
spl35_232,
inference(avatar_split_clause,[],[f5417,f8174]) ).
fof(f8174,plain,
( spl35_232
<=> class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_232])]) ).
fof(f5417,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1145]) ).
fof(f1145,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(f8172,plain,
spl35_231,
inference(avatar_split_clause,[],[f5225,f8169]) ).
fof(f8169,plain,
( spl35_231
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_231])]) ).
fof(f5225,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1142]) ).
fof(f1142,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f8149,plain,
spl35_230,
inference(avatar_split_clause,[],[f8144,f8146]) ).
fof(f8144,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f8143,f4335]) ).
fof(f8143,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f8142,f5637]) ).
fof(f8142,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)),
inference(forward_demodulation,[],[f8141,f4335]) ).
fof(f8141,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),
inference(forward_demodulation,[],[f5963,f5637]) ).
fof(f5963,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(definition_unfolding,[],[f5062,f5442]) ).
fof(f5062,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f473]) ).
fof(f473,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).
fof(f8137,plain,
spl35_229,
inference(avatar_split_clause,[],[f4998,f8134]) ).
fof(f8134,plain,
( spl35_229
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_229])]) ).
fof(f4998,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1025]) ).
fof(f1025,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f8132,plain,
~ spl35_228,
inference(avatar_split_clause,[],[f5736,f8129]) ).
fof(f5736,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f292]) ).
fof(f292,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f8115,plain,
spl35_48,
inference(avatar_split_clause,[],[f8114,f6556]) ).
fof(f8114,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(forward_demodulation,[],[f5044,f4248]) ).
fof(f4248,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
inference(cnf_transformation,[],[f1280]) ).
fof(f1280,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
inference(rectify,[],[f239]) ).
fof(f239,axiom,
! [X20] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X20) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f5044,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
inference(cnf_transformation,[],[f246]) ).
fof(f246,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
fof(f8113,plain,
spl35_227,
inference(avatar_split_clause,[],[f4827,f8110]) ).
fof(f8110,plain,
( spl35_227
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_227])]) ).
fof(f4827,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1141]) ).
fof(f1141,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f8107,plain,
spl35_226,
inference(avatar_split_clause,[],[f5450,f8104]) ).
fof(f8104,plain,
( spl35_226
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_226])]) ).
fof(f5450,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1021]) ).
fof(f1021,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f8101,plain,
spl35_225,
inference(avatar_split_clause,[],[f6155,f8098]) ).
fof(f6155,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_resolution,[],[f5083]) ).
fof(f5083,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(cnf_transformation,[],[f3647]) ).
fof(f3647,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ),
inference(nnf_transformation,[],[f1681]) ).
fof(f1681,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(rectify,[],[f294]) ).
fof(f294,axiom,
! [X11] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X11
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X11),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(f8096,plain,
spl35_224,
inference(avatar_split_clause,[],[f4956,f8093]) ).
fof(f8093,plain,
( spl35_224
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_224])]) ).
fof(f4956,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1026]) ).
fof(f1026,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f8091,plain,
spl35_223,
inference(avatar_split_clause,[],[f4348,f8088]) ).
fof(f8088,plain,
( spl35_223
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_223])]) ).
fof(f4348,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1093]) ).
fof(f1093,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f8085,plain,
spl35_222,
inference(avatar_split_clause,[],[f4725,f8082]) ).
fof(f8082,plain,
( spl35_222
<=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_222])]) ).
fof(f4725,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1149]) ).
fof(f1149,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(f8074,plain,
spl35_221,
inference(avatar_split_clause,[],[f4885,f8071]) ).
fof(f8071,plain,
( spl35_221
<=> class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_221])]) ).
fof(f4885,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1117]) ).
fof(f1117,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(f8068,plain,
spl35_220,
inference(avatar_split_clause,[],[f4728,f8065]) ).
fof(f8065,plain,
( spl35_220
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_220])]) ).
fof(f4728,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f1056]) ).
fof(f1056,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f8063,plain,
spl35_219,
inference(avatar_split_clause,[],[f4705,f8060]) ).
fof(f8060,plain,
( spl35_219
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_219])]) ).
fof(f4705,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1059]) ).
fof(f1059,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f8058,plain,
spl35_218,
inference(avatar_split_clause,[],[f4964,f8055]) ).
fof(f8055,plain,
( spl35_218
<=> class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_218])]) ).
fof(f4964,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1148]) ).
fof(f1148,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(f8053,plain,
spl35_217,
inference(avatar_split_clause,[],[f4810,f8050]) ).
fof(f8050,plain,
( spl35_217
<=> class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_217])]) ).
fof(f4810,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1144]) ).
fof(f1144,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(f8048,plain,
spl35_216,
inference(avatar_split_clause,[],[f5319,f8045]) ).
fof(f8045,plain,
( spl35_216
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_216])]) ).
fof(f5319,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(f8043,plain,
spl35_215,
inference(avatar_split_clause,[],[f4032,f8040]) ).
fof(f8040,plain,
( spl35_215
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_215])]) ).
fof(f4032,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f1002]) ).
fof(f1002,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(f8038,plain,
~ spl35_214,
inference(avatar_split_clause,[],[f8033,f8035]) ).
fof(f8033,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8032,f7524]) ).
fof(f8032,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8031,f4335]) ).
fof(f8031,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8030,f5723]) ).
fof(f8030,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8029,f5637]) ).
fof(f8029,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8028,f4335]) ).
fof(f8028,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8027,f5723]) ).
fof(f8027,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8026,f5637]) ).
fof(f8026,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8025,f4335]) ).
fof(f8025,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8024,f5723]) ).
fof(f8024,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8023,f5637]) ).
fof(f8023,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8022,f4335]) ).
fof(f8022,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8021,f5723]) ).
fof(f8021,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8020,f5537]) ).
fof(f8020,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f8019,f5723]) ).
fof(f8019,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f5922,f7524]) ).
fof(f5922,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(definition_unfolding,[],[f4848,f4431,f5442,f4431,f5442]) ).
fof(f4848,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(cnf_transformation,[],[f1281]) ).
fof(f1281,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(flattening,[],[f1172]) ).
fof(f1172,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(negated_conjecture,[],[f1171]) ).
fof(f1171,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f8018,plain,
spl35_213,
inference(avatar_split_clause,[],[f5098,f8015]) ).
fof(f8015,plain,
( spl35_213
<=> class_Rings_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_213])]) ).
fof(f5098,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1126]) ).
fof(f1126,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(f8013,plain,
spl35_212,
inference(avatar_split_clause,[],[f5308,f8010]) ).
fof(f8010,plain,
( spl35_212
<=> class_Rings_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_212])]) ).
fof(f5308,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1160]) ).
fof(f1160,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(f8008,plain,
spl35_211,
inference(avatar_split_clause,[],[f5001,f8005]) ).
fof(f8005,plain,
( spl35_211
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_211])]) ).
fof(f5001,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1074]) ).
fof(f1074,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f7996,plain,
spl35_210,
inference(avatar_split_clause,[],[f5744,f7993]) ).
fof(f7993,plain,
( spl35_210
<=> class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_210])]) ).
fof(f5744,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(f7990,plain,
spl35_209,
inference(avatar_split_clause,[],[f4300,f7987]) ).
fof(f7987,plain,
( spl35_209
<=> class_Groups_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_209])]) ).
fof(f4300,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1116]) ).
fof(f1116,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(f7985,plain,
~ spl35_208,
inference(avatar_split_clause,[],[f5526,f7982]) ).
fof(f5526,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f244]) ).
fof(f244,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(f7973,plain,
~ spl35_207,
inference(avatar_split_clause,[],[f4461,f7970]) ).
fof(f7970,plain,
( spl35_207
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_207])]) ).
fof(f4461,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f254]) ).
fof(f254,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(f7968,plain,
spl35_206,
inference(avatar_split_clause,[],[f7963,f7965]) ).
fof(f7963,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7962,f4335]) ).
fof(f7962,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7961,f5723]) ).
fof(f7961,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7960,f5637]) ).
fof(f7960,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7959,f4335]) ).
fof(f7959,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7958,f5723]) ).
fof(f7958,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7957,f5637]) ).
fof(f7957,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7956,f4335]) ).
fof(f7956,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7955,f5723]) ).
fof(f7955,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7954,f5637]) ).
fof(f7954,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7953,f4335]) ).
fof(f7953,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7952,f5723]) ).
fof(f7952,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7951,f5537]) ).
fof(f7951,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f7950,f5723]) ).
fof(f7950,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(forward_demodulation,[],[f5910,f7524]) ).
fof(f5910,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(definition_unfolding,[],[f4768,f4431,f5442]) ).
fof(f4768,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_N2) ).
fof(f7943,plain,
spl35_205,
inference(avatar_split_clause,[],[f4566,f7940]) ).
fof(f7940,plain,
( spl35_205
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_205])]) ).
fof(f4566,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1049]) ).
fof(f1049,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f7938,plain,
spl35_204,
inference(avatar_split_clause,[],[f5613,f7935]) ).
fof(f7935,plain,
( spl35_204
<=> class_Rings_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_204])]) ).
fof(f5613,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1114]) ).
fof(f1114,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(f7933,plain,
spl35_203,
inference(avatar_split_clause,[],[f4866,f7930]) ).
fof(f7930,plain,
( spl35_203
<=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_203])]) ).
fof(f4866,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(f7928,plain,
spl35_202,
inference(avatar_split_clause,[],[f4266,f7925]) ).
fof(f7925,plain,
( spl35_202
<=> class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_202])]) ).
fof(f4266,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1095]) ).
fof(f1095,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(f7923,plain,
spl35_201,
inference(avatar_split_clause,[],[f4706,f7920]) ).
fof(f4706,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(f7918,plain,
spl35_200,
inference(avatar_split_clause,[],[f4832,f7915]) ).
fof(f7915,plain,
( spl35_200
<=> class_Groups_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_200])]) ).
fof(f4832,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1121]) ).
fof(f1121,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(f7913,plain,
spl35_199,
inference(avatar_split_clause,[],[f4769,f7910]) ).
fof(f7910,plain,
( spl35_199
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_199])]) ).
fof(f4769,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1035]) ).
fof(f1035,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(f7904,plain,
spl35_198,
inference(avatar_split_clause,[],[f5293,f7901]) ).
fof(f5293,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f243]) ).
fof(f243,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).
fof(f7899,plain,
( ~ spl35_195
| ~ spl35_196
| spl35_197 ),
inference(avatar_split_clause,[],[f7886,f7896,f7892,f7888]) ).
fof(f7886,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7885,f4335]) ).
fof(f7885,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7884,f5723]) ).
fof(f7884,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7883,f4335]) ).
fof(f7883,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7882,f5637]) ).
fof(f7882,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7881,f4335]) ).
fof(f7881,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7880,f5723]) ).
fof(f7880,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7879,f5637]) ).
fof(f7879,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7878,f4335]) ).
fof(f7878,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7877,f5723]) ).
fof(f7877,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7876,f5723]) ).
fof(f7876,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7875,f5637]) ).
fof(f7875,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7874,f5023]) ).
fof(f7874,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7873,f5637]) ).
fof(f7873,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7872,f4335]) ).
fof(f7872,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7871,f5723]) ).
fof(f7871,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7870,f5615]) ).
fof(f7870,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7869,f5637]) ).
fof(f7869,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7868,f4335]) ).
fof(f7868,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7867,f4335]) ).
fof(f7867,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7866,f5723]) ).
fof(f7866,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7865,f5723]) ).
fof(f7865,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7864,f5637]) ).
fof(f7864,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7863,f5537]) ).
fof(f7863,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7862,f4335]) ).
fof(f7862,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7861,f4335]) ).
fof(f7861,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7860,f5723]) ).
fof(f7860,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7859,f5637]) ).
fof(f7859,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7858,f5723]) ).
fof(f7858,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7857,f5637]) ).
fof(f7857,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7856,f4335]) ).
fof(f7856,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7855,f5723]) ).
fof(f7855,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7854,f5723]) ).
fof(f7854,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7853,f5637]) ).
fof(f7853,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7852,f4335]) ).
fof(f7852,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7851,f5723]) ).
fof(f7851,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7850,f4335]) ).
fof(f7850,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7849,f7524]) ).
fof(f7849,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7848,f5723]) ).
fof(f7848,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7847,f5537]) ).
fof(f7847,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7846,f5723]) ).
fof(f7846,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ),
inference(forward_demodulation,[],[f7845,f5537]) ).
fof(f7845,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7844,f5023]) ).
fof(f7844,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_N2____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f7843,f5615]) ).
fof(f7843,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7842,f5723]) ).
fof(f7842,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))) ),
inference(forward_demodulation,[],[f7841,f7524]) ).
fof(f7841,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))))) ),
inference(forward_demodulation,[],[f5858,f7524]) ).
fof(f5858,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))) ),
inference(definition_unfolding,[],[f4524,f4497,f4431,f5442,f4431,f5442,f4431,f5442,f4497]) ).
fof(f4524,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(cnf_transformation,[],[f2826]) ).
fof(f2826,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(flattening,[],[f2825]) ).
fof(f2825,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(ennf_transformation,[],[f230]) ).
fof(f230,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096) ).
fof(f7840,plain,
spl35_194,
inference(avatar_split_clause,[],[f4940,f7837]) ).
fof(f7837,plain,
( spl35_194
<=> class_Rings_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_194])]) ).
fof(f4940,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1167]) ).
fof(f1167,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(f7691,plain,
spl35_193,
inference(avatar_split_clause,[],[f5603,f7688]) ).
fof(f7688,plain,
( spl35_193
<=> c_SEQ_Osubseq(v_f____) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_193])]) ).
fof(f5603,plain,
c_SEQ_Osubseq(v_f____),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
c_SEQ_Osubseq(v_f____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fz_I1_J) ).
fof(f7686,plain,
spl35_123,
inference(avatar_split_clause,[],[f7685,f7053]) ).
fof(f7685,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f7684,f5637]) ).
fof(f7684,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),
inference(forward_demodulation,[],[f5795,f5637]) ).
fof(f5795,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(definition_unfolding,[],[f4126,f5442]) ).
fof(f4126,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f474]) ).
fof(f474,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(f7665,plain,
spl35_192,
inference(avatar_split_clause,[],[f4851,f7662]) ).
fof(f7662,plain,
( spl35_192
<=> class_Rings_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_192])]) ).
fof(f4851,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1132]) ).
fof(f1132,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(f7660,plain,
spl35_191,
inference(avatar_split_clause,[],[f4186,f7657]) ).
fof(f7657,plain,
( spl35_191
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_191])]) ).
fof(f4186,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f7655,plain,
spl35_190,
inference(avatar_split_clause,[],[f7650,f7652]) ).
fof(f7652,plain,
( spl35_190
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_190])]) ).
fof(f7650,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f7649,f5637]) ).
fof(f7649,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),
inference(forward_demodulation,[],[f5843,f5637]) ).
fof(f5843,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(definition_unfolding,[],[f4439,f5442]) ).
fof(f4439,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f305]) ).
fof(f305,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__num__one) ).
fof(f7648,plain,
spl35_189,
inference(avatar_split_clause,[],[f5685,f7645]) ).
fof(f7645,plain,
( spl35_189
<=> class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_189])]) ).
fof(f5685,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1092]) ).
fof(f1092,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(f7643,plain,
spl35_188,
inference(avatar_split_clause,[],[f5004,f7640]) ).
fof(f5004,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1125]) ).
fof(f1125,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f7638,plain,
spl35_187,
inference(avatar_split_clause,[],[f5027,f7635]) ).
fof(f5027,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18),
inference(cnf_transformation,[],[f3607]) ).
fof(f3607,plain,
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),sK18)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f2590,f3606]) ).
fof(f3606,plain,
( ? [X0] :
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
=> ( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),sK18)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f2590,plain,
? [X0] :
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(flattening,[],[f2589]) ).
fof(f2589,plain,
? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),X0) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f1765]) ).
fof(f1765,plain,
? [X0] :
( ! [X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),X0) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(rectify,[],[f225]) ).
fof(f225,axiom,
? [X54] :
( ! [X35] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X35,v_z____)),X54)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X35,v_z____))) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X35),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).
fof(f7633,plain,
spl35_186,
inference(avatar_split_clause,[],[f5118,f7630]) ).
fof(f7630,plain,
( spl35_186
<=> class_Groups_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_186])]) ).
fof(f5118,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1170]) ).
fof(f1170,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(f7605,plain,
spl35_185,
inference(avatar_split_clause,[],[f4388,f7602]) ).
fof(f7602,plain,
( spl35_185
<=> class_Rings_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_185])]) ).
fof(f4388,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1123]) ).
fof(f1123,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(f7600,plain,
spl35_184,
inference(avatar_split_clause,[],[f4903,f7597]) ).
fof(f7597,plain,
( spl35_184
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_184])]) ).
fof(f4903,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f1041]) ).
fof(f1041,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(f7595,plain,
spl35_183,
inference(avatar_split_clause,[],[f4897,f7592]) ).
fof(f4897,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14),
inference(cnf_transformation,[],[f3531]) ).
fof(f3531,plain,
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),sK14)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f3024,f3530]) ).
fof(f3530,plain,
( ? [X0] :
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
=> ( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),sK14)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f3024,plain,
? [X0] :
( ! [X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(flattening,[],[f3023]) ).
fof(f3023,plain,
? [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),X0) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f2080]) ).
fof(f2080,plain,
~ ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> ~ ! [X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,v_z____)),X0) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
inference(rectify,[],[f750]) ).
fof(f750,axiom,
~ ! [X54] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54)
=> ~ ! [X35] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X35,v_z____)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X35,v_z____)),X54) )
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X35),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(f7590,plain,
spl35_182,
inference(avatar_split_clause,[],[f4318,f7587]) ).
fof(f7587,plain,
( spl35_182
<=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_182])]) ).
fof(f4318,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1157]) ).
fof(f1157,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(f7585,plain,
spl35_181,
inference(avatar_split_clause,[],[f4511,f7582]) ).
fof(f7582,plain,
( spl35_181
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_181])]) ).
fof(f4511,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1054]) ).
fof(f1054,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f7580,plain,
spl35_180,
inference(avatar_split_clause,[],[f4059,f7577]) ).
fof(f7577,plain,
( spl35_180
<=> class_Groups_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_180])]) ).
fof(f4059,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1130]) ).
fof(f1130,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(f7575,plain,
spl35_179,
inference(avatar_split_clause,[],[f7570,f7572]) ).
fof(f7570,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f7569,f7524]) ).
fof(f7569,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f7568,f7524]) ).
fof(f7568,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f7567,f5723]) ).
fof(f7567,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f7566,f5637]) ).
fof(f7566,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f7565,f5723]) ).
fof(f7565,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f7564,f5637]) ).
fof(f7564,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))),
inference(forward_demodulation,[],[f7563,f5723]) ).
fof(f7563,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))),
inference(forward_demodulation,[],[f7562,f5637]) ).
fof(f7562,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f7561,f5723]) ).
fof(f7561,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f7560,f5537]) ).
fof(f7560,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f5948,f5723]) ).
fof(f5948,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(definition_unfolding,[],[f5000,f4431,f5442]) ).
fof(f5000,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_thc1) ).
fof(f7559,plain,
spl35_178,
inference(avatar_split_clause,[],[f5253,f7556]) ).
fof(f7556,plain,
( spl35_178
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_178])]) ).
fof(f5253,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f7553,plain,
spl35_177,
inference(avatar_split_clause,[],[f4917,f7550]) ).
fof(f7550,plain,
( spl35_177
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_177])]) ).
fof(f4917,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f1046]) ).
fof(f1046,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f7548,plain,
spl35_135,
inference(avatar_split_clause,[],[f4627,f7125]) ).
fof(f4627,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp) ).
fof(f7545,plain,
spl35_176,
inference(avatar_split_clause,[],[f4080,f7542]) ).
fof(f7542,plain,
( spl35_176
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_176])]) ).
fof(f4080,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1062]) ).
fof(f1062,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f7534,plain,
spl35_175,
inference(avatar_split_clause,[],[f4183,f7531]) ).
fof(f7531,plain,
( spl35_175
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_175])]) ).
fof(f4183,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1042]) ).
fof(f1042,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(f7521,plain,
spl35_174,
inference(avatar_split_clause,[],[f4420,f7518]) ).
fof(f7518,plain,
( spl35_174
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_174])]) ).
fof(f4420,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1000]) ).
fof(f1000,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f7516,plain,
spl35_173,
inference(avatar_split_clause,[],[f4600,f7513]) ).
fof(f7513,plain,
( spl35_173
<=> class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_173])]) ).
fof(f4600,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1088]) ).
fof(f1088,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(f7511,plain,
spl35_172,
inference(avatar_split_clause,[],[f4487,f7508]) ).
fof(f7508,plain,
( spl35_172
<=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_172])]) ).
fof(f4487,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1166]) ).
fof(f1166,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f7397,plain,
spl35_171,
inference(avatar_split_clause,[],[f4055,f7394]) ).
fof(f7394,plain,
( spl35_171
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_171])]) ).
fof(f4055,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1161]) ).
fof(f1161,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f7392,plain,
spl35_170,
inference(avatar_split_clause,[],[f5269,f7389]) ).
fof(f7389,plain,
( spl35_170
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_170])]) ).
fof(f5269,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1001]) ).
fof(f1001,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f7387,plain,
spl35_169,
inference(avatar_split_clause,[],[f6239,f7384]) ).
fof(f6239,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(equality_resolution,[],[f6238]) ).
fof(f6238,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(equality_resolution,[],[f5679]) ).
fof(f5679,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X1
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(cnf_transformation,[],[f3988]) ).
fof(f7382,plain,
spl35_168,
inference(avatar_split_clause,[],[f4214,f7379]) ).
fof(f4214,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f236]) ).
fof(f236,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th000_I1_J) ).
fof(f7377,plain,
spl35_167,
inference(avatar_split_clause,[],[f4430,f7374]) ).
fof(f7374,plain,
( spl35_167
<=> class_Groups_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_167])]) ).
fof(f4430,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1158]) ).
fof(f1158,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(f7361,plain,
spl35_166,
inference(avatar_split_clause,[],[f5369,f7358]) ).
fof(f7358,plain,
( spl35_166
<=> c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_166])]) ).
fof(f5369,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
inference(cnf_transformation,[],[f237]) ).
fof(f237,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r)
& c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096) ).
fof(f7356,plain,
spl35_49,
inference(avatar_split_clause,[],[f4589,f6566]) ).
fof(f4589,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(cnf_transformation,[],[f471]) ).
fof(f471,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
fof(f7351,plain,
spl35_165,
inference(avatar_split_clause,[],[f4938,f7348]) ).
fof(f7348,plain,
( spl35_165
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_165])]) ).
fof(f4938,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1029]) ).
fof(f1029,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f7345,plain,
spl35_164,
inference(avatar_split_clause,[],[f4805,f7342]) ).
fof(f7342,plain,
( spl35_164
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_164])]) ).
fof(f4805,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f1034]) ).
fof(f1034,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(f7340,plain,
spl35_163,
inference(avatar_split_clause,[],[f4256,f7337]) ).
fof(f7337,plain,
( spl35_163
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_163])]) ).
fof(f4256,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f1072]) ).
fof(f1072,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(f7324,plain,
spl35_162,
inference(avatar_split_clause,[],[f5215,f7321]) ).
fof(f7321,plain,
( spl35_162
<=> class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_162])]) ).
fof(f5215,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1136]) ).
fof(f1136,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(f7319,plain,
spl35_161,
inference(avatar_split_clause,[],[f5378,f7316]) ).
fof(f7316,plain,
( spl35_161
<=> class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_161])]) ).
fof(f5378,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1155]) ).
fof(f1155,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(f7311,plain,
spl35_160,
inference(avatar_split_clause,[],[f5280,f7308]) ).
fof(f7308,plain,
( spl35_160
<=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_160])]) ).
fof(f5280,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1156]) ).
fof(f1156,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(f7306,plain,
spl35_159,
inference(avatar_split_clause,[],[f5756,f7303]) ).
fof(f7303,plain,
( spl35_159
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_159])]) ).
fof(f5756,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f250]) ).
fof(f250,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(f7300,plain,
spl35_158,
inference(avatar_split_clause,[],[f5170,f7297]) ).
fof(f7297,plain,
( spl35_158
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_158])]) ).
fof(f5170,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1112]) ).
fof(f1112,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f7295,plain,
spl35_157,
inference(avatar_split_clause,[],[f5666,f7292]) ).
fof(f7292,plain,
( spl35_157
<=> class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_157])]) ).
fof(f5666,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1087]) ).
fof(f1087,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(f7290,plain,
spl35_156,
inference(avatar_split_clause,[],[f5753,f7287]) ).
fof(f7287,plain,
( spl35_156
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_156])]) ).
fof(f5753,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1085]) ).
fof(f1085,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f7277,plain,
spl35_155,
inference(avatar_split_clause,[],[f4523,f7274]) ).
fof(f7274,plain,
( spl35_155
<=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_155])]) ).
fof(f4523,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1101]) ).
fof(f1101,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(f7272,plain,
spl35_154,
inference(avatar_split_clause,[],[f4240,f7269]) ).
fof(f7269,plain,
( spl35_154
<=> class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_154])]) ).
fof(f4240,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1122]) ).
fof(f1122,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f7267,plain,
spl35_153,
inference(avatar_split_clause,[],[f5144,f7264]) ).
fof(f7264,plain,
( spl35_153
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_153])]) ).
fof(f5144,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f998]) ).
fof(f998,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f7258,plain,
spl35_152,
inference(avatar_split_clause,[],[f5277,f7255]) ).
fof(f7255,plain,
( spl35_152
<=> class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_152])]) ).
fof(f5277,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1094]) ).
fof(f1094,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(f7253,plain,
spl35_151,
inference(avatar_split_clause,[],[f5370,f7250]) ).
fof(f5370,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r),
inference(cnf_transformation,[],[f237]) ).
fof(f7248,plain,
spl35_150,
inference(avatar_split_clause,[],[f5707,f7245]) ).
fof(f7245,plain,
( spl35_150
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_150])]) ).
fof(f5707,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1012]) ).
fof(f1012,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f7234,plain,
spl35_149,
inference(avatar_split_clause,[],[f5303,f7231]) ).
fof(f7231,plain,
( spl35_149
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_149])]) ).
fof(f5303,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1067]) ).
fof(f1067,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f7229,plain,
spl35_148,
inference(avatar_split_clause,[],[f4907,f7226]) ).
fof(f7226,plain,
( spl35_148
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_148])]) ).
fof(f4907,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f1020]) ).
fof(f1020,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(f7224,plain,
spl35_147,
inference(avatar_split_clause,[],[f4751,f7221]) ).
fof(f7221,plain,
( spl35_147
<=> class_Groups_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_147])]) ).
fof(f4751,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1159]) ).
fof(f1159,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f7217,plain,
spl35_146,
inference(avatar_split_clause,[],[f4484,f7214]) ).
fof(f7214,plain,
( spl35_146
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_146])]) ).
fof(f4484,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1070]) ).
fof(f1070,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(f7210,plain,
spl35_145,
inference(avatar_split_clause,[],[f5030,f7207]) ).
fof(f5030,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
inference(cnf_transformation,[],[f84]) ).
fof(f84,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d_I1_J) ).
fof(f7205,plain,
spl35_144,
inference(avatar_split_clause,[],[f4819,f7202]) ).
fof(f7202,plain,
( spl35_144
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_144])]) ).
fof(f4819,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1119]) ).
fof(f1119,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f7196,plain,
spl35_143,
inference(avatar_split_clause,[],[f5902,f7193]) ).
fof(f5902,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(definition_unfolding,[],[f4743,f4497]) ).
fof(f4743,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(cnf_transformation,[],[f227]) ).
fof(f227,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096abs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_060_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).
fof(f7189,plain,
spl35_142,
inference(avatar_split_clause,[],[f5400,f7186]) ).
fof(f7186,plain,
( spl35_142
<=> class_Rings_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_142])]) ).
fof(f5400,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1163]) ).
fof(f1163,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(f7173,plain,
spl35_141,
inference(avatar_split_clause,[],[f4717,f7170]) ).
fof(f4717,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096abs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_060_061_Aabs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_L_Acmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_A_N_Apoly_Ap_Az_J_096) ).
fof(f7166,plain,
spl35_140,
inference(avatar_split_clause,[],[f4857,f7163]) ).
fof(f7163,plain,
( spl35_140
<=> class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_140])]) ).
fof(f4857,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1147]) ).
fof(f1147,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(f7160,plain,
spl35_139,
inference(avatar_split_clause,[],[f5673,f7157]) ).
fof(f5673,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wr) ).
fof(f7149,plain,
spl35_138,
inference(avatar_split_clause,[],[f4659,f7146]) ).
fof(f7146,plain,
( spl35_138
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_138])]) ).
fof(f4659,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1027]) ).
fof(f1027,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f7144,plain,
spl35_137,
inference(avatar_split_clause,[],[f6243,f7141]) ).
fof(f7141,plain,
( spl35_137
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_137])]) ).
fof(f6243,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(equality_resolution,[],[f5755]) ).
fof(f5755,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f4022]) ).
fof(f4022,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(nnf_transformation,[],[f1432]) ).
fof(f1432,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f270]) ).
fof(f270,axiom,
! [X50] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X50
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X50),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
fof(f7133,plain,
spl35_136,
inference(avatar_split_clause,[],[f5607,f7130]) ).
fof(f7130,plain,
( spl35_136
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_136])]) ).
fof(f5607,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1068]) ).
fof(f1068,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f7128,plain,
( spl35_134
| spl35_135 ),
inference(avatar_split_clause,[],[f4742,f7125,f7122]) ).
fof(f7122,plain,
( spl35_134
<=> ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sK13)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_134])]) ).
fof(f4742,plain,
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sK13)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) ),
inference(cnf_transformation,[],[f3445]) ).
fof(f3445,plain,
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sK13)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f2691,f3444]) ).
fof(f3444,plain,
( ? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) )
=> ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sK13)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) ) ),
introduced(choice_axiom,[]) ).
fof(f2691,plain,
( ? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
inference(ennf_transformation,[],[f1331]) ).
fof(f1331,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
=> ? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1))) ) ),
inference(rectify,[],[f233]) ).
fof(f233,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
=> ? [X19] :
! [X35] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X35),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X19)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X35))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation) ).
fof(f7120,plain,
spl35_133,
inference(avatar_split_clause,[],[f5452,f7117]) ).
fof(f7117,plain,
( spl35_133
<=> c_Int_OPls = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_133])]) ).
fof(f5452,plain,
c_Int_OPls = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls),
inference(cnf_transformation,[],[f132]) ).
fof(f132,axiom,
c_Int_OPls = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Pls) ).
fof(f7110,plain,
spl35_132,
inference(avatar_split_clause,[],[f5566,f7107]) ).
fof(f7107,plain,
( spl35_132
<=> class_Int_Onumber(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_132])]) ).
fof(f5566,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1169]) ).
fof(f1169,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).
fof(f7105,plain,
( spl35_130
| spl35_131 ),
inference(avatar_split_clause,[],[f4449,f7102,f7099]) ).
fof(f7099,plain,
( spl35_130
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_130])]) ).
fof(f4449,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
inference(cnf_transformation,[],[f3279]) ).
fof(f3279,plain,
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK6),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sK6)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f3277,f3278]) ).
fof(f3278,plain,
( ? [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK6),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sK6)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ),
introduced(choice_axiom,[]) ).
fof(f3277,plain,
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) )
& ( ? [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X1)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ),
inference(rectify,[],[f3276]) ).
fof(f3276,plain,
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
| ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) )
& ( ? [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ),
inference(nnf_transformation,[],[f1769]) ).
fof(f1769,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
<=> ? [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X0),v_r)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X0)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ),
inference(rectify,[],[f78]) ).
fof(f78,axiom,
( ? [X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,X19)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X19),v_r) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096) ).
fof(f7092,plain,
spl35_129,
inference(avatar_split_clause,[],[f4189,f7089]) ).
fof(f7089,plain,
( spl35_129
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_129])]) ).
fof(f4189,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f1024]) ).
fof(f1024,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f7087,plain,
spl35_128,
inference(avatar_split_clause,[],[f5041,f7084]) ).
fof(f7084,plain,
( spl35_128
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_128])]) ).
fof(f5041,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f1043]) ).
fof(f1043,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(f7082,plain,
spl35_125,
inference(avatar_split_clause,[],[f7081,f7065]) ).
fof(f7065,plain,
( spl35_125
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_125])]) ).
fof(f7081,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f7080,f6110]) ).
fof(f7080,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f6133,f5023]) ).
fof(f6133,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f6132]) ).
fof(f6132,plain,
! [X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f5929]) ).
fof(f5929,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(definition_unfolding,[],[f4868,f4497,f4497,f4497]) ).
fof(f4868,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3515]) ).
fof(f3515,plain,
! [X0,X1] :
( ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ),
inference(flattening,[],[f3514]) ).
fof(f3514,plain,
! [X0,X1] :
( ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ),
inference(nnf_transformation,[],[f2077]) ).
fof(f2077,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
<=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f478]) ).
fof(f478,axiom,
! [X6,X50] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X6,X50)
<=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X50
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
fof(f7078,plain,
spl35_127,
inference(avatar_split_clause,[],[f4874,f7075]) ).
fof(f7075,plain,
( spl35_127
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_127])]) ).
fof(f4874,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1084]) ).
fof(f1084,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(f7073,plain,
spl35_126,
inference(avatar_split_clause,[],[f5737,f7070]) ).
fof(f7070,plain,
( spl35_126
<=> class_Groups_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_126])]) ).
fof(f5737,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1120]) ).
fof(f1120,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(f7068,plain,
spl35_125,
inference(avatar_split_clause,[],[f6096,f7065]) ).
fof(f6096,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(equality_resolution,[],[f6095]) ).
fof(f6095,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ),
inference(equality_resolution,[],[f4522]) ).
fof(f4522,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3317]) ).
fof(f3317,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
& ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) ) ),
inference(flattening,[],[f3316]) ).
fof(f3316,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
& ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1) ) ),
inference(nnf_transformation,[],[f1395]) ).
fof(f1395,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f355]) ).
fof(f355,axiom,
! [X6,X50] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X50
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X6 )
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X6,X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(f7063,plain,
spl35_124,
inference(avatar_split_clause,[],[f7058,f7060]) ).
fof(f7060,plain,
( spl35_124
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_124])]) ).
fof(f7058,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f7057,f6110]) ).
fof(f7057,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f6208,f5023]) ).
fof(f6208,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f6207]) ).
fof(f6207,plain,
! [X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f6029]) ).
fof(f6029,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(definition_unfolding,[],[f5489,f4497,f4497]) ).
fof(f5489,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3874]) ).
fof(f7056,plain,
spl35_123,
inference(avatar_split_clause,[],[f7051,f7053]) ).
fof(f7051,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f7050,f5637]) ).
fof(f7050,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),
inference(forward_demodulation,[],[f7049,f6110]) ).
fof(f7049,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f7048,f5023]) ).
fof(f7048,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f5944,f5637]) ).
fof(f5944,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(definition_unfolding,[],[f4955,f4497,f5442]) ).
fof(f4955,plain,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f544]) ).
fof(f544,axiom,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
fof(f7044,plain,
spl35_122,
inference(avatar_split_clause,[],[f5703,f7041]) ).
fof(f5703,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_e) ).
fof(f7039,plain,
spl35_121,
inference(avatar_split_clause,[],[f4924,f7036]) ).
fof(f7036,plain,
( spl35_121
<=> class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_121])]) ).
fof(f4924,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1102]) ).
fof(f1102,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(f7034,plain,
spl35_120,
inference(avatar_split_clause,[],[f4195,f7031]) ).
fof(f7031,plain,
( spl35_120
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_120])]) ).
fof(f4195,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1069]) ).
fof(f1069,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f7028,plain,
spl35_119,
inference(avatar_split_clause,[],[f5653,f7025]) ).
fof(f7025,plain,
( spl35_119
<=> class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_119])]) ).
fof(f5653,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1096]) ).
fof(f1096,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(f7021,plain,
spl35_118,
inference(avatar_split_clause,[],[f5458,f7018]) ).
fof(f7018,plain,
( spl35_118
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_118])]) ).
fof(f5458,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1139]) ).
fof(f1139,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(f7016,plain,
spl35_117,
inference(avatar_split_clause,[],[f5007,f7013]) ).
fof(f7013,plain,
( spl35_117
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_117])]) ).
fof(f5007,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f1063]) ).
fof(f1063,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f7011,plain,
spl35_116,
inference(avatar_split_clause,[],[f5399,f7008]) ).
fof(f7008,plain,
( spl35_116
<=> class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_116])]) ).
fof(f5399,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1103]) ).
fof(f1103,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(f7003,plain,
spl35_115,
inference(avatar_split_clause,[],[f5625,f7000]) ).
fof(f7000,plain,
( spl35_115
<=> class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_115])]) ).
fof(f5625,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1104]) ).
fof(f1104,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(f6998,plain,
spl35_114,
inference(avatar_split_clause,[],[f5163,f6995]) ).
fof(f6995,plain,
( spl35_114
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_114])]) ).
fof(f5163,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1079]) ).
fof(f1079,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f6992,plain,
spl35_113,
inference(avatar_split_clause,[],[f5456,f6989]) ).
fof(f6989,plain,
( spl35_113
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_113])]) ).
fof(f5456,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1011]) ).
fof(f1011,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f6987,plain,
spl35_112,
inference(avatar_split_clause,[],[f4344,f6984]) ).
fof(f6984,plain,
( spl35_112
<=> class_Rings_Oring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_112])]) ).
fof(f4344,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1128]) ).
fof(f1128,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(f6981,plain,
spl35_111,
inference(avatar_split_clause,[],[f4442,f6978]) ).
fof(f6978,plain,
( spl35_111
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_111])]) ).
fof(f4442,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1009]) ).
fof(f1009,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f6976,plain,
spl35_110,
inference(avatar_split_clause,[],[f4639,f6973]) ).
fof(f6973,plain,
( spl35_110
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_110])]) ).
fof(f4639,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1047]) ).
fof(f1047,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f6971,plain,
spl35_109,
inference(avatar_split_clause,[],[f4968,f6968]) ).
fof(f6968,plain,
( spl35_109
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_109])]) ).
fof(f4968,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1075]) ).
fof(f1075,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6966,plain,
spl35_108,
inference(avatar_split_clause,[],[f4765,f6963]) ).
fof(f6963,plain,
( spl35_108
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_108])]) ).
fof(f4765,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1013]) ).
fof(f1013,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f6961,plain,
spl35_107,
inference(avatar_split_clause,[],[f4287,f6958]) ).
fof(f6958,plain,
( spl35_107
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_107])]) ).
fof(f4287,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f235]) ).
fof(f235,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th000_I2_J) ).
fof(f6956,plain,
spl35_106,
inference(avatar_split_clause,[],[f5060,f6953]) ).
fof(f6953,plain,
( spl35_106
<=> class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_106])]) ).
fof(f5060,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1150]) ).
fof(f1150,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(f6951,plain,
spl35_105,
inference(avatar_split_clause,[],[f5694,f6948]) ).
fof(f6948,plain,
( spl35_105
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_105])]) ).
fof(f5694,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1064]) ).
fof(f1064,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f6946,plain,
spl35_104,
inference(avatar_split_clause,[],[f4799,f6943]) ).
fof(f6943,plain,
( spl35_104
<=> class_Rings_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_104])]) ).
fof(f4799,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1164]) ).
fof(f1164,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(f6941,plain,
spl35_103,
inference(avatar_split_clause,[],[f4051,f6938]) ).
fof(f6938,plain,
( spl35_103
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_103])]) ).
fof(f4051,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f1040]) ).
fof(f1040,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(f6936,plain,
spl35_102,
inference(avatar_split_clause,[],[f5182,f6933]) ).
fof(f5182,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1165]) ).
fof(f1165,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(f6931,plain,
spl35_101,
inference(avatar_split_clause,[],[f6926,f6928]) ).
fof(f6926,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f6925,f5637]) ).
fof(f6925,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f6924,f5637]) ).
fof(f6924,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))),
inference(forward_demodulation,[],[f6923,f5537]) ).
fof(f6923,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f5884,f5537]) ).
fof(f5884,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(definition_unfolding,[],[f4634,f4497,f4431,f5442]) ).
fof(f4634,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f226]) ).
fof(f226,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0961_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).
fof(f6921,plain,
spl35_100,
inference(avatar_split_clause,[],[f5739,f6918]) ).
fof(f6918,plain,
( spl35_100
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_100])]) ).
fof(f5739,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1008]) ).
fof(f1008,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f6911,plain,
spl35_99,
inference(avatar_split_clause,[],[f5476,f6908]) ).
fof(f6908,plain,
( spl35_99
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_99])]) ).
fof(f5476,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1023]) ).
fof(f1023,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f6905,plain,
spl35_98,
inference(avatar_split_clause,[],[f5145,f6902]) ).
fof(f6902,plain,
( spl35_98
<=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_98])]) ).
fof(f5145,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1124]) ).
fof(f1124,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(f6900,plain,
spl35_97,
inference(avatar_split_clause,[],[f6895,f6897]) ).
fof(f6895,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)),
inference(forward_demodulation,[],[f6894,f5637]) ).
fof(f6894,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)),
inference(forward_demodulation,[],[f6893,f5637]) ).
fof(f6893,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)),
inference(forward_demodulation,[],[f6892,f5537]) ).
fof(f6892,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)),
inference(forward_demodulation,[],[f6013,f5537]) ).
fof(f6013,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)),
inference(definition_unfolding,[],[f5418,f4431,f5442]) ).
fof(f5418,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)),
inference(cnf_transformation,[],[f3827]) ).
fof(f3827,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f1221,f3826]) ).
fof(f3826,plain,
( ? [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X0))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK25)) ),
introduced(choice_axiom,[]) ).
fof(f1221,plain,
? [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(rectify,[],[f75]) ).
fof(f75,axiom,
? [X5] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_An_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_An_096) ).
fof(f6891,plain,
spl35_64,
inference(avatar_split_clause,[],[f6890,f6657]) ).
fof(f6890,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f6889,f6110]) ).
fof(f6889,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f6049,f5023]) ).
fof(f6049,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definition_unfolding,[],[f5675,f4497]) ).
fof(f5675,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f242]) ).
fof(f242,axiom,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__one) ).
fof(f6888,plain,
spl35_96,
inference(avatar_split_clause,[],[f6883,f6885]) ).
fof(f6883,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f6882,f5637]) ).
fof(f6882,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),
inference(forward_demodulation,[],[f6881,f5637]) ).
fof(f6881,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f6880,f5537]) ).
fof(f6880,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f6034,f5537]) ).
fof(f6034,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(definition_unfolding,[],[f5562,f4431,f5442]) ).
fof(f5562,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f546]) ).
fof(f546,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(f6878,plain,
spl35_95,
inference(avatar_split_clause,[],[f4609,f6875]) ).
fof(f6875,plain,
( spl35_95
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_95])]) ).
fof(f4609,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(cnf_transformation,[],[f141]) ).
fof(f141,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).
fof(f6873,plain,
spl35_94,
inference(avatar_split_clause,[],[f5577,f6870]) ).
fof(f6870,plain,
( spl35_94
<=> class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_94])]) ).
fof(f5577,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1143]) ).
fof(f1143,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(f6867,plain,
spl35_93,
inference(avatar_split_clause,[],[f5255,f6864]) ).
fof(f6864,plain,
( spl35_93
<=> class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_93])]) ).
fof(f5255,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1105]) ).
fof(f1105,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(f6860,plain,
spl35_92,
inference(avatar_split_clause,[],[f4890,f6857]) ).
fof(f4890,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1162]) ).
fof(f1162,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f6855,plain,
spl35_91,
inference(avatar_split_clause,[],[f5088,f6852]) ).
fof(f6852,plain,
( spl35_91
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_91])]) ).
fof(f5088,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1091]) ).
fof(f1091,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f6850,plain,
spl35_90,
inference(avatar_split_clause,[],[f4219,f6847]) ).
fof(f4219,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f696]) ).
fof(f696,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f6842,plain,
spl35_89,
inference(avatar_split_clause,[],[f6837,f6839]) ).
fof(f6837,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f6836,f5637]) ).
fof(f6836,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))))),
inference(forward_demodulation,[],[f6835,f5637]) ).
fof(f6835,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f6834,f5537]) ).
fof(f6834,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f6833,f5537]) ).
fof(f6833,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f6832,f5637]) ).
fof(f6832,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f6831,f6110]) ).
fof(f6831,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(forward_demodulation,[],[f6022,f5023]) ).
fof(f6022,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(definition_unfolding,[],[f5467,f5442,f5442,f4497,f4497,f4497]) ).
fof(f5467,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(cnf_transformation,[],[f543]) ).
fof(f543,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
fof(f6830,plain,
spl35_88,
inference(avatar_split_clause,[],[f4036,f6827]) ).
fof(f6827,plain,
( spl35_88
<=> class_Groups_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_88])]) ).
fof(f4036,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1134]) ).
fof(f1134,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(f6825,plain,
spl35_87,
inference(avatar_split_clause,[],[f5714,f6822]) ).
fof(f6822,plain,
( spl35_87
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_87])]) ).
fof(f5714,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1048]) ).
fof(f1048,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f6820,plain,
spl35_86,
inference(avatar_split_clause,[],[f5708,f6817]) ).
fof(f6817,plain,
( spl35_86
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_86])]) ).
fof(f5708,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(cnf_transformation,[],[f1038]) ).
fof(f1038,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(f6807,plain,
spl35_85,
inference(avatar_split_clause,[],[f4507,f6804]) ).
fof(f6804,plain,
( spl35_85
<=> class_Int_Onumber(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_85])]) ).
fof(f4507,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
fof(f6802,plain,
spl35_84,
inference(avatar_split_clause,[],[f6797,f6799]) ).
fof(f6797,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f6796,f5637]) ).
fof(f6796,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f6795,f5637]) ).
fof(f6795,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))),
inference(forward_demodulation,[],[f6794,f5537]) ).
fof(f6794,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f6061,f5537]) ).
fof(f6061,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(definition_unfolding,[],[f5776,f4431,f5442]) ).
fof(f5776,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th2) ).
fof(f6793,plain,
spl35_83,
inference(avatar_split_clause,[],[f4973,f6790]) ).
fof(f6790,plain,
( spl35_83
<=> class_Groups_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_83])]) ).
fof(f4973,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,axiom,
class_Groups_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).
fof(f6787,plain,
spl35_82,
inference(avatar_split_clause,[],[f4045,f6784]) ).
fof(f6784,plain,
( spl35_82
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_82])]) ).
fof(f4045,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1135]) ).
fof(f1135,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f6782,plain,
spl35_81,
inference(avatar_split_clause,[],[f4691,f6779]) ).
fof(f6779,plain,
( spl35_81
<=> class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_81])]) ).
fof(f4691,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1099]) ).
fof(f1099,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(f6771,plain,
spl35_80,
inference(avatar_split_clause,[],[f4783,f6768]) ).
fof(f6768,plain,
( spl35_80
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_80])]) ).
fof(f4783,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f1065]) ).
fof(f1065,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f6766,plain,
spl35_79,
inference(avatar_split_clause,[],[f4098,f6763]) ).
fof(f6763,plain,
( spl35_79
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_79])]) ).
fof(f4098,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1004]) ).
fof(f1004,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f6761,plain,
spl35_78,
inference(avatar_split_clause,[],[f4681,f6758]) ).
fof(f4681,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f293]) ).
fof(f293,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(f6750,plain,
spl35_77,
inference(avatar_split_clause,[],[f4744,f6747]) ).
fof(f6747,plain,
( spl35_77
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_77])]) ).
fof(f4744,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1031]) ).
fof(f1031,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f6742,plain,
spl35_76,
inference(avatar_split_clause,[],[f5524,f6739]) ).
fof(f6739,plain,
( spl35_76
<=> class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_76])]) ).
fof(f5524,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1097]) ).
fof(f1097,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(f6737,plain,
( spl35_74
| spl35_75 ),
inference(avatar_split_clause,[],[f6729,f6734,f6731]) ).
fof(f6731,plain,
( spl35_74
<=> ! [X0] : ~ class_RealVector_Oreal__normed__vector(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_74])]) ).
fof(f6729,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(forward_subsumption_demodulation,[],[f6082,f4289]) ).
fof(f4289,plain,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f2721]) ).
fof(f2721,plain,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(ennf_transformation,[],[f1856]) ).
fof(f1856,plain,
! [X0] :
( class_RealVector_Oreal__normed__vector(X0)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f684]) ).
fof(f684,axiom,
! [X15] :
( class_RealVector_Oreal__normed__vector(X15)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X15,c_Groups_Ozero__class_Ozero(X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(f6082,plain,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,c_Groups_Ozero__class_Ozero(X0)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(equality_resolution,[],[f4312]) ).
fof(f4312,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(X0) != X1
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f3200]) ).
fof(f3200,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X0) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(X0) != X1 ) )
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(rectify,[],[f3199]) ).
fof(f3199,plain,
! [X1,X0] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(X1) != X0 ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(nnf_transformation,[],[f2553]) ).
fof(f2553,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(X1) = X0
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1334]) ).
fof(f1334,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = X0
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(rectify,[],[f726]) ).
fof(f726,axiom,
! [X13,X15] :
( class_RealVector_Oreal__normed__vector(X15)
=> ( c_Groups_Ozero__class_Ozero(X15) = X13
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X15,X13),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(f6728,plain,
spl35_73,
inference(avatar_split_clause,[],[f4391,f6725]) ).
fof(f6725,plain,
( spl35_73
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_73])]) ).
fof(f4391,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1071]) ).
fof(f1071,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(f6722,plain,
spl35_72,
inference(avatar_split_clause,[],[f4406,f6719]) ).
fof(f6719,plain,
( spl35_72
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_72])]) ).
fof(f4406,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f997]) ).
fof(f997,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6712,plain,
spl35_71,
inference(avatar_split_clause,[],[f6707,f6709]) ).
fof(f6709,plain,
( spl35_71
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_71])]) ).
fof(f6707,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_OPls),
inference(forward_demodulation,[],[f5298,f4248]) ).
fof(f5298,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(cnf_transformation,[],[f539]) ).
fof(f539,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of2) ).
fof(f6706,plain,
spl35_70,
inference(avatar_split_clause,[],[f4534,f6703]) ).
fof(f6703,plain,
( spl35_70
<=> class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_70])]) ).
fof(f4534,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1083]) ).
fof(f1083,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(f6691,plain,
spl35_69,
inference(avatar_split_clause,[],[f4852,f6688]) ).
fof(f6688,plain,
( spl35_69
<=> class_Rings_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_69])]) ).
fof(f4852,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1106]) ).
fof(f1106,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(f6684,plain,
spl35_68,
inference(avatar_split_clause,[],[f5630,f6681]) ).
fof(f6681,plain,
( spl35_68
<=> class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_68])]) ).
fof(f5630,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1154]) ).
fof(f1154,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(f6679,plain,
spl35_67,
inference(avatar_split_clause,[],[f5680,f6676]) ).
fof(f6676,plain,
( spl35_67
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_67])]) ).
fof(f5680,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1015]) ).
fof(f1015,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f6674,plain,
spl35_66,
inference(avatar_split_clause,[],[f4423,f6671]) ).
fof(f6671,plain,
( spl35_66
<=> class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_66])]) ).
fof(f4423,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1140]) ).
fof(f1140,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(f6665,plain,
spl35_65,
inference(avatar_split_clause,[],[f4896,f6662]) ).
fof(f6662,plain,
( spl35_65
<=> class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_65])]) ).
fof(f4896,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1146]) ).
fof(f1146,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(f6660,plain,
spl35_64,
inference(avatar_split_clause,[],[f4115,f6657]) ).
fof(f4115,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f304]) ).
fof(f304,axiom,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
fof(f6655,plain,
spl35_63,
inference(avatar_split_clause,[],[f4668,f6652]) ).
fof(f6652,plain,
( spl35_63
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_63])]) ).
fof(f4668,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1019]) ).
fof(f1019,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f6650,plain,
spl35_62,
inference(avatar_split_clause,[],[f4188,f6647]) ).
fof(f6647,plain,
( spl35_62
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_62])]) ).
fof(f4188,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(f6645,plain,
spl35_61,
inference(avatar_split_clause,[],[f5779,f6642]) ).
fof(f6642,plain,
( spl35_61
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_61])]) ).
fof(f5779,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1082]) ).
fof(f1082,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f6640,plain,
spl35_60,
inference(avatar_split_clause,[],[f4677,f6637]) ).
fof(f6637,plain,
( spl35_60
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_60])]) ).
fof(f4677,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f1073]) ).
fof(f1073,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(f6635,plain,
spl35_59,
inference(avatar_split_clause,[],[f4696,f6632]) ).
fof(f6632,plain,
( spl35_59
<=> class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_59])]) ).
fof(f4696,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1080]) ).
fof(f1080,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(f6630,plain,
spl35_58,
inference(avatar_split_clause,[],[f6625,f6627]) ).
fof(f6625,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f6624,f5023]) ).
fof(f6624,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f6623,f5637]) ).
fof(f6623,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),
inference(forward_demodulation,[],[f6622,f5637]) ).
fof(f6622,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f6621,f5537]) ).
fof(f6621,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f5837,f5537]) ).
fof(f5837,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(definition_unfolding,[],[f4410,f4431,f5442,f4497,f4497]) ).
fof(f4410,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f552]) ).
fof(f552,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(f6617,plain,
spl35_19,
inference(avatar_split_clause,[],[f6038,f6362]) ).
fof(f6362,plain,
( spl35_19
<=> c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_19])]) ).
fof(f6038,plain,
c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(definition_unfolding,[],[f5617,f4431]) ).
fof(f5617,plain,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
fof(f6615,plain,
spl35_57,
inference(avatar_split_clause,[],[f4210,f6612]) ).
fof(f6612,plain,
( spl35_57
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_57])]) ).
fof(f4210,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f1028]) ).
fof(f1028,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f6610,plain,
~ spl35_56,
inference(avatar_split_clause,[],[f5212,f6607]) ).
fof(f5212,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(cnf_transformation,[],[f136]) ).
fof(f136,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).
fof(f6605,plain,
spl35_55,
inference(avatar_split_clause,[],[f5635,f6602]) ).
fof(f6602,plain,
( spl35_55
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_55])]) ).
fof(f5635,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1036]) ).
fof(f1036,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(f6600,plain,
spl35_54,
inference(avatar_split_clause,[],[f5240,f6597]) ).
fof(f6597,plain,
( spl35_54
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_54])]) ).
fof(f5240,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1113]) ).
fof(f1113,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f6595,plain,
spl35_53,
inference(avatar_split_clause,[],[f6590,f6592]) ).
fof(f6590,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f6589,f5637]) ).
fof(f6589,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))))),
inference(forward_demodulation,[],[f6588,f5637]) ).
fof(f6588,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f6587,f5537]) ).
fof(f6587,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f5790,f5537]) ).
fof(f5790,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(definition_unfolding,[],[f4102,f4431,f5442]) ).
fof(f4102,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f562]) ).
fof(f562,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos2) ).
fof(f6586,plain,
spl35_52,
inference(avatar_split_clause,[],[f4238,f6583]) ).
fof(f6583,plain,
( spl35_52
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_52])]) ).
fof(f4238,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1057]) ).
fof(f1057,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f6579,plain,
spl35_51,
inference(avatar_split_clause,[],[f5422,f6576]) ).
fof(f6576,plain,
( spl35_51
<=> class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_51])]) ).
fof(f5422,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1107]) ).
fof(f1107,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
fof(f6574,plain,
spl35_50,
inference(avatar_split_clause,[],[f5381,f6571]) ).
fof(f6571,plain,
( spl35_50
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_50])]) ).
fof(f5381,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1045]) ).
fof(f1045,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6569,plain,
spl35_49,
inference(avatar_split_clause,[],[f4794,f6566]) ).
fof(f4794,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(cnf_transformation,[],[f470]) ).
fof(f470,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(f6559,plain,
spl35_48,
inference(avatar_split_clause,[],[f4875,f6556]) ).
fof(f4875,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f247]) ).
fof(f247,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(f6554,plain,
spl35_47,
inference(avatar_split_clause,[],[f5997,f6551]) ).
fof(f5997,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(definition_unfolding,[],[f5267,f4497,f4497]) ).
fof(f5267,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(cnf_transformation,[],[f234]) ).
fof(f234,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0961_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_A_060_061_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).
fof(f6549,plain,
spl35_46,
inference(avatar_split_clause,[],[f5695,f6546]) ).
fof(f6546,plain,
( spl35_46
<=> class_Rings_Olinordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_46])]) ).
fof(f5695,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(f6544,plain,
spl35_45,
inference(avatar_split_clause,[],[f5891,f6541]) ).
fof(f6541,plain,
( spl35_45
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_45])]) ).
fof(f5891,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(definition_unfolding,[],[f4716,f4497]) ).
fof(f4716,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(cnf_transformation,[],[f87]) ).
fof(f87,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th000_I3_J) ).
fof(f6539,plain,
spl35_44,
inference(avatar_split_clause,[],[f4610,f6536]) ).
fof(f6536,plain,
( spl35_44
<=> class_Rings_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_44])]) ).
fof(f4610,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1153]) ).
fof(f1153,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(f6530,plain,
spl35_43,
inference(avatar_split_clause,[],[f5349,f6527]) ).
fof(f6527,plain,
( spl35_43
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_43])]) ).
fof(f5349,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1039]) ).
fof(f1039,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(f6525,plain,
~ spl35_42,
inference(avatar_split_clause,[],[f6147,f6522]) ).
fof(f6147,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(equality_resolution,[],[f5015]) ).
fof(f5015,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X0,X0))
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != X0 ),
inference(cnf_transformation,[],[f3600]) ).
fof(f6520,plain,
spl35_41,
inference(avatar_split_clause,[],[f4599,f6517]) ).
fof(f6517,plain,
( spl35_41
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_41])]) ).
fof(f4599,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1066]) ).
fof(f1066,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f6511,plain,
spl35_40,
inference(avatar_split_clause,[],[f6506,f6508]) ).
fof(f6506,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f6505,f5637]) ).
fof(f6505,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),
inference(forward_demodulation,[],[f6504,f5637]) ).
fof(f6504,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f6503,f5537]) ).
fof(f6503,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f6502,f5537]) ).
fof(f6502,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f5828,f4248]) ).
fof(f5828,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(definition_unfolding,[],[f4332,f4431,f5442]) ).
fof(f4332,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f561]) ).
fof(f561,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(f6490,plain,
spl35_39,
inference(avatar_split_clause,[],[f5471,f6487]) ).
fof(f6487,plain,
( spl35_39
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_39])]) ).
fof(f5471,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1018]) ).
fof(f1018,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f6485,plain,
spl35_38,
inference(avatar_split_clause,[],[f4370,f6482]) ).
fof(f4370,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1129]) ).
fof(f1129,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
fof(f6479,plain,
spl35_37,
inference(avatar_split_clause,[],[f5693,f6476]) ).
fof(f5693,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th22) ).
fof(f6474,plain,
spl35_36,
inference(avatar_split_clause,[],[f4709,f6471]) ).
fof(f6471,plain,
( spl35_36
<=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_36])]) ).
fof(f4709,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1098]) ).
fof(f1098,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(f6467,plain,
spl35_35,
inference(avatar_split_clause,[],[f5726,f6464]) ).
fof(f5726,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f257]) ).
fof(f257,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(f6462,plain,
spl35_34,
inference(avatar_split_clause,[],[f4724,f6459]) ).
fof(f6459,plain,
( spl35_34
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_34])]) ).
fof(f4724,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1022]) ).
fof(f1022,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f6457,plain,
spl35_33,
inference(avatar_split_clause,[],[f4491,f6454]) ).
fof(f6454,plain,
( spl35_33
<=> class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_33])]) ).
fof(f4491,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1078]) ).
fof(f1078,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(f6452,plain,
spl35_32,
inference(avatar_split_clause,[],[f5506,f6449]) ).
fof(f6449,plain,
( spl35_32
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_32])]) ).
fof(f5506,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1014]) ).
fof(f1014,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f6442,plain,
spl35_31,
inference(avatar_split_clause,[],[f4158,f6439]) ).
fof(f4158,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(cnf_transformation,[],[f85]) ).
fof(f85,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).
fof(f6437,plain,
spl35_30,
inference(avatar_split_clause,[],[f4820,f6434]) ).
fof(f6434,plain,
( spl35_30
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_30])]) ).
fof(f4820,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f1061]) ).
fof(f1061,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f6432,plain,
spl35_29,
inference(avatar_split_clause,[],[f4886,f6429]) ).
fof(f6429,plain,
( spl35_29
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_29])]) ).
fof(f4886,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f6426,plain,
spl35_28,
inference(avatar_split_clause,[],[f5141,f6423]) ).
fof(f6423,plain,
( spl35_28
<=> class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_28])]) ).
fof(f5141,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1081]) ).
fof(f1081,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(f6421,plain,
spl35_27,
inference(avatar_split_clause,[],[f4937,f6418]) ).
fof(f6418,plain,
( spl35_27
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_27])]) ).
fof(f4937,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1151]) ).
fof(f1151,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f6416,plain,
spl35_26,
inference(avatar_split_clause,[],[f6411,f6413]) ).
fof(f6411,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(forward_demodulation,[],[f6410,f5637]) ).
fof(f6410,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(forward_demodulation,[],[f6409,f5637]) ).
fof(f6409,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(forward_demodulation,[],[f6408,f5537]) ).
fof(f6408,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(forward_demodulation,[],[f5956,f5537]) ).
fof(f5956,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(definition_unfolding,[],[f5036,f4431,f5442,f4497]) ).
fof(f5036,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(cnf_transformation,[],[f76]) ).
fof(f76,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).
fof(f6407,plain,
spl35_25,
inference(avatar_split_clause,[],[f6210,f6404]) ).
fof(f6404,plain,
( spl35_25
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_25])]) ).
fof(f6210,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f6209]) ).
fof(f6209,plain,
! [X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f6030]) ).
fof(f6030,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(definition_unfolding,[],[f5488,f4497,f4497]) ).
fof(f5488,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3874]) ).
fof(f6402,plain,
spl35_24,
inference(avatar_split_clause,[],[f5081,f6399]) ).
fof(f6399,plain,
( spl35_24
<=> class_Rings_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_24])]) ).
fof(f5081,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1131]) ).
fof(f1131,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(f6397,plain,
spl35_23,
inference(avatar_split_clause,[],[f5802,f6394]) ).
fof(f5802,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
inference(definition_unfolding,[],[f4184,f4497,f4497]) ).
fof(f4184,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
inference(cnf_transformation,[],[f232]) ).
fof(f232,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th00) ).
fof(f6390,plain,
spl35_22,
inference(avatar_split_clause,[],[f4057,f6387]) ).
fof(f6387,plain,
( spl35_22
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_22])]) ).
fof(f4057,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1006]) ).
fof(f1006,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f6376,plain,
spl35_19,
inference(avatar_split_clause,[],[f6200,f6362]) ).
fof(f6200,plain,
c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(equality_resolution,[],[f6015]) ).
fof(f6015,plain,
! [X0] :
( c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)
| c_Int_OPls != X0 ),
inference(definition_unfolding,[],[f5423,f4431]) ).
fof(f5423,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ),
inference(cnf_transformation,[],[f3830]) ).
fof(f3830,plain,
! [X0] :
( ( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) )
& ( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ) ),
inference(nnf_transformation,[],[f1544]) ).
fof(f1544,plain,
! [X0] :
( c_Int_OPls = X0
<=> c_Int_OPls = c_Int_OBit0(X0) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X26] :
( c_Int_OPls = c_Int_OBit0(X26)
<=> c_Int_OPls = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
fof(f6375,plain,
spl35_21,
inference(avatar_split_clause,[],[f4727,f6372]) ).
fof(f6372,plain,
( spl35_21
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_21])]) ).
fof(f4727,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1053]) ).
fof(f1053,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f6370,plain,
spl35_20,
inference(avatar_split_clause,[],[f5728,f6367]) ).
fof(f5728,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1077]) ).
fof(f1077,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(f6365,plain,
spl35_19,
inference(avatar_split_clause,[],[f6241,f6362]) ).
fof(f6241,plain,
c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(equality_resolution,[],[f6054]) ).
fof(f6054,plain,
! [X0] :
( c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0)
| c_Int_OPls != X0 ),
inference(definition_unfolding,[],[f5700,f4431]) ).
fof(f5700,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ),
inference(cnf_transformation,[],[f3994]) ).
fof(f3994,plain,
! [X0] :
( ( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 )
& ( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
inference(nnf_transformation,[],[f1486]) ).
fof(f1486,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
<=> c_Int_OPls = X0 ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X27] :
( c_Int_OPls = c_Int_OBit0(X27)
<=> c_Int_OPls = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
fof(f6354,plain,
spl35_18,
inference(avatar_split_clause,[],[f5386,f6351]) ).
fof(f6351,plain,
( spl35_18
<=> class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_18])]) ).
fof(f5386,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1076]) ).
fof(f1076,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(f6349,plain,
spl35_17,
inference(avatar_split_clause,[],[f4697,f6346]) ).
fof(f6346,plain,
( spl35_17
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_17])]) ).
fof(f4697,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1016]) ).
fof(f1016,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f6344,plain,
spl35_16,
inference(avatar_split_clause,[],[f5505,f6341]) ).
fof(f6341,plain,
( spl35_16
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_16])]) ).
fof(f5505,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1003]) ).
fof(f1003,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f6339,plain,
spl35_15,
inference(avatar_split_clause,[],[f5005,f6336]) ).
fof(f6336,plain,
( spl35_15
<=> class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_15])]) ).
fof(f5005,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1115]) ).
fof(f1115,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(f6334,plain,
spl35_14,
inference(avatar_split_clause,[],[f4544,f6331]) ).
fof(f6331,plain,
( spl35_14
<=> class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_14])]) ).
fof(f4544,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1100]) ).
fof(f1100,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(f6329,plain,
spl35_13,
inference(avatar_split_clause,[],[f4187,f6326]) ).
fof(f6326,plain,
( spl35_13
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_13])]) ).
fof(f4187,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1060]) ).
fof(f1060,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f6324,plain,
spl35_12,
inference(avatar_split_clause,[],[f4828,f6321]) ).
fof(f6321,plain,
( spl35_12
<=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_12])]) ).
fof(f4828,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1168]) ).
fof(f1168,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f6319,plain,
spl35_11,
inference(avatar_split_clause,[],[f4071,f6316]) ).
fof(f6316,plain,
( spl35_11
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_11])]) ).
fof(f4071,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1007]) ).
fof(f1007,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f6314,plain,
spl35_10,
inference(avatar_split_clause,[],[f5040,f6311]) ).
fof(f6311,plain,
( spl35_10
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_10])]) ).
fof(f5040,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1044]) ).
fof(f1044,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(f6299,plain,
spl35_9,
inference(avatar_split_clause,[],[f5257,f6296]) ).
fof(f6296,plain,
( spl35_9
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_9])]) ).
fof(f5257,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f996]) ).
fof(f996,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6294,plain,
spl35_8,
inference(avatar_split_clause,[],[f4583,f6291]) ).
fof(f6291,plain,
( spl35_8
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_8])]) ).
fof(f4583,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1005]) ).
fof(f1005,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f6289,plain,
spl35_7,
inference(avatar_split_clause,[],[f4829,f6286]) ).
fof(f6286,plain,
( spl35_7
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_7])]) ).
fof(f4829,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1010]) ).
fof(f1010,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f6284,plain,
spl35_6,
inference(avatar_split_clause,[],[f6279,f6281]) ).
fof(f6279,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f6033,f4248]) ).
fof(f6033,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(definition_unfolding,[],[f5560,f5442,f5442]) ).
fof(f5560,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f741]) ).
fof(f741,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(f6278,plain,
spl35_5,
inference(avatar_split_clause,[],[f5589,f6275]) ).
fof(f6275,plain,
( spl35_5
<=> class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_5])]) ).
fof(f5589,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1090]) ).
fof(f1090,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(f6273,plain,
spl35_4,
inference(avatar_split_clause,[],[f5901,f6270]) ).
fof(f5901,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK12)),
inference(definition_unfolding,[],[f4741,f4431,f5442]) ).
fof(f4741,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK12)),
inference(cnf_transformation,[],[f3443]) ).
fof(f3443,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK12)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f2359,f3442]) ).
fof(f3442,plain,
( ? [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X0))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,sK12)) ),
introduced(choice_axiom,[]) ).
fof(f2359,plain,
? [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(ennf_transformation,[],[f1292]) ).
fof(f1292,plain,
~ ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X0)),
inference(rectify,[],[f74]) ).
fof(f74,axiom,
~ ! [X33] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BN2_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_AN2_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(f6264,plain,
spl35_3,
inference(avatar_split_clause,[],[f5874,f6261]) ).
fof(f5874,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(definition_unfolding,[],[f4558,f4431,f5442]) ).
fof(f4558,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_e2) ).
fof(f6259,plain,
spl35_2,
inference(avatar_split_clause,[],[f4048,f6256]) ).
fof(f6256,plain,
( spl35_2
<=> class_Rings_Oordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_2])]) ).
fof(f4048,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1118]) ).
fof(f1118,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(f6254,plain,
spl35_1,
inference(avatar_split_clause,[],[f4831,f6251]) ).
fof(f6251,plain,
( spl35_1
<=> class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl35_1])]) ).
fof(f4831,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1089]) ).
fof(f1089,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW230+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 20:37:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.56 % (18412)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.56 % (18405)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.57 % (18408)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.57 % (18393)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.57 % (18400)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.57 % (18396)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.57 % (18391)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.58 % (18403)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.58 % (18415)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.58 % (18394)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.59 % (18395)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.59 % (18392)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.59 % (18396)Instruction limit reached!
% 0.19/0.59 % (18396)------------------------------
% 0.19/0.59 % (18396)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59 % (18396)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59 % (18396)Termination reason: Unknown
% 0.19/0.59 % (18396)Termination phase: Preprocessing 1
% 0.19/0.59
% 0.19/0.59 % (18396)Memory used [KB]: 2430
% 0.19/0.59 % (18396)Time elapsed: 0.009 s
% 0.19/0.59 % (18396)Instructions burned: 8 (million)
% 0.19/0.59 % (18396)------------------------------
% 0.19/0.59 % (18396)------------------------------
% 0.19/0.59 % (18389)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.59 % (18390)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.59 % (18410)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.59 % (18409)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.59 % (18416)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.59 % (18402)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.39/0.59 % (18411)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.39/0.60 % (18418)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.39/0.60 % (18406)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.39/0.60 % (18399)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.39/0.60 % (18398)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.39/0.60 % (18397)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.39/0.60 % (18397)Instruction limit reached!
% 1.39/0.60 % (18397)------------------------------
% 1.39/0.60 % (18397)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.39/0.60 % (18417)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.39/0.60 % (18413)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.39/0.61 % (18404)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.39/0.61 % (18414)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.39/0.61 % (18401)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.39/0.61 % (18407)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.61/0.62 % (18397)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.61/0.62 % (18397)Termination reason: Unknown
% 1.61/0.62 % (18397)Termination phase: shuffling
% 1.61/0.62
% 1.61/0.62 % (18397)Memory used [KB]: 1918
% 1.61/0.62 % (18397)Time elapsed: 0.003 s
% 1.61/0.62 % (18397)Instructions burned: 2 (million)
% 1.61/0.62 % (18397)------------------------------
% 1.61/0.62 % (18397)------------------------------
% 1.61/0.64 % (18393)Instruction limit reached!
% 1.61/0.64 % (18393)------------------------------
% 1.61/0.64 % (18393)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.66 % (18394)Instruction limit reached!
% 1.81/0.66 % (18394)------------------------------
% 1.81/0.66 % (18394)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.66 % (18391)Instruction limit reached!
% 1.81/0.66 % (18391)------------------------------
% 1.81/0.66 % (18391)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.66 % (18393)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.66 % (18393)Termination reason: Unknown
% 1.81/0.66 % (18393)Termination phase: Property scanning
% 1.81/0.66
% 1.81/0.66 % (18393)Memory used [KB]: 4349
% 1.81/0.66 % (18393)Time elapsed: 0.027 s
% 1.81/0.66 % (18393)Instructions burned: 51 (million)
% 1.81/0.66 % (18393)------------------------------
% 1.81/0.66 % (18393)------------------------------
% 1.81/0.66 % (18392)Instruction limit reached!
% 1.81/0.66 % (18392)------------------------------
% 1.81/0.66 % (18392)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.66 % (18392)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.66 % (18392)Termination reason: Unknown
% 1.81/0.66 % (18392)Termination phase: Property scanning
% 1.81/0.66
% 1.81/0.66 % (18392)Memory used [KB]: 4093
% 1.81/0.66 % (18392)Time elapsed: 0.026 s
% 1.81/0.66 % (18392)Instructions burned: 51 (million)
% 1.81/0.66 % (18392)------------------------------
% 1.81/0.66 % (18392)------------------------------
% 1.81/0.66 % (18391)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.66 % (18391)Termination reason: Unknown
% 1.81/0.66 % (18391)Termination phase: Preprocessing 3
% 1.81/0.66
% 1.81/0.66 % (18391)Memory used [KB]: 3837
% 1.81/0.66 % (18391)Time elapsed: 0.024 s
% 1.81/0.66 % (18391)Instructions burned: 38 (million)
% 1.81/0.66 % (18391)------------------------------
% 1.81/0.66 % (18391)------------------------------
% 1.81/0.66 % (18394)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.66 % (18394)Termination reason: Unknown
% 1.81/0.66 % (18394)Termination phase: Property scanning
% 1.81/0.66
% 1.81/0.66 % (18394)Memory used [KB]: 4349
% 1.81/0.66 % (18394)Time elapsed: 0.024 s
% 1.81/0.66 % (18394)Instructions burned: 48 (million)
% 1.81/0.66 % (18394)------------------------------
% 1.81/0.66 % (18394)------------------------------
% 1.81/0.67 % (18415)Instruction limit reached!
% 1.81/0.67 % (18415)------------------------------
% 1.81/0.67 % (18415)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.68 % (18398)Instruction limit reached!
% 1.81/0.68 % (18398)------------------------------
% 1.81/0.68 % (18398)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.69 % (18390)Instruction limit reached!
% 1.81/0.69 % (18390)------------------------------
% 1.81/0.69 % (18390)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.69 % (18390)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.69 % (18390)Termination reason: Unknown
% 1.81/0.69 % (18390)Termination phase: Property scanning
% 1.81/0.69
% 1.81/0.69 % (18390)Memory used [KB]: 4349
% 1.81/0.69 % (18390)Time elapsed: 0.026 s
% 1.81/0.69 % (18390)Instructions burned: 50 (million)
% 1.81/0.69 % (18390)------------------------------
% 1.81/0.69 % (18390)------------------------------
% 1.81/0.69 % (18399)Instruction limit reached!
% 1.81/0.69 % (18399)------------------------------
% 1.81/0.69 % (18399)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.69 % (18399)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.69 % (18399)Termination reason: Unknown
% 1.81/0.69 % (18399)Termination phase: Property scanning
% 1.81/0.69
% 1.81/0.69 % (18399)Memory used [KB]: 4349
% 1.81/0.69 % (18399)Time elapsed: 0.025 s
% 1.81/0.69 % (18399)Instructions burned: 50 (million)
% 1.81/0.69 % (18399)------------------------------
% 1.81/0.69 % (18399)------------------------------
% 1.81/0.69 % (18403)Instruction limit reached!
% 1.81/0.69 % (18403)------------------------------
% 1.81/0.69 % (18403)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.70 % (18403)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.70 % (18415)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.70 % (18415)Termination reason: Unknown
% 1.81/0.70 % (18415)Termination phase: Property scanning
% 1.81/0.70
% 1.81/0.70 % (18415)Memory used [KB]: 4733
% 1.81/0.70 % (18415)Time elapsed: 0.033 s
% 1.81/0.70 % (18415)Instructions burned: 69 (million)
% 1.81/0.70 % (18415)------------------------------
% 1.81/0.70 % (18415)------------------------------
% 1.81/0.70 % (18403)Termination reason: Unknown
% 1.81/0.70 % (18403)Termination phase: Property scanning
% 1.81/0.70
% 1.81/0.70 % (18403)Memory used [KB]: 4733
% 1.81/0.70 % (18403)Time elapsed: 0.050 s
% 1.81/0.70 % (18403)Instructions burned: 69 (million)
% 1.81/0.70 % (18403)------------------------------
% 1.81/0.70 % (18403)------------------------------
% 1.81/0.70 % (18395)Instruction limit reached!
% 1.81/0.70 % (18395)------------------------------
% 1.81/0.70 % (18395)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.70 % (18395)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.70 % (18395)Termination reason: Unknown
% 1.81/0.70 % (18395)Termination phase: Property scanning
% 1.81/0.70
% 1.81/0.70 % (18395)Memory used [KB]: 4477
% 1.81/0.70 % (18395)Time elapsed: 0.028 s
% 1.81/0.70 % (18395)Instructions burned: 53 (million)
% 1.81/0.70 % (18395)------------------------------
% 1.81/0.70 % (18395)------------------------------
% 1.81/0.70 % (18406)Instruction limit reached!
% 1.81/0.70 % (18406)------------------------------
% 1.81/0.70 % (18406)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.70 % (18406)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.70 % (18406)Termination reason: Unknown
% 1.81/0.70 % (18406)Termination phase: Function definition elimination
% 1.81/0.70
% 1.81/0.70 % (18406)Memory used [KB]: 4349
% 1.81/0.70 % (18406)Time elapsed: 0.041 s
% 1.81/0.70 % (18406)Instructions burned: 60 (million)
% 1.81/0.70 % (18406)------------------------------
% 1.81/0.70 % (18406)------------------------------
% 1.81/0.70 % (18398)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.70 % (18398)Termination reason: Unknown
% 1.81/0.70 % (18398)Termination phase: Property scanning
% 1.81/0.70
% 1.81/0.70 % (18398)Memory used [KB]: 4349
% 1.81/0.70 % (18398)Time elapsed: 0.026 s
% 1.81/0.70 % (18398)Instructions burned: 52 (million)
% 1.81/0.70 % (18398)------------------------------
% 1.81/0.70 % (18398)------------------------------
% 1.81/0.71 % (18405)Instruction limit reached!
% 1.81/0.71 % (18405)------------------------------
% 1.81/0.71 % (18405)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.71 % (18405)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.71 % (18405)Termination reason: Unknown
% 1.81/0.71 % (18405)Termination phase: Saturation
% 1.81/0.71
% 1.81/0.71 % (18405)Memory used [KB]: 9083
% 1.81/0.71 % (18405)Time elapsed: 0.065 s
% 1.81/0.71 % (18405)Instructions burned: 99 (million)
% 1.81/0.71 % (18405)------------------------------
% 1.81/0.71 % (18405)------------------------------
% 1.81/0.72 % (18408)Instruction limit reached!
% 1.81/0.72 % (18408)------------------------------
% 1.81/0.72 % (18408)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.72 % (18400)Instruction limit reached!
% 2.43/0.72 % (18400)------------------------------
% 2.43/0.72 % (18400)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.72 % (18400)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.72 % (18400)Termination reason: Unknown
% 2.43/0.72 % (18400)Termination phase: Saturation
% 2.43/0.72
% 2.43/0.72 % (18400)Memory used [KB]: 8955
% 2.43/0.72 % (18400)Time elapsed: 0.047 s
% 2.43/0.72 % (18400)Instructions burned: 101 (million)
% 2.43/0.72 % (18400)------------------------------
% 2.43/0.72 % (18400)------------------------------
% 2.43/0.72 % (18408)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.72 % (18408)Termination reason: Unknown
% 2.43/0.72 % (18408)Termination phase: Saturation
% 2.43/0.72
% 2.43/0.72 % (18408)Memory used [KB]: 4861
% 2.43/0.72 % (18408)Time elapsed: 0.048 s
% 2.43/0.72 % (18408)Instructions burned: 101 (million)
% 2.43/0.72 % (18408)------------------------------
% 2.43/0.72 % (18408)------------------------------
% 2.43/0.72 % (18404)Instruction limit reached!
% 2.43/0.72 % (18404)------------------------------
% 2.43/0.72 % (18404)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.72 % (18404)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.72 % (18404)Termination reason: Unknown
% 2.43/0.72 % (18404)Termination phase: Property scanning
% 2.43/0.72
% 2.43/0.72 % (18404)Memory used [KB]: 4349
% 2.43/0.72 % (18404)Time elapsed: 0.036 s
% 2.43/0.72 % (18404)Instructions burned: 77 (million)
% 2.43/0.72 % (18404)------------------------------
% 2.43/0.72 % (18404)------------------------------
% 2.43/0.73 % (18419)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/388Mi)
% 2.43/0.74 % (18402)Instruction limit reached!
% 2.43/0.74 % (18402)------------------------------
% 2.43/0.74 % (18402)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.74 % (18402)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.74 % (18402)Termination reason: Unknown
% 2.43/0.74 % (18402)Termination phase: Saturation
% 2.43/0.74
% 2.43/0.74 % (18402)Memory used [KB]: 9338
% 2.43/0.74 % (18402)Time elapsed: 0.049 s
% 2.43/0.74 % (18402)Instructions burned: 99 (million)
% 2.43/0.74 % (18402)------------------------------
% 2.43/0.74 % (18402)------------------------------
% 2.43/0.76 % (18407)Instruction limit reached!
% 2.43/0.76 % (18407)------------------------------
% 2.43/0.76 % (18407)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.76 % (18420)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=211:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/211Mi)
% 2.43/0.76 % (18401)Instruction limit reached!
% 2.43/0.76 % (18401)------------------------------
% 2.43/0.76 % (18401)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.43/0.76 % (18401)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.76 % (18401)Termination reason: Unknown
% 2.43/0.76 % (18401)Termination phase: Saturation
% 2.43/0.76
% 2.43/0.76 % (18401)Memory used [KB]: 9338
% 2.43/0.76 % (18401)Time elapsed: 0.051 s
% 2.43/0.76 % (18401)Instructions burned: 101 (million)
% 2.43/0.76 % (18401)------------------------------
% 2.43/0.76 % (18401)------------------------------
% 2.43/0.77 % (18407)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.43/0.77 % (18407)Termination reason: Unknown
% 2.43/0.77 % (18407)Termination phase: Saturation
% 2.43/0.77
% 2.43/0.77 % (18407)Memory used [KB]: 9338
% 2.43/0.77 % (18407)Time elapsed: 0.048 s
% 2.43/0.77 % (18407)Instructions burned: 101 (million)
% 2.43/0.77 % (18407)------------------------------
% 2.43/0.77 % (18407)------------------------------
% 2.43/0.78 % (18423)ott+1_1:7_bd=off:i=934:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/934Mi)
% 2.65/0.78 % (18421)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/90Mi)
% 2.65/0.79 % (18422)ott+1_1:2_i=920:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/920Mi)
% 2.65/0.80 % (18424)ott+10_1:50_bsr=unit_only:drc=off:fd=preordered:sp=frequency:i=747:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/747Mi)
% 2.65/0.80 % (18410)Instruction limit reached!
% 2.65/0.80 % (18410)------------------------------
% 2.65/0.80 % (18410)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.65/0.80 % (18410)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.65/0.80 % (18410)Termination reason: Unknown
% 2.65/0.80 % (18410)Termination phase: Saturation
% 2.65/0.80
% 2.65/0.80 % (18410)Memory used [KB]: 9722
% 2.65/0.80 % (18410)Time elapsed: 0.079 s
% 2.65/0.80 % (18410)Instructions burned: 139 (million)
% 2.65/0.80 % (18410)------------------------------
% 2.65/0.80 % (18410)------------------------------
% 2.65/0.81 % (18416)Instruction limit reached!
% 2.65/0.81 % (18416)------------------------------
% 2.65/0.81 % (18416)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.65/0.81 % (18427)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=940:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/940Mi)
% 2.65/0.82 % (18409)Instruction limit reached!
% 2.65/0.82 % (18409)------------------------------
% 2.65/0.82 % (18409)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.65/0.82 % (18409)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.65/0.82 % (18409)Termination reason: Unknown
% 2.65/0.82 % (18409)Termination phase: Saturation
% 2.65/0.82
% 2.65/0.82 % (18409)Memory used [KB]: 10106
% 2.65/0.82 % (18409)Time elapsed: 0.111 s
% 2.65/0.82 % (18409)Instructions burned: 176 (million)
% 2.65/0.82 % (18409)------------------------------
% 2.65/0.82 % (18409)------------------------------
% 2.65/0.82 % (18425)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=655:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/655Mi)
% 2.65/0.82 % (18430)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/2016Mi)
% 2.65/0.82 % (18426)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/68Mi)
% 2.65/0.83 % (18416)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.65/0.83 % (18416)Termination reason: Unknown
% 2.65/0.83 % (18416)Termination phase: Saturation
% 2.65/0.83
% 2.65/0.83 % (18416)Memory used [KB]: 5500
% 2.65/0.83 % (18416)Time elapsed: 0.115 s
% 2.65/0.83 % (18416)Instructions burned: 177 (million)
% 2.65/0.83 % (18416)------------------------------
% 2.65/0.83 % (18416)------------------------------
% 2.65/0.83 % (18429)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/90Mi)
% 2.65/0.84 % (18432)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4958Mi)
% 2.65/0.85 % (18435)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=4931:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4931Mi)
% 2.65/0.85 % (18433)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=4959:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4959Mi)
% 2.65/0.85 WARNING Broken Constraint: if sine_depth(2) has been set then sine_selection(off) is not equal to off
% 2.65/0.85 % (18428)ott+11_4:1_br=off:fde=none:s2a=on:sd=2:sp=frequency:urr=on:i=981:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/981Mi)
% 2.65/0.85 % (18431)dis+10_1:2_atotf=0.3:i=3735:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/3735Mi)
% 2.83/0.86 % (18434)ott+10_1:1_kws=precedence:tgt=ground:i=4756:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4756Mi)
% 2.83/0.86 % (18436)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/68Mi)
% 2.89/0.89 % (18421)Instruction limit reached!
% 2.89/0.89 % (18421)------------------------------
% 2.89/0.89 % (18421)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.89/0.89 % (18421)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.89/0.89 % (18421)Termination reason: Unknown
% 2.89/0.89 % (18421)Termination phase: Property scanning
% 2.89/0.89
% 2.89/0.89 % (18421)Memory used [KB]: 4605
% 2.89/0.89 % (18421)Time elapsed: 0.067 s
% 2.89/0.89 % (18421)Instructions burned: 91 (million)
% 2.89/0.89 % (18421)------------------------------
% 2.89/0.89 % (18421)------------------------------
% 2.89/0.90 % (18438)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=2134:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/2134Mi)
% 2.89/0.90 % (18437)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/1824Mi)
% 2.89/0.91 % (18439)ott-1_1:1_sp=const_frequency:i=2891:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/2891Mi)
% 3.04/0.93 % (18426)Instruction limit reached!
% 3.04/0.93 % (18426)------------------------------
% 3.04/0.93 % (18426)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.04/0.93 % (18426)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.04/0.93 % (18426)Termination reason: Unknown
% 3.04/0.93 % (18426)Termination phase: Property scanning
% 3.04/0.93
% 3.04/0.93 % (18426)Memory used [KB]: 4733
% 3.04/0.93 % (18426)Time elapsed: 0.030 s
% 3.04/0.93 % (18426)Instructions burned: 68 (million)
% 3.04/0.93 % (18426)------------------------------
% 3.04/0.93 % (18426)------------------------------
% 3.14/0.95 % (18440)dis+2_1:64_add=large:bce=on:bd=off:i=4585:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/4585Mi)
% 3.14/0.97 % (18441)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/90Mi)
% 3.14/0.98 % (18429)Instruction limit reached!
% 3.14/0.98 % (18429)------------------------------
% 3.14/0.98 % (18429)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.14/0.98 % (18429)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.14/0.98 % (18429)Termination reason: Unknown
% 3.14/0.98 % (18429)Termination phase: Property scanning
% 3.14/0.98
% 3.14/0.98 % (18429)Memory used [KB]: 4605
% 3.14/0.98 % (18429)Time elapsed: 0.040 s
% 3.14/0.98 % (18429)Instructions burned: 91 (million)
% 3.14/0.98 % (18429)------------------------------
% 3.14/0.98 % (18429)------------------------------
% 3.14/0.98 % (18436)Instruction limit reached!
% 3.14/0.98 % (18436)------------------------------
% 3.14/0.98 % (18436)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.14/0.98 % (18436)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.14/0.98 % (18436)Termination reason: Unknown
% 3.14/0.98 % (18436)Termination phase: Property scanning
% 3.14/0.98
% 3.14/0.98 % (18436)Memory used [KB]: 4733
% 3.14/0.98 % (18436)Time elapsed: 0.033 s
% 3.14/0.98 % (18436)Instructions burned: 69 (million)
% 3.14/0.98 % (18436)------------------------------
% 3.14/0.98 % (18436)------------------------------
% 3.14/1.00 % (18442)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/2016Mi)
% 3.41/1.06 % (18443)dis+10_1:2_atotf=0.3:i=8004:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/8004Mi)
% 3.54/1.08 % (18441)Instruction limit reached!
% 3.54/1.08 % (18441)------------------------------
% 3.54/1.08 % (18441)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.54/1.09 % (18441)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.54/1.09 % (18441)Termination reason: Unknown
% 3.54/1.09 % (18441)Termination phase: Property scanning
% 3.54/1.09
% 3.54/1.09 % (18441)Memory used [KB]: 4733
% 3.54/1.09 % (18441)Time elapsed: 0.038 s
% 3.54/1.09 % (18441)Instructions burned: 90 (million)
% 3.54/1.09 % (18441)------------------------------
% 3.54/1.09 % (18441)------------------------------
% 3.54/1.11 % (18444)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=9965:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/9965Mi)
% 3.54/1.11 % (18420)Instruction limit reached!
% 3.54/1.11 % (18420)------------------------------
% 3.54/1.11 % (18420)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.54/1.11 % (18420)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.54/1.11 % (18420)Termination reason: Unknown
% 3.54/1.11 % (18420)Termination phase: Saturation
% 3.54/1.11
% 3.54/1.11 % (18420)Memory used [KB]: 6140
% 3.54/1.11 % (18420)Time elapsed: 0.459 s
% 3.54/1.11 % (18420)Instructions burned: 211 (million)
% 3.54/1.11 % (18420)------------------------------
% 3.54/1.11 % (18420)------------------------------
% 3.54/1.12 % (18445)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=9877:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/9877Mi)
% 6.18/1.22 % (18418)Instruction limit reached!
% 6.18/1.22 % (18418)------------------------------
% 6.18/1.22 % (18418)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.18/1.23 % (18418)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.18/1.23 % (18418)Termination reason: Unknown
% 6.18/1.23 % (18418)Termination phase: Saturation
% 6.18/1.23
% 6.18/1.23 % (18418)Memory used [KB]: 11641
% 6.18/1.23 % (18418)Time elapsed: 0.742 s
% 6.18/1.23 % (18418)Instructions burned: 355 (million)
% 6.18/1.23 % (18418)------------------------------
% 6.18/1.23 % (18418)------------------------------
% 6.18/1.23 % (18446)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=9902:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/9902Mi)
% 6.53/1.25 % (18447)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/1824Mi)
% 6.53/1.29 % (18417)Instruction limit reached!
% 6.53/1.29 % (18417)------------------------------
% 6.53/1.29 % (18417)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.53/1.29 % (18419)Instruction limit reached!
% 6.53/1.29 % (18419)------------------------------
% 6.53/1.29 % (18419)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.53/1.30 % (18417)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.53/1.30 % (18417)Termination reason: Unknown
% 6.53/1.30 % (18417)Termination phase: Saturation
% 6.53/1.30
% 6.53/1.30 % (18417)Memory used [KB]: 11897
% 6.53/1.30 % (18417)Time elapsed: 0.833 s
% 6.53/1.30 % (18417)Instructions burned: 440 (million)
% 6.53/1.30 % (18417)------------------------------
% 6.53/1.30 % (18417)------------------------------
% 6.53/1.30 % (18419)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.53/1.30 % (18419)Termination reason: Unknown
% 6.53/1.30 % (18419)Termination phase: Saturation
% 6.53/1.30
% 6.53/1.30 % (18419)Memory used [KB]: 11641
% 6.53/1.30 % (18419)Time elapsed: 0.663 s
% 6.53/1.30 % (18419)Instructions burned: 388 (million)
% 6.53/1.30 % (18419)------------------------------
% 6.53/1.30 % (18419)------------------------------
% 6.53/1.32 % (18411)Instruction limit reached!
% 6.53/1.32 % (18411)------------------------------
% 6.53/1.32 % (18411)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.53/1.32 % (18411)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.53/1.32 % (18411)Termination reason: Unknown
% 6.53/1.32 % (18411)Termination phase: Saturation
% 6.53/1.32
% 6.53/1.32 % (18411)Memory used [KB]: 6780
% 6.53/1.32 % (18411)Time elapsed: 0.822 s
% 6.53/1.32 % (18411)Instructions burned: 498 (million)
% 6.53/1.32 % (18411)------------------------------
% 6.53/1.32 % (18411)------------------------------
% 7.35/1.36 % (18412)Instruction limit reached!
% 7.35/1.36 % (18412)------------------------------
% 7.35/1.36 % (18412)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.35/1.36 % (18412)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.35/1.36 % (18412)Termination reason: Unknown
% 7.35/1.36 % (18412)Termination phase: Saturation
% 7.35/1.36
% 7.35/1.36 % (18412)Memory used [KB]: 12025
% 7.35/1.36 % (18412)Time elapsed: 0.879 s
% 7.35/1.36 % (18412)Instructions burned: 468 (million)
% 7.35/1.36 % (18412)------------------------------
% 7.35/1.36 % (18412)------------------------------
% 7.35/1.38 % (18448)dis+2_1:64_add=large:bce=on:bd=off:i=9989:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/9989Mi)
% 7.71/1.40 % (18449)ott-11_1:32_i=9707:si=on:rawr=on:rtra=on_0 on theBenchmark for (2990ds/9707Mi)
% 7.71/1.40 % (18450)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2990ds/90Mi)
% 8.11/1.46 % (18414)Instruction limit reached!
% 8.11/1.46 % (18414)------------------------------
% 8.11/1.46 % (18414)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.11/1.46 % (18451)ott+3_1:1_abs=on:anc=none:bs=on:fsr=off:spb=goal_then_units:i=44001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2990ds/44001Mi)
% 8.11/1.47 % (18413)Instruction limit reached!
% 8.11/1.47 % (18413)------------------------------
% 8.11/1.47 % (18413)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.11/1.48 % (18414)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.11/1.48 % (18414)Termination reason: Unknown
% 8.11/1.48 % (18414)Termination phase: Saturation
% 8.11/1.48
% 8.11/1.48 % (18414)Memory used [KB]: 13432
% 8.11/1.48 % (18414)Time elapsed: 0.994 s
% 8.11/1.48 % (18414)Instructions burned: 500 (million)
% 8.11/1.48 % (18414)------------------------------
% 8.11/1.48 % (18414)------------------------------
% 8.11/1.49 % (18413)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.11/1.49 % (18413)Termination reason: Unknown
% 8.11/1.49 % (18413)Termination phase: Saturation
% 8.11/1.49
% 8.11/1.49 % (18413)Memory used [KB]: 12665
% 8.11/1.49 % (18413)Time elapsed: 0.991 s
% 8.11/1.49 % (18413)Instructions burned: 483 (million)
% 8.11/1.49 % (18413)------------------------------
% 8.11/1.49 % (18413)------------------------------
% 8.11/1.52 % (18450)Instruction limit reached!
% 8.11/1.52 % (18450)------------------------------
% 8.11/1.52 % (18450)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.11/1.52 % (18452)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2989ds/4958Mi)
% 8.11/1.53 % (18450)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.11/1.53 % (18450)Termination reason: Unknown
% 8.11/1.53 % (18450)Termination phase: Property scanning
% 8.11/1.53
% 8.11/1.53 % (18450)Memory used [KB]: 4605
% 8.11/1.53 % (18450)Time elapsed: 0.061 s
% 8.11/1.53 % (18450)Instructions burned: 90 (million)
% 8.11/1.53 % (18450)------------------------------
% 8.11/1.53 % (18450)------------------------------
% 8.85/1.58 TRYING [1]
% 8.85/1.59 % (18453)ott+1_27:428_av=off:awrs=converge:awrsf=8:bsr=unit_only:drc=off:fd=preordered:newcnf=on:nwc=1.5:skr=on:slsq=on:slsqc=2:slsql=off:slsqr=1,4:sp=reverse_frequency:uwa=one_side_constant:i=35256:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/35256Mi)
% 9.08/1.62 % (18454)dis+1002_1:1_fde=unused:nwc=10.0:s2a=on:s2at=3.0:sac=on:i=32293:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/32293Mi)
% 9.36/1.68 % (18455)ott+21_1:28_afr=on:anc=all_dependent:bs=on:bsr=unit_only:nicw=on:sp=const_frequency:uhcvi=on:i=37001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/37001Mi)
% 9.36/1.69 TRYING [2]
% 9.36/1.73 % (18425)Instruction limit reached!
% 9.36/1.73 % (18425)------------------------------
% 9.36/1.73 % (18425)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 9.36/1.73 % (18425)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 9.36/1.73 % (18425)Termination reason: Unknown
% 9.36/1.73 % (18425)Termination phase: Saturation
% 9.36/1.73
% 9.36/1.73 % (18425)Memory used [KB]: 6908
% 9.36/1.73 % (18425)Time elapsed: 0.981 s
% 9.36/1.73 % (18425)Instructions burned: 655 (million)
% 9.36/1.73 % (18425)------------------------------
% 9.36/1.73 % (18425)------------------------------
% 11.60/1.88 % (18456)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=10187:si=on:rawr=on:rtra=on_0 on theBenchmark for (2986ds/10187Mi)
% 14.03/2.18 % (18424)Instruction limit reached!
% 14.03/2.18 % (18424)------------------------------
% 14.03/2.18 % (18424)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 14.03/2.18 % (18424)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 14.03/2.18 % (18424)Termination reason: Unknown
% 14.03/2.18 % (18424)Termination phase: Saturation
% 14.03/2.18
% 14.03/2.18 % (18424)Memory used [KB]: 15479
% 14.03/2.18 % (18424)Time elapsed: 1.464 s
% 14.03/2.18 % (18424)Instructions burned: 747 (million)
% 14.03/2.18 % (18424)------------------------------
% 14.03/2.18 % (18424)------------------------------
% 14.50/2.30 % (18457)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=29337:si=on:rawr=on:rtra=on_0 on theBenchmark for (2981ds/29337Mi)
% 15.08/2.35 % (18423)Instruction limit reached!
% 15.08/2.35 % (18423)------------------------------
% 15.08/2.35 % (18423)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.08/2.35 % (18423)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.08/2.35 % (18423)Termination reason: Unknown
% 15.08/2.35 % (18423)Termination phase: Saturation
% 15.08/2.35
% 15.08/2.35 % (18423)Memory used [KB]: 16502
% 15.08/2.35 % (18423)Time elapsed: 1.660 s
% 15.08/2.35 % (18423)Instructions burned: 934 (million)
% 15.08/2.35 % (18423)------------------------------
% 15.08/2.35 % (18423)------------------------------
% 15.64/2.40 % (18427)Instruction limit reached!
% 15.64/2.40 % (18427)------------------------------
% 15.64/2.40 % (18427)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.64/2.40 % (18427)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.64/2.40 % (18427)Termination reason: Unknown
% 15.64/2.40 % (18427)Termination phase: Saturation
% 15.64/2.40
% 15.64/2.40 % (18427)Memory used [KB]: 15863
% 15.64/2.40 % (18427)Time elapsed: 1.659 s
% 15.64/2.40 % (18427)Instructions burned: 941 (million)
% 15.64/2.40 % (18427)------------------------------
% 15.64/2.40 % (18427)------------------------------
% 15.64/2.41 % (18422)Instruction limit reached!
% 15.64/2.41 % (18422)------------------------------
% 15.64/2.41 % (18422)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.64/2.41 % (18422)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.64/2.41 % (18422)Termination reason: Unknown
% 15.64/2.41 % (18422)Termination phase: Saturation
% 15.64/2.41
% 15.64/2.41 % (18422)Memory used [KB]: 14583
% 15.64/2.41 % (18422)Time elapsed: 1.715 s
% 15.64/2.41 % (18422)Instructions burned: 920 (million)
% 15.64/2.41 % (18422)------------------------------
% 15.64/2.41 % (18422)------------------------------
% 15.64/2.45 % (18428)Instruction limit reached!
% 15.64/2.45 % (18428)------------------------------
% 15.64/2.45 % (18428)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.64/2.45 % (18428)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.64/2.45 % (18428)Termination reason: Unknown
% 15.64/2.45 % (18428)Termination phase: Saturation
% 15.64/2.45
% 15.64/2.45 % (18428)Memory used [KB]: 17910
% 15.64/2.45 % (18428)Time elapsed: 1.682 s
% 15.64/2.45 % (18428)Instructions burned: 981 (million)
% 15.64/2.45 % (18428)------------------------------
% 15.64/2.45 % (18428)------------------------------
% 15.64/2.47 % (18458)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=10147:si=on:rawr=on:rtra=on_0 on theBenchmark for (2979ds/10147Mi)
% 16.66/2.54 % (18460)fmb+10_1:1_dr=on:fmbsr=2.0:newcnf=on:nm=2:i=33239:si=on:rawr=on:rtra=on_0 on theBenchmark for (2979ds/33239Mi)
% 16.66/2.55 % (18459)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=38056:si=on:rawr=on:rtra=on_0 on theBenchmark for (2979ds/38056Mi)
% 16.66/2.58 % (18461)fmb+10_1:1_fmbas=predicate:gsp=on:nm=2:i=20987:si=on:rawr=on:rtra=on_0 on theBenchmark for (2978ds/20987Mi)
% 18.56/2.83 % (18442)Instruction limit reached!
% 18.56/2.83 % (18442)------------------------------
% 18.56/2.83 % (18442)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 18.56/2.83 % (18442)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 18.56/2.83 % (18442)Termination reason: Unknown
% 18.56/2.83 % (18442)Termination phase: Saturation
% 18.56/2.83
% 18.56/2.83 % (18442)Memory used [KB]: 9594
% 18.56/2.83 % (18442)Time elapsed: 1.890 s
% 18.56/2.83 % (18442)Instructions burned: 2016 (million)
% 18.56/2.83 % (18442)------------------------------
% 18.56/2.83 % (18442)------------------------------
% 19.39/2.90 % (18462)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=49917:si=on:rawr=on:rtra=on_0 on theBenchmark for (2975ds/49917Mi)
% 20.25/3.04 % (18430)Instruction limit reached!
% 20.25/3.04 % (18430)------------------------------
% 20.25/3.04 % (18430)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 20.25/3.04 % (18430)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 20.25/3.04 % (18430)Termination reason: Unknown
% 20.25/3.04 % (18430)Termination phase: Saturation
% 20.25/3.04
% 20.25/3.04 % (18430)Memory used [KB]: 9850
% 20.25/3.04 % (18430)Time elapsed: 2.316 s
% 20.25/3.04 % (18430)Instructions burned: 2017 (million)
% 20.25/3.04 % (18430)------------------------------
% 20.25/3.04 % (18430)------------------------------
% 21.41/3.15 % (18463)dis+2_1:64_add=large:bce=on:bd=off:i=19144:si=on:rawr=on:rtra=on_0 on theBenchmark for (2973ds/19144Mi)
% 23.72/3.43 % (18437)Instruction limit reached!
% 23.72/3.43 % (18437)------------------------------
% 23.72/3.43 % (18437)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 23.72/3.44 TRYING [1]
% 23.72/3.44 % (18437)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 23.72/3.44 % (18437)Termination reason: Unknown
% 23.72/3.44 % (18437)Termination phase: Saturation
% 23.72/3.44
% 23.72/3.44 % (18437)Memory used [KB]: 12792
% 23.72/3.44 % (18437)Time elapsed: 2.614 s
% 23.72/3.44 % (18437)Instructions burned: 1824 (million)
% 23.72/3.44 % (18437)------------------------------
% 23.72/3.44 % (18437)------------------------------
% 23.72/3.46 TRYING [1]
% 23.72/3.49 TRYING [1]
% 24.49/3.55 % (18464)dis+10_1:128_bd=off:lcm=predicate:sac=on:sp=reverse_arity:urr=on:i=27492:si=on:rawr=on:rtra=on_0 on theBenchmark for (2969ds/27492Mi)
% 24.49/3.55 TRYING [2]
% 24.49/3.57 TRYING [2]
% 24.49/3.59 TRYING [2]
% 25.25/3.61 % (18432)First to succeed.
% 25.25/3.62 TRYING [1]
% 26.07/3.72 TRYING [2]
% 26.07/3.79 % (18432)Refutation found. Thanks to Tanya!
% 26.07/3.79 % SZS status Theorem for theBenchmark
% 26.07/3.79 % SZS output start Proof for theBenchmark
% See solution above
% 27.01/3.82 % (18432)------------------------------
% 27.01/3.82 % (18432)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 27.01/3.82 % (18432)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 27.01/3.82 % (18432)Termination reason: Refutation
% 27.01/3.82
% 27.01/3.82 % (18432)Memory used [KB]: 12537
% 27.01/3.82 % (18432)Time elapsed: 2.885 s
% 27.01/3.82 % (18432)Instructions burned: 2084 (million)
% 27.01/3.82 % (18432)------------------------------
% 27.01/3.82 % (18432)------------------------------
% 27.01/3.82 % (18388)Success in time 3.466 s
%------------------------------------------------------------------------------