TSTP Solution File: NUM925+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:38:38 EDT 2024
% Result : Theorem 1.73s 0.67s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 872
% Syntax : Number of formulae : 2662 (1099 unt; 0 def)
% Number of atoms : 6011 (1983 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 5179 (1830 ~;1816 |; 594 &)
% ( 689 <=>; 246 =>; 0 <=; 4 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 508 ( 506 usr; 484 prp; 0-3 aty)
% Number of functors : 97 ( 97 usr; 44 con; 0-3 aty)
% Number of variables : 3152 (3041 !; 111 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12514,plain,
$false,
inference(avatar_sat_refutation,[],[f7014,f7019,f7024,f7029,f7034,f7039,f7044,f7049,f7054,f7059,f7064,f7069,f7074,f7079,f7084,f7089,f7094,f7099,f7104,f7109,f7114,f7119,f7124,f7129,f7134,f7139,f7144,f7149,f7154,f7159,f7163,f7168,f7173,f7177,f7181,f7186,f7191,f7196,f7201,f7206,f7211,f7220,f7224,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7256,f7260,f7264,f7268,f7272,f7276,f7280,f7284,f7288,f7292,f7296,f7300,f7304,f7308,f7312,f7316,f7321,f7327,f7332,f7336,f7340,f7344,f7349,f7353,f7362,f7373,f7378,f7384,f7389,f7394,f7399,f7404,f7409,f7414,f7419,f7424,f7429,f7434,f7439,f7444,f7449,f7453,f7457,f7461,f7465,f7469,f7473,f7477,f7481,f7485,f7489,f7493,f7497,f7501,f7505,f7509,f7513,f7517,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7550,f7555,f7560,f7565,f7570,f7574,f7578,f7583,f7588,f7593,f7598,f7603,f7638,f7646,f7650,f7654,f7658,f7662,f7666,f7670,f7674,f7678,f7682,f7687,f7691,f7695,f7699,f7703,f7707,f7711,f7715,f7719,f7723,f7728,f7733,f7737,f7741,f7745,f7750,f7903,f7987,f8025,f8029,f8047,f8063,f8068,f8072,f8076,f8080,f8084,f8088,f8092,f8096,f8101,f8105,f8109,f8113,f8117,f8121,f8125,f8129,f8133,f8137,f8141,f8146,f8150,f8154,f8158,f8162,f8166,f8170,f8174,f8178,f8182,f8186,f8191,f8195,f8199,f8203,f8207,f8211,f8215,f8220,f8225,f8229,f8233,f8238,f8242,f8246,f8255,f8258,f8265,f8270,f8274,f8278,f8283,f8289,f8294,f8299,f8304,f8309,f8314,f8329,f8396,f8526,f8559,f8564,f8587,f8592,f8598,f8606,f8611,f8616,f8620,f8624,f8628,f8632,f8636,f8640,f8644,f8648,f8652,f8656,f8661,f8665,f8669,f8673,f8677,f8681,f8686,f8691,f8695,f8699,f8703,f8708,f8713,f8718,f8722,f8726,f8810,f8823,f8871,f8877,f8881,f8885,f8889,f8893,f8897,f8901,f8905,f8909,f8913,f8917,f8922,f8926,f8930,f8934,f8938,f8942,f8947,f8953,f8958,f8965,f8969,f8974,f8980,f8985,f8991,f8995,f8999,f9003,f9007,f9011,f9015,f9019,f9023,f9027,f9031,f9035,f9039,f9043,f9047,f9051,f9055,f9059,f9064,f9069,f9073,f9077,f9081,f9085,f9089,f9093,f9097,f9101,f9106,f9262,f9517,f9575,f9588,f9593,f9597,f9601,f9605,f9609,f9613,f9617,f9621,f9625,f9636,f9640,f9644,f9648,f9652,f9656,f9660,f9664,f9668,f9672,f9683,f9687,f9691,f9695,f9699,f9703,f9707,f9711,f9715,f9719,f9730,f9734,f9738,f9742,f9746,f9751,f9755,f9759,f9763,f9767,f9778,f9782,f9786,f9790,f9794,f9798,f9803,f9810,f9816,f9827,f9832,f9838,f9843,f9847,f9851,f9855,f9859,f9863,f9867,f9879,f9884,f10062,f10763,f10816,f10934,f10939,f10945,f10949,f11375,f11379,f11383,f11466,f11470,f11474,f11483,f11487,f11491,f11495,f11499,f11503,f11507,f11511,f11515,f11519,f11523,f11529,f11533,f11537,f11541,f11545,f11550,f11554,f11558,f11562,f11566,f11571,f11575,f11579,f11583,f11587,f11591,f11595,f11599,f11604,f11611,f11619,f11625,f12058,f12176,f12258,f12262,f12267,f12274,f12278,f12282,f12286,f12290,f12295,f12299,f12303,f12307,f12311,f12315,f12319,f12323,f12327,f12331,f12335,f12340,f12344,f12348,f12352,f12356,f12360,f12364,f12368,f12372,f12376,f12381,f12385,f12389,f12393,f12397,f12401,f12405,f12409,f12413,f12417,f12422,f12426,f12430,f12434,f12438,f12442,f12447,f12451,f12455,f12459,f12463,f12475,f12479,f12483,f12487,f12491,f12495,f12499,f12503,f12508,f12513]) ).
fof(f12513,plain,
( spl63_24
| ~ spl63_32
| ~ spl63_129
| ~ spl63_351
| ~ spl63_464 ),
inference(avatar_split_clause,[],[f12470,f12419,f9749,f7635,f7165,f7126]) ).
fof(f7126,plain,
( spl63_24
<=> one_one_nat = zero_zero_nat ),
introduced(avatar_definition,[new_symbols(naming,[spl63_24])]) ).
fof(f7165,plain,
( spl63_32
<=> one_one_nat = nat(one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_32])]) ).
fof(f7635,plain,
( spl63_129
<=> one_one_int = number_number_of_int(one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_129])]) ).
fof(f9749,plain,
( spl63_351
<=> ! [X0] :
( zero_zero_nat = nat(number_number_of_int(X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_351])]) ).
fof(f12419,plain,
( spl63_464
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_464])]) ).
fof(f12470,plain,
( one_one_nat = zero_zero_nat
| ~ spl63_32
| ~ spl63_129
| ~ spl63_351
| ~ spl63_464 ),
inference(forward_demodulation,[],[f12469,f7167]) ).
fof(f7167,plain,
( one_one_nat = nat(one_one_int)
| ~ spl63_32 ),
inference(avatar_component_clause,[],[f7165]) ).
fof(f12469,plain,
( zero_zero_nat = nat(one_one_int)
| ~ spl63_129
| ~ spl63_351
| ~ spl63_464 ),
inference(forward_demodulation,[],[f12465,f7637]) ).
fof(f7637,plain,
( one_one_int = number_number_of_int(one_one_int)
| ~ spl63_129 ),
inference(avatar_component_clause,[],[f7635]) ).
fof(f12465,plain,
( zero_zero_nat = nat(number_number_of_int(one_one_int))
| ~ spl63_351
| ~ spl63_464 ),
inference(resolution,[],[f12421,f9750]) ).
fof(f9750,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| zero_zero_nat = nat(number_number_of_int(X0)) )
| ~ spl63_351 ),
inference(avatar_component_clause,[],[f9749]) ).
fof(f12421,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls))
| ~ spl63_464 ),
inference(avatar_component_clause,[],[f12419]) ).
fof(f12508,plain,
( spl63_483
| ~ spl63_32
| ~ spl63_129
| ~ spl63_351
| ~ spl63_464
| ~ spl63_482 ),
inference(avatar_split_clause,[],[f12504,f12501,f12419,f9749,f7635,f7165,f12506]) ).
fof(f12506,plain,
( spl63_483
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,one_one_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_483])]) ).
fof(f12501,plain,
( spl63_482
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_482])]) ).
fof(f12504,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,one_one_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ sP5(X0,X1) )
| ~ spl63_32
| ~ spl63_129
| ~ spl63_351
| ~ spl63_464
| ~ spl63_482 ),
inference(forward_demodulation,[],[f12502,f12470]) ).
fof(f12502,plain,
( ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ sP5(X0,X1) )
| ~ spl63_482 ),
inference(avatar_component_clause,[],[f12501]) ).
fof(f12503,plain,
spl63_482,
inference(avatar_split_clause,[],[f5934,f12501]) ).
fof(f5934,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ sP5(X0,X1) ),
inference(definition_unfolding,[],[f4433,f3772]) ).
fof(f3772,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f127]) ).
fof(f127,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(f4433,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3351]) ).
fof(f3351,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
| ( ~ hBOOL(hAPP_nat_bool(X0,sK43(X0,X1)))
& hAPP_nat_int(semiri1621563631at_int,sK43(X0,X1)) = X1 ) )
& ( ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_int(semiri1621563631at_int,X3) != X1 ) )
| ~ sP5(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f3349,f3350]) ).
fof(f3350,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& hAPP_nat_int(semiri1621563631at_int,X2) = X1 )
=> ( ~ hBOOL(hAPP_nat_bool(X0,sK43(X0,X1)))
& hAPP_nat_int(semiri1621563631at_int,sK43(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3349,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& hAPP_nat_int(semiri1621563631at_int,X2) = X1 ) )
& ( ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_int(semiri1621563631at_int,X3) != X1 ) )
| ~ sP5(X0,X1) ) ),
inference(rectify,[],[f3348]) ).
fof(f3348,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& hAPP_nat_int(semiri1621563631at_int,X2) = X1 ) )
& ( ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X2] :
( hBOOL(hAPP_nat_bool(X0,X2))
| hAPP_nat_int(semiri1621563631at_int,X2) != X1 ) )
| ~ sP5(X0,X1) ) ),
inference(flattening,[],[f3347]) ).
fof(f3347,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,X2))
& hAPP_nat_int(semiri1621563631at_int,X2) = X1 ) )
& ( ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X2] :
( hBOOL(hAPP_nat_bool(X0,X2))
| hAPP_nat_int(semiri1621563631at_int,X2) != X1 ) )
| ~ sP5(X0,X1) ) ),
inference(nnf_transformation,[],[f3180]) ).
fof(f3180,plain,
! [X0,X1] :
( sP5(X0,X1)
<=> ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X2] :
( hBOOL(hAPP_nat_bool(X0,X2))
| hAPP_nat_int(semiri1621563631at_int,X2) != X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f12499,plain,
spl63_481,
inference(avatar_split_clause,[],[f5880,f12497]) ).
fof(f12497,plain,
( spl63_481
<=> ! [X2,X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK41(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_481])]) ).
fof(f5880,plain,
! [X2,X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK41(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(definition_unfolding,[],[f4292,f3772]) ).
fof(f4292,plain,
! [X2,X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK41(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(cnf_transformation,[],[f3332]) ).
fof(f3332,plain,
! [X0] :
( ( ( hBOOL(hAPP_int_bool(X0,sK41(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK41(X0)))
& is_int(sK41(X0)) )
| ! [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK42(X0))))
| ! [X4] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
| ~ is_int(X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f3329,f3331,f3330]) ).
fof(f3330,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& is_int(X1) )
=> ( hBOOL(hAPP_int_bool(X0,sK41(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK41(X0)))
& is_int(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3331,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
=> hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK42(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f3329,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& is_int(X1) )
| ! [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ? [X3] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ! [X4] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
| ~ is_int(X4) ) ) ),
inference(rectify,[],[f3328]) ).
fof(f3328,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& is_int(X1) )
| ! [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ? [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
| ! [X1] :
( ~ hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) ) ) ),
inference(nnf_transformation,[],[f1515]) ).
fof(f1515,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& is_int(X1) )
<=> ? [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(rectify,[],[f814]) ).
fof(f814,axiom,
! [X54] :
( ? [X152] :
( hBOOL(hAPP_int_bool(X54,X152))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
& is_int(X152) )
<=> ? [X152] : hBOOL(hAPP_int_bool(X54,hAPP_nat_int(semiri1621563631at_int,X152))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_785_transfer__int__nat__quantifiers_I2_J) ).
fof(f12495,plain,
spl63_480,
inference(avatar_split_clause,[],[f5877,f12493]) ).
fof(f12493,plain,
( spl63_480
<=> ! [X0,X3] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK38(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_480])]) ).
fof(f5877,plain,
! [X3,X0] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK38(X0))) ),
inference(definition_unfolding,[],[f4283,f3772]) ).
fof(f4283,plain,
! [X3,X0] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK38(X0))) ),
inference(cnf_transformation,[],[f3322]) ).
fof(f3322,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK37(X0)))) )
& ( ! [X3] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ( ~ hBOOL(hAPP_int_bool(X0,sK38(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK38(X0)))
& is_int(sK38(X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f3319,f3321,f3320]) ).
fof(f3320,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
=> ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,sK37(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f3321,plain,
! [X0] :
( ? [X4] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
& is_int(X4) )
=> ( ~ hBOOL(hAPP_int_bool(X0,sK38(X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK38(X0)))
& is_int(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3319,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
| ? [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ! [X3] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ? [X4] :
( ~ hBOOL(hAPP_int_bool(X0,X4))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X4))
& is_int(X4) ) ) ),
inference(rectify,[],[f3318]) ).
fof(f3318,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
| ? [X2] : ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) )
& ( ! [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2)))
| ? [X1] :
( ~ hBOOL(hAPP_int_bool(X0,X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& is_int(X1) ) ) ),
inference(nnf_transformation,[],[f2414]) ).
fof(f2414,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
<=> ! [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(flattening,[],[f2413]) ).
fof(f2413,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP_int_bool(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
<=> ! [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(ennf_transformation,[],[f1513]) ).
fof(f1513,plain,
! [X0] :
( ! [X1] :
( is_int(X1)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> hBOOL(hAPP_int_bool(X0,X1)) ) )
<=> ! [X2] : hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(rectify,[],[f815]) ).
fof(f815,axiom,
! [X54] :
( ! [X152] :
( is_int(X152)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
=> hBOOL(hAPP_int_bool(X54,X152)) ) )
<=> ! [X152] : hBOOL(hAPP_int_bool(X54,hAPP_nat_int(semiri1621563631at_int,X152))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_786_transfer__int__nat__quantifiers_I1_J) ).
fof(f12491,plain,
spl63_479,
inference(avatar_split_clause,[],[f5847,f12489]) ).
fof(f12489,plain,
( spl63_479
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_479])]) ).
fof(f5847,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls)) ),
inference(definition_unfolding,[],[f4238,f3772]) ).
fof(f4238,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int)) ),
inference(cnf_transformation,[],[f3293]) ).
fof(f3293,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int)) ) ),
inference(nnf_transformation,[],[f1492]) ).
fof(f1492,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(rectify,[],[f760]) ).
fof(f760,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X3)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_le__special_I3_J) ).
fof(f12487,plain,
spl63_478,
inference(avatar_split_clause,[],[f5846,f12485]) ).
fof(f12485,plain,
( spl63_478
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_478])]) ).
fof(f5846,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(definition_unfolding,[],[f4239,f3772]) ).
fof(f4239,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X0)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(cnf_transformation,[],[f3293]) ).
fof(f12483,plain,
spl63_477,
inference(avatar_split_clause,[],[f5831,f12481]) ).
fof(f12481,plain,
( spl63_477
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_477])]) ).
fof(f5831,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls)) ),
inference(definition_unfolding,[],[f4222,f3772]) ).
fof(f4222,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int)) ),
inference(cnf_transformation,[],[f3285]) ).
fof(f3285,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int)) ) ),
inference(nnf_transformation,[],[f1484]) ).
fof(f1484,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(rectify,[],[f98]) ).
fof(f98,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X3)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__special_I3_J) ).
fof(f12479,plain,
spl63_476,
inference(avatar_split_clause,[],[f5830,f12477]) ).
fof(f12477,plain,
( spl63_476
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_476])]) ).
fof(f5830,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(definition_unfolding,[],[f4223,f3772]) ).
fof(f4223,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(X0)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(cnf_transformation,[],[f3285]) ).
fof(f12475,plain,
spl63_475,
inference(avatar_split_clause,[],[f5827,f12473]) ).
fof(f12473,plain,
( spl63_475
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_475])]) ).
fof(f5827,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0))) ),
inference(definition_unfolding,[],[f4218,f3772]) ).
fof(f4218,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f3283]) ).
fof(f3283,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0))) ) ),
inference(nnf_transformation,[],[f1482]) ).
fof(f1482,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(rectify,[],[f758]) ).
fof(f758,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_le__special_I1_J) ).
fof(f12463,plain,
spl63_474,
inference(avatar_split_clause,[],[f5826,f12461]) ).
fof(f12461,plain,
( spl63_474
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_474])]) ).
fof(f5826,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(definition_unfolding,[],[f4219,f3772]) ).
fof(f4219,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(cnf_transformation,[],[f3283]) ).
fof(f12459,plain,
spl63_473,
inference(avatar_split_clause,[],[f5815,f12457]) ).
fof(f12457,plain,
( spl63_473
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_473])]) ).
fof(f5815,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0))) ),
inference(definition_unfolding,[],[f4206,f3772]) ).
fof(f4206,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0))) ),
inference(cnf_transformation,[],[f3277]) ).
fof(f3277,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0))) ) ),
inference(nnf_transformation,[],[f1476]) ).
fof(f1476,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(rectify,[],[f100]) ).
fof(f100,axiom,
! [X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__special_I1_J) ).
fof(f12455,plain,
spl63_472,
inference(avatar_split_clause,[],[f5814,f12453]) ).
fof(f12453,plain,
( spl63_472
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_472])]) ).
fof(f5814,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(definition_unfolding,[],[f4207,f3772]) ).
fof(f4207,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(cnf_transformation,[],[f3277]) ).
fof(f12451,plain,
spl63_471,
inference(avatar_split_clause,[],[f5801,f12449]) ).
fof(f12449,plain,
( spl63_471
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_471])]) ).
fof(f5801,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0))) ),
inference(definition_unfolding,[],[f4192,f3772]) ).
fof(f4192,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0))) ),
inference(cnf_transformation,[],[f3270]) ).
fof(f3270,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0))) ) ),
inference(nnf_transformation,[],[f1469]) ).
fof(f1469,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(rectify,[],[f844]) ).
fof(f844,axiom,
! [X30] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X30)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_zero__less__nat__eq) ).
fof(f12447,plain,
spl63_470,
inference(avatar_split_clause,[],[f5800,f12445]) ).
fof(f12445,plain,
( spl63_470
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_470])]) ).
fof(f5800,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(definition_unfolding,[],[f4193,f3772]) ).
fof(f4193,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),nat(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f3270]) ).
fof(f12442,plain,
spl63_469,
inference(avatar_split_clause,[],[f5732,f12440]) ).
fof(f12440,plain,
( spl63_469
<=> ! [X0] :
( one_one_nat = plus_plus_nat(nat(number_number_of_int(X0)),one_one_nat)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_469])]) ).
fof(f5732,plain,
! [X0] :
( one_one_nat = plus_plus_nat(nat(number_number_of_int(X0)),one_one_nat)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(definition_unfolding,[],[f4061,f3978]) ).
fof(f3978,plain,
! [X0] : number_number_of_nat(X0) = nat(number_number_of_int(X0)),
inference(cnf_transformation,[],[f1313]) ).
fof(f1313,plain,
! [X0] : number_number_of_nat(X0) = nat(number_number_of_int(X0)),
inference(rectify,[],[f796]) ).
fof(f796,axiom,
! [X13] : number_number_of_nat(X13) = nat(number_number_of_int(X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_nat__number__of__def) ).
fof(f4061,plain,
! [X0] :
( one_one_nat = plus_plus_nat(number_number_of_nat(X0),one_one_nat)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(cnf_transformation,[],[f2345]) ).
fof(f2345,plain,
! [X0] :
( ( number_number_of_nat(succ(X0)) = plus_plus_nat(number_number_of_nat(X0),one_one_nat)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
& ( one_one_nat = plus_plus_nat(number_number_of_nat(X0),one_one_nat)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
inference(ennf_transformation,[],[f1389]) ).
fof(f1389,plain,
! [X0] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
=> number_number_of_nat(succ(X0)) = plus_plus_nat(number_number_of_nat(X0),one_one_nat) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
=> one_one_nat = plus_plus_nat(number_number_of_nat(X0),one_one_nat) ) ),
inference(rectify,[],[f435]) ).
fof(f435,axiom,
! [X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> plus_plus_nat(number_number_of_nat(X13),one_one_nat) = number_number_of_nat(succ(X13)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> one_one_nat = plus_plus_nat(number_number_of_nat(X13),one_one_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_nat__number__of__add__1) ).
fof(f12438,plain,
spl63_468,
inference(avatar_split_clause,[],[f5730,f12436]) ).
fof(f12436,plain,
( spl63_468
<=> ! [X0] :
( one_one_nat = plus_plus_nat(one_one_nat,nat(number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_468])]) ).
fof(f5730,plain,
! [X0] :
( one_one_nat = plus_plus_nat(one_one_nat,nat(number_number_of_int(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(definition_unfolding,[],[f4059,f3978]) ).
fof(f4059,plain,
! [X0] :
( one_one_nat = plus_plus_nat(one_one_nat,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(cnf_transformation,[],[f2344]) ).
fof(f2344,plain,
! [X0] :
( ( number_number_of_nat(succ(X0)) = plus_plus_nat(one_one_nat,number_number_of_nat(X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
& ( one_one_nat = plus_plus_nat(one_one_nat,number_number_of_nat(X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
inference(ennf_transformation,[],[f1388]) ).
fof(f1388,plain,
! [X0] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
=> number_number_of_nat(succ(X0)) = plus_plus_nat(one_one_nat,number_number_of_nat(X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
=> one_one_nat = plus_plus_nat(one_one_nat,number_number_of_nat(X0)) ) ),
inference(rectify,[],[f436]) ).
fof(f436,axiom,
! [X13] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> number_number_of_nat(succ(X13)) = plus_plus_nat(one_one_nat,number_number_of_nat(X13)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X13),pls))
=> one_one_nat = plus_plus_nat(one_one_nat,number_number_of_nat(X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_nat__1__add__number__of) ).
fof(f12434,plain,
spl63_467,
inference(avatar_split_clause,[],[f5698,f12432]) ).
fof(f12432,plain,
( spl63_467
<=> ! [X0] : minus_minus_int(pls,plus_plus_int(X0,X0)) = plus_plus_int(minus_minus_int(pls,X0),minus_minus_int(pls,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_467])]) ).
fof(f5698,plain,
! [X0] : minus_minus_int(pls,plus_plus_int(X0,X0)) = plus_plus_int(minus_minus_int(pls,X0),minus_minus_int(pls,X0)),
inference(definition_unfolding,[],[f4020,f3979,f3979]) ).
fof(f3979,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f1314]) ).
fof(f1314,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X21] : bit0(X21) = plus_plus_int(X21,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(f4020,plain,
! [X0] : minus_minus_int(pls,bit0(X0)) = bit0(minus_minus_int(pls,X0)),
inference(cnf_transformation,[],[f1355]) ).
fof(f1355,plain,
! [X0] : minus_minus_int(pls,bit0(X0)) = bit0(minus_minus_int(pls,X0)),
inference(rectify,[],[f943]) ).
fof(f943,axiom,
! [X31] : minus_minus_int(pls,bit0(X31)) = bit0(minus_minus_int(pls,X31)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_914_diff__bin__simps_I3_J) ).
fof(f12430,plain,
spl63_466,
inference(avatar_split_clause,[],[f5346,f12428]) ).
fof(f12428,plain,
( spl63_466
<=> ! [X2,X0,X1] :
( zero_zero_nat = X0
| X1 = X2
| times_times_nat(X0,X1) != times_times_nat(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_466])]) ).
fof(f5346,plain,
! [X2,X0,X1] :
( zero_zero_nat = X0
| X1 = X2
| times_times_nat(X0,X1) != times_times_nat(X0,X2) ),
inference(cnf_transformation,[],[f3659]) ).
fof(f3659,plain,
! [X0,X1,X2] :
( ( times_times_nat(X0,X1) = times_times_nat(X0,X2)
| ( zero_zero_nat != X0
& X1 != X2 ) )
& ( zero_zero_nat = X0
| X1 = X2
| times_times_nat(X0,X1) != times_times_nat(X0,X2) ) ),
inference(flattening,[],[f3658]) ).
fof(f3658,plain,
! [X0,X1,X2] :
( ( times_times_nat(X0,X1) = times_times_nat(X0,X2)
| ( zero_zero_nat != X0
& X1 != X2 ) )
& ( zero_zero_nat = X0
| X1 = X2
| times_times_nat(X0,X1) != times_times_nat(X0,X2) ) ),
inference(nnf_transformation,[],[f2186]) ).
fof(f2186,plain,
! [X0,X1,X2] :
( times_times_nat(X0,X1) = times_times_nat(X0,X2)
<=> ( zero_zero_nat = X0
| X1 = X2 ) ),
inference(rectify,[],[f897]) ).
fof(f897,axiom,
! [X11,X29,X18] :
( times_times_nat(X11,X29) = times_times_nat(X11,X18)
<=> ( zero_zero_nat = X11
| X18 = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_mult__cancel1) ).
fof(f12426,plain,
spl63_465,
inference(avatar_split_clause,[],[f5343,f12424]) ).
fof(f12424,plain,
( spl63_465
<=> ! [X2,X0,X1] :
( zero_zero_nat = X1
| X0 = X2
| times_times_nat(X0,X1) != times_times_nat(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_465])]) ).
fof(f5343,plain,
! [X2,X0,X1] :
( zero_zero_nat = X1
| X0 = X2
| times_times_nat(X0,X1) != times_times_nat(X2,X1) ),
inference(cnf_transformation,[],[f3657]) ).
fof(f3657,plain,
! [X0,X1,X2] :
( ( times_times_nat(X0,X1) = times_times_nat(X2,X1)
| ( zero_zero_nat != X1
& X0 != X2 ) )
& ( zero_zero_nat = X1
| X0 = X2
| times_times_nat(X0,X1) != times_times_nat(X2,X1) ) ),
inference(flattening,[],[f3656]) ).
fof(f3656,plain,
! [X0,X1,X2] :
( ( times_times_nat(X0,X1) = times_times_nat(X2,X1)
| ( zero_zero_nat != X1
& X0 != X2 ) )
& ( zero_zero_nat = X1
| X0 = X2
| times_times_nat(X0,X1) != times_times_nat(X2,X1) ) ),
inference(nnf_transformation,[],[f2185]) ).
fof(f2185,plain,
! [X0,X1,X2] :
( times_times_nat(X0,X1) = times_times_nat(X2,X1)
<=> ( zero_zero_nat = X1
| X0 = X2 ) ),
inference(rectify,[],[f898]) ).
fof(f898,axiom,
! [X29,X11,X18] :
( times_times_nat(X29,X11) = times_times_nat(X18,X11)
<=> ( zero_zero_nat = X11
| X18 = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_mult__cancel2) ).
fof(f12422,plain,
( spl63_464
| ~ spl63_314
| ~ spl63_390
| ~ spl63_409 ),
inference(avatar_split_clause,[],[f12098,f11556,f11476,f9514,f12419]) ).
fof(f9514,plain,
( spl63_314
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_314])]) ).
fof(f11476,plain,
( spl63_390
<=> pls = minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_390])]) ).
fof(f11556,plain,
( spl63_409
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_409])]) ).
fof(f12098,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls))
| ~ spl63_314
| ~ spl63_390
| ~ spl63_409 ),
inference(forward_demodulation,[],[f12092,f11478]) ).
fof(f11478,plain,
( pls = minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)
| ~ spl63_390 ),
inference(avatar_component_clause,[],[f11476]) ).
fof(f12092,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl63_314
| ~ spl63_409 ),
inference(resolution,[],[f11557,f9516]) ).
fof(f9516,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl63_314 ),
inference(avatar_component_clause,[],[f9514]) ).
fof(f11557,plain,
( ! [X0] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) )
| ~ spl63_409 ),
inference(avatar_component_clause,[],[f11556]) ).
fof(f12417,plain,
spl63_463,
inference(avatar_split_clause,[],[f5056,f12415]) ).
fof(f12415,plain,
( spl63_463
<=> ! [X2,X0,X1] :
( X0 = X1
| times_times_real(X1,X2) != times_times_real(X0,X2)
| zero_zero_real = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_463])]) ).
fof(f5056,plain,
! [X2,X0,X1] :
( X0 = X1
| times_times_real(X1,X2) != times_times_real(X0,X2)
| zero_zero_real = X2 ),
inference(cnf_transformation,[],[f3588]) ).
fof(f3588,plain,
! [X0,X1,X2] :
( ( ( times_times_real(X1,X2) = times_times_real(X0,X2)
| X0 != X1 )
& ( X0 = X1
| times_times_real(X1,X2) != times_times_real(X0,X2) ) )
| zero_zero_real = X2 ),
inference(nnf_transformation,[],[f2736]) ).
fof(f2736,plain,
! [X0,X1,X2] :
( ( times_times_real(X1,X2) = times_times_real(X0,X2)
<=> X0 = X1 )
| zero_zero_real = X2 ),
inference(ennf_transformation,[],[f1979]) ).
fof(f1979,plain,
! [X0,X1,X2] :
( zero_zero_real != X2
=> ( times_times_real(X1,X2) = times_times_real(X0,X2)
<=> X0 = X1 ) ),
inference(rectify,[],[f902]) ).
fof(f902,axiom,
! [X5,X81,X110] :
( zero_zero_real != X110
=> ( times_times_real(X5,X110) = times_times_real(X81,X110)
<=> X5 = X81 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_real__mult__right__cancel) ).
fof(f12413,plain,
spl63_462,
inference(avatar_split_clause,[],[f5054,f12411]) ).
fof(f12411,plain,
( spl63_462
<=> ! [X2,X0,X1] :
( X0 = X1
| times_times_real(X2,X1) != times_times_real(X2,X0)
| zero_zero_real = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_462])]) ).
fof(f5054,plain,
! [X2,X0,X1] :
( X0 = X1
| times_times_real(X2,X1) != times_times_real(X2,X0)
| zero_zero_real = X2 ),
inference(cnf_transformation,[],[f3587]) ).
fof(f3587,plain,
! [X0,X1,X2] :
( ( ( times_times_real(X2,X1) = times_times_real(X2,X0)
| X0 != X1 )
& ( X0 = X1
| times_times_real(X2,X1) != times_times_real(X2,X0) ) )
| zero_zero_real = X2 ),
inference(nnf_transformation,[],[f2735]) ).
fof(f2735,plain,
! [X0,X1,X2] :
( ( times_times_real(X2,X1) = times_times_real(X2,X0)
<=> X0 = X1 )
| zero_zero_real = X2 ),
inference(ennf_transformation,[],[f1978]) ).
fof(f1978,plain,
! [X0,X1,X2] :
( zero_zero_real != X2
=> ( times_times_real(X2,X1) = times_times_real(X2,X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f901]) ).
fof(f901,axiom,
! [X5,X81,X110] :
( zero_zero_real != X110
=> ( times_times_real(X110,X5) = times_times_real(X110,X81)
<=> X5 = X81 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_real__mult__left__cancel) ).
fof(f12409,plain,
spl63_461,
inference(avatar_split_clause,[],[f5051,f12407]) ).
fof(f12407,plain,
( spl63_461
<=> ! [X2,X0,X1] :
( is_int(sK56(X0,X1,X2))
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
| ~ is_int(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_461])]) ).
fof(f5051,plain,
! [X2,X0,X1] :
( is_int(sK56(X0,X1,X2))
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
| ~ is_int(X1) ),
inference(cnf_transformation,[],[f3586]) ).
fof(f3586,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
| ! [X3] :
( plus_plus_int(X0,times_times_int(X2,X3)) != X1
| ~ is_int(X3) ) )
& ( ( plus_plus_int(X0,times_times_int(X2,sK56(X0,X1,X2))) = X1
& is_int(sK56(X0,X1,X2)) )
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) )
| ~ is_int(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f3584,f3585]) ).
fof(f3585,plain,
! [X0,X1,X2] :
( ? [X4] :
( plus_plus_int(X0,times_times_int(X2,X4)) = X1
& is_int(X4) )
=> ( plus_plus_int(X0,times_times_int(X2,sK56(X0,X1,X2))) = X1
& is_int(sK56(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3584,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
| ! [X3] :
( plus_plus_int(X0,times_times_int(X2,X3)) != X1
| ~ is_int(X3) ) )
& ( ? [X4] :
( plus_plus_int(X0,times_times_int(X2,X4)) = X1
& is_int(X4) )
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) )
| ~ is_int(X1) ),
inference(rectify,[],[f3583]) ).
fof(f3583,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
| ! [X3] :
( plus_plus_int(X0,times_times_int(X2,X3)) != X1
| ~ is_int(X3) ) )
& ( ? [X3] :
( plus_plus_int(X0,times_times_int(X2,X3)) = X1
& is_int(X3) )
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) )
| ~ is_int(X1) ),
inference(nnf_transformation,[],[f2734]) ).
fof(f2734,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
<=> ? [X3] :
( plus_plus_int(X0,times_times_int(X2,X3)) = X1
& is_int(X3) ) )
| ~ is_int(X1) ),
inference(ennf_transformation,[],[f1977]) ).
fof(f1977,plain,
! [X0,X1,X2] :
( is_int(X1)
=> ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
<=> ? [X3] :
( plus_plus_int(X0,times_times_int(X2,X3)) = X1
& is_int(X3) ) ) ),
inference(rectify,[],[f1165]) ).
fof(f1165,axiom,
! [X5,X81,X29] :
( is_int(X81)
=> ( hBOOL(hAPP_int_bool(zcong(X5,X81),X29))
<=> ? [X91] :
( plus_plus_int(X5,times_times_int(X29,X91)) = X81
& is_int(X91) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_zcong__iff__lin) ).
fof(f12405,plain,
spl63_460,
inference(avatar_split_clause,[],[f5010,f12403]) ).
fof(f12403,plain,
( spl63_460
<=> ! [X2,X0,X1] : times_times_int(plus_plus_int(X0,X1),X2) = plus_plus_int(times_times_int(X0,X2),times_times_int(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_460])]) ).
fof(f5010,plain,
! [X2,X0,X1] : times_times_int(plus_plus_int(X0,X1),X2) = plus_plus_int(times_times_int(X0,X2),times_times_int(X1,X2)),
inference(cnf_transformation,[],[f1946]) ).
fof(f1946,plain,
! [X0,X1,X2] : times_times_int(plus_plus_int(X0,X1),X2) = plus_plus_int(times_times_int(X0,X2),times_times_int(X1,X2)),
inference(rectify,[],[f674]) ).
fof(f674,axiom,
! [X322,X323,X324] : times_times_int(plus_plus_int(X322,X323),X324) = plus_plus_int(times_times_int(X322,X324),times_times_int(X323,X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(f12401,plain,
spl63_459,
inference(avatar_split_clause,[],[f5009,f12399]) ).
fof(f12399,plain,
( spl63_459
<=> ! [X2,X0,X1] : times_times_int(minus_minus_int(X0,X1),X2) = minus_minus_int(times_times_int(X0,X2),times_times_int(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_459])]) ).
fof(f5009,plain,
! [X2,X0,X1] : times_times_int(minus_minus_int(X0,X1),X2) = minus_minus_int(times_times_int(X0,X2),times_times_int(X1,X2)),
inference(cnf_transformation,[],[f1945]) ).
fof(f1945,plain,
! [X0,X1,X2] : times_times_int(minus_minus_int(X0,X1),X2) = minus_minus_int(times_times_int(X0,X2),times_times_int(X1,X2)),
inference(rectify,[],[f892]) ).
fof(f892,axiom,
! [X26,X27,X14] : times_times_int(minus_minus_int(X26,X27),X14) = minus_minus_int(times_times_int(X26,X14),times_times_int(X27,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_zdiff__zmult__distrib) ).
fof(f12397,plain,
spl63_458,
inference(avatar_split_clause,[],[f5007,f12395]) ).
fof(f12395,plain,
( spl63_458
<=> ! [X2,X0,X1] : times_times_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(times_times_int(X0,X1),times_times_int(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_458])]) ).
fof(f5007,plain,
! [X2,X0,X1] : times_times_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(times_times_int(X0,X1),times_times_int(X0,X2)),
inference(cnf_transformation,[],[f1943]) ).
fof(f1943,plain,
! [X0,X1,X2] : times_times_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(times_times_int(X0,X1),times_times_int(X0,X2)),
inference(rectify,[],[f748]) ).
fof(f748,axiom,
! [X14,X26,X27] : times_times_int(X14,plus_plus_int(X26,X27)) = plus_plus_int(times_times_int(X14,X26),times_times_int(X14,X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_zadd__zmult__distrib2) ).
fof(f12393,plain,
spl63_457,
inference(avatar_split_clause,[],[f5006,f12391]) ).
fof(f12391,plain,
( spl63_457
<=> ! [X2,X0,X1] : times_times_int(X0,minus_minus_int(X1,X2)) = minus_minus_int(times_times_int(X0,X1),times_times_int(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_457])]) ).
fof(f5006,plain,
! [X2,X0,X1] : times_times_int(X0,minus_minus_int(X1,X2)) = minus_minus_int(times_times_int(X0,X1),times_times_int(X0,X2)),
inference(cnf_transformation,[],[f1942]) ).
fof(f1942,plain,
! [X0,X1,X2] : times_times_int(X0,minus_minus_int(X1,X2)) = minus_minus_int(times_times_int(X0,X1),times_times_int(X0,X2)),
inference(rectify,[],[f893]) ).
fof(f893,axiom,
! [X14,X26,X27] : times_times_int(X14,minus_minus_int(X26,X27)) = minus_minus_int(times_times_int(X14,X26),times_times_int(X14,X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_864_zdiff__zmult__distrib2) ).
fof(f12389,plain,
spl63_456,
inference(avatar_split_clause,[],[f5003,f12387]) ).
fof(f12387,plain,
( spl63_456
<=> ! [X2,X0,X1] : times_times_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(times_times_nat(X0,X2),times_times_nat(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_456])]) ).
fof(f5003,plain,
! [X2,X0,X1] : times_times_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(times_times_nat(X0,X2),times_times_nat(X1,X2)),
inference(cnf_transformation,[],[f1939]) ).
fof(f1939,plain,
! [X0,X1,X2] : times_times_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(times_times_nat(X0,X2),times_times_nat(X1,X2)),
inference(rectify,[],[f910]) ).
fof(f910,axiom,
! [X15,X16,X21] : times_times_nat(plus_plus_nat(X15,X16),X21) = plus_plus_nat(times_times_nat(X15,X21),times_times_nat(X16,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_add__mult__distrib) ).
fof(f12385,plain,
spl63_455,
inference(avatar_split_clause,[],[f5002,f12383]) ).
fof(f12383,plain,
( spl63_455
<=> ! [X2,X0,X1] : times_times_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(times_times_nat(X0,X2),times_times_nat(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_455])]) ).
fof(f5002,plain,
! [X2,X0,X1] : times_times_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(times_times_nat(X0,X2),times_times_nat(X1,X2)),
inference(cnf_transformation,[],[f1938]) ).
fof(f1938,plain,
! [X0,X1,X2] : times_times_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(times_times_nat(X0,X2),times_times_nat(X1,X2)),
inference(rectify,[],[f928]) ).
fof(f928,axiom,
! [X15,X16,X21] : times_times_nat(minus_minus_nat(X15,X16),X21) = minus_minus_nat(times_times_nat(X15,X21),times_times_nat(X16,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_899_diff__mult__distrib) ).
fof(f12381,plain,
spl63_454,
inference(avatar_split_clause,[],[f5000,f12379]) ).
fof(f12379,plain,
( spl63_454
<=> ! [X2,X0,X1] : times_times_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(times_times_nat(X0,X1),times_times_nat(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_454])]) ).
fof(f5000,plain,
! [X2,X0,X1] : times_times_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(times_times_nat(X0,X1),times_times_nat(X0,X2)),
inference(cnf_transformation,[],[f1936]) ).
fof(f1936,plain,
! [X0,X1,X2] : times_times_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(times_times_nat(X0,X1),times_times_nat(X0,X2)),
inference(rectify,[],[f911]) ).
fof(f911,axiom,
! [X21,X15,X16] : times_times_nat(X21,plus_plus_nat(X15,X16)) = plus_plus_nat(times_times_nat(X21,X15),times_times_nat(X21,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_882_add__mult__distrib2) ).
fof(f12376,plain,
spl63_453,
inference(avatar_split_clause,[],[f4999,f12374]) ).
fof(f12374,plain,
( spl63_453
<=> ! [X2,X0,X1] : times_times_nat(X0,minus_minus_nat(X1,X2)) = minus_minus_nat(times_times_nat(X0,X1),times_times_nat(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_453])]) ).
fof(f4999,plain,
! [X2,X0,X1] : times_times_nat(X0,minus_minus_nat(X1,X2)) = minus_minus_nat(times_times_nat(X0,X1),times_times_nat(X0,X2)),
inference(cnf_transformation,[],[f1935]) ).
fof(f1935,plain,
! [X0,X1,X2] : times_times_nat(X0,minus_minus_nat(X1,X2)) = minus_minus_nat(times_times_nat(X0,X1),times_times_nat(X0,X2)),
inference(rectify,[],[f929]) ).
fof(f929,axiom,
! [X21,X15,X16] : times_times_nat(X21,minus_minus_nat(X15,X16)) = minus_minus_nat(times_times_nat(X21,X15),times_times_nat(X21,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_diff__mult__distrib2) ).
fof(f12372,plain,
spl63_452,
inference(avatar_split_clause,[],[f4996,f12370]) ).
fof(f12370,plain,
( spl63_452
<=> ! [X2,X0,X1] : times_times_real(plus_plus_real(X0,X1),X2) = plus_plus_real(times_times_real(X0,X2),times_times_real(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_452])]) ).
fof(f4996,plain,
! [X2,X0,X1] : times_times_real(plus_plus_real(X0,X1),X2) = plus_plus_real(times_times_real(X0,X2),times_times_real(X1,X2)),
inference(cnf_transformation,[],[f1932]) ).
fof(f1932,plain,
! [X0,X1,X2] : times_times_real(plus_plus_real(X0,X1),X2) = plus_plus_real(times_times_real(X0,X2),times_times_real(X1,X2)),
inference(rectify,[],[f938]) ).
fof(f938,axiom,
! [X26,X27,X14] : times_times_real(plus_plus_real(X26,X27),X14) = plus_plus_real(times_times_real(X26,X14),times_times_real(X27,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_real__add__mult__distrib) ).
fof(f12368,plain,
spl63_451,
inference(avatar_split_clause,[],[f4995,f12366]) ).
fof(f12366,plain,
( spl63_451
<=> ! [X2,X0,X1] : times_times_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(times_times_real(X0,X1),times_times_real(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_451])]) ).
fof(f4995,plain,
! [X2,X0,X1] : times_times_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(times_times_real(X0,X1),times_times_real(X0,X2)),
inference(cnf_transformation,[],[f1931]) ).
fof(f1931,plain,
! [X0,X1,X2] : times_times_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(times_times_real(X0,X1),times_times_real(X0,X2)),
inference(rectify,[],[f678]) ).
fof(f678,axiom,
! [X325,X326,X327] : times_times_real(X325,plus_plus_real(X326,X327)) = plus_plus_real(times_times_real(X325,X326),times_times_real(X325,X327)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(f12364,plain,
spl63_450,
inference(avatar_split_clause,[],[f4745,f12362]) ).
fof(f12362,plain,
( spl63_450
<=> ! [X0,X1] :
( plus_plus_nat(X0,sK51(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_450])]) ).
fof(f4745,plain,
! [X0,X1] :
( plus_plus_nat(X0,sK51(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3462]) ).
fof(f3462,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ! [X2] : plus_plus_nat(X0,X2) != X1 )
& ( plus_plus_nat(X0,sK51(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f3460,f3461]) ).
fof(f3461,plain,
! [X0,X1] :
( ? [X3] : plus_plus_nat(X0,X3) = X1
=> plus_plus_nat(X0,sK51(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f3460,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ! [X2] : plus_plus_nat(X0,X2) != X1 )
& ( ? [X3] : plus_plus_nat(X0,X3) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
inference(rectify,[],[f3459]) ).
fof(f3459,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ! [X2] : plus_plus_nat(X0,X2) != X1 )
& ( ? [X2] : plus_plus_nat(X0,X2) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
inference(nnf_transformation,[],[f1811]) ).
fof(f1811,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
<=> ? [X2] : plus_plus_nat(X0,X2) = X1 ),
inference(rectify,[],[f920]) ).
fof(f920,axiom,
! [X29,X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18))
<=> ? [X91] : plus_plus_nat(X29,X91) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_le__iff__add) ).
fof(f12360,plain,
spl63_449,
inference(avatar_split_clause,[],[f4575,f12358]) ).
fof(f12358,plain,
( spl63_449
<=> ! [X0,X1] :
( plus_plus_nat(X0,sK49(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_449])]) ).
fof(f4575,plain,
! [X0,X1] :
( plus_plus_nat(X0,sK49(X0,X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f3380]) ).
fof(f3380,plain,
! [X0,X1] :
( ( plus_plus_nat(X0,sK49(X0,X1)) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK49(X0,X1))) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f2627,f3379]) ).
fof(f3379,plain,
! [X0,X1] :
( ? [X2] :
( plus_plus_nat(X0,X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) )
=> ( plus_plus_nat(X0,sK49(X0,X1)) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK49(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f2627,plain,
! [X0,X1] :
( ? [X2] :
( plus_plus_nat(X0,X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1733]) ).
fof(f1733,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> ? [X2] :
( plus_plus_nat(X0,X2) = X1
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ) ),
inference(rectify,[],[f327]) ).
fof(f327,axiom,
! [X22,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X23))
=> ? [X91] :
( plus_plus_nat(X22,X91) = X23
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X91)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_less__imp__add__positive) ).
fof(f12356,plain,
spl63_448,
inference(avatar_split_clause,[],[f4562,f12354]) ).
fof(f12354,plain,
( spl63_448
<=> ! [X0,X1] :
( plus_plus_nat(X0,minus_minus_nat(X1,X0)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_448])]) ).
fof(f4562,plain,
! [X0,X1] :
( plus_plus_nat(X0,minus_minus_nat(X1,X0)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2613]) ).
fof(f2613,plain,
! [X0,X1] :
( plus_plus_nat(X0,minus_minus_nat(X1,X0)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1721]) ).
fof(f1721,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> plus_plus_nat(X0,minus_minus_nat(X1,X0)) = X1 ),
inference(rectify,[],[f967]) ).
fof(f967,axiom,
! [X16,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X15))
=> plus_plus_nat(X16,minus_minus_nat(X15,X16)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_938_le__add__diff__inverse) ).
fof(f12352,plain,
spl63_447,
inference(avatar_split_clause,[],[f4561,f12350]) ).
fof(f12350,plain,
( spl63_447
<=> ! [X0,X1] :
( minus_minus_nat(X1,minus_minus_nat(X1,X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_447])]) ).
fof(f4561,plain,
! [X0,X1] :
( minus_minus_nat(X1,minus_minus_nat(X1,X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2612]) ).
fof(f2612,plain,
! [X0,X1] :
( minus_minus_nat(X1,minus_minus_nat(X1,X0)) = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1720]) ).
fof(f1720,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> minus_minus_nat(X1,minus_minus_nat(X1,X0)) = X0 ),
inference(rectify,[],[f934]) ).
fof(f934,axiom,
! [X22,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X16))
=> minus_minus_nat(X16,minus_minus_nat(X16,X22)) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_diff__diff__cancel) ).
fof(f12348,plain,
spl63_446,
inference(avatar_split_clause,[],[f4470,f12346]) ).
fof(f12346,plain,
( spl63_446
<=> ! [X0,X1] :
( plus_plus_nat(X1,minus_minus_nat(X0,X1)) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_446])]) ).
fof(f4470,plain,
! [X0,X1] :
( plus_plus_nat(X1,minus_minus_nat(X0,X1)) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2481]) ).
fof(f2481,plain,
! [X0,X1] :
( plus_plus_nat(X1,minus_minus_nat(X0,X1)) = X0
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1644]) ).
fof(f1644,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> plus_plus_nat(X1,minus_minus_nat(X0,X1)) = X0 ),
inference(rectify,[],[f802]) ).
fof(f802,axiom,
! [X15,X16] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
=> plus_plus_nat(X16,minus_minus_nat(X15,X16)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_add__diff__inverse) ).
fof(f12344,plain,
spl63_445,
inference(avatar_split_clause,[],[f4466,f12342]) ).
fof(f12342,plain,
( spl63_445
<=> ! [X0,X1] :
( X0 = X1
| zero_zero_nat != minus_minus_nat(X1,X0)
| zero_zero_nat != minus_minus_nat(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_445])]) ).
fof(f4466,plain,
! [X0,X1] :
( X0 = X1
| zero_zero_nat != minus_minus_nat(X1,X0)
| zero_zero_nat != minus_minus_nat(X0,X1) ),
inference(cnf_transformation,[],[f2475]) ).
fof(f2475,plain,
! [X0,X1] :
( X0 = X1
| zero_zero_nat != minus_minus_nat(X1,X0)
| zero_zero_nat != minus_minus_nat(X0,X1) ),
inference(flattening,[],[f2474]) ).
fof(f2474,plain,
! [X0,X1] :
( X0 = X1
| zero_zero_nat != minus_minus_nat(X1,X0)
| zero_zero_nat != minus_minus_nat(X0,X1) ),
inference(ennf_transformation,[],[f1640]) ).
fof(f1640,plain,
! [X0,X1] :
( zero_zero_nat = minus_minus_nat(X0,X1)
=> ( zero_zero_nat = minus_minus_nat(X1,X0)
=> X0 = X1 ) ),
inference(rectify,[],[f656]) ).
fof(f656,axiom,
! [X15,X16] :
( zero_zero_nat = minus_minus_nat(X15,X16)
=> ( zero_zero_nat = minus_minus_nat(X16,X15)
=> X15 = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_diffs0__imp__equal) ).
fof(f12340,plain,
spl63_444,
inference(avatar_split_clause,[],[f4437,f12338]) ).
fof(f12338,plain,
( spl63_444
<=> ! [X0,X1] :
( sP5(X0,X1)
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X0,sK43(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_444])]) ).
fof(f4437,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X0,sK43(X0,X1))) ),
inference(cnf_transformation,[],[f3351]) ).
fof(f12335,plain,
spl63_443,
inference(avatar_split_clause,[],[f4358,f12333]) ).
fof(f12333,plain,
( spl63_443
<=> ! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X0),X1)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_443])]) ).
fof(f4358,plain,
! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X0),X1)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X0)),X1),
inference(cnf_transformation,[],[f1578]) ).
fof(f1578,plain,
! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X0),X1)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X0)),X1),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X73,X74] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(power_power_nat(X73),X74)) = hAPP_nat_int(power_power_int(hAPP_nat_int(semiri1621563631at_int,X73)),X74),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_of__nat__power) ).
fof(f12331,plain,
spl63_442,
inference(avatar_split_clause,[],[f4356,f12329]) ).
fof(f12329,plain,
( spl63_442
<=> ! [X0,X1] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X0),X1)) = hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_442])]) ).
fof(f4356,plain,
! [X0,X1] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X0),X1)) = hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X0)),X1),
inference(cnf_transformation,[],[f1576]) ).
fof(f1576,plain,
! [X0,X1] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X0),X1)) = hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X0)),X1),
inference(rectify,[],[f282]) ).
fof(f282,axiom,
! [X73,X74] : hAPP_nat_real(semiri132038758t_real,hAPP_nat_nat(power_power_nat(X73),X74)) = hAPP_nat_real(power_power_real(hAPP_nat_real(semiri132038758t_real,X73)),X74),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_of__nat__power) ).
fof(f12327,plain,
spl63_441,
inference(avatar_split_clause,[],[f4355,f12325]) ).
fof(f12325,plain,
( spl63_441
<=> ! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,times_times_nat(X0,X1)) = times_times_int(hAPP_nat_int(semiri1621563631at_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_441])]) ).
fof(f4355,plain,
! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,times_times_nat(X0,X1)) = times_times_int(hAPP_nat_int(semiri1621563631at_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)),
inference(cnf_transformation,[],[f1575]) ).
fof(f1575,plain,
! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,times_times_nat(X0,X1)) = times_times_int(hAPP_nat_int(semiri1621563631at_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)),
inference(rectify,[],[f500]) ).
fof(f500,axiom,
! [X204,X205] : hAPP_nat_int(semiri1621563631at_int,times_times_nat(X204,X205)) = times_times_int(hAPP_nat_int(semiri1621563631at_int,X204),hAPP_nat_int(semiri1621563631at_int,X205)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_of__nat__mult) ).
fof(f12323,plain,
spl63_440,
inference(avatar_split_clause,[],[f4353,f12321]) ).
fof(f12321,plain,
( spl63_440
<=> ! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(X0,X1)) = plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_440])]) ).
fof(f4353,plain,
! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(X0,X1)) = plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)),
inference(cnf_transformation,[],[f1573]) ).
fof(f1573,plain,
! [X0,X1] : hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(X0,X1)) = plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)),
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X15,X16] : hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(X15,X16)) = plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X15),hAPP_nat_int(semiri1621563631at_int,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zadd__int) ).
fof(f12319,plain,
spl63_439,
inference(avatar_split_clause,[],[f4350,f12317]) ).
fof(f12317,plain,
( spl63_439
<=> ! [X0,X1] : hAPP_nat_real(semiri132038758t_real,times_times_nat(X0,X1)) = times_times_real(hAPP_nat_real(semiri132038758t_real,X0),hAPP_nat_real(semiri132038758t_real,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_439])]) ).
fof(f4350,plain,
! [X0,X1] : hAPP_nat_real(semiri132038758t_real,times_times_nat(X0,X1)) = times_times_real(hAPP_nat_real(semiri132038758t_real,X0),hAPP_nat_real(semiri132038758t_real,X1)),
inference(cnf_transformation,[],[f1570]) ).
fof(f1570,plain,
! [X0,X1] : hAPP_nat_real(semiri132038758t_real,times_times_nat(X0,X1)) = times_times_real(hAPP_nat_real(semiri132038758t_real,X0),hAPP_nat_real(semiri132038758t_real,X1)),
inference(rectify,[],[f498]) ).
fof(f498,axiom,
! [X204,X205] : hAPP_nat_real(semiri132038758t_real,times_times_nat(X204,X205)) = times_times_real(hAPP_nat_real(semiri132038758t_real,X204),hAPP_nat_real(semiri132038758t_real,X205)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_of__nat__mult) ).
fof(f12315,plain,
spl63_438,
inference(avatar_split_clause,[],[f4349,f12313]) ).
fof(f12313,plain,
( spl63_438
<=> ! [X0,X1] : hAPP_nat_real(semiri132038758t_real,plus_plus_nat(X0,X1)) = plus_plus_real(hAPP_nat_real(semiri132038758t_real,X0),hAPP_nat_real(semiri132038758t_real,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_438])]) ).
fof(f4349,plain,
! [X0,X1] : hAPP_nat_real(semiri132038758t_real,plus_plus_nat(X0,X1)) = plus_plus_real(hAPP_nat_real(semiri132038758t_real,X0),hAPP_nat_real(semiri132038758t_real,X1)),
inference(cnf_transformation,[],[f1569]) ).
fof(f1569,plain,
! [X0,X1] : hAPP_nat_real(semiri132038758t_real,plus_plus_nat(X0,X1)) = plus_plus_real(hAPP_nat_real(semiri132038758t_real,X0),hAPP_nat_real(semiri132038758t_real,X1)),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X71,X72] : hAPP_nat_real(semiri132038758t_real,plus_plus_nat(X71,X72)) = plus_plus_real(hAPP_nat_real(semiri132038758t_real,X71),hAPP_nat_real(semiri132038758t_real,X72)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_of__nat__add) ).
fof(f12311,plain,
spl63_437,
inference(avatar_split_clause,[],[f4348,f12309]) ).
fof(f12309,plain,
( spl63_437
<=> ! [X0,X1] : nat(abs_abs_int(times_times_int(X0,X1))) = times_times_nat(nat(abs_abs_int(X0)),nat(abs_abs_int(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_437])]) ).
fof(f4348,plain,
! [X0,X1] : nat(abs_abs_int(times_times_int(X0,X1))) = times_times_nat(nat(abs_abs_int(X0)),nat(abs_abs_int(X1))),
inference(cnf_transformation,[],[f1568]) ).
fof(f1568,plain,
! [X0,X1] : nat(abs_abs_int(times_times_int(X0,X1))) = times_times_nat(nat(abs_abs_int(X0)),nat(abs_abs_int(X1))),
inference(rectify,[],[f1185]) ).
fof(f1185,axiom,
! [X14,X17] : nat(abs_abs_int(times_times_int(X14,X17))) = times_times_nat(nat(abs_abs_int(X14)),nat(abs_abs_int(X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_nat__abs__mult__distrib) ).
fof(f12307,plain,
spl63_436,
inference(avatar_split_clause,[],[f4191,f12305]) ).
fof(f12305,plain,
( spl63_436
<=> ! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_436])]) ).
fof(f4191,plain,
! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(cnf_transformation,[],[f3269]) ).
fof(f3269,plain,
! [X0] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real)) ) ),
inference(nnf_transformation,[],[f1468]) ).
fof(f1468,plain,
! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(rectify,[],[f759]) ).
fof(f759,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X3)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_le__special_I3_J) ).
fof(f12303,plain,
spl63_435,
inference(avatar_split_clause,[],[f4190,f12301]) ).
fof(f12301,plain,
( spl63_435
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_435])]) ).
fof(f4190,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,number267125858f_real(X0)),zero_zero_real)) ),
inference(cnf_transformation,[],[f3269]) ).
fof(f12299,plain,
spl63_434,
inference(avatar_split_clause,[],[f4187,f12297]) ).
fof(f12297,plain,
( spl63_434
<=> ! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_434])]) ).
fof(f4187,plain,
! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(cnf_transformation,[],[f3267]) ).
fof(f3267,plain,
! [X0] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real)) ) ),
inference(nnf_transformation,[],[f1466]) ).
fof(f1466,plain,
! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls)) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X3] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X3)),zero_zero_real))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__special_I3_J) ).
fof(f12295,plain,
( spl63_433
| ~ spl63_6
| ~ spl63_72
| ~ spl63_130
| ~ spl63_375
| ~ spl63_390 ),
inference(avatar_split_clause,[],[f12087,f11476,f9876,f7644,f7338,f7036,f12292]) ).
fof(f12292,plain,
( spl63_433
<=> x = sK30 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_433])]) ).
fof(f7036,plain,
( spl63_6
<=> is_int(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_6])]) ).
fof(f7338,plain,
( spl63_72
<=> ! [X0] : pls = times_times_int(X0,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_72])]) ).
fof(f7644,plain,
( spl63_130
<=> ! [X0] :
( minus_minus_int(X0,pls) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_130])]) ).
fof(f9876,plain,
( spl63_375
<=> sK30 = minus_minus_int(x,times_times_int(sK29,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_375])]) ).
fof(f12087,plain,
( x = sK30
| ~ spl63_6
| ~ spl63_72
| ~ spl63_130
| ~ spl63_375
| ~ spl63_390 ),
inference(forward_demodulation,[],[f12086,f7766]) ).
fof(f7766,plain,
( x = minus_minus_int(x,pls)
| ~ spl63_6
| ~ spl63_130 ),
inference(resolution,[],[f7645,f7038]) ).
fof(f7038,plain,
( is_int(x)
| ~ spl63_6 ),
inference(avatar_component_clause,[],[f7036]) ).
fof(f7645,plain,
( ! [X0] :
( ~ is_int(X0)
| minus_minus_int(X0,pls) = X0 )
| ~ spl63_130 ),
inference(avatar_component_clause,[],[f7644]) ).
fof(f12086,plain,
( sK30 = minus_minus_int(x,pls)
| ~ spl63_72
| ~ spl63_375
| ~ spl63_390 ),
inference(forward_demodulation,[],[f12077,f7339]) ).
fof(f7339,plain,
( ! [X0] : pls = times_times_int(X0,pls)
| ~ spl63_72 ),
inference(avatar_component_clause,[],[f7338]) ).
fof(f12077,plain,
( sK30 = minus_minus_int(x,times_times_int(sK29,pls))
| ~ spl63_375
| ~ spl63_390 ),
inference(superposition,[],[f9878,f11478]) ).
fof(f9878,plain,
( sK30 = minus_minus_int(x,times_times_int(sK29,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl63_375 ),
inference(avatar_component_clause,[],[f9876]) ).
fof(f12290,plain,
spl63_432,
inference(avatar_split_clause,[],[f4186,f12288]) ).
fof(f12288,plain,
( spl63_432
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_432])]) ).
fof(f4186,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),pls))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,number267125858f_real(X0)),zero_zero_real)) ),
inference(cnf_transformation,[],[f3267]) ).
fof(f12286,plain,
spl63_431,
inference(avatar_split_clause,[],[f4183,f12284]) ).
fof(f12284,plain,
( spl63_431
<=> ! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_431])]) ).
fof(f4183,plain,
! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(cnf_transformation,[],[f3265]) ).
fof(f3265,plain,
! [X0] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0))) ) ),
inference(nnf_transformation,[],[f1464]) ).
fof(f1464,plain,
! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0)) ),
inference(rectify,[],[f757]) ).
fof(f757,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_le__special_I1_J) ).
fof(f12282,plain,
spl63_430,
inference(avatar_split_clause,[],[f4182,f12280]) ).
fof(f12280,plain,
( spl63_430
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_430])]) ).
fof(f4182,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X0))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),number267125858f_real(X0))) ),
inference(cnf_transformation,[],[f3265]) ).
fof(f12278,plain,
spl63_429,
inference(avatar_split_clause,[],[f4179,f12276]) ).
fof(f12276,plain,
( spl63_429
<=> ! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_429])]) ).
fof(f4179,plain,
! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(cnf_transformation,[],[f3263]) ).
fof(f3263,plain,
! [X0] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ) ),
inference(nnf_transformation,[],[f1462]) ).
fof(f1462,plain,
! [X0] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(rectify,[],[f101]) ).
fof(f101,axiom,
! [X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X4)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__special_I1_J) ).
fof(f12274,plain,
spl63_428,
inference(avatar_split_clause,[],[f4178,f12272]) ).
fof(f12272,plain,
( spl63_428
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_428])]) ).
fof(f4178,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),number267125858f_real(X0))) ),
inference(cnf_transformation,[],[f3263]) ).
fof(f12267,plain,
( spl63_427
| ~ spl63_140
| ~ spl63_426 ),
inference(avatar_split_clause,[],[f12263,f12260,f7684,f12265]) ).
fof(f12265,plain,
( spl63_427
<=> ! [X0] :
( min = X0
| one_one_int = X0
| abs_abs_int(X0) != one_one_int
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_427])]) ).
fof(f7684,plain,
( spl63_140
<=> min = number_number_of_int(min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_140])]) ).
fof(f12260,plain,
( spl63_426
<=> ! [X0] :
( number_number_of_int(min) = X0
| one_one_int = X0
| abs_abs_int(X0) != one_one_int
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_426])]) ).
fof(f12263,plain,
( ! [X0] :
( min = X0
| one_one_int = X0
| abs_abs_int(X0) != one_one_int
| ~ is_int(X0) )
| ~ spl63_140
| ~ spl63_426 ),
inference(forward_demodulation,[],[f12261,f7686]) ).
fof(f7686,plain,
( min = number_number_of_int(min)
| ~ spl63_140 ),
inference(avatar_component_clause,[],[f7684]) ).
fof(f12261,plain,
( ! [X0] :
( number_number_of_int(min) = X0
| one_one_int = X0
| abs_abs_int(X0) != one_one_int
| ~ is_int(X0) )
| ~ spl63_426 ),
inference(avatar_component_clause,[],[f12260]) ).
fof(f12262,plain,
spl63_426,
inference(avatar_split_clause,[],[f4109,f12260]) ).
fof(f4109,plain,
! [X0] :
( number_number_of_int(min) = X0
| one_one_int = X0
| abs_abs_int(X0) != one_one_int
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3233]) ).
fof(f3233,plain,
! [X0] :
( ( ( abs_abs_int(X0) = one_one_int
| ( number_number_of_int(min) != X0
& one_one_int != X0 ) )
& ( number_number_of_int(min) = X0
| one_one_int = X0
| abs_abs_int(X0) != one_one_int ) )
| ~ is_int(X0) ),
inference(flattening,[],[f3232]) ).
fof(f3232,plain,
! [X0] :
( ( ( abs_abs_int(X0) = one_one_int
| ( number_number_of_int(min) != X0
& one_one_int != X0 ) )
& ( number_number_of_int(min) = X0
| one_one_int = X0
| abs_abs_int(X0) != one_one_int ) )
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2391]) ).
fof(f2391,plain,
! [X0] :
( ( abs_abs_int(X0) = one_one_int
<=> ( number_number_of_int(min) = X0
| one_one_int = X0 ) )
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1427]) ).
fof(f1427,plain,
! [X0] :
( is_int(X0)
=> ( abs_abs_int(X0) = one_one_int
<=> ( number_number_of_int(min) = X0
| one_one_int = X0 ) ) ),
inference(rectify,[],[f1192]) ).
fof(f1192,axiom,
! [X30] :
( is_int(X30)
=> ( one_one_int = abs_abs_int(X30)
<=> ( number_number_of_int(min) = X30
| one_one_int = X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_abs__eq__1__iff) ).
fof(f12258,plain,
spl63_425,
inference(avatar_split_clause,[],[f4038,f12256]) ).
fof(f12256,plain,
( spl63_425
<=> ! [X0] : minus_minus_real(times_times_real(X0,X0),one_one_real) = times_times_real(plus_plus_real(X0,one_one_real),minus_minus_real(X0,one_one_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_425])]) ).
fof(f4038,plain,
! [X0] : minus_minus_real(times_times_real(X0,X0),one_one_real) = times_times_real(plus_plus_real(X0,one_one_real),minus_minus_real(X0,one_one_real)),
inference(cnf_transformation,[],[f1373]) ).
fof(f1373,plain,
! [X0] : minus_minus_real(times_times_real(X0,X0),one_one_real) = times_times_real(plus_plus_real(X0,one_one_real),minus_minus_real(X0,one_one_real)),
inference(rectify,[],[f568]) ).
fof(f568,axiom,
! [X250] : minus_minus_real(times_times_real(X250,X250),one_one_real) = times_times_real(plus_plus_real(X250,one_one_real),minus_minus_real(X250,one_one_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_real__squared__diff__one__factored) ).
fof(f12176,plain,
( spl63_424
| ~ spl63_7
| ~ spl63_72
| ~ spl63_130
| ~ spl63_376
| ~ spl63_390 ),
inference(avatar_split_clause,[],[f12085,f11476,f9881,f7644,f7338,f7041,f12173]) ).
fof(f12173,plain,
( spl63_424
<=> y = sK32 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_424])]) ).
fof(f7041,plain,
( spl63_7
<=> is_int(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_7])]) ).
fof(f9881,plain,
( spl63_376
<=> sK32 = minus_minus_int(y,times_times_int(sK31,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_376])]) ).
fof(f12085,plain,
( y = sK32
| ~ spl63_7
| ~ spl63_72
| ~ spl63_130
| ~ spl63_376
| ~ spl63_390 ),
inference(forward_demodulation,[],[f12084,f7767]) ).
fof(f7767,plain,
( y = minus_minus_int(y,pls)
| ~ spl63_7
| ~ spl63_130 ),
inference(resolution,[],[f7645,f7043]) ).
fof(f7043,plain,
( is_int(y)
| ~ spl63_7 ),
inference(avatar_component_clause,[],[f7041]) ).
fof(f12084,plain,
( sK32 = minus_minus_int(y,pls)
| ~ spl63_72
| ~ spl63_376
| ~ spl63_390 ),
inference(forward_demodulation,[],[f12076,f7339]) ).
fof(f12076,plain,
( sK32 = minus_minus_int(y,times_times_int(sK31,pls))
| ~ spl63_376
| ~ spl63_390 ),
inference(superposition,[],[f9883,f11478]) ).
fof(f9883,plain,
( sK32 = minus_minus_int(y,times_times_int(sK31,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl63_376 ),
inference(avatar_component_clause,[],[f9881]) ).
fof(f12058,plain,
( spl63_423
| ~ spl63_37
| ~ spl63_269
| ~ spl63_406 ),
inference(avatar_split_clause,[],[f11546,f11543,f8915,f7188,f12056]) ).
fof(f12056,plain,
( spl63_423
<=> ! [X0] : number_number_of_int(plus_plus_int(X0,X0)) = plus_plus_int(number_number_of_int(plus_plus_int(pls,X0)),number_number_of_int(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_423])]) ).
fof(f7188,plain,
( spl63_37
<=> pls = number_number_of_int(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_37])]) ).
fof(f8915,plain,
( spl63_269
<=> ! [X0,X1] : number_number_of_int(plus_plus_int(X0,X1)) = plus_plus_int(number_number_of_int(X0),number_number_of_int(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_269])]) ).
fof(f11543,plain,
( spl63_406
<=> ! [X0] : number_number_of_int(plus_plus_int(X0,X0)) = plus_plus_int(plus_plus_int(pls,number_number_of_int(X0)),number_number_of_int(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_406])]) ).
fof(f11546,plain,
( ! [X0] : number_number_of_int(plus_plus_int(X0,X0)) = plus_plus_int(number_number_of_int(plus_plus_int(pls,X0)),number_number_of_int(X0))
| ~ spl63_37
| ~ spl63_269
| ~ spl63_406 ),
inference(forward_demodulation,[],[f11544,f9205]) ).
fof(f9205,plain,
( ! [X0] : plus_plus_int(pls,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(pls,X0))
| ~ spl63_37
| ~ spl63_269 ),
inference(superposition,[],[f8916,f7190]) ).
fof(f7190,plain,
( pls = number_number_of_int(pls)
| ~ spl63_37 ),
inference(avatar_component_clause,[],[f7188]) ).
fof(f8916,plain,
( ! [X0,X1] : number_number_of_int(plus_plus_int(X0,X1)) = plus_plus_int(number_number_of_int(X0),number_number_of_int(X1))
| ~ spl63_269 ),
inference(avatar_component_clause,[],[f8915]) ).
fof(f11544,plain,
( ! [X0] : number_number_of_int(plus_plus_int(X0,X0)) = plus_plus_int(plus_plus_int(pls,number_number_of_int(X0)),number_number_of_int(X0))
| ~ spl63_406 ),
inference(avatar_component_clause,[],[f11543]) ).
fof(f11625,plain,
( ~ spl63_31
| spl63_412 ),
inference(avatar_contradiction_clause,[],[f11624]) ).
fof(f11624,plain,
( $false
| ~ spl63_31
| spl63_412 ),
inference(resolution,[],[f11570,f7162]) ).
fof(f7162,plain,
( ! [X0,X1] : is_int(hAPP_nat_int(X0,X1))
| ~ spl63_31 ),
inference(avatar_component_clause,[],[f7161]) ).
fof(f7161,plain,
( spl63_31
<=> ! [X0,X1] : is_int(hAPP_nat_int(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_31])]) ).
fof(f11570,plain,
( ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| spl63_412 ),
inference(avatar_component_clause,[],[f11568]) ).
fof(f11568,plain,
( spl63_412
<=> is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_412])]) ).
fof(f11619,plain,
spl63_422,
inference(avatar_split_clause,[],[f6714,f11616]) ).
fof(f11616,plain,
( spl63_422
<=> zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat(number_number_of_int(minus_minus_int(minus_minus_int(pls,min),min)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_422])]) ).
fof(f6714,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat(number_number_of_int(minus_minus_int(minus_minus_int(pls,min),min)))),
inference(forward_demodulation,[],[f6713,f5593]) ).
fof(f5593,plain,
pls = plus_plus_int(pls,pls),
inference(definition_unfolding,[],[f3785,f3979]) ).
fof(f3785,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f126]) ).
fof(f126,axiom,
pls = bit0(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).
fof(f6713,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat(number_number_of_int(minus_minus_int(minus_minus_int(plus_plus_int(pls,pls),min),min)))),
inference(forward_demodulation,[],[f6712,f5593]) ).
fof(f6712,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat(number_number_of_int(minus_minus_int(minus_minus_int(plus_plus_int(plus_plus_int(pls,pls),plus_plus_int(pls,pls)),min),min)))),
inference(forward_demodulation,[],[f6241,f5687]) ).
fof(f5687,plain,
! [X0] : minus_minus_int(minus_minus_int(plus_plus_int(X0,X0),min),min) = plus_plus_int(minus_minus_int(X0,min),minus_minus_int(X0,min)),
inference(definition_unfolding,[],[f3997,f3976,f5578,f3979,f3976]) ).
fof(f5578,plain,
! [X0] : bit1(X0) = minus_minus_int(plus_plus_int(X0,X0),min),
inference(definition_unfolding,[],[f3980,f3976,f3979]) ).
fof(f3980,plain,
! [X0] : bit1(X0) = succ(bit0(X0)),
inference(cnf_transformation,[],[f1315]) ).
fof(f1315,plain,
! [X0] : bit1(X0) = succ(bit0(X0)),
inference(rectify,[],[f838]) ).
fof(f838,axiom,
! [X21] : bit1(X21) = succ(bit0(X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_succ__Bit0) ).
fof(f3976,plain,
! [X0] : succ(X0) = minus_minus_int(X0,min),
inference(cnf_transformation,[],[f1311]) ).
fof(f1311,plain,
! [X0] : succ(X0) = minus_minus_int(X0,min),
inference(rectify,[],[f1050]) ).
fof(f1050,axiom,
! [X21] : succ(X21) = minus_minus_int(X21,min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_diff__bin__simps_I2_J) ).
fof(f3997,plain,
! [X0] : succ(bit1(X0)) = bit0(succ(X0)),
inference(cnf_transformation,[],[f1332]) ).
fof(f1332,plain,
! [X0] : succ(bit1(X0)) = bit0(succ(X0)),
inference(rectify,[],[f839]) ).
fof(f839,axiom,
! [X21] : succ(bit1(X21)) = bit0(succ(X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_succ__Bit1) ).
fof(f6241,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(equality_resolution,[],[f5868]) ).
fof(f5868,plain,
! [X0] :
( zero_zero_real = hAPP_nat_real(power_power_real(X0),nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min)))))
| zero_zero_real != X0 ),
inference(definition_unfolding,[],[f4273,f3978,f3979,f5578]) ).
fof(f4273,plain,
! [X0] :
( zero_zero_real = hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))
| zero_zero_real != X0 ),
inference(cnf_transformation,[],[f3310]) ).
fof(f3310,plain,
! [X0] :
( ( zero_zero_real = hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))
| zero_zero_real != X0 )
& ( zero_zero_real = X0
| zero_zero_real != hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls)))) ) ),
inference(nnf_transformation,[],[f1509]) ).
fof(f1509,plain,
! [X0] :
( zero_zero_real = hAPP_nat_real(power_power_real(X0),number_number_of_nat(bit0(bit1(pls))))
<=> zero_zero_real = X0 ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X5] :
( zero_zero_real = hAPP_nat_real(power_power_real(X5),number_number_of_nat(bit0(bit1(pls))))
<=> zero_zero_real = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__eq__power2) ).
fof(f11611,plain,
spl63_421,
inference(avatar_split_clause,[],[f6468,f11608]) ).
fof(f11608,plain,
( spl63_421
<=> plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_421])]) ).
fof(f6468,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))),
inference(forward_demodulation,[],[f5623,f5593]) ).
fof(f5623,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))),
inference(definition_unfolding,[],[f3840,f3979,f5578]) ).
fof(f3840,plain,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_semiring__one__add__one__is__two) ).
fof(f11604,plain,
spl63_420,
inference(avatar_split_clause,[],[f6466,f11601]) ).
fof(f11601,plain,
( spl63_420
<=> plus_plus_real(one_one_real,one_one_real) = number267125858f_real(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_420])]) ).
fof(f6466,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))),
inference(forward_demodulation,[],[f5621,f5593]) ).
fof(f5621,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))),
inference(definition_unfolding,[],[f3838,f3979,f5578]) ).
fof(f3838,plain,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
plus_plus_real(one_one_real,one_one_real) = number267125858f_real(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_one__add__one__is__two) ).
fof(f11599,plain,
spl63_419,
inference(avatar_split_clause,[],[f6055,f11597]) ).
fof(f11597,plain,
( spl63_419
<=> ! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_419])]) ).
fof(f6055,plain,
! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP9(X0,X1) ),
inference(definition_unfolding,[],[f4779,f3772]) ).
fof(f4779,plain,
! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f3482]) ).
fof(f3482,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( zero_zero_nat != X0
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(semiri1621563631at_int,X0)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( ( ( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(semiri1621563631at_int,X0)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP9(X0,X1) ) ),
inference(rectify,[],[f3481]) ).
fof(f3481,plain,
! [X1,X0] :
( ( sP9(X1,X0)
| ( zero_zero_nat != X1
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
& ( ( ( zero_zero_nat = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
| ~ sP9(X1,X0) ) ),
inference(flattening,[],[f3480]) ).
fof(f3480,plain,
! [X1,X0] :
( ( sP9(X1,X0)
| ( zero_zero_nat != X1
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
| ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
& ( ( ( zero_zero_nat = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
| ~ sP9(X1,X0) ) ),
inference(nnf_transformation,[],[f3186]) ).
fof(f3186,plain,
! [X1,X0] :
( sP9(X1,X0)
<=> ( ( zero_zero_nat = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f11595,plain,
spl63_418,
inference(avatar_split_clause,[],[f6037,f11593]) ).
fof(f11593,plain,
( spl63_418
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_418])]) ).
fof(f6037,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
inference(definition_unfolding,[],[f4750,f3772]) ).
fof(f4750,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3465]) ).
fof(f3465,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) ) ),
inference(nnf_transformation,[],[f1813]) ).
fof(f1813,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
inference(rectify,[],[f1072]) ).
fof(f1072,axiom,
! [X3,X391] :
( hBOOL(hAPP_int_bool(zcong(X3,zero_zero_int),X391))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X391),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_zcong__eq__zdvd__prop) ).
fof(f11591,plain,
spl63_417,
inference(avatar_split_clause,[],[f6036,f11589]) ).
fof(f11589,plain,
( spl63_417
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_417])]) ).
fof(f6036,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(zcong(X0,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
inference(definition_unfolding,[],[f4751,f3772]) ).
fof(f4751,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0)) ),
inference(cnf_transformation,[],[f3465]) ).
fof(f11587,plain,
spl63_416,
inference(avatar_split_clause,[],[f6010,f11585]) ).
fof(f11585,plain,
( spl63_416
<=> ! [X0,X1] :
( pls = X1
| plus_plus_int(X0,X1) != X0
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_416])]) ).
fof(f6010,plain,
! [X0,X1] :
( pls = X1
| plus_plus_int(X0,X1) != X0
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f4625,f3772]) ).
fof(f4625,plain,
! [X0,X1] :
( zero_zero_int = X1
| plus_plus_int(X0,X1) != X0
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3397]) ).
fof(f3397,plain,
! [X0,X1] :
( ( ( plus_plus_int(X0,X1) = X0
| zero_zero_int != X1 )
& ( zero_zero_int = X1
| plus_plus_int(X0,X1) != X0 ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2682]) ).
fof(f2682,plain,
! [X0,X1] :
( ( plus_plus_int(X0,X1) = X0
<=> zero_zero_int = X1 )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2681]) ).
fof(f2681,plain,
! [X0,X1] :
( ( plus_plus_int(X0,X1) = X0
<=> zero_zero_int = X1 )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1760]) ).
fof(f1760,plain,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ( plus_plus_int(X0,X1) = X0
<=> zero_zero_int = X1 ) ),
inference(rectify,[],[f384]) ).
fof(f384,axiom,
! [X81,X5] :
( ( is_int(X5)
& is_int(X81) )
=> ( plus_plus_int(X81,X5) = X81
<=> zero_zero_int = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_add__0__iff) ).
fof(f11583,plain,
spl63_415,
inference(avatar_split_clause,[],[f5998,f11581]) ).
fof(f11581,plain,
( spl63_415
<=> ! [X0,X1] :
( X0 = X1
| minus_minus_int(X0,X1) != pls
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_415])]) ).
fof(f5998,plain,
! [X0,X1] :
( X0 = X1
| minus_minus_int(X0,X1) != pls
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f4602,f3772]) ).
fof(f4602,plain,
! [X0,X1] :
( X0 = X1
| minus_minus_int(X0,X1) != zero_zero_int
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3385]) ).
fof(f3385,plain,
! [X0,X1] :
( ( ( X0 = X1
| minus_minus_int(X0,X1) != zero_zero_int )
& ( minus_minus_int(X0,X1) = zero_zero_int
| X0 != X1 ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2666]) ).
fof(f2666,plain,
! [X0,X1] :
( ( X0 = X1
<=> minus_minus_int(X0,X1) = zero_zero_int )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2665]) ).
fof(f2665,plain,
! [X0,X1] :
( ( X0 = X1
<=> minus_minus_int(X0,X1) = zero_zero_int )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1752]) ).
fof(f1752,plain,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ( X0 = X1
<=> minus_minus_int(X0,X1) = zero_zero_int ) ),
inference(rectify,[],[f623]) ).
fof(f623,axiom,
! [X5,X81] :
( ( is_int(X81)
& is_int(X5) )
=> ( X5 = X81
<=> zero_zero_int = minus_minus_int(X5,X81) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_eq__iff__diff__eq__0) ).
fof(f11579,plain,
spl63_414,
inference(avatar_split_clause,[],[f5928,f11577]) ).
fof(f11577,plain,
( spl63_414
<=> ! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_414])]) ).
fof(f5928,plain,
! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP3(X0,X1) ),
inference(definition_unfolding,[],[f4419,f3772]) ).
fof(f4419,plain,
! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f3341]) ).
fof(f3341,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( zero_zero_nat != X0
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( ( ( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( hAPP_nat_int(semiri1621563631at_int,X0) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP3(X0,X1) ) ),
inference(flattening,[],[f3340]) ).
fof(f3340,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( zero_zero_nat != X0
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( ( ( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( hAPP_nat_int(semiri1621563631at_int,X0) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP3(X0,X1) ) ),
inference(nnf_transformation,[],[f3177]) ).
fof(f3177,plain,
! [X0,X1] :
( sP3(X0,X1)
<=> ( ( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( hAPP_nat_int(semiri1621563631at_int,X0) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f11575,plain,
spl63_413,
inference(avatar_split_clause,[],[f5923,f11573]) ).
fof(f11573,plain,
( spl63_413
<=> ! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_413])]) ).
fof(f5923,plain,
! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ sP1(X0,X1) ),
inference(definition_unfolding,[],[f4410,f3772]) ).
fof(f4410,plain,
! [X0,X1] :
( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3337]) ).
fof(f3337,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( zero_zero_nat != X0
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
| ( hAPP_nat_int(semiri1621563631at_int,X0) != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
& ( ( ( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( hAPP_nat_int(semiri1621563631at_int,X0) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f3336]) ).
fof(f3336,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( zero_zero_nat != X1
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
| ( hAPP_nat_int(semiri1621563631at_int,X1) != X0
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
& ( ( ( zero_zero_nat = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hAPP_nat_int(semiri1621563631at_int,X1) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f3335]) ).
fof(f3335,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( zero_zero_nat != X1
& ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
| ( hAPP_nat_int(semiri1621563631at_int,X1) != X0
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
& ( ( ( zero_zero_nat = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hAPP_nat_int(semiri1621563631at_int,X1) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) )
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f3174]) ).
fof(f3174,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ( zero_zero_nat = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hAPP_nat_int(semiri1621563631at_int,X1) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f11571,plain,
( ~ spl63_412
| ~ spl63_123
| spl63_391 ),
inference(avatar_split_clause,[],[f11524,f11480,f7576,f11568]) ).
fof(f7576,plain,
( spl63_123
<=> ! [X0] :
( is_int(minus_minus_int(X0,min))
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_123])]) ).
fof(f11480,plain,
( spl63_391
<=> is_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_391])]) ).
fof(f11524,plain,
( ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ spl63_123
| spl63_391 ),
inference(resolution,[],[f11482,f7577]) ).
fof(f7577,plain,
( ! [X0] :
( is_int(minus_minus_int(X0,min))
| ~ is_int(X0) )
| ~ spl63_123 ),
inference(avatar_component_clause,[],[f7576]) ).
fof(f11482,plain,
( ~ is_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min))
| spl63_391 ),
inference(avatar_component_clause,[],[f11480]) ).
fof(f11566,plain,
spl63_411,
inference(avatar_split_clause,[],[f5894,f11564]) ).
fof(f11564,plain,
( spl63_411
<=> ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_411])]) ).
fof(f5894,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)))),
inference(definition_unfolding,[],[f4347,f3772]) ).
fof(f4347,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)))),
inference(cnf_transformation,[],[f1567]) ).
fof(f1567,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)))),
inference(rectify,[],[f605]) ).
fof(f605,axiom,
! [X285,X286] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),plus_plus_int(times_times_int(X285,X285),times_times_int(X286,X286)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_sum__squares__ge__zero) ).
fof(f11562,plain,
spl63_410,
inference(avatar_split_clause,[],[f5791,f11560]) ).
fof(f11560,plain,
( spl63_410
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_410])]) ).
fof(f5791,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
inference(definition_unfolding,[],[f4172,f3772]) ).
fof(f4172,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ),
inference(cnf_transformation,[],[f3260]) ).
fof(f3260,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0)) ) ),
inference(nnf_transformation,[],[f1459]) ).
fof(f1459,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(rectify,[],[f835]) ).
fof(f835,axiom,
! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X30))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_806_int__one__le__iff__zero__less) ).
fof(f11558,plain,
spl63_409,
inference(avatar_split_clause,[],[f5790,f11556]) ).
fof(f5790,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X0)) ),
inference(definition_unfolding,[],[f4173,f3772]) ).
fof(f4173,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X0)) ),
inference(cnf_transformation,[],[f3260]) ).
fof(f11554,plain,
spl63_408,
inference(avatar_split_clause,[],[f5767,f11552]) ).
fof(f11552,plain,
( spl63_408
<=> ! [X0] :
( pls = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_408])]) ).
fof(f5767,plain,
! [X0] :
( pls = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f4129,f3772]) ).
fof(f4129,plain,
! [X0] :
( zero_zero_int = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3244]) ).
fof(f3244,plain,
! [X0] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| zero_zero_int != X0 )
& ( zero_zero_int = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int)) ) )
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2398]) ).
fof(f2398,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
<=> zero_zero_int = X0 )
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1433]) ).
fof(f1433,plain,
! [X0] :
( is_int(X0)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
<=> zero_zero_int = X0 ) ),
inference(rectify,[],[f1191]) ).
fof(f1191,axiom,
! [X30] :
( is_int(X30)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X30)),one_one_int))
<=> zero_zero_int = X30 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_zabs__less__one__iff) ).
fof(f11550,plain,
spl63_407,
inference(avatar_split_clause,[],[f5753,f11548]) ).
fof(f11548,plain,
( spl63_407
<=> ! [X0] :
( min = X0
| min != minus_minus_int(plus_plus_int(X0,X0),min)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_407])]) ).
fof(f5753,plain,
! [X0] :
( min = X0
| min != minus_minus_int(plus_plus_int(X0,X0),min)
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f4105,f5578]) ).
fof(f4105,plain,
! [X0] :
( min = X0
| bit1(X0) != min
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3230]) ).
fof(f3230,plain,
! [X0] :
( ( ( bit1(X0) = min
| min != X0 )
& ( min = X0
| bit1(X0) != min ) )
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2389]) ).
fof(f2389,plain,
! [X0] :
( ( bit1(X0) = min
<=> min = X0 )
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1425]) ).
fof(f1425,plain,
! [X0] :
( is_int(X0)
=> ( bit1(X0) = min
<=> min = X0 ) ),
inference(rectify,[],[f1048]) ).
fof(f1048,axiom,
! [X11] :
( is_int(X11)
=> ( min = bit1(X11)
<=> min = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_rel__simps_I47_J) ).
fof(f11545,plain,
spl63_406,
inference(avatar_split_clause,[],[f5708,f11543]) ).
fof(f5708,plain,
! [X0] : number_number_of_int(plus_plus_int(X0,X0)) = plus_plus_int(plus_plus_int(pls,number_number_of_int(X0)),number_number_of_int(X0)),
inference(definition_unfolding,[],[f4032,f3979,f3772]) ).
fof(f4032,plain,
! [X0] : number_number_of_int(bit0(X0)) = plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(X0)),number_number_of_int(X0)),
inference(cnf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0] : number_number_of_int(bit0(X0)) = plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(X0)),number_number_of_int(X0)),
inference(rectify,[],[f170]) ).
fof(f170,axiom,
! [X45] : number_number_of_int(bit0(X45)) = plus_plus_int(plus_plus_int(zero_zero_int,number_number_of_int(X45)),number_number_of_int(X45)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_number__of__Bit0) ).
fof(f11541,plain,
spl63_405,
inference(avatar_split_clause,[],[f5363,f11539]) ).
fof(f11539,plain,
( spl63_405
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2))))
| ~ sP19(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_405])]) ).
fof(f5363,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2))))
| ~ sP19(X0,X2,X1) ),
inference(cnf_transformation,[],[f3667]) ).
fof(f3667,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2))))
| ~ sP19(X0,X2,X1) )
& ( sP19(X0,X2,X1)
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2)))) ) ),
inference(nnf_transformation,[],[f3207]) ).
fof(f3207,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2))))
<=> sP19(X0,X2,X1) ),
inference(definition_folding,[],[f3048,f3206]) ).
fof(f3206,plain,
! [X0,X2,X1] :
( sP19(X0,X2,X1)
<=> ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
& ( hBOOL(hAPP_int_bool(X0,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,X1),hAPP_nat_int(semiri1621563631at_int,X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f3048,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2))))
<=> ( ( hBOOL(hAPP_int_bool(X0,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
& ( hBOOL(hAPP_int_bool(X0,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,X1),hAPP_nat_int(semiri1621563631at_int,X2))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ) ) ),
inference(ennf_transformation,[],[f2190]) ).
fof(f2190,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2))))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_int_bool(X0,zero_zero_int)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
=> hBOOL(hAPP_int_bool(X0,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)))) ) ) ),
inference(rectify,[],[f1173]) ).
fof(f1173,axiom,
! [X54,X3,X4] :
( hBOOL(hAPP_int_bool(X54,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X3,X4))))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4))
=> hBOOL(hAPP_int_bool(X54,zero_zero_int)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X3))
=> hBOOL(hAPP_int_bool(X54,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,X3),hAPP_nat_int(semiri1621563631at_int,X4)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_zdiff__int__split) ).
fof(f11537,plain,
spl63_404,
inference(avatar_split_clause,[],[f5362,f11535]) ).
fof(f11535,plain,
( spl63_404
<=> ! [X2,X0,X1] :
( sP19(X0,X2,X1)
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_404])]) ).
fof(f5362,plain,
! [X2,X0,X1] :
( sP19(X0,X2,X1)
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,minus_minus_nat(X1,X2)))) ),
inference(cnf_transformation,[],[f3667]) ).
fof(f11533,plain,
spl63_403,
inference(avatar_split_clause,[],[f5328,f11531]) ).
fof(f11531,plain,
( spl63_403
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
| ~ hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_403])]) ).
fof(f5328,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
| ~ hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ),
inference(cnf_transformation,[],[f3648]) ).
fof(f3648,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
| ~ hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) )
& ( hBOOL(hAPP_int_bool(zcong(X1,X0),X2))
| ~ hBOOL(hAPP_int_bool(zcong(X0,X1),X2)) ) ),
inference(nnf_transformation,[],[f2177]) ).
fof(f2177,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_int_bool(zcong(X0,X1),X2))
<=> hBOOL(hAPP_int_bool(zcong(X1,X0),X2)) ),
inference(rectify,[],[f1154]) ).
fof(f1154,axiom,
! [X5,X81,X29] :
( hBOOL(hAPP_int_bool(zcong(X5,X81),X29))
<=> hBOOL(hAPP_int_bool(zcong(X81,X5),X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_zcong__sym) ).
fof(f11529,plain,
spl63_402,
inference(avatar_split_clause,[],[f5036,f11527]) ).
fof(f11527,plain,
( spl63_402
<=> ! [X2,X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,if_nat(X2,X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_402])]) ).
fof(f5036,plain,
! [X2,X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,if_nat(X2,X0,X1))
| hBOOL(X2) ),
inference(cnf_transformation,[],[f2722]) ).
fof(f2722,plain,
! [X0,X1,X2] :
( ( hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,if_nat(X2,X0,X1))
| hBOOL(X2) )
& ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,if_nat(X2,X0,X1))
| ~ hBOOL(X2) ) ),
inference(ennf_transformation,[],[f1970]) ).
fof(f1970,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(X2)
=> hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,if_nat(X2,X0,X1)) )
& ( hBOOL(X2)
=> hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,if_nat(X2,X0,X1)) ) ),
inference(rectify,[],[f251]) ).
fof(f251,axiom,
! [X3,X4,X54] :
( ( ~ hBOOL(X54)
=> hAPP_nat_int(semiri1621563631at_int,X4) = hAPP_nat_int(semiri1621563631at_int,if_nat(X54,X3,X4)) )
& ( hBOOL(X54)
=> hAPP_nat_int(semiri1621563631at_int,X3) = hAPP_nat_int(semiri1621563631at_int,if_nat(X54,X3,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_int__if__cong) ).
fof(f11523,plain,
spl63_401,
inference(avatar_split_clause,[],[f5035,f11521]) ).
fof(f11521,plain,
( spl63_401
<=> ! [X2,X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,if_nat(X2,X0,X1))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_401])]) ).
fof(f5035,plain,
! [X2,X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,if_nat(X2,X0,X1))
| ~ hBOOL(X2) ),
inference(cnf_transformation,[],[f2722]) ).
fof(f11519,plain,
spl63_400,
inference(avatar_split_clause,[],[f4893,f11517]) ).
fof(f11517,plain,
( spl63_400
<=> ! [X0,X1] :
( zero_zero_real = X1
| zero_zero_real != plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_400])]) ).
fof(f4893,plain,
! [X0,X1] :
( zero_zero_real = X1
| zero_zero_real != plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)) ),
inference(cnf_transformation,[],[f3540]) ).
fof(f3540,plain,
! [X0,X1] :
( ( zero_zero_real = plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1))
| zero_zero_real != X1
| zero_zero_real != X0 )
& ( ( zero_zero_real = X1
& zero_zero_real = X0 )
| zero_zero_real != plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)) ) ),
inference(flattening,[],[f3539]) ).
fof(f3539,plain,
! [X0,X1] :
( ( zero_zero_real = plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1))
| zero_zero_real != X1
| zero_zero_real != X0 )
& ( ( zero_zero_real = X1
& zero_zero_real = X0 )
| zero_zero_real != plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)) ) ),
inference(nnf_transformation,[],[f1865]) ).
fof(f1865,plain,
! [X0,X1] :
( zero_zero_real = plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1))
<=> ( zero_zero_real = X1
& zero_zero_real = X0 ) ),
inference(rectify,[],[f958]) ).
fof(f958,axiom,
! [X3,X4] :
( zero_zero_real = plus_plus_real(times_times_real(X3,X3),times_times_real(X4,X4))
<=> ( zero_zero_real = X4
& zero_zero_real = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_929_real__two__squares__add__zero__iff) ).
fof(f11515,plain,
spl63_399,
inference(avatar_split_clause,[],[f4892,f11513]) ).
fof(f11513,plain,
( spl63_399
<=> ! [X0,X1] :
( zero_zero_real = X0
| zero_zero_real != plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_399])]) ).
fof(f4892,plain,
! [X0,X1] :
( zero_zero_real = X0
| zero_zero_real != plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)) ),
inference(cnf_transformation,[],[f3540]) ).
fof(f11511,plain,
spl63_398,
inference(avatar_split_clause,[],[f4726,f11509]) ).
fof(f11509,plain,
( spl63_398
<=> ! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_398])]) ).
fof(f4726,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1))
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
inference(cnf_transformation,[],[f3449]) ).
fof(f3449,plain,
! [X0,X1] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
inference(flattening,[],[f3448]) ).
fof(f3448,plain,
! [X0,X1] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ) ),
inference(nnf_transformation,[],[f1804]) ).
fof(f1804,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1))
<=> ( X0 != X1
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
inference(rectify,[],[f908]) ).
fof(f908,axiom,
! [X3,X4] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X3),X4))
<=> ( X3 != X4
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X3),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_real__less__def) ).
fof(f11507,plain,
spl63_397,
inference(avatar_split_clause,[],[f4709,f11505]) ).
fof(f11505,plain,
( spl63_397
<=> ! [X0,X1] :
( zero_zero_nat = X1
| one_one_nat = X0
| one_one_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_397])]) ).
fof(f4709,plain,
! [X0,X1] :
( zero_zero_nat = X1
| one_one_nat = X0
| one_one_nat != hAPP_nat_nat(power_power_nat(X0),X1) ),
inference(cnf_transformation,[],[f3438]) ).
fof(f3438,plain,
! [X0,X1] :
( ( one_one_nat = hAPP_nat_nat(power_power_nat(X0),X1)
| ( zero_zero_nat != X1
& one_one_nat != X0 ) )
& ( zero_zero_nat = X1
| one_one_nat = X0
| one_one_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ),
inference(flattening,[],[f3437]) ).
fof(f3437,plain,
! [X0,X1] :
( ( one_one_nat = hAPP_nat_nat(power_power_nat(X0),X1)
| ( zero_zero_nat != X1
& one_one_nat != X0 ) )
& ( zero_zero_nat = X1
| one_one_nat = X0
| one_one_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ),
inference(nnf_transformation,[],[f1798]) ).
fof(f1798,plain,
! [X0,X1] :
( one_one_nat = hAPP_nat_nat(power_power_nat(X0),X1)
<=> ( zero_zero_nat = X1
| one_one_nat = X0 ) ),
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X3,X18] :
( one_one_nat = hAPP_nat_nat(power_power_nat(X3),X18)
<=> ( zero_zero_nat = X18
| one_one_nat = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_exp__eq__1) ).
fof(f11503,plain,
spl63_396,
inference(avatar_split_clause,[],[f4619,f11501]) ).
fof(f11501,plain,
( spl63_396
<=> ! [X0,X1] :
( X0 = X1
| number_number_of_int(X0) != number_number_of_int(X1)
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_396])]) ).
fof(f4619,plain,
! [X0,X1] :
( X0 = X1
| number_number_of_int(X0) != number_number_of_int(X1)
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3394]) ).
fof(f3394,plain,
! [X0,X1] :
( ( ( number_number_of_int(X0) = number_number_of_int(X1)
| X0 != X1 )
& ( X0 = X1
| number_number_of_int(X0) != number_number_of_int(X1) ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2676]) ).
fof(f2676,plain,
! [X0,X1] :
( ( number_number_of_int(X0) = number_number_of_int(X1)
<=> X0 = X1 )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2675]) ).
fof(f2675,plain,
! [X0,X1] :
( ( number_number_of_int(X0) = number_number_of_int(X1)
<=> X0 = X1 )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1757]) ).
fof(f1757,plain,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ( number_number_of_int(X0) = number_number_of_int(X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f85]) ).
fof(f85,axiom,
! [X3,X4] :
( ( is_int(X4)
& is_int(X3) )
=> ( number_number_of_int(X3) = number_number_of_int(X4)
<=> X3 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_eq__number__of) ).
fof(f11499,plain,
spl63_395,
inference(avatar_split_clause,[],[f4617,f11497]) ).
fof(f11497,plain,
( spl63_395
<=> ! [X0,X1] :
( X0 = X1
| number267125858f_real(X0) != number267125858f_real(X1)
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_395])]) ).
fof(f4617,plain,
! [X0,X1] :
( X0 = X1
| number267125858f_real(X0) != number267125858f_real(X1)
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3393]) ).
fof(f3393,plain,
! [X0,X1] :
( ( ( number267125858f_real(X0) = number267125858f_real(X1)
| X0 != X1 )
& ( X0 = X1
| number267125858f_real(X0) != number267125858f_real(X1) ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2674]) ).
fof(f2674,plain,
! [X0,X1] :
( ( number267125858f_real(X0) = number267125858f_real(X1)
<=> X0 = X1 )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2673]) ).
fof(f2673,plain,
! [X0,X1] :
( ( number267125858f_real(X0) = number267125858f_real(X1)
<=> X0 = X1 )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1756]) ).
fof(f1756,plain,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ( number267125858f_real(X0) = number267125858f_real(X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X3,X4] :
( ( is_int(X4)
& is_int(X3) )
=> ( number267125858f_real(X3) = number267125858f_real(X4)
<=> X3 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_eq__number__of) ).
fof(f11495,plain,
spl63_394,
inference(avatar_split_clause,[],[f4570,f11493]) ).
fof(f11493,plain,
( spl63_394
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_394])]) ).
fof(f4570,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2623]) ).
fof(f2623,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1729]) ).
fof(f1729,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f905]) ).
fof(f905,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_876_less__imp__le__nat) ).
fof(f11491,plain,
spl63_393,
inference(avatar_split_clause,[],[f4392,f11489]) ).
fof(f11489,plain,
( spl63_393
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_393])]) ).
fof(f4392,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(cnf_transformation,[],[f1605]) ).
fof(f1605,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X0))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ),
inference(rectify,[],[f479]) ).
fof(f479,axiom,
! [X17,X14] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X14),X17))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X17),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_zle__linear) ).
fof(f11487,plain,
spl63_392,
inference(avatar_split_clause,[],[f4391,f11485]) ).
fof(f11485,plain,
( spl63_392
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_392])]) ).
fof(f4391,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f1604]) ).
fof(f1604,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X0))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f876]) ).
fof(f876,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X15))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_nat__le__linear) ).
fof(f11483,plain,
( spl63_390
| ~ spl63_391
| ~ spl63_77
| ~ spl63_143
| ~ spl63_153
| ~ spl63_357 ),
inference(avatar_split_clause,[],[f10850,f9780,f7739,f7697,f7370,f11480,f11476]) ).
fof(f7370,plain,
( spl63_77
<=> pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(minus_minus_int(minus_minus_int(pls,min),min)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_77])]) ).
fof(f7697,plain,
( spl63_143
<=> ! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_143])]) ).
fof(f7739,plain,
( spl63_153
<=> ! [X0] : minus_minus_int(X0,min) = plus_plus_int(X0,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_153])]) ).
fof(f9780,plain,
( spl63_357
<=> ! [X0,X1] :
( pls != hAPP_nat_int(power_power_int(X1),X0)
| pls = X1
| ~ is_int(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_357])]) ).
fof(f10850,plain,
( ~ is_int(minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min))
| pls = minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)
| ~ spl63_77
| ~ spl63_143
| ~ spl63_153
| ~ spl63_357 ),
inference(forward_demodulation,[],[f10849,f8005]) ).
fof(f8005,plain,
( ! [X0] : minus_minus_int(X0,min) = plus_plus_int(one_one_int,X0)
| ~ spl63_143
| ~ spl63_153 ),
inference(superposition,[],[f7740,f7698]) ).
fof(f7698,plain,
( ! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0)
| ~ spl63_143 ),
inference(avatar_component_clause,[],[f7697]) ).
fof(f7740,plain,
( ! [X0] : minus_minus_int(X0,min) = plus_plus_int(X0,one_one_int)
| ~ spl63_153 ),
inference(avatar_component_clause,[],[f7739]) ).
fof(f10849,plain,
( pls = minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ spl63_77
| ~ spl63_143
| ~ spl63_153
| ~ spl63_357 ),
inference(forward_demodulation,[],[f10848,f8005]) ).
fof(f10848,plain,
( pls = plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ spl63_77
| ~ spl63_357 ),
inference(trivial_inequality_removal,[],[f10847]) ).
fof(f10847,plain,
( pls != pls
| pls = plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ spl63_77
| ~ spl63_357 ),
inference(superposition,[],[f9781,f7372]) ).
fof(f7372,plain,
( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(minus_minus_int(minus_minus_int(pls,min),min))))
| ~ spl63_77 ),
inference(avatar_component_clause,[],[f7370]) ).
fof(f9781,plain,
( ! [X0,X1] :
( pls != hAPP_nat_int(power_power_int(X1),X0)
| pls = X1
| ~ is_int(X1) )
| ~ spl63_357 ),
inference(avatar_component_clause,[],[f9780]) ).
fof(f11474,plain,
spl63_389,
inference(avatar_split_clause,[],[f4390,f11472]) ).
fof(f11472,plain,
( spl63_389
<=> ! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_389])]) ).
fof(f4390,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
inference(cnf_transformation,[],[f1603]) ).
fof(f1603,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),X0))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X1)) ),
inference(rectify,[],[f1008]) ).
fof(f1008,axiom,
! [X17,X14] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X14),X17))
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X17),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_real__le__linear) ).
fof(f11470,plain,
spl63_388,
inference(avatar_split_clause,[],[f4346,f11468]) ).
fof(f11468,plain,
( spl63_388
<=> ! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_388])]) ).
fof(f4346,plain,
! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)))),
inference(cnf_transformation,[],[f1566]) ).
fof(f1566,plain,
! [X0,X1] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),plus_plus_real(times_times_real(X0,X0),times_times_real(X1,X1)))),
inference(rectify,[],[f604]) ).
fof(f604,axiom,
! [X285,X286] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),plus_plus_real(times_times_real(X285,X285),times_times_real(X286,X286)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_sum__squares__ge__zero) ).
fof(f11466,plain,
spl63_387,
inference(avatar_split_clause,[],[f4122,f11464]) ).
fof(f11464,plain,
( spl63_387
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(zprime,X0))
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_387])]) ).
fof(f4122,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0))
| ~ hBOOL(hAPP_int_bool(zprime,X0))
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3241]) ).
fof(f3241,plain,
! [X0] :
( ( ( hBOOL(hAPP_int_bool(zprime,X0))
| ~ sP0(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
& ( ( sP0(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
| ~ hBOOL(hAPP_int_bool(zprime,X0)) ) )
| ~ is_int(X0) ),
inference(flattening,[],[f3240]) ).
fof(f3240,plain,
! [X0] :
( ( ( hBOOL(hAPP_int_bool(zprime,X0))
| ~ sP0(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
& ( ( sP0(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) )
| ~ hBOOL(hAPP_int_bool(zprime,X0)) ) )
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f3173]) ).
fof(f3173,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(zprime,X0))
<=> ( sP0(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) )
| ~ is_int(X0) ),
inference(definition_folding,[],[f2395,f3172]) ).
fof(f3172,plain,
! [X0] :
( sP0(X0)
<=> ! [X1] :
( X0 = X1
| one_one_int = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f2395,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(zprime,X0))
<=> ( ! [X1] :
( X0 = X1
| one_one_int = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) )
| ~ is_int(X0) ),
inference(flattening,[],[f2394]) ).
fof(f2394,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(zprime,X0))
<=> ( ! [X1] :
( X0 = X1
| one_one_int = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) )
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1430]) ).
fof(f1430,plain,
! [X0] :
( is_int(X0)
=> ( hBOOL(hAPP_int_bool(zprime,X0))
<=> ( ! [X1] :
( is_int(X1)
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
=> ( X0 = X1
| one_one_int = X1 ) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X0)) ) ) ),
inference(rectify,[],[f1171]) ).
fof(f1171,axiom,
! [X391] :
( is_int(X391)
=> ( hBOOL(hAPP_int_bool(zprime,X391))
<=> ( ! [X394] :
( is_int(X394)
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X394),X391))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X394)) )
=> ( X391 = X394
| one_one_int = X394 ) ) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),X391)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_zprime__def) ).
fof(f11383,plain,
( spl63_386
| ~ spl63_153
| ~ spl63_346
| ~ spl63_383 ),
inference(avatar_split_clause,[],[f10950,f10947,f9728,f7739,f11381]) ).
fof(f11381,plain,
( spl63_386
<=> ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(minus_minus_int(plus_plus_int(X0,pls),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_386])]) ).
fof(f9728,plain,
( spl63_346
<=> ! [X2,X0,X1] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(plus_plus_int(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_346])]) ).
fof(f10947,plain,
( spl63_383
<=> ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(plus_plus_int(X0,minus_minus_int(pls,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_383])]) ).
fof(f10950,plain,
( ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(minus_minus_int(plus_plus_int(X0,pls),min))
| ~ spl63_153
| ~ spl63_346
| ~ spl63_383 ),
inference(forward_demodulation,[],[f10948,f10650]) ).
fof(f10650,plain,
( ! [X0,X1] : plus_plus_int(X0,minus_minus_int(X1,min)) = minus_minus_int(plus_plus_int(X0,X1),min)
| ~ spl63_153
| ~ spl63_346 ),
inference(forward_demodulation,[],[f10626,f7740]) ).
fof(f10626,plain,
( ! [X0,X1] : plus_plus_int(X0,plus_plus_int(X1,one_one_int)) = minus_minus_int(plus_plus_int(X0,X1),min)
| ~ spl63_153
| ~ spl63_346 ),
inference(superposition,[],[f9729,f7740]) ).
fof(f9729,plain,
( ! [X2,X0,X1] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(plus_plus_int(X0,X1),X2)
| ~ spl63_346 ),
inference(avatar_component_clause,[],[f9728]) ).
fof(f10948,plain,
( ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(plus_plus_int(X0,minus_minus_int(pls,min)))
| ~ spl63_383 ),
inference(avatar_component_clause,[],[f10947]) ).
fof(f11379,plain,
( spl63_385
| ~ spl63_143
| ~ spl63_153
| ~ spl63_346
| ~ spl63_381 ),
inference(avatar_split_clause,[],[f10941,f10937,f9728,f7739,f7697,f11377]) ).
fof(f11377,plain,
( spl63_385
<=> ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(minus_minus_int(plus_plus_int(pls,X0),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_385])]) ).
fof(f10937,plain,
( spl63_381
<=> ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_381])]) ).
fof(f10941,plain,
( ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(minus_minus_int(plus_plus_int(pls,X0),min))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_346
| ~ spl63_381 ),
inference(forward_demodulation,[],[f10940,f10650]) ).
fof(f10940,plain,
( ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(plus_plus_int(pls,minus_minus_int(X0,min)))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_346
| ~ spl63_381 ),
inference(forward_demodulation,[],[f10938,f10645]) ).
fof(f10645,plain,
( ! [X0,X1] : plus_plus_int(X0,minus_minus_int(X1,min)) = plus_plus_int(minus_minus_int(X0,min),X1)
| ~ spl63_143
| ~ spl63_153
| ~ spl63_346 ),
inference(forward_demodulation,[],[f10618,f8005]) ).
fof(f10618,plain,
( ! [X0,X1] : plus_plus_int(minus_minus_int(X0,min),X1) = plus_plus_int(X0,plus_plus_int(one_one_int,X1))
| ~ spl63_153
| ~ spl63_346 ),
inference(superposition,[],[f9729,f7740]) ).
fof(f10938,plain,
( ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),X0))
| ~ spl63_381 ),
inference(avatar_component_clause,[],[f10937]) ).
fof(f11375,plain,
( spl63_384
| ~ spl63_153
| ~ spl63_346
| ~ spl63_380 ),
inference(avatar_split_clause,[],[f10935,f10932,f9728,f7739,f11373]) ).
fof(f11373,plain,
( spl63_384
<=> ! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(minus_minus_int(plus_plus_int(X0,pls),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_384])]) ).
fof(f10932,plain,
( spl63_380
<=> ! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(plus_plus_int(X0,minus_minus_int(pls,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_380])]) ).
fof(f10935,plain,
( ! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(minus_minus_int(plus_plus_int(X0,pls),min))
| ~ spl63_153
| ~ spl63_346
| ~ spl63_380 ),
inference(forward_demodulation,[],[f10933,f10650]) ).
fof(f10933,plain,
( ! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(plus_plus_int(X0,minus_minus_int(pls,min)))
| ~ spl63_380 ),
inference(avatar_component_clause,[],[f10932]) ).
fof(f10949,plain,
( spl63_383
| ~ spl63_140
| ~ spl63_268
| ~ spl63_367 ),
inference(avatar_split_clause,[],[f9839,f9836,f8911,f7684,f10947]) ).
fof(f8911,plain,
( spl63_268
<=> ! [X0,X1] : number_number_of_int(minus_minus_int(X0,X1)) = minus_minus_int(number_number_of_int(X0),number_number_of_int(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_268])]) ).
fof(f9836,plain,
( spl63_367
<=> ! [X0] : number_number_of_int(plus_plus_int(X0,minus_minus_int(pls,min))) = minus_minus_int(number_number_of_int(X0),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_367])]) ).
fof(f9839,plain,
( ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(plus_plus_int(X0,minus_minus_int(pls,min)))
| ~ spl63_140
| ~ spl63_268
| ~ spl63_367 ),
inference(forward_demodulation,[],[f9837,f9195]) ).
fof(f9195,plain,
( ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = minus_minus_int(number_number_of_int(X0),min)
| ~ spl63_140
| ~ spl63_268 ),
inference(superposition,[],[f8912,f7686]) ).
fof(f8912,plain,
( ! [X0,X1] : number_number_of_int(minus_minus_int(X0,X1)) = minus_minus_int(number_number_of_int(X0),number_number_of_int(X1))
| ~ spl63_268 ),
inference(avatar_component_clause,[],[f8911]) ).
fof(f9837,plain,
( ! [X0] : number_number_of_int(plus_plus_int(X0,minus_minus_int(pls,min))) = minus_minus_int(number_number_of_int(X0),min)
| ~ spl63_367 ),
inference(avatar_component_clause,[],[f9836]) ).
fof(f10945,plain,
( spl63_382
| ~ spl63_204
| ~ spl63_359 ),
inference(avatar_split_clause,[],[f10860,f9788,f8240,f10943]) ).
fof(f10943,plain,
( spl63_382
<=> ! [X0] : sP12(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_382])]) ).
fof(f8240,plain,
( spl63_204
<=> ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_204])]) ).
fof(f9788,plain,
( spl63_359
<=> ! [X0,X1] :
( sP12(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_359])]) ).
fof(f10860,plain,
( ! [X0] : sP12(X0,X0)
| ~ spl63_204
| ~ spl63_359 ),
inference(resolution,[],[f9789,f8241]) ).
fof(f8241,plain,
( ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X0)))
| ~ spl63_204 ),
inference(avatar_component_clause,[],[f8240]) ).
fof(f9789,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X1)))
| sP12(X1,X0) )
| ~ spl63_359 ),
inference(avatar_component_clause,[],[f9788]) ).
fof(f10939,plain,
( spl63_381
| ~ spl63_140
| ~ spl63_143
| ~ spl63_153
| ~ spl63_268
| ~ spl63_366 ),
inference(avatar_split_clause,[],[f9834,f9830,f8911,f7739,f7697,f7684,f10937]) ).
fof(f9830,plain,
( spl63_366
<=> ! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_366])]) ).
fof(f9834,plain,
( ! [X0] : number_number_of_int(minus_minus_int(X0,min)) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),X0))
| ~ spl63_140
| ~ spl63_143
| ~ spl63_153
| ~ spl63_268
| ~ spl63_366 ),
inference(forward_demodulation,[],[f9833,f9195]) ).
fof(f9833,plain,
( ! [X0] : number_number_of_int(plus_plus_int(minus_minus_int(pls,min),X0)) = minus_minus_int(number_number_of_int(X0),min)
| ~ spl63_143
| ~ spl63_153
| ~ spl63_366 ),
inference(forward_demodulation,[],[f9831,f8005]) ).
fof(f9831,plain,
( ! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),X0))
| ~ spl63_366 ),
inference(avatar_component_clause,[],[f9830]) ).
fof(f10934,plain,
( spl63_380
| ~ spl63_138
| ~ spl63_365 ),
inference(avatar_split_clause,[],[f9828,f9825,f7676,f10932]) ).
fof(f7676,plain,
( spl63_138
<=> ! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_138])]) ).
fof(f9825,plain,
( spl63_365
<=> ! [X0] : plus_plus_real(number267125858f_real(X0),one_one_real) = number267125858f_real(plus_plus_int(X0,minus_minus_int(pls,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_365])]) ).
fof(f9828,plain,
( ! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(plus_plus_int(X0,minus_minus_int(pls,min)))
| ~ spl63_138
| ~ spl63_365 ),
inference(forward_demodulation,[],[f9826,f7677]) ).
fof(f7677,plain,
( ! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0)
| ~ spl63_138 ),
inference(avatar_component_clause,[],[f7676]) ).
fof(f9826,plain,
( ! [X0] : plus_plus_real(number267125858f_real(X0),one_one_real) = number267125858f_real(plus_plus_int(X0,minus_minus_int(pls,min)))
| ~ spl63_365 ),
inference(avatar_component_clause,[],[f9825]) ).
fof(f10816,plain,
( spl63_379
| ~ spl63_70
| ~ spl63_165 ),
inference(avatar_split_clause,[],[f8323,f8078,f7329,f10813]) ).
fof(f10813,plain,
( spl63_379
<=> pls = abs_abs_int(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_379])]) ).
fof(f7329,plain,
( spl63_70
<=> pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_70])]) ).
fof(f8078,plain,
( spl63_165
<=> ! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_165])]) ).
fof(f8323,plain,
( pls = abs_abs_int(pls)
| ~ spl63_70
| ~ spl63_165 ),
inference(superposition,[],[f8079,f7331]) ).
fof(f7331,plain,
( pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)
| ~ spl63_70 ),
inference(avatar_component_clause,[],[f7329]) ).
fof(f8079,plain,
( ! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0))
| ~ spl63_165 ),
inference(avatar_component_clause,[],[f8078]) ).
fof(f10763,plain,
( spl63_378
| ~ spl63_143
| ~ spl63_153
| ~ spl63_350 ),
inference(avatar_split_clause,[],[f9747,f9744,f7739,f7697,f10761]) ).
fof(f10761,plain,
( spl63_378
<=> ! [X0] : minus_minus_int(plus_plus_int(X0,X0),min) = plus_plus_int(minus_minus_int(X0,min),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_378])]) ).
fof(f9744,plain,
( spl63_350
<=> ! [X0] : plus_plus_int(plus_plus_int(one_one_int,X0),X0) = minus_minus_int(plus_plus_int(X0,X0),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_350])]) ).
fof(f9747,plain,
( ! [X0] : minus_minus_int(plus_plus_int(X0,X0),min) = plus_plus_int(minus_minus_int(X0,min),X0)
| ~ spl63_143
| ~ spl63_153
| ~ spl63_350 ),
inference(forward_demodulation,[],[f9745,f8005]) ).
fof(f9745,plain,
( ! [X0] : plus_plus_int(plus_plus_int(one_one_int,X0),X0) = minus_minus_int(plus_plus_int(X0,X0),min)
| ~ spl63_350 ),
inference(avatar_component_clause,[],[f9744]) ).
fof(f10062,plain,
( spl63_377
| ~ spl63_167
| ~ spl63_330 ),
inference(avatar_split_clause,[],[f10002,f9650,f8086,f10060]) ).
fof(f10060,plain,
( spl63_377
<=> ! [X0] : sP10(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_377])]) ).
fof(f8086,plain,
( spl63_167
<=> ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_167])]) ).
fof(f9650,plain,
( spl63_330
<=> ! [X0,X1] :
( sP10(X1,X0)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_330])]) ).
fof(f10002,plain,
( ! [X0] : sP10(X0,X0)
| ~ spl63_167
| ~ spl63_330 ),
inference(resolution,[],[f9651,f8087]) ).
fof(f8087,plain,
( ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X0)))
| ~ spl63_167 ),
inference(avatar_component_clause,[],[f8086]) ).
fof(f9651,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1)))
| sP10(X1,X0) )
| ~ spl63_330 ),
inference(avatar_component_clause,[],[f9650]) ).
fof(f9884,plain,
( spl63_376
| ~ spl63_143
| ~ spl63_153
| ~ spl63_316 ),
inference(avatar_split_clause,[],[f9589,f9585,f7739,f7697,f9881]) ).
fof(f9585,plain,
( spl63_316
<=> sK32 = minus_minus_int(y,times_times_int(sK31,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_316])]) ).
fof(f9589,plain,
( sK32 = minus_minus_int(y,times_times_int(sK31,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_316 ),
inference(forward_demodulation,[],[f9587,f8005]) ).
fof(f9587,plain,
( sK32 = minus_minus_int(y,times_times_int(sK31,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
| ~ spl63_316 ),
inference(avatar_component_clause,[],[f9585]) ).
fof(f9879,plain,
( spl63_375
| ~ spl63_143
| ~ spl63_153
| ~ spl63_315 ),
inference(avatar_split_clause,[],[f9576,f9572,f7739,f7697,f9876]) ).
fof(f9572,plain,
( spl63_315
<=> sK30 = minus_minus_int(x,times_times_int(sK29,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_315])]) ).
fof(f9576,plain,
( sK30 = minus_minus_int(x,times_times_int(sK29,minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_315 ),
inference(forward_demodulation,[],[f9574,f8005]) ).
fof(f9574,plain,
( sK30 = minus_minus_int(x,times_times_int(sK29,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
| ~ spl63_315 ),
inference(avatar_component_clause,[],[f9572]) ).
fof(f9867,plain,
spl63_374,
inference(avatar_split_clause,[],[f6891,f9865]) ).
fof(f9865,plain,
( spl63_374
<=> ! [X2,X0,X1] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_374])]) ).
fof(f6891,plain,
! [X2,X0,X1] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(X0,times_times_int(X2,X1)),
inference(forward_demodulation,[],[f4994,f4990]) ).
fof(f4990,plain,
! [X2,X0,X1] : times_times_int(X0,times_times_int(X1,X2)) = times_times_int(times_times_int(X0,X1),X2),
inference(cnf_transformation,[],[f1926]) ).
fof(f1926,plain,
! [X0,X1,X2] : times_times_int(X0,times_times_int(X1,X2)) = times_times_int(times_times_int(X0,X1),X2),
inference(rectify,[],[f449]) ).
fof(f449,axiom,
! [X161,X162,X163] : times_times_int(X161,times_times_int(X162,X163)) = times_times_int(times_times_int(X161,X162),X163),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(f4994,plain,
! [X2,X0,X1] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(times_times_int(X0,X2),X1),
inference(cnf_transformation,[],[f1930]) ).
fof(f1930,plain,
! [X0,X1,X2] : times_times_int(times_times_int(X0,X1),X2) = times_times_int(times_times_int(X0,X2),X1),
inference(rectify,[],[f458]) ).
fof(f458,axiom,
! [X170,X171,X172] : times_times_int(times_times_int(X170,X171),X172) = times_times_int(times_times_int(X170,X172),X171),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(f9863,plain,
spl63_373,
inference(avatar_split_clause,[],[f6890,f9861]) ).
fof(f9861,plain,
( spl63_373
<=> ! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_373])]) ).
fof(f6890,plain,
! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(X0,plus_plus_int(X2,X1)),
inference(forward_demodulation,[],[f4988,f4984]) ).
fof(f4984,plain,
! [X2,X0,X1] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(plus_plus_int(X0,X1),X2),
inference(cnf_transformation,[],[f1920]) ).
fof(f1920,plain,
! [X0,X1,X2] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(plus_plus_int(X0,X1),X2),
inference(rectify,[],[f372]) ).
fof(f372,axiom,
! [X120,X121,X122] : plus_plus_int(X120,plus_plus_int(X121,X122)) = plus_plus_int(plus_plus_int(X120,X121),X122),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f4988,plain,
! [X2,X0,X1] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(plus_plus_int(X0,X2),X1),
inference(cnf_transformation,[],[f1924]) ).
fof(f1924,plain,
! [X0,X1,X2] : plus_plus_int(plus_plus_int(X0,X1),X2) = plus_plus_int(plus_plus_int(X0,X2),X1),
inference(rectify,[],[f363]) ).
fof(f363,axiom,
! [X111,X112,X113] : plus_plus_int(plus_plus_int(X111,X112),X113) = plus_plus_int(plus_plus_int(X111,X113),X112),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(f9859,plain,
spl63_372,
inference(avatar_split_clause,[],[f6889,f9857]) ).
fof(f9857,plain,
( spl63_372
<=> ! [X2,X0,X1] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_372])]) ).
fof(f6889,plain,
! [X2,X0,X1] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(X0,times_times_nat(X2,X1)),
inference(forward_demodulation,[],[f4981,f4977]) ).
fof(f4977,plain,
! [X2,X0,X1] : times_times_nat(X0,times_times_nat(X1,X2)) = times_times_nat(times_times_nat(X0,X1),X2),
inference(cnf_transformation,[],[f1913]) ).
fof(f1913,plain,
! [X0,X1,X2] : times_times_nat(X0,times_times_nat(X1,X2)) = times_times_nat(times_times_nat(X0,X1),X2),
inference(rectify,[],[f450]) ).
fof(f450,axiom,
! [X161,X162,X163] : times_times_nat(X161,times_times_nat(X162,X163)) = times_times_nat(times_times_nat(X161,X162),X163),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(f4981,plain,
! [X2,X0,X1] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(times_times_nat(X0,X2),X1),
inference(cnf_transformation,[],[f1917]) ).
fof(f1917,plain,
! [X0,X1,X2] : times_times_nat(times_times_nat(X0,X1),X2) = times_times_nat(times_times_nat(X0,X2),X1),
inference(rectify,[],[f459]) ).
fof(f459,axiom,
! [X170,X171,X172] : times_times_nat(times_times_nat(X170,X171),X172) = times_times_nat(times_times_nat(X170,X172),X171),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(f9855,plain,
spl63_371,
inference(avatar_split_clause,[],[f6888,f9853]) ).
fof(f9853,plain,
( spl63_371
<=> ! [X2,X0,X1] : plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(X0,plus_plus_nat(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_371])]) ).
fof(f6888,plain,
! [X2,X0,X1] : plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(X0,plus_plus_nat(X2,X1)),
inference(forward_demodulation,[],[f4975,f4971]) ).
fof(f4971,plain,
! [X2,X0,X1] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2),
inference(cnf_transformation,[],[f1907]) ).
fof(f1907,plain,
! [X0,X1,X2] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2),
inference(rectify,[],[f373]) ).
fof(f373,axiom,
! [X120,X121,X122] : plus_plus_nat(X120,plus_plus_nat(X121,X122)) = plus_plus_nat(plus_plus_nat(X120,X121),X122),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f4975,plain,
! [X2,X0,X1] : plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(plus_plus_nat(X0,X2),X1),
inference(cnf_transformation,[],[f1911]) ).
fof(f1911,plain,
! [X0,X1,X2] : plus_plus_nat(plus_plus_nat(X0,X1),X2) = plus_plus_nat(plus_plus_nat(X0,X2),X1),
inference(rectify,[],[f364]) ).
fof(f364,axiom,
! [X111,X112,X113] : plus_plus_nat(plus_plus_nat(X111,X112),X113) = plus_plus_nat(plus_plus_nat(X111,X113),X112),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(f9851,plain,
spl63_370,
inference(avatar_split_clause,[],[f6887,f9849]) ).
fof(f9849,plain,
( spl63_370
<=> ! [X2,X0,X1] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_370])]) ).
fof(f6887,plain,
! [X2,X0,X1] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(X0,times_times_real(X2,X1)),
inference(forward_demodulation,[],[f4968,f4964]) ).
fof(f4964,plain,
! [X2,X0,X1] : times_times_real(X0,times_times_real(X1,X2)) = times_times_real(times_times_real(X0,X1),X2),
inference(cnf_transformation,[],[f1900]) ).
fof(f1900,plain,
! [X0,X1,X2] : times_times_real(X0,times_times_real(X1,X2)) = times_times_real(times_times_real(X0,X1),X2),
inference(rectify,[],[f451]) ).
fof(f451,axiom,
! [X161,X162,X163] : times_times_real(X161,times_times_real(X162,X163)) = times_times_real(times_times_real(X161,X162),X163),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(f4968,plain,
! [X2,X0,X1] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(times_times_real(X0,X2),X1),
inference(cnf_transformation,[],[f1904]) ).
fof(f1904,plain,
! [X0,X1,X2] : times_times_real(times_times_real(X0,X1),X2) = times_times_real(times_times_real(X0,X2),X1),
inference(rectify,[],[f460]) ).
fof(f460,axiom,
! [X170,X171,X172] : times_times_real(times_times_real(X170,X171),X172) = times_times_real(times_times_real(X170,X172),X171),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(f9847,plain,
spl63_369,
inference(avatar_split_clause,[],[f6886,f9845]) ).
fof(f9845,plain,
( spl63_369
<=> ! [X2,X0,X1] : plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(X0,plus_plus_real(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_369])]) ).
fof(f6886,plain,
! [X2,X0,X1] : plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(X0,plus_plus_real(X2,X1)),
inference(forward_demodulation,[],[f4962,f4959]) ).
fof(f4959,plain,
! [X2,X0,X1] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2),
inference(cnf_transformation,[],[f1895]) ).
fof(f1895,plain,
! [X0,X1,X2] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2),
inference(rectify,[],[f374]) ).
fof(f374,axiom,
! [X120,X121,X122] : plus_plus_real(X120,plus_plus_real(X121,X122)) = plus_plus_real(plus_plus_real(X120,X121),X122),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(f4962,plain,
! [X2,X0,X1] : plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(plus_plus_real(X0,X2),X1),
inference(cnf_transformation,[],[f1898]) ).
fof(f1898,plain,
! [X0,X1,X2] : plus_plus_real(plus_plus_real(X0,X1),X2) = plus_plus_real(plus_plus_real(X0,X2),X1),
inference(rectify,[],[f365]) ).
fof(f365,axiom,
! [X111,X112,X113] : plus_plus_real(plus_plus_real(X111,X112),X113) = plus_plus_real(plus_plus_real(X111,X113),X112),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(f9843,plain,
spl63_368,
inference(avatar_split_clause,[],[f6885,f9841]) ).
fof(f9841,plain,
( spl63_368
<=> ! [X2,X0,X1] : minus_minus_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(X0,plus_plus_nat(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_368])]) ).
fof(f6885,plain,
! [X2,X0,X1] : minus_minus_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(X0,plus_plus_nat(X2,X1)),
inference(forward_demodulation,[],[f4957,f4956]) ).
fof(f4956,plain,
! [X2,X0,X1] : minus_minus_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(X0,plus_plus_nat(X1,X2)),
inference(cnf_transformation,[],[f1892]) ).
fof(f1892,plain,
! [X0,X1,X2] : minus_minus_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(X0,plus_plus_nat(X1,X2)),
inference(rectify,[],[f734]) ).
fof(f734,axiom,
! [X22,X23,X21] : minus_minus_nat(minus_minus_nat(X22,X23),X21) = minus_minus_nat(X22,plus_plus_nat(X23,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_diff__diff__left) ).
fof(f4957,plain,
! [X2,X0,X1] : minus_minus_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(minus_minus_nat(X0,X2),X1),
inference(cnf_transformation,[],[f1893]) ).
fof(f1893,plain,
! [X0,X1,X2] : minus_minus_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(minus_minus_nat(X0,X2),X1),
inference(rectify,[],[f504]) ).
fof(f504,axiom,
! [X22,X23,X21] : minus_minus_nat(minus_minus_nat(X22,X23),X21) = minus_minus_nat(minus_minus_nat(X22,X21),X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_diff__commute) ).
fof(f9838,plain,
spl63_367,
inference(avatar_split_clause,[],[f6580,f9836]) ).
fof(f6580,plain,
! [X0] : number_number_of_int(plus_plus_int(X0,minus_minus_int(pls,min))) = minus_minus_int(number_number_of_int(X0),min),
inference(forward_demodulation,[],[f6579,f5683]) ).
fof(f5683,plain,
! [X0] : minus_minus_int(X0,min) = plus_plus_int(X0,one_one_int),
inference(definition_unfolding,[],[f3977,f3976]) ).
fof(f3977,plain,
! [X0] : succ(X0) = plus_plus_int(X0,one_one_int),
inference(cnf_transformation,[],[f1312]) ).
fof(f1312,plain,
! [X0] : succ(X0) = plus_plus_int(X0,one_one_int),
inference(rectify,[],[f843]) ).
fof(f843,axiom,
! [X21] : succ(X21) = plus_plus_int(X21,one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_succ__def) ).
fof(f6579,plain,
! [X0] : plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,minus_minus_int(pls,min))),
inference(forward_demodulation,[],[f5704,f5593]) ).
fof(f5704,plain,
! [X0] : plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,minus_minus_int(plus_plus_int(pls,pls),min))),
inference(definition_unfolding,[],[f4027,f5578]) ).
fof(f4027,plain,
! [X0] : plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,bit1(pls))),
inference(cnf_transformation,[],[f1362]) ).
fof(f1362,plain,
! [X0] : plus_plus_int(number_number_of_int(X0),one_one_int) = number_number_of_int(plus_plus_int(X0,bit1(pls))),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X7] : plus_plus_int(number_number_of_int(X7),one_one_int) = number_number_of_int(plus_plus_int(X7,bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_add__special_I3_J) ).
fof(f9832,plain,
spl63_366,
inference(avatar_split_clause,[],[f6578,f9830]) ).
fof(f6578,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(minus_minus_int(pls,min),X0)),
inference(forward_demodulation,[],[f5703,f5593]) ).
fof(f5703,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),X0)),
inference(definition_unfolding,[],[f4026,f5578]) ).
fof(f4026,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(bit1(pls),X0)),
inference(cnf_transformation,[],[f1361]) ).
fof(f1361,plain,
! [X0] : plus_plus_int(one_one_int,number_number_of_int(X0)) = number_number_of_int(plus_plus_int(bit1(pls),X0)),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X6] : plus_plus_int(one_one_int,number_number_of_int(X6)) = number_number_of_int(plus_plus_int(bit1(pls),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_add__special_I2_J) ).
fof(f9827,plain,
spl63_365,
inference(avatar_split_clause,[],[f6577,f9825]) ).
fof(f6577,plain,
! [X0] : plus_plus_real(number267125858f_real(X0),one_one_real) = number267125858f_real(plus_plus_int(X0,minus_minus_int(pls,min))),
inference(forward_demodulation,[],[f5702,f5593]) ).
fof(f5702,plain,
! [X0] : plus_plus_real(number267125858f_real(X0),one_one_real) = number267125858f_real(plus_plus_int(X0,minus_minus_int(plus_plus_int(pls,pls),min))),
inference(definition_unfolding,[],[f4025,f5578]) ).
fof(f4025,plain,
! [X0] : plus_plus_real(number267125858f_real(X0),one_one_real) = number267125858f_real(plus_plus_int(X0,bit1(pls))),
inference(cnf_transformation,[],[f1360]) ).
fof(f1360,plain,
! [X0] : plus_plus_real(number267125858f_real(X0),one_one_real) = number267125858f_real(plus_plus_int(X0,bit1(pls))),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X7] : plus_plus_real(number267125858f_real(X7),one_one_real) = number267125858f_real(plus_plus_int(X7,bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__special_I3_J) ).
fof(f9816,plain,
spl63_364,
inference(avatar_split_clause,[],[f6576,f9814]) ).
fof(f9814,plain,
( spl63_364
<=> ! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(plus_plus_int(minus_minus_int(pls,min),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_364])]) ).
fof(f6576,plain,
! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(plus_plus_int(minus_minus_int(pls,min),X0)),
inference(forward_demodulation,[],[f5701,f5593]) ).
fof(f5701,plain,
! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),X0)),
inference(definition_unfolding,[],[f4024,f5578]) ).
fof(f4024,plain,
! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(plus_plus_int(bit1(pls),X0)),
inference(cnf_transformation,[],[f1359]) ).
fof(f1359,plain,
! [X0] : plus_plus_real(one_one_real,number267125858f_real(X0)) = number267125858f_real(plus_plus_int(bit1(pls),X0)),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X6] : plus_plus_real(one_one_real,number267125858f_real(X6)) = number267125858f_real(plus_plus_int(bit1(pls),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_add__special_I2_J) ).
fof(f9810,plain,
( spl63_363
| ~ spl63_143
| ~ spl63_153
| ~ spl63_362 ),
inference(avatar_split_clause,[],[f9805,f9800,f7739,f7697,f9807]) ).
fof(f9807,plain,
( spl63_363
<=> hBOOL(hAPP_int_bool(zprime,minus_minus_int(one_one_int,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_363])]) ).
fof(f9800,plain,
( spl63_362
<=> hBOOL(hAPP_int_bool(zprime,number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_362])]) ).
fof(f9805,plain,
( hBOOL(hAPP_int_bool(zprime,minus_minus_int(one_one_int,min)))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_362 ),
inference(forward_demodulation,[],[f9804,f8005]) ).
fof(f9804,plain,
( hBOOL(hAPP_int_bool(zprime,plus_plus_int(one_one_int,one_one_int)))
| ~ spl63_362 ),
inference(forward_demodulation,[],[f9802,f6468]) ).
fof(f9802,plain,
( hBOOL(hAPP_int_bool(zprime,number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min)))))
| ~ spl63_362 ),
inference(avatar_component_clause,[],[f9800]) ).
fof(f9803,plain,
spl63_362,
inference(avatar_split_clause,[],[f6464,f9800]) ).
fof(f6464,plain,
hBOOL(hAPP_int_bool(zprime,number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5619,f5593]) ).
fof(f5619,plain,
hBOOL(hAPP_int_bool(zprime,number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3836,f3979,f5578]) ).
fof(f3836,plain,
hBOOL(hAPP_int_bool(zprime,number_number_of_int(bit0(bit1(pls))))),
inference(cnf_transformation,[],[f1012]) ).
fof(f1012,axiom,
hBOOL(hAPP_int_bool(zprime,number_number_of_int(bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_zprime__2) ).
fof(f9798,plain,
spl63_361,
inference(avatar_split_clause,[],[f6113,f9796]) ).
fof(f9796,plain,
( spl63_361
<=> ! [X0,X1] :
( sP13(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_361])]) ).
fof(f6113,plain,
! [X0,X1] :
( sP13(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),pls)) ),
inference(definition_unfolding,[],[f4888,f3772]) ).
fof(f4888,plain,
! [X0,X1] :
( sP13(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),zero_zero_int)) ),
inference(cnf_transformation,[],[f3537]) ).
fof(f3537,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),zero_zero_int))
| ~ sP13(X1,X0) )
& ( sP13(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),zero_zero_int)) ) ),
inference(nnf_transformation,[],[f3195]) ).
fof(f3195,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),zero_zero_int))
<=> sP13(X1,X0) ),
inference(definition_folding,[],[f1863,f3194]) ).
fof(f3194,plain,
! [X1,X0] :
( sP13(X1,X0)
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f1863,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),zero_zero_int))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
inference(rectify,[],[f557]) ).
fof(f557,axiom,
! [X5,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X5,X81)),zero_zero_int))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X81))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X81),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_mult__le__0__iff) ).
fof(f9794,plain,
spl63_360,
inference(avatar_split_clause,[],[f6112,f9792]) ).
fof(f9792,plain,
( spl63_360
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),pls))
| ~ sP13(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_360])]) ).
fof(f6112,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),pls))
| ~ sP13(X1,X0) ),
inference(definition_unfolding,[],[f4889,f3772]) ).
fof(f4889,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(X0,X1)),zero_zero_int))
| ~ sP13(X1,X0) ),
inference(cnf_transformation,[],[f3537]) ).
fof(f9790,plain,
spl63_359,
inference(avatar_split_clause,[],[f6073,f9788]) ).
fof(f6073,plain,
! [X0,X1] :
( sP12(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X1))) ),
inference(definition_unfolding,[],[f4830,f3772]) ).
fof(f4830,plain,
! [X0,X1] :
( sP12(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X1))) ),
inference(cnf_transformation,[],[f3508]) ).
fof(f3508,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X1)))
| ~ sP12(X1,X0) )
& ( sP12(X1,X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X1))) ) ),
inference(nnf_transformation,[],[f3193]) ).
fof(f3193,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X1)))
<=> sP12(X1,X0) ),
inference(definition_folding,[],[f1837,f3192]) ).
fof(f3192,plain,
! [X1,X0] :
( sP12(X1,X0)
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f1837,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X1)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
inference(rectify,[],[f559]) ).
fof(f559,axiom,
! [X5,X81] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X5,X81)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X81),zero_zero_int))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),zero_zero_int)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X81))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_zero__le__mult__iff) ).
fof(f9786,plain,
spl63_358,
inference(avatar_split_clause,[],[f6072,f9784]) ).
fof(f9784,plain,
( spl63_358
<=> ! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X1)))
| ~ sP12(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_358])]) ).
fof(f6072,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X1)))
| ~ sP12(X1,X0) ),
inference(definition_unfolding,[],[f4831,f3772]) ).
fof(f4831,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X1)))
| ~ sP12(X1,X0) ),
inference(cnf_transformation,[],[f3508]) ).
fof(f9782,plain,
spl63_357,
inference(avatar_split_clause,[],[f5912,f9780]) ).
fof(f5912,plain,
! [X0,X1] :
( pls != hAPP_nat_int(power_power_int(X1),X0)
| pls = X1
| ~ is_int(X1) ),
inference(definition_unfolding,[],[f4398,f3772,f3772]) ).
fof(f4398,plain,
! [X0,X1] :
( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0)
| zero_zero_int = X1
| ~ is_int(X1) ),
inference(cnf_transformation,[],[f2427]) ).
fof(f2427,plain,
! [X0,X1] :
( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0)
| zero_zero_int = X1
| ~ is_int(X1) ),
inference(flattening,[],[f2426]) ).
fof(f2426,plain,
! [X0,X1] :
( zero_zero_int != hAPP_nat_int(power_power_int(X1),X0)
| zero_zero_int = X1
| ~ is_int(X1) ),
inference(ennf_transformation,[],[f1610]) ).
fof(f1610,plain,
! [X0,X1] :
( is_int(X1)
=> ( zero_zero_int != X1
=> zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) ) ),
inference(rectify,[],[f260]) ).
fof(f260,axiom,
! [X64,X65] :
( is_int(X65)
=> ( zero_zero_int != X65
=> zero_zero_int != hAPP_nat_int(power_power_int(X65),X64) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
fof(f9778,plain,
spl63_356,
inference(avatar_split_clause,[],[f5911,f9776]) ).
fof(f9776,plain,
( spl63_356
<=> ! [X0,X1] :
( pls = legendre(X0,X1)
| ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_356])]) ).
fof(f5911,plain,
! [X0,X1] :
( pls = legendre(X0,X1)
| ~ hBOOL(hAPP_int_bool(zcong(X0,pls),X1)) ),
inference(definition_unfolding,[],[f4387,f3772,f3772]) ).
fof(f4387,plain,
! [X0,X1] :
( zero_zero_int = legendre(X0,X1)
| ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f2420]) ).
fof(f2420,plain,
! [X0,X1] :
( ( ( ( legendre(X0,X1) = number_number_of_int(min)
| hBOOL(hAPP_int_bool(quadRes(X1),X0)) )
& ( one_one_int = legendre(X0,X1)
| ~ hBOOL(hAPP_int_bool(quadRes(X1),X0)) ) )
| hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) )
& ( zero_zero_int = legendre(X0,X1)
| ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1)) ) ),
inference(ennf_transformation,[],[f1602]) ).
fof(f1602,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
=> ( ( ~ hBOOL(hAPP_int_bool(quadRes(X1),X0))
=> legendre(X0,X1) = number_number_of_int(min) )
& ( hBOOL(hAPP_int_bool(quadRes(X1),X0))
=> one_one_int = legendre(X0,X1) ) ) )
& ( hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X1))
=> zero_zero_int = legendre(X0,X1) ) ),
inference(rectify,[],[f1148]) ).
fof(f1148,axiom,
! [X151,X381] :
( ( ~ hBOOL(hAPP_int_bool(zcong(X151,zero_zero_int),X381))
=> ( ( ~ hBOOL(hAPP_int_bool(quadRes(X381),X151))
=> number_number_of_int(min) = legendre(X151,X381) )
& ( hBOOL(hAPP_int_bool(quadRes(X381),X151))
=> one_one_int = legendre(X151,X381) ) ) )
& ( hBOOL(hAPP_int_bool(zcong(X151,zero_zero_int),X381))
=> zero_zero_int = legendre(X151,X381) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_Legendre__def) ).
fof(f9767,plain,
spl63_355,
inference(avatar_split_clause,[],[f5879,f9765]) ).
fof(f9765,plain,
( spl63_355
<=> ! [X4,X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK40(X0)))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_355])]) ).
fof(f5879,plain,
! [X0,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK40(X0)))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ),
inference(definition_unfolding,[],[f4287,f3772]) ).
fof(f4287,plain,
! [X0,X4] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK40(X0)))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ),
inference(cnf_transformation,[],[f3327]) ).
fof(f3327,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(X0,sK39(X0)))
| ! [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ is_int(X2) ) )
& ( ( hBOOL(hAPP_nat_bool(X0,nat(sK40(X0))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK40(X0)))
& is_int(sK40(X0)) )
| ! [X4] : ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f3324,f3326,f3325]) ).
fof(f3325,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_nat_bool(X0,X1))
=> hBOOL(hAPP_nat_bool(X0,sK39(X0))) ),
introduced(choice_axiom,[]) ).
fof(f3326,plain,
! [X0] :
( ? [X3] :
( hBOOL(hAPP_nat_bool(X0,nat(X3)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
& is_int(X3) )
=> ( hBOOL(hAPP_nat_bool(X0,nat(sK40(X0))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK40(X0)))
& is_int(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3324,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP_nat_bool(X0,X1))
| ! [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ is_int(X2) ) )
& ( ? [X3] :
( hBOOL(hAPP_nat_bool(X0,nat(X3)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
& is_int(X3) )
| ! [X4] : ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
inference(rectify,[],[f3323]) ).
fof(f3323,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP_nat_bool(X0,X1))
| ! [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ is_int(X2) ) )
& ( ? [X2] :
( hBOOL(hAPP_nat_bool(X0,nat(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
& is_int(X2) )
| ! [X1] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
inference(nnf_transformation,[],[f1514]) ).
fof(f1514,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP_nat_bool(X0,X1))
<=> ? [X2] :
( hBOOL(hAPP_nat_bool(X0,nat(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
& is_int(X2) ) ),
inference(rectify,[],[f561]) ).
fof(f561,axiom,
! [X54] :
( ? [X248] : hBOOL(hAPP_nat_bool(X54,X248))
<=> ? [X152] :
( hBOOL(hAPP_nat_bool(X54,nat(X152)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
& is_int(X152) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_ex__nat) ).
fof(f9763,plain,
spl63_354,
inference(avatar_split_clause,[],[f5874,f9761]) ).
fof(f9761,plain,
( spl63_354
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK35(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_354])]) ).
fof(f5874,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK35(X0))) ),
inference(definition_unfolding,[],[f4280,f3772]) ).
fof(f4280,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(X0))) ),
inference(cnf_transformation,[],[f3317]) ).
fof(f3317,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP_nat_bool(X0,X1))
| ( ~ hBOOL(hAPP_nat_bool(X0,nat(sK35(X0))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(X0)))
& is_int(sK35(X0)) ) )
& ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,nat(X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ is_int(X3) )
| ~ hBOOL(hAPP_nat_bool(X0,sK36(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f3314,f3316,f3315]) ).
fof(f3315,plain,
! [X0] :
( ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,nat(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
& is_int(X2) )
=> ( ~ hBOOL(hAPP_nat_bool(X0,nat(sK35(X0))))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK35(X0)))
& is_int(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3316,plain,
! [X0] :
( ? [X4] : ~ hBOOL(hAPP_nat_bool(X0,X4))
=> ~ hBOOL(hAPP_nat_bool(X0,sK36(X0))) ),
introduced(choice_axiom,[]) ).
fof(f3314,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP_nat_bool(X0,X1))
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,nat(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
& is_int(X2) ) )
& ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,nat(X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ is_int(X3) )
| ? [X4] : ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
inference(rectify,[],[f3313]) ).
fof(f3313,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP_nat_bool(X0,X1))
| ? [X2] :
( ~ hBOOL(hAPP_nat_bool(X0,nat(X2)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
& is_int(X2) ) )
& ( ! [X2] :
( hBOOL(hAPP_nat_bool(X0,nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ is_int(X2) )
| ? [X1] : ~ hBOOL(hAPP_nat_bool(X0,X1)) ) ),
inference(nnf_transformation,[],[f2412]) ).
fof(f2412,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP_nat_bool(X0,X1))
<=> ! [X2] :
( hBOOL(hAPP_nat_bool(X0,nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ is_int(X2) ) ),
inference(flattening,[],[f2411]) ).
fof(f2411,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP_nat_bool(X0,X1))
<=> ! [X2] :
( hBOOL(hAPP_nat_bool(X0,nat(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ is_int(X2) ) ),
inference(ennf_transformation,[],[f1512]) ).
fof(f1512,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP_nat_bool(X0,X1))
<=> ! [X2] :
( is_int(X2)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> hBOOL(hAPP_nat_bool(X0,nat(X2))) ) ) ),
inference(rectify,[],[f560]) ).
fof(f560,axiom,
! [X54] :
( ! [X248] : hBOOL(hAPP_nat_bool(X54,X248))
<=> ! [X152] :
( is_int(X152)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
=> hBOOL(hAPP_nat_bool(X54,nat(X152))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_all__nat) ).
fof(f9759,plain,
spl63_353,
inference(avatar_split_clause,[],[f5861,f9757]) ).
fof(f9757,plain,
( spl63_353
<=> ! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_353])]) ).
fof(f5861,plain,
! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ),
inference(definition_unfolding,[],[f4258,f3772]) ).
fof(f4258,plain,
! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)) ),
inference(cnf_transformation,[],[f3303]) ).
fof(f3303,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int))
| zero_zero_nat != X0 )
& ( zero_zero_nat = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)) ) ),
inference(nnf_transformation,[],[f1502]) ).
fof(f1502,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int))
<=> zero_zero_nat = X0 ),
inference(rectify,[],[f836]) ).
fof(f836,axiom,
! [X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X18)),zero_zero_int))
<=> zero_zero_nat = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_int__le__0__conv) ).
fof(f9755,plain,
spl63_352,
inference(avatar_split_clause,[],[f5785,f9753]) ).
fof(f9753,plain,
( spl63_352
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| zero_zero_nat != nat(number_number_of_int(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_352])]) ).
fof(f5785,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| zero_zero_nat != nat(number_number_of_int(X0)) ),
inference(definition_unfolding,[],[f4158,f3978]) ).
fof(f4158,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| zero_zero_nat != number_number_of_nat(X0) ),
inference(cnf_transformation,[],[f3253]) ).
fof(f3253,plain,
! [X0] :
( ( zero_zero_nat = number_number_of_nat(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| zero_zero_nat != number_number_of_nat(X0) ) ),
inference(nnf_transformation,[],[f1452]) ).
fof(f1452,plain,
! [X0] :
( zero_zero_nat = number_number_of_nat(X0)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(rectify,[],[f825]) ).
fof(f825,axiom,
! [X59] :
( zero_zero_nat = number_number_of_nat(X59)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_eq__0__number__of) ).
fof(f9751,plain,
spl63_351,
inference(avatar_split_clause,[],[f5784,f9749]) ).
fof(f5784,plain,
! [X0] :
( zero_zero_nat = nat(number_number_of_int(X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(definition_unfolding,[],[f4159,f3978]) ).
fof(f4159,plain,
! [X0] :
( zero_zero_nat = number_number_of_nat(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(cnf_transformation,[],[f3253]) ).
fof(f9746,plain,
spl63_350,
inference(avatar_split_clause,[],[f5691,f9744]) ).
fof(f5691,plain,
! [X0] : plus_plus_int(plus_plus_int(one_one_int,X0),X0) = minus_minus_int(plus_plus_int(X0,X0),min),
inference(definition_unfolding,[],[f4004,f5578]) ).
fof(f4004,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f1339]) ).
fof(f1339,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X21] : bit1(X21) = plus_plus_int(plus_plus_int(one_one_int,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
fof(f9742,plain,
spl63_349,
inference(avatar_split_clause,[],[f5274,f9740]) ).
fof(f9740,plain,
( spl63_349
<=> ! [X2,X0,X1] :
( is_int(if_int(X0,X1,X2))
| ~ is_int(X2)
| ~ is_int(X1)
| ~ is_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_349])]) ).
fof(f5274,plain,
! [X2,X0,X1] :
( is_int(if_int(X0,X1,X2))
| ~ is_int(X2)
| ~ is_int(X1)
| ~ is_bool(X0) ),
inference(cnf_transformation,[],[f3019]) ).
fof(f3019,plain,
! [X0,X1,X2] :
( is_int(if_int(X0,X1,X2))
| ~ is_int(X2)
| ~ is_int(X1)
| ~ is_bool(X0) ),
inference(flattening,[],[f3018]) ).
fof(f3018,plain,
! [X0,X1,X2] :
( is_int(if_int(X0,X1,X2))
| ~ is_int(X2)
| ~ is_int(X1)
| ~ is_bool(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( is_int(X2)
& is_int(X1)
& is_bool(X0) )
=> is_int(if_int(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_If_000tc__Int__Oint) ).
fof(f9738,plain,
spl63_348,
inference(avatar_split_clause,[],[f4990,f9736]) ).
fof(f9736,plain,
( spl63_348
<=> ! [X2,X0,X1] : times_times_int(X0,times_times_int(X1,X2)) = times_times_int(times_times_int(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_348])]) ).
fof(f9734,plain,
spl63_347,
inference(avatar_split_clause,[],[f4989,f9732]) ).
fof(f9732,plain,
( spl63_347
<=> ! [X2,X0,X1] : times_times_int(X0,times_times_int(X1,X2)) = times_times_int(X1,times_times_int(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_347])]) ).
fof(f4989,plain,
! [X2,X0,X1] : times_times_int(X0,times_times_int(X1,X2)) = times_times_int(X1,times_times_int(X0,X2)),
inference(cnf_transformation,[],[f1925]) ).
fof(f1925,plain,
! [X0,X1,X2] : times_times_int(X0,times_times_int(X1,X2)) = times_times_int(X1,times_times_int(X0,X2)),
inference(rectify,[],[f446]) ).
fof(f446,axiom,
! [X158,X159,X160] : times_times_int(X158,times_times_int(X159,X160)) = times_times_int(X159,times_times_int(X158,X160)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f9730,plain,
spl63_346,
inference(avatar_split_clause,[],[f4984,f9728]) ).
fof(f9719,plain,
spl63_345,
inference(avatar_split_clause,[],[f4982,f9717]) ).
fof(f9717,plain,
( spl63_345
<=> ! [X2,X0,X1] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_345])]) ).
fof(f4982,plain,
! [X2,X0,X1] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)),
inference(cnf_transformation,[],[f1918]) ).
fof(f1918,plain,
! [X0,X1,X2] : plus_plus_int(X0,plus_plus_int(X1,X2)) = plus_plus_int(X1,plus_plus_int(X0,X2)),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X8,X10,X17] : plus_plus_int(X8,plus_plus_int(X10,X17)) = plus_plus_int(X10,plus_plus_int(X8,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zadd__left__commute) ).
fof(f9715,plain,
spl63_344,
inference(avatar_split_clause,[],[f4977,f9713]) ).
fof(f9713,plain,
( spl63_344
<=> ! [X2,X0,X1] : times_times_nat(X0,times_times_nat(X1,X2)) = times_times_nat(times_times_nat(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_344])]) ).
fof(f9711,plain,
spl63_343,
inference(avatar_split_clause,[],[f4976,f9709]) ).
fof(f9709,plain,
( spl63_343
<=> ! [X2,X0,X1] : times_times_nat(X0,times_times_nat(X1,X2)) = times_times_nat(X1,times_times_nat(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_343])]) ).
fof(f4976,plain,
! [X2,X0,X1] : times_times_nat(X0,times_times_nat(X1,X2)) = times_times_nat(X1,times_times_nat(X0,X2)),
inference(cnf_transformation,[],[f1912]) ).
fof(f1912,plain,
! [X0,X1,X2] : times_times_nat(X0,times_times_nat(X1,X2)) = times_times_nat(X1,times_times_nat(X0,X2)),
inference(rectify,[],[f447]) ).
fof(f447,axiom,
! [X158,X159,X160] : times_times_nat(X158,times_times_nat(X159,X160)) = times_times_nat(X159,times_times_nat(X158,X160)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f9707,plain,
spl63_342,
inference(avatar_split_clause,[],[f4971,f9705]) ).
fof(f9705,plain,
( spl63_342
<=> ! [X2,X0,X1] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(plus_plus_nat(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_342])]) ).
fof(f9703,plain,
spl63_341,
inference(avatar_split_clause,[],[f4969,f9701]) ).
fof(f9701,plain,
( spl63_341
<=> ! [X2,X0,X1] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(X1,plus_plus_nat(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_341])]) ).
fof(f4969,plain,
! [X2,X0,X1] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(X1,plus_plus_nat(X0,X2)),
inference(cnf_transformation,[],[f1905]) ).
fof(f1905,plain,
! [X0,X1,X2] : plus_plus_nat(X0,plus_plus_nat(X1,X2)) = plus_plus_nat(X1,plus_plus_nat(X0,X2)),
inference(rectify,[],[f376]) ).
fof(f376,axiom,
! [X123,X124,X125] : plus_plus_nat(X123,plus_plus_nat(X124,X125)) = plus_plus_nat(X124,plus_plus_nat(X123,X125)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(f9699,plain,
spl63_340,
inference(avatar_split_clause,[],[f4964,f9697]) ).
fof(f9697,plain,
( spl63_340
<=> ! [X2,X0,X1] : times_times_real(X0,times_times_real(X1,X2)) = times_times_real(times_times_real(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_340])]) ).
fof(f9695,plain,
spl63_339,
inference(avatar_split_clause,[],[f4963,f9693]) ).
fof(f9693,plain,
( spl63_339
<=> ! [X2,X0,X1] : times_times_real(X0,times_times_real(X1,X2)) = times_times_real(X1,times_times_real(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_339])]) ).
fof(f4963,plain,
! [X2,X0,X1] : times_times_real(X0,times_times_real(X1,X2)) = times_times_real(X1,times_times_real(X0,X2)),
inference(cnf_transformation,[],[f1899]) ).
fof(f1899,plain,
! [X0,X1,X2] : times_times_real(X0,times_times_real(X1,X2)) = times_times_real(X1,times_times_real(X0,X2)),
inference(rectify,[],[f448]) ).
fof(f448,axiom,
! [X158,X159,X160] : times_times_real(X158,times_times_real(X159,X160)) = times_times_real(X159,times_times_real(X158,X160)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f9691,plain,
spl63_338,
inference(avatar_split_clause,[],[f4959,f9689]) ).
fof(f9689,plain,
( spl63_338
<=> ! [X2,X0,X1] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(plus_plus_real(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_338])]) ).
fof(f9687,plain,
spl63_337,
inference(avatar_split_clause,[],[f4958,f9685]) ).
fof(f9685,plain,
( spl63_337
<=> ! [X2,X0,X1] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(X1,plus_plus_real(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_337])]) ).
fof(f4958,plain,
! [X2,X0,X1] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(X1,plus_plus_real(X0,X2)),
inference(cnf_transformation,[],[f1894]) ).
fof(f1894,plain,
! [X0,X1,X2] : plus_plus_real(X0,plus_plus_real(X1,X2)) = plus_plus_real(X1,plus_plus_real(X0,X2)),
inference(rectify,[],[f377]) ).
fof(f377,axiom,
! [X123,X124,X125] : plus_plus_real(X123,plus_plus_real(X124,X125)) = plus_plus_real(X124,plus_plus_real(X123,X125)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(f9683,plain,
spl63_336,
inference(avatar_split_clause,[],[f4956,f9681]) ).
fof(f9681,plain,
( spl63_336
<=> ! [X2,X0,X1] : minus_minus_nat(minus_minus_nat(X0,X1),X2) = minus_minus_nat(X0,plus_plus_nat(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_336])]) ).
fof(f9672,plain,
spl63_335,
inference(avatar_split_clause,[],[f4955,f9670]) ).
fof(f9670,plain,
( spl63_335
<=> ! [X2,X0,X1] : minus_minus_nat(X1,X2) = minus_minus_nat(plus_plus_nat(X0,X1),plus_plus_nat(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_335])]) ).
fof(f4955,plain,
! [X2,X0,X1] : minus_minus_nat(X1,X2) = minus_minus_nat(plus_plus_nat(X0,X1),plus_plus_nat(X0,X2)),
inference(cnf_transformation,[],[f1891]) ).
fof(f1891,plain,
! [X0,X1,X2] : minus_minus_nat(X1,X2) = minus_minus_nat(plus_plus_nat(X0,X1),plus_plus_nat(X0,X2)),
inference(rectify,[],[f735]) ).
fof(f735,axiom,
! [X21,X15,X16] : minus_minus_nat(X15,X16) = minus_minus_nat(plus_plus_nat(X21,X15),plus_plus_nat(X21,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_Nat_Odiff__cancel) ).
fof(f9668,plain,
spl63_334,
inference(avatar_split_clause,[],[f4954,f9666]) ).
fof(f9666,plain,
( spl63_334
<=> ! [X2,X0,X1] : minus_minus_nat(X0,X2) = minus_minus_nat(plus_plus_nat(X0,X1),plus_plus_nat(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_334])]) ).
fof(f4954,plain,
! [X2,X0,X1] : minus_minus_nat(X0,X2) = minus_minus_nat(plus_plus_nat(X0,X1),plus_plus_nat(X2,X1)),
inference(cnf_transformation,[],[f1890]) ).
fof(f1890,plain,
! [X0,X1,X2] : minus_minus_nat(X0,X2) = minus_minus_nat(plus_plus_nat(X0,X1),plus_plus_nat(X2,X1)),
inference(rectify,[],[f736]) ).
fof(f736,axiom,
! [X15,X21,X16] : minus_minus_nat(X15,X16) = minus_minus_nat(plus_plus_nat(X15,X21),plus_plus_nat(X16,X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_diff__cancel2) ).
fof(f9664,plain,
spl63_333,
inference(avatar_split_clause,[],[f4805,f9662]) ).
fof(f9662,plain,
( spl63_333
<=> ! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X0,X1)),zero_zero_real))
| ~ sP11(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_333])]) ).
fof(f4805,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X0,X1)),zero_zero_real))
| ~ sP11(X1,X0) ),
inference(cnf_transformation,[],[f3493]) ).
fof(f3493,plain,
! [X0,X1] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X0,X1)),zero_zero_real))
| ~ sP11(X1,X0) )
& ( sP11(X1,X0)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X0,X1)),zero_zero_real)) ) ),
inference(nnf_transformation,[],[f3191]) ).
fof(f3191,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X0,X1)),zero_zero_real))
<=> sP11(X1,X0) ),
inference(definition_folding,[],[f1830,f3190]) ).
fof(f3190,plain,
! [X1,X0] :
( sP11(X1,X0)
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f1830,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X0,X1)),zero_zero_real))
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) ) ),
inference(rectify,[],[f556]) ).
fof(f556,axiom,
! [X5,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X5,X81)),zero_zero_real))
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X81))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X81),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_mult__le__0__iff) ).
fof(f9660,plain,
spl63_332,
inference(avatar_split_clause,[],[f4804,f9658]) ).
fof(f9658,plain,
( spl63_332
<=> ! [X0,X1] :
( sP11(X1,X0)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X0,X1)),zero_zero_real)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_332])]) ).
fof(f4804,plain,
! [X0,X1] :
( sP11(X1,X0)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,times_times_real(X0,X1)),zero_zero_real)) ),
inference(cnf_transformation,[],[f3493]) ).
fof(f9656,plain,
spl63_331,
inference(avatar_split_clause,[],[f4793,f9654]) ).
fof(f9654,plain,
( spl63_331
<=> ! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1)))
| ~ sP10(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_331])]) ).
fof(f4793,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1)))
| ~ sP10(X1,X0) ),
inference(cnf_transformation,[],[f3487]) ).
fof(f3487,plain,
! [X0,X1] :
( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1)))
| ~ sP10(X1,X0) )
& ( sP10(X1,X0)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1))) ) ),
inference(nnf_transformation,[],[f3189]) ).
fof(f3189,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1)))
<=> sP10(X1,X0) ),
inference(definition_folding,[],[f1827,f3188]) ).
fof(f3188,plain,
! [X1,X0] :
( sP10(X1,X0)
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f1827,plain,
! [X0,X1] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1)))
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X1),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X1))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X0)) ) ) ),
inference(rectify,[],[f558]) ).
fof(f558,axiom,
! [X5,X81] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X5,X81)))
<=> ( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X81),zero_zero_real))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X5),zero_zero_real)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X81))
& hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_zero__le__mult__iff) ).
fof(f9652,plain,
spl63_330,
inference(avatar_split_clause,[],[f4792,f9650]) ).
fof(f4792,plain,
! [X0,X1] :
( sP10(X1,X0)
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X1))) ),
inference(cnf_transformation,[],[f3487]) ).
fof(f9648,plain,
spl63_329,
inference(avatar_split_clause,[],[f4721,f9646]) ).
fof(f9646,plain,
( spl63_329
<=> ! [X0,X1] :
( nat(number_number_of_int(X1)) = X0
| hAPP_nat_int(semiri1621563631at_int,X0) != number_number_of_int(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_329])]) ).
fof(f4721,plain,
! [X0,X1] :
( nat(number_number_of_int(X1)) = X0
| hAPP_nat_int(semiri1621563631at_int,X0) != number_number_of_int(X1) ),
inference(cnf_transformation,[],[f3446]) ).
fof(f3446,plain,
! [X0,X1] :
( ( hAPP_nat_int(semiri1621563631at_int,X0) = number_number_of_int(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| nat(number_number_of_int(X1)) != X0 )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
& nat(number_number_of_int(X1)) = X0 )
| hAPP_nat_int(semiri1621563631at_int,X0) != number_number_of_int(X1) ) ),
inference(flattening,[],[f3445]) ).
fof(f3445,plain,
! [X0,X1] :
( ( hAPP_nat_int(semiri1621563631at_int,X0) = number_number_of_int(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
| nat(number_number_of_int(X1)) != X0 )
& ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
& nat(number_number_of_int(X1)) = X0 )
| hAPP_nat_int(semiri1621563631at_int,X0) != number_number_of_int(X1) ) ),
inference(nnf_transformation,[],[f1802]) ).
fof(f1802,plain,
! [X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X0) = number_number_of_int(X1)
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X1)))
& nat(number_number_of_int(X1)) = X0 ) ),
inference(rectify,[],[f774]) ).
fof(f774,axiom,
! [X29,X59] :
( hAPP_nat_int(semiri1621563631at_int,X29) = number_number_of_int(X59)
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(X59)))
& nat(number_number_of_int(X59)) = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_int__eq__iff__number__of) ).
fof(f9644,plain,
spl63_328,
inference(avatar_split_clause,[],[f4694,f9642]) ).
fof(f9642,plain,
( spl63_328
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| zero_zero_nat != minus_minus_nat(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_328])]) ).
fof(f4694,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| zero_zero_nat != minus_minus_nat(X0,X1) ),
inference(cnf_transformation,[],[f3426]) ).
fof(f3426,plain,
! [X0,X1] :
( ( zero_zero_nat = minus_minus_nat(X0,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
| zero_zero_nat != minus_minus_nat(X0,X1) ) ),
inference(nnf_transformation,[],[f1792]) ).
fof(f1792,plain,
! [X0,X1] :
( zero_zero_nat = minus_minus_nat(X0,X1)
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(rectify,[],[f956]) ).
fof(f956,axiom,
! [X29,X18] :
( zero_zero_nat = minus_minus_nat(X29,X18)
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_927_diff__is__0__eq) ).
fof(f9640,plain,
spl63_327,
inference(avatar_split_clause,[],[f4604,f9638]) ).
fof(f9638,plain,
( spl63_327
<=> ! [X0,X1] :
( one_one_int = times_times_int(X0,X1)
| ~ sP7(X1,X0)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_327])]) ).
fof(f4604,plain,
! [X0,X1] :
( one_one_int = times_times_int(X0,X1)
| ~ sP7(X1,X0)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f3386]) ).
fof(f3386,plain,
! [X0,X1] :
( ( ( one_one_int = times_times_int(X0,X1)
| ~ sP7(X1,X0) )
& ( sP7(X1,X0)
| one_one_int != times_times_int(X0,X1) ) )
| ~ sP8(X0,X1) ),
inference(nnf_transformation,[],[f3184]) ).
fof(f3184,plain,
! [X0,X1] :
( ( one_one_int = times_times_int(X0,X1)
<=> sP7(X1,X0) )
| ~ sP8(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f9636,plain,
spl63_326,
inference(avatar_split_clause,[],[f4603,f9634]) ).
fof(f9634,plain,
( spl63_326
<=> ! [X0,X1] :
( sP7(X1,X0)
| one_one_int != times_times_int(X0,X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_326])]) ).
fof(f4603,plain,
! [X0,X1] :
( sP7(X1,X0)
| one_one_int != times_times_int(X0,X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f3386]) ).
fof(f9625,plain,
spl63_325,
inference(avatar_split_clause,[],[f4560,f9623]) ).
fof(f9623,plain,
( spl63_325
<=> ! [X0,X1] :
( zero_zero_nat = minus_minus_nat(X0,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_325])]) ).
fof(f4560,plain,
! [X0,X1] :
( zero_zero_nat = minus_minus_nat(X0,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(cnf_transformation,[],[f2611]) ).
fof(f2611,plain,
! [X0,X1] :
( zero_zero_nat = minus_minus_nat(X0,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1)) ),
inference(ennf_transformation,[],[f1719]) ).
fof(f1719,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X1))
=> zero_zero_nat = minus_minus_nat(X0,X1) ),
inference(rectify,[],[f957]) ).
fof(f957,axiom,
! [X15,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X16))
=> zero_zero_nat = minus_minus_nat(X15,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_928_diff__is__0__eq_H) ).
fof(f9621,plain,
spl63_324,
inference(avatar_split_clause,[],[f4469,f9619]) ).
fof(f9619,plain,
( spl63_324
<=> ! [X0,X1] :
( zero_zero_nat = X0
| one_one_nat = X1
| times_times_nat(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_324])]) ).
fof(f4469,plain,
! [X0,X1] :
( zero_zero_nat = X0
| one_one_nat = X1
| times_times_nat(X0,X1) != X0 ),
inference(cnf_transformation,[],[f2480]) ).
fof(f2480,plain,
! [X0,X1] :
( zero_zero_nat = X0
| one_one_nat = X1
| times_times_nat(X0,X1) != X0 ),
inference(flattening,[],[f2479]) ).
fof(f2479,plain,
! [X0,X1] :
( zero_zero_nat = X0
| one_one_nat = X1
| times_times_nat(X0,X1) != X0 ),
inference(ennf_transformation,[],[f1643]) ).
fof(f1643,plain,
! [X0,X1] :
( times_times_nat(X0,X1) = X0
=> ( zero_zero_nat = X0
| one_one_nat = X1 ) ),
inference(rectify,[],[f955]) ).
fof(f955,axiom,
! [X15,X16] :
( times_times_nat(X15,X16) = X15
=> ( zero_zero_nat = X15
| one_one_nat = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_mult__eq__self__implies__10) ).
fof(f9617,plain,
spl63_323,
inference(avatar_split_clause,[],[f4456,f9615]) ).
fof(f9615,plain,
( spl63_323
<=> ! [X0,X1] :
( zero_zero_nat != times_times_nat(X1,X0)
| zero_zero_nat = X0
| zero_zero_nat = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_323])]) ).
fof(f4456,plain,
! [X0,X1] :
( zero_zero_nat != times_times_nat(X1,X0)
| zero_zero_nat = X0
| zero_zero_nat = X1 ),
inference(cnf_transformation,[],[f2461]) ).
fof(f2461,plain,
! [X0,X1] :
( zero_zero_nat != times_times_nat(X1,X0)
| zero_zero_nat = X0
| zero_zero_nat = X1 ),
inference(flattening,[],[f2460]) ).
fof(f2460,plain,
! [X0,X1] :
( zero_zero_nat != times_times_nat(X1,X0)
| zero_zero_nat = X0
| zero_zero_nat = X1 ),
inference(ennf_transformation,[],[f1632]) ).
fof(f1632,plain,
! [X0,X1] :
( zero_zero_nat != X1
=> ( zero_zero_nat != X0
=> zero_zero_nat != times_times_nat(X1,X0) ) ),
inference(rectify,[],[f645]) ).
fof(f645,axiom,
! [X306,X307] :
( zero_zero_nat != X307
=> ( zero_zero_nat != X306
=> zero_zero_nat != times_times_nat(X307,X306) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_no__zero__divisors) ).
fof(f9613,plain,
spl63_322,
inference(avatar_split_clause,[],[f4455,f9611]) ).
fof(f9611,plain,
( spl63_322
<=> ! [X0,X1] :
( zero_zero_real != times_times_real(X1,X0)
| zero_zero_real = X0
| zero_zero_real = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_322])]) ).
fof(f4455,plain,
! [X0,X1] :
( zero_zero_real != times_times_real(X1,X0)
| zero_zero_real = X0
| zero_zero_real = X1 ),
inference(cnf_transformation,[],[f2459]) ).
fof(f2459,plain,
! [X0,X1] :
( zero_zero_real != times_times_real(X1,X0)
| zero_zero_real = X0
| zero_zero_real = X1 ),
inference(flattening,[],[f2458]) ).
fof(f2458,plain,
! [X0,X1] :
( zero_zero_real != times_times_real(X1,X0)
| zero_zero_real = X0
| zero_zero_real = X1 ),
inference(ennf_transformation,[],[f1631]) ).
fof(f1631,plain,
! [X0,X1] :
( zero_zero_real != X1
=> ( zero_zero_real != X0
=> zero_zero_real != times_times_real(X1,X0) ) ),
inference(rectify,[],[f644]) ).
fof(f644,axiom,
! [X306,X307] :
( zero_zero_real != X307
=> ( zero_zero_real != X306
=> zero_zero_real != times_times_real(X307,X306) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_no__zero__divisors) ).
fof(f9609,plain,
spl63_321,
inference(avatar_split_clause,[],[f4431,f9607]) ).
fof(f9607,plain,
( spl63_321
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,nat(X0)))
| ~ sP5(X1,X0)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_321])]) ).
fof(f4431,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X1,nat(X0)))
| ~ sP5(X1,X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3346]) ).
fof(f3346,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP_nat_bool(X1,nat(X0)))
| ~ sP5(X1,X0) )
& ( sP5(X1,X0)
| ~ hBOOL(hAPP_nat_bool(X1,nat(X0))) ) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f3345]) ).
fof(f3345,plain,
! [X1,X0] :
( ( ( hBOOL(hAPP_nat_bool(X0,nat(X1)))
| ~ sP5(X0,X1) )
& ( sP5(X0,X1)
| ~ hBOOL(hAPP_nat_bool(X0,nat(X1))) ) )
| ~ sP6(X1,X0) ),
inference(nnf_transformation,[],[f3181]) ).
fof(f3181,plain,
! [X1,X0] :
( ( hBOOL(hAPP_nat_bool(X0,nat(X1)))
<=> sP5(X0,X1) )
| ~ sP6(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f9605,plain,
spl63_320,
inference(avatar_split_clause,[],[f4430,f9603]) ).
fof(f9603,plain,
( spl63_320
<=> ! [X0,X1] :
( sP5(X1,X0)
| ~ hBOOL(hAPP_nat_bool(X1,nat(X0)))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_320])]) ).
fof(f4430,plain,
! [X0,X1] :
( sP5(X1,X0)
| ~ hBOOL(hAPP_nat_bool(X1,nat(X0)))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3346]) ).
fof(f9601,plain,
spl63_319,
inference(avatar_split_clause,[],[f4293,f9599]) ).
fof(f9599,plain,
( spl63_319
<=> ! [X2,X0] :
( hBOOL(hAPP_int_bool(X0,sK41(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_319])]) ).
fof(f4293,plain,
! [X2,X0] :
( hBOOL(hAPP_int_bool(X0,sK41(X0)))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(cnf_transformation,[],[f3332]) ).
fof(f9597,plain,
spl63_318,
inference(avatar_split_clause,[],[f4284,f9595]) ).
fof(f9595,plain,
( spl63_318
<=> ! [X0,X3] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ~ hBOOL(hAPP_int_bool(X0,sK38(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_318])]) ).
fof(f4284,plain,
! [X3,X0] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| ~ hBOOL(hAPP_int_bool(X0,sK38(X0))) ),
inference(cnf_transformation,[],[f3322]) ).
fof(f9593,plain,
spl63_317,
inference(avatar_split_clause,[],[f4248,f9591]) ).
fof(f9591,plain,
( spl63_317
<=> ! [X0] :
( zero_zero_real = X0
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),times_times_real(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_317])]) ).
fof(f4248,plain,
! [X0] :
( zero_zero_real = X0
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),times_times_real(X0,X0))) ),
inference(cnf_transformation,[],[f3298]) ).
fof(f3298,plain,
! [X0] :
( ( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),times_times_real(X0,X0)))
| zero_zero_real != X0 )
& ( zero_zero_real = X0
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),times_times_real(X0,X0))) ) ),
inference(nnf_transformation,[],[f1497]) ).
fof(f1497,plain,
! [X0] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),times_times_real(X0,X0)))
<=> zero_zero_real = X0 ),
inference(rectify,[],[f951]) ).
fof(f951,axiom,
! [X3] :
( ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),times_times_real(X3,X3)))
<=> zero_zero_real = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_922_not__real__square__gt__zero) ).
fof(f9588,plain,
spl63_316,
inference(avatar_split_clause,[],[f3906,f9585]) ).
fof(f3906,plain,
sK32 = minus_minus_int(y,times_times_int(sK31,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f3225]) ).
fof(f3225,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(sK32))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& sK32 = minus_minus_int(y,times_times_int(sK31,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& is_int(sK32)
& is_int(sK31) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f2337,f3224]) ).
fof(f3224,plain,
( ? [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X1))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(y,times_times_int(X0,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X1
& is_int(X1)
& is_int(X0) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(sK32))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& sK32 = minus_minus_int(y,times_times_int(sK31,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& is_int(sK32)
& is_int(sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f2337,plain,
? [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X1))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(y,times_times_int(X0,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X1
& is_int(X1)
& is_int(X0) ),
inference(flattening,[],[f2336]) ).
fof(f2336,plain,
? [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X1))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(y,times_times_int(X0,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X1
& is_int(X1)
& is_int(X0) ),
inference(ennf_transformation,[],[f1242]) ).
fof(f1242,plain,
~ ! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ~ ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X1))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(y,times_times_int(X0,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X1 ) ),
inference(rectify,[],[f1182]) ).
fof(f1182,axiom,
~ ! [X393,X396] :
( ( is_int(X396)
& is_int(X393) )
=> ~ ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X396))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(y,times_times_int(X393,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X396 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153__096_B_Bthesis_O_A_I_B_Bs_Aw_O_Aw_A_061_Ay_A_N_As_A_K_A_I1_A_L_Aint_An) ).
fof(f9575,plain,
spl63_315,
inference(avatar_split_clause,[],[f3902,f9572]) ).
fof(f3902,plain,
sK30 = minus_minus_int(x,times_times_int(sK29,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f3223]) ).
fof(f3223,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(sK30))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& sK30 = minus_minus_int(x,times_times_int(sK29,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& is_int(sK30)
& is_int(sK29) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f2335,f3222]) ).
fof(f3222,plain,
( ? [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X1))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(x,times_times_int(X0,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X1
& is_int(X1)
& is_int(X0) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(sK30))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& sK30 = minus_minus_int(x,times_times_int(sK29,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& is_int(sK30)
& is_int(sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f2335,plain,
? [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X1))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(x,times_times_int(X0,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X1
& is_int(X1)
& is_int(X0) ),
inference(flattening,[],[f2334]) ).
fof(f2334,plain,
? [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X1))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(x,times_times_int(X0,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X1
& is_int(X1)
& is_int(X0) ),
inference(ennf_transformation,[],[f1241]) ).
fof(f1241,plain,
~ ! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ~ ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X1))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(x,times_times_int(X0,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X1 ) ),
inference(rectify,[],[f1183]) ).
fof(f1183,axiom,
~ ! [X154,X397] :
( ( is_int(X397)
& is_int(X154) )
=> ~ ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(X397))),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
& minus_minus_int(x,times_times_int(X154,plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) = X397 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154__096_B_Bthesis_O_A_I_B_Br_Av_O_Av_A_061_Ax_A_N_Ar_A_K_A_I1_A_L_Aint_An) ).
fof(f9517,plain,
( spl63_314
| ~ spl63_143
| ~ spl63_153
| ~ spl63_302 ),
inference(avatar_split_clause,[],[f9065,f9061,f7739,f7697,f9514]) ).
fof(f9061,plain,
( spl63_302
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_302])]) ).
fof(f9065,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_302 ),
inference(forward_demodulation,[],[f9063,f8005]) ).
fof(f9063,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
| ~ spl63_302 ),
inference(avatar_component_clause,[],[f9061]) ).
fof(f9262,plain,
( spl63_313
| ~ spl63_31
| ~ spl63_257 ),
inference(avatar_split_clause,[],[f8866,f8820,f7161,f9259]) ).
fof(f9259,plain,
( spl63_313
<=> is_int(minus_minus_int(one_one_int,min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_313])]) ).
fof(f8820,plain,
( spl63_257
<=> hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)) = minus_minus_int(one_one_int,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_257])]) ).
fof(f8866,plain,
( is_int(minus_minus_int(one_one_int,min))
| ~ spl63_31
| ~ spl63_257 ),
inference(superposition,[],[f7162,f8822]) ).
fof(f8822,plain,
( hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)) = minus_minus_int(one_one_int,min)
| ~ spl63_257 ),
inference(avatar_component_clause,[],[f8820]) ).
fof(f9106,plain,
( spl63_312
| ~ spl63_143
| ~ spl63_153
| ~ spl63_258 ),
inference(avatar_split_clause,[],[f8872,f8868,f7739,f7697,f9103]) ).
fof(f9103,plain,
( spl63_312
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_312])]) ).
fof(f8868,plain,
( spl63_258
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_258])]) ).
fof(f8872,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),minus_minus_int(hAPP_nat_int(semiri1621563631at_int,n),min)))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_258 ),
inference(forward_demodulation,[],[f8870,f8005]) ).
fof(f8870,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
| ~ spl63_258 ),
inference(avatar_component_clause,[],[f8868]) ).
fof(f9101,plain,
spl63_311,
inference(avatar_split_clause,[],[f6389,f9099]) ).
fof(f9099,plain,
( spl63_311
<=> ! [X4,X0,X2] :
( hBOOL(hAPP_nat_bool(X0,X4))
| ~ sP18(X0,plus_plus_nat(X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_311])]) ).
fof(f6389,plain,
! [X2,X0,X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| ~ sP18(X0,plus_plus_nat(X2,X4),X2) ),
inference(equality_resolution,[],[f5320]) ).
fof(f5320,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| plus_plus_nat(X2,X4) != X1
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f3646]) ).
fof(f3646,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ( ~ hBOOL(hAPP_nat_bool(X0,sK61(X0,X1,X2)))
& plus_plus_nat(X2,sK61(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| plus_plus_nat(X2,X4) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f3644,f3645]) ).
fof(f3645,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
=> ( ~ hBOOL(hAPP_nat_bool(X0,sK61(X0,X1,X2)))
& plus_plus_nat(X2,sK61(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3644,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| plus_plus_nat(X2,X4) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(rectify,[],[f3643]) ).
fof(f3643,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| plus_plus_nat(X2,X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(flattening,[],[f3642]) ).
fof(f3642,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| plus_plus_nat(X2,X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3204]) ).
fof(f3204,plain,
! [X0,X1,X2] :
( sP18(X0,X1,X2)
<=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| plus_plus_nat(X2,X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f9097,plain,
spl63_310,
inference(avatar_split_clause,[],[f6388,f9095]) ).
fof(f9095,plain,
( spl63_310
<=> ! [X4,X0,X2] :
( hBOOL(hAPP_nat_bool(X0,X4))
| ~ sP17(X0,plus_plus_nat(X2,X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_310])]) ).
fof(f6388,plain,
! [X2,X0,X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| ~ sP17(X0,plus_plus_nat(X2,X4),X2) ),
inference(equality_resolution,[],[f5312]) ).
fof(f5312,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| plus_plus_nat(X2,X4) != X1
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f3640]) ).
fof(f3640,plain,
! [X0,X1,X2] :
( ( sP17(X0,X1,X2)
| ( ~ hBOOL(hAPP_nat_bool(X0,sK60(X0,X1,X2)))
& plus_plus_nat(X2,sK60(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| plus_plus_nat(X2,X4) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f3638,f3639]) ).
fof(f3639,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
=> ( ~ hBOOL(hAPP_nat_bool(X0,sK60(X0,X1,X2)))
& plus_plus_nat(X2,sK60(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3638,plain,
! [X0,X1,X2] :
( ( sP17(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP_nat_bool(X0,X4))
| plus_plus_nat(X2,X4) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(rectify,[],[f3637]) ).
fof(f3637,plain,
! [X0,X1,X2] :
( ( sP17(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| plus_plus_nat(X2,X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(flattening,[],[f3636]) ).
fof(f3636,plain,
! [X0,X1,X2] :
( ( sP17(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| plus_plus_nat(X2,X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3202]) ).
fof(f3202,plain,
! [X0,X1,X2] :
( sP17(X0,X1,X2)
<=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| plus_plus_nat(X2,X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f9093,plain,
spl63_309,
inference(avatar_split_clause,[],[f6182,f9091]) ).
fof(f9091,plain,
( spl63_309
<=> ! [X2,X0,X1] :
( sP15(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_309])]) ).
fof(f6182,plain,
! [X2,X0,X1] :
( sP15(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ),
inference(definition_unfolding,[],[f5302,f3772]) ).
fof(f5302,plain,
! [X2,X0,X1] :
( sP15(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(cnf_transformation,[],[f3633]) ).
fof(f3633,plain,
! [X0,X1,X2] :
( sP15(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(flattening,[],[f3632]) ).
fof(f3632,plain,
! [X0,X1,X2] :
( sP15(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(nnf_transformation,[],[f3199]) ).
fof(f3199,plain,
! [X0,X1,X2] :
( sP15(X0,X2,X1)
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(definition_folding,[],[f3043,f3198]) ).
fof(f3198,plain,
! [X0,X2,X1] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ~ sP15(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f3043,plain,
! [X0,X1,X2] :
( ( ( hBOOL(X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(ennf_transformation,[],[f2173]) ).
fof(f2173,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> ( hBOOL(X1)
<=> hBOOL(X0) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> hBOOL(X1) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> hBOOL(X0) ) ) ),
inference(rectify,[],[f1176]) ).
fof(f1176,axiom,
! [X395,X54,X3] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> ( hBOOL(X54)
<=> hBOOL(X395) ) )
=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> hBOOL(X54) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> hBOOL(X395) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_imp__le__cong) ).
fof(f9089,plain,
spl63_308,
inference(avatar_split_clause,[],[f6177,f9087]) ).
fof(f9087,plain,
( spl63_308
<=> ! [X2,X0,X1] :
( sP14(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_308])]) ).
fof(f6177,plain,
! [X2,X0,X1] :
( sP14(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X2)) ),
inference(definition_unfolding,[],[f5295,f3772]) ).
fof(f5295,plain,
! [X2,X0,X1] :
( sP14(X0,X2,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(cnf_transformation,[],[f3628]) ).
fof(f3628,plain,
! [X0,X1,X2] :
( sP14(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(flattening,[],[f3627]) ).
fof(f3627,plain,
! [X0,X1,X2] :
( sP14(X0,X2,X1)
| ( ( ~ hBOOL(X0)
| ~ hBOOL(X1) )
& ( hBOOL(X0)
| hBOOL(X1) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(nnf_transformation,[],[f3197]) ).
fof(f3197,plain,
! [X0,X1,X2] :
( sP14(X0,X2,X1)
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(definition_folding,[],[f3042,f3196]) ).
fof(f3196,plain,
! [X0,X2,X1] :
( ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ~ sP14(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f3042,plain,
! [X0,X1,X2] :
( ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) )
| ( ( hBOOL(X1)
<~> hBOOL(X0) )
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ),
inference(ennf_transformation,[],[f2172]) ).
fof(f2172,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
=> ( hBOOL(X1)
<=> hBOOL(X0) ) )
=> ( ( hBOOL(X1)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) )
<=> ( hBOOL(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ) ) ),
inference(rectify,[],[f1175]) ).
fof(f1175,axiom,
! [X395,X54,X3] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
=> ( hBOOL(X54)
<=> hBOOL(X395) ) )
=> ( ( hBOOL(X54)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) )
<=> ( hBOOL(X395)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_conj__le__cong) ).
fof(f9085,plain,
spl63_307,
inference(avatar_split_clause,[],[f5954,f9083]) ).
fof(f9083,plain,
( spl63_307
<=> ! [X0,X1] :
( is_int(sK48(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_307])]) ).
fof(f5954,plain,
! [X0,X1] :
( is_int(sK48(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),X1)) ),
inference(definition_unfolding,[],[f4515,f3772]) ).
fof(f4515,plain,
! [X0,X1] :
( is_int(sK48(X0,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3372]) ).
fof(f3372,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(minus_minus_int(X0,times_times_int(sK48(X0,X1),X1))))),X1))
& is_int(sK48(X0,X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f2547,f3371]) ).
fof(f3371,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(minus_minus_int(X0,times_times_int(X2,X1))))),X1))
& is_int(X2) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(minus_minus_int(X0,times_times_int(sK48(X0,X1),X1))))),X1))
& is_int(sK48(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2547,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(minus_minus_int(X0,times_times_int(X2,X1))))),X1))
& is_int(X2) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(ennf_transformation,[],[f1683]) ).
fof(f1683,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
=> ? [X2] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(minus_minus_int(X0,times_times_int(X2,X1))))),X1))
& is_int(X2) ) ),
inference(rectify,[],[f1203]) ).
fof(f1203,axiom,
! [X10,X8] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X8))
=> ? [X90] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,times_times_int(number_number_of_int(bit0(bit1(pls))),abs_abs_int(minus_minus_int(X10,times_times_int(X90,X8))))),X8))
& is_int(X90) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_best__division__abs) ).
fof(f9081,plain,
spl63_306,
inference(avatar_split_clause,[],[f5891,f9079]) ).
fof(f9079,plain,
( spl63_306
<=> ! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(abs_abs_int(X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_306])]) ).
fof(f5891,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(power_power_int(abs_abs_int(X0)),X1))),
inference(definition_unfolding,[],[f4343,f3772]) ).
fof(f4343,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(abs_abs_int(X0)),X1))),
inference(cnf_transformation,[],[f1563]) ).
fof(f1563,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(abs_abs_int(X0)),X1))),
inference(rectify,[],[f1190]) ).
fof(f1190,axiom,
! [X8,X16] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(power_power_int(abs_abs_int(X8)),X16))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_zero__le__zpower__abs) ).
fof(f9077,plain,
spl63_305,
inference(avatar_split_clause,[],[f5783,f9075]) ).
fof(f9075,plain,
( spl63_305
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| zero_zero_nat != nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_305])]) ).
fof(f5783,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls))
| zero_zero_nat != nat(X0) ),
inference(definition_unfolding,[],[f4156,f3772]) ).
fof(f4156,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
| zero_zero_nat != nat(X0) ),
inference(cnf_transformation,[],[f3252]) ).
fof(f3252,plain,
! [X0] :
( ( zero_zero_nat = nat(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
| zero_zero_nat != nat(X0) ) ),
inference(nnf_transformation,[],[f1451]) ).
fof(f1451,plain,
! [X0] :
( zero_zero_nat = nat(X0)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) ),
inference(rectify,[],[f613]) ).
fof(f613,axiom,
! [X55] :
( zero_zero_nat = nat(X55)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X55),zero_zero_int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_nat__0__iff) ).
fof(f9073,plain,
spl63_304,
inference(avatar_split_clause,[],[f5773,f9071]) ).
fof(f9071,plain,
( spl63_304
<=> ! [X0] :
( zero_zero_nat = nat(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_304])]) ).
fof(f5773,plain,
! [X0] :
( zero_zero_nat = nat(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),pls)) ),
inference(definition_unfolding,[],[f4137,f3772]) ).
fof(f4137,plain,
! [X0] :
( zero_zero_nat = nat(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) ),
inference(cnf_transformation,[],[f2403]) ).
fof(f2403,plain,
! [X0] :
( zero_zero_nat = nat(X0)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int)) ),
inference(ennf_transformation,[],[f1438]) ).
fof(f1438,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),zero_zero_int))
=> zero_zero_nat = nat(X0) ),
inference(rectify,[],[f612]) ).
fof(f612,axiom,
! [X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X17),zero_zero_int))
=> zero_zero_nat = nat(X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_nat__le__0) ).
fof(f9069,plain,
spl63_303,
inference(avatar_split_clause,[],[f5757,f9067]) ).
fof(f9067,plain,
( spl63_303
<=> ! [X0] :
( pls = X0
| pls != plus_plus_int(X0,X0)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_303])]) ).
fof(f5757,plain,
! [X0] :
( pls = X0
| pls != plus_plus_int(X0,X0)
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f4112,f3979]) ).
fof(f4112,plain,
! [X0] :
( pls = X0
| bit0(X0) != pls
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3234]) ).
fof(f3234,plain,
! [X0] :
( ( ( bit0(X0) = pls
| pls != X0 )
& ( pls = X0
| bit0(X0) != pls ) )
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2392]) ).
fof(f2392,plain,
! [X0] :
( ( bit0(X0) = pls
<=> pls = X0 )
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1428]) ).
fof(f1428,plain,
! [X0] :
( is_int(X0)
=> ( bit0(X0) = pls
<=> pls = X0 ) ),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X11] :
( is_int(X11)
=> ( pls = bit0(X11)
<=> pls = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rel__simps_I44_J) ).
fof(f9064,plain,
spl63_302,
inference(avatar_split_clause,[],[f5639,f9061]) ).
fof(f5639,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(definition_unfolding,[],[f3860,f3772]) ).
fof(f3860,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(f9059,plain,
spl63_301,
inference(avatar_split_clause,[],[f5326,f9057]) ).
fof(f9057,plain,
( spl63_301
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_301])]) ).
fof(f5326,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f3647]) ).
fof(f3647,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP18(X0,X1,X2) )
& ( sP18(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ) ),
inference(nnf_transformation,[],[f3205]) ).
fof(f3205,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> sP18(X0,X1,X2) ),
inference(definition_folding,[],[f3047,f3204]) ).
fof(f3047,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| plus_plus_nat(X2,X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(ennf_transformation,[],[f2176]) ).
fof(f2176,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> ~ ( ? [X3] :
( ~ hBOOL(hAPP_nat_bool(X0,X3))
& plus_plus_nat(X2,X3) = X1 )
| ( ~ hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(rectify,[],[f823]) ).
fof(f823,axiom,
! [X54,X5,X81] :
( hBOOL(hAPP_nat_bool(X54,minus_minus_nat(X5,X81)))
<=> ~ ( ? [X380] :
( ~ hBOOL(hAPP_nat_bool(X54,X380))
& plus_plus_nat(X81,X380) = X5 )
| ( ~ hBOOL(hAPP_nat_bool(X54,zero_zero_nat))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X81)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_nat__diff__split__asm) ).
fof(f9055,plain,
spl63_300,
inference(avatar_split_clause,[],[f5325,f9053]) ).
fof(f9053,plain,
( spl63_300
<=> ! [X2,X0,X1] :
( sP18(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_300])]) ).
fof(f5325,plain,
! [X2,X0,X1] :
( sP18(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ),
inference(cnf_transformation,[],[f3647]) ).
fof(f9051,plain,
spl63_299,
inference(avatar_split_clause,[],[f5318,f9049]) ).
fof(f9049,plain,
( spl63_299
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_299])]) ).
fof(f5318,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f3641]) ).
fof(f3641,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
| ~ sP17(X0,X1,X2) )
& ( sP17(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ) ),
inference(nnf_transformation,[],[f3203]) ).
fof(f3203,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> sP17(X0,X1,X2) ),
inference(definition_folding,[],[f3046,f3202]) ).
fof(f3046,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> ( ! [X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| plus_plus_nat(X2,X3) != X1 )
& ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ) ) ),
inference(ennf_transformation,[],[f2175]) ).
fof(f2175,plain,
! [X0,X1,X2] :
( hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2)))
<=> ( ! [X3] :
( plus_plus_nat(X2,X3) = X1
=> hBOOL(hAPP_nat_bool(X0,X3)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
=> hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) ) ) ),
inference(rectify,[],[f824]) ).
fof(f824,axiom,
! [X54,X5,X81] :
( hBOOL(hAPP_nat_bool(X54,minus_minus_nat(X5,X81)))
<=> ( ! [X380] :
( plus_plus_nat(X81,X380) = X5
=> hBOOL(hAPP_nat_bool(X54,X380)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5),X81))
=> hBOOL(hAPP_nat_bool(X54,zero_zero_nat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_nat__diff__split) ).
fof(f9047,plain,
spl63_298,
inference(avatar_split_clause,[],[f5317,f9045]) ).
fof(f9045,plain,
( spl63_298
<=> ! [X2,X0,X1] :
( sP17(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_298])]) ).
fof(f5317,plain,
! [X2,X0,X1] :
( sP17(X0,X1,X2)
| ~ hBOOL(hAPP_nat_bool(X0,minus_minus_nat(X1,X2))) ),
inference(cnf_transformation,[],[f3641]) ).
fof(f9043,plain,
spl63_297,
inference(avatar_split_clause,[],[f5306,f9041]) ).
fof(f9041,plain,
( spl63_297
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_297])]) ).
fof(f5306,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f3635]) ).
fof(f3635,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X2,X1),X0))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1)) )
| ~ sP16(X0,X1,X2) ),
inference(rectify,[],[f3634]) ).
fof(f3634,plain,
! [X1,X2,X0] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
| ~ sP16(X1,X2,X0) ),
inference(nnf_transformation,[],[f3200]) ).
fof(f3200,plain,
! [X1,X2,X0] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X0,X2),X1))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) )
| ~ sP16(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f9039,plain,
spl63_296,
inference(avatar_split_clause,[],[f5305,f9037]) ).
fof(f9037,plain,
( spl63_296
<=> ! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_296])]) ).
fof(f5305,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X1))
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f3635]) ).
fof(f9035,plain,
spl63_295,
inference(avatar_split_clause,[],[f5228,f9033]) ).
fof(f9033,plain,
( spl63_295
<=> ! [X2,X0,X1] :
( X0 = X2
| plus_plus_nat(X0,X1) != plus_plus_nat(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_295])]) ).
fof(f5228,plain,
! [X2,X0,X1] :
( X0 = X2
| plus_plus_nat(X0,X1) != plus_plus_nat(X2,X1) ),
inference(cnf_transformation,[],[f2946]) ).
fof(f2946,plain,
! [X0,X1,X2] :
( X0 = X2
| plus_plus_nat(X0,X1) != plus_plus_nat(X2,X1) ),
inference(ennf_transformation,[],[f2116]) ).
fof(f2116,plain,
! [X0,X1,X2] :
( plus_plus_nat(X0,X1) = plus_plus_nat(X2,X1)
=> X0 = X2 ),
inference(rectify,[],[f346]) ).
fof(f346,axiom,
! [X97,X98,X99] :
( plus_plus_nat(X97,X98) = plus_plus_nat(X99,X98)
=> X97 = X99 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_add__right__imp__eq) ).
fof(f9031,plain,
spl63_294,
inference(avatar_split_clause,[],[f5227,f9029]) ).
fof(f9029,plain,
( spl63_294
<=> ! [X2,X0,X1] :
( X1 = X2
| plus_plus_nat(X0,X1) != plus_plus_nat(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_294])]) ).
fof(f5227,plain,
! [X2,X0,X1] :
( X1 = X2
| plus_plus_nat(X0,X1) != plus_plus_nat(X0,X2) ),
inference(cnf_transformation,[],[f2945]) ).
fof(f2945,plain,
! [X0,X1,X2] :
( X1 = X2
| plus_plus_nat(X0,X1) != plus_plus_nat(X0,X2) ),
inference(ennf_transformation,[],[f2115]) ).
fof(f2115,plain,
! [X0,X1,X2] :
( plus_plus_nat(X0,X1) = plus_plus_nat(X0,X2)
=> X1 = X2 ),
inference(rectify,[],[f349]) ).
fof(f349,axiom,
! [X100,X101,X102] :
( plus_plus_nat(X100,X101) = plus_plus_nat(X100,X102)
=> X101 = X102 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_add__imp__eq) ).
fof(f9027,plain,
spl63_293,
inference(avatar_split_clause,[],[f5225,f9025]) ).
fof(f9025,plain,
( spl63_293
<=> ! [X2,X0,X1] :
( X0 = X2
| plus_plus_real(X0,X1) != plus_plus_real(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_293])]) ).
fof(f5225,plain,
! [X2,X0,X1] :
( X0 = X2
| plus_plus_real(X0,X1) != plus_plus_real(X2,X1) ),
inference(cnf_transformation,[],[f2943]) ).
fof(f2943,plain,
! [X0,X1,X2] :
( X0 = X2
| plus_plus_real(X0,X1) != plus_plus_real(X2,X1) ),
inference(ennf_transformation,[],[f2113]) ).
fof(f2113,plain,
! [X0,X1,X2] :
( plus_plus_real(X0,X1) = plus_plus_real(X2,X1)
=> X0 = X2 ),
inference(rectify,[],[f347]) ).
fof(f347,axiom,
! [X97,X98,X99] :
( plus_plus_real(X97,X98) = plus_plus_real(X99,X98)
=> X97 = X99 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_add__right__imp__eq) ).
fof(f9023,plain,
spl63_292,
inference(avatar_split_clause,[],[f5224,f9021]) ).
fof(f9021,plain,
( spl63_292
<=> ! [X2,X0,X1] :
( X1 = X2
| plus_plus_real(X0,X1) != plus_plus_real(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_292])]) ).
fof(f5224,plain,
! [X2,X0,X1] :
( X1 = X2
| plus_plus_real(X0,X1) != plus_plus_real(X0,X2) ),
inference(cnf_transformation,[],[f2942]) ).
fof(f2942,plain,
! [X0,X1,X2] :
( X1 = X2
| plus_plus_real(X0,X1) != plus_plus_real(X0,X2) ),
inference(ennf_transformation,[],[f2112]) ).
fof(f2112,plain,
! [X0,X1,X2] :
( plus_plus_real(X0,X1) = plus_plus_real(X0,X2)
=> X1 = X2 ),
inference(rectify,[],[f350]) ).
fof(f350,axiom,
! [X100,X101,X102] :
( plus_plus_real(X100,X101) = plus_plus_real(X100,X102)
=> X101 = X102 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_add__imp__eq) ).
fof(f9019,plain,
spl63_291,
inference(avatar_split_clause,[],[f5034,f9017]) ).
fof(f9017,plain,
( spl63_291
<=> ! [X2,X0,X1] :
( nat(X1) = nat(if_int(X2,X0,X1))
| hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_291])]) ).
fof(f5034,plain,
! [X2,X0,X1] :
( nat(X1) = nat(if_int(X2,X0,X1))
| hBOOL(X2) ),
inference(cnf_transformation,[],[f2721]) ).
fof(f2721,plain,
! [X0,X1,X2] :
( ( nat(X1) = nat(if_int(X2,X0,X1))
| hBOOL(X2) )
& ( nat(X0) = nat(if_int(X2,X0,X1))
| ~ hBOOL(X2) ) ),
inference(ennf_transformation,[],[f1969]) ).
fof(f1969,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(X2)
=> nat(X1) = nat(if_int(X2,X0,X1)) )
& ( hBOOL(X2)
=> nat(X0) = nat(if_int(X2,X0,X1)) ) ),
inference(rectify,[],[f505]) ).
fof(f505,axiom,
! [X3,X4,X54] :
( ( ~ hBOOL(X54)
=> nat(if_int(X54,X3,X4)) = nat(X4) )
& ( hBOOL(X54)
=> nat(X3) = nat(if_int(X54,X3,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_nat__if__cong) ).
fof(f9015,plain,
spl63_290,
inference(avatar_split_clause,[],[f5033,f9013]) ).
fof(f9013,plain,
( spl63_290
<=> ! [X2,X0,X1] :
( nat(X0) = nat(if_int(X2,X0,X1))
| ~ hBOOL(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_290])]) ).
fof(f5033,plain,
! [X2,X0,X1] :
( nat(X0) = nat(if_int(X2,X0,X1))
| ~ hBOOL(X2) ),
inference(cnf_transformation,[],[f2721]) ).
fof(f9011,plain,
spl63_289,
inference(avatar_split_clause,[],[f4953,f9009]) ).
fof(f9009,plain,
( spl63_289
<=> ! [X2,X0,X1] : hBOOL(hAPP_int_bool(zcong(times_times_int(X0,X1),times_times_int(X2,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_289])]) ).
fof(f4953,plain,
! [X2,X0,X1] : hBOOL(hAPP_int_bool(zcong(times_times_int(X0,X1),times_times_int(X2,X1)),X1)),
inference(cnf_transformation,[],[f1889]) ).
fof(f1889,plain,
! [X0,X1,X2] : hBOOL(hAPP_int_bool(zcong(times_times_int(X0,X1),times_times_int(X2,X1)),X1)),
inference(rectify,[],[f1157]) ).
fof(f1157,axiom,
! [X151,X15,X155] : hBOOL(hAPP_int_bool(zcong(times_times_int(X151,X15),times_times_int(X155,X15)),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_zcong__zmult__self) ).
fof(f9007,plain,
spl63_288,
inference(avatar_split_clause,[],[f4785,f9005]) ).
fof(f9005,plain,
( spl63_288
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1))
| ~ sP9(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_288])]) ).
fof(f4785,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1))
| ~ sP9(X1,X0) ),
inference(cnf_transformation,[],[f3483]) ).
fof(f3483,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1))
| ~ sP9(X1,X0) )
& ( sP9(X1,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1)) ) ),
inference(nnf_transformation,[],[f3187]) ).
fof(f3187,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1))
<=> sP9(X1,X0) ),
inference(definition_folding,[],[f2718,f3186]) ).
fof(f2718,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1))
<=> ( ( zero_zero_nat = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) ),
inference(ennf_transformation,[],[f1826]) ).
fof(f1826,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1))
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> zero_zero_nat = X1 )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),hAPP_nat_int(semiri1621563631at_int,X1))) ) ) ),
inference(rectify,[],[f1106]) ).
fof(f1106,axiom,
! [X30,X29] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X30)),X29))
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X30))
=> zero_zero_nat = X29 )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X30))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X30),hAPP_nat_int(semiri1621563631at_int,X29))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_nat__dvd__iff) ).
fof(f9003,plain,
spl63_287,
inference(avatar_split_clause,[],[f4784,f9001]) ).
fof(f9001,plain,
( spl63_287
<=> ! [X0,X1] :
( sP9(X1,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_287])]) ).
fof(f4784,plain,
! [X0,X1] :
( sP9(X1,X0)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,nat(X0)),X1)) ),
inference(cnf_transformation,[],[f3483]) ).
fof(f8999,plain,
spl63_286,
inference(avatar_split_clause,[],[f4770,f8997]) ).
fof(f8997,plain,
( spl63_286
<=> ! [X0,X1] :
( X0 = X1
| hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_286])]) ).
fof(f4770,plain,
! [X0,X1] :
( X0 = X1
| hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ),
inference(cnf_transformation,[],[f3476]) ).
fof(f3476,plain,
! [X0,X1] :
( ( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP_nat_int(semiri1621563631at_int,X0) != hAPP_nat_int(semiri1621563631at_int,X1) ) ),
inference(nnf_transformation,[],[f1822]) ).
fof(f1822,plain,
! [X0,X1] :
( hAPP_nat_int(semiri1621563631at_int,X0) = hAPP_nat_int(semiri1621563631at_int,X1)
<=> X0 = X1 ),
inference(rectify,[],[f250]) ).
fof(f250,axiom,
! [X3,X4] :
( hAPP_nat_int(semiri1621563631at_int,X3) = hAPP_nat_int(semiri1621563631at_int,X4)
<=> X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
fof(f8995,plain,
spl63_285,
inference(avatar_split_clause,[],[f4768,f8993]) ).
fof(f8993,plain,
( spl63_285
<=> ! [X0,X1] :
( X0 = X1
| hAPP_nat_nat(semiri984289939at_nat,X0) != hAPP_nat_nat(semiri984289939at_nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_285])]) ).
fof(f4768,plain,
! [X0,X1] :
( X0 = X1
| hAPP_nat_nat(semiri984289939at_nat,X0) != hAPP_nat_nat(semiri984289939at_nat,X1) ),
inference(cnf_transformation,[],[f3475]) ).
fof(f3475,plain,
! [X0,X1] :
( ( hAPP_nat_nat(semiri984289939at_nat,X0) = hAPP_nat_nat(semiri984289939at_nat,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP_nat_nat(semiri984289939at_nat,X0) != hAPP_nat_nat(semiri984289939at_nat,X1) ) ),
inference(nnf_transformation,[],[f1821]) ).
fof(f1821,plain,
! [X0,X1] :
( hAPP_nat_nat(semiri984289939at_nat,X0) = hAPP_nat_nat(semiri984289939at_nat,X1)
<=> X0 = X1 ),
inference(rectify,[],[f248]) ).
fof(f248,axiom,
! [X29,X18] :
( hAPP_nat_nat(semiri984289939at_nat,X18) = hAPP_nat_nat(semiri984289939at_nat,X29)
<=> X18 = X29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_of__nat__eq__iff) ).
fof(f8991,plain,
spl63_284,
inference(avatar_split_clause,[],[f4766,f8989]) ).
fof(f8989,plain,
( spl63_284
<=> ! [X0,X1] :
( X0 = X1
| hAPP_nat_real(semiri132038758t_real,X0) != hAPP_nat_real(semiri132038758t_real,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_284])]) ).
fof(f4766,plain,
! [X0,X1] :
( X0 = X1
| hAPP_nat_real(semiri132038758t_real,X0) != hAPP_nat_real(semiri132038758t_real,X1) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f3474,plain,
! [X0,X1] :
( ( hAPP_nat_real(semiri132038758t_real,X0) = hAPP_nat_real(semiri132038758t_real,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP_nat_real(semiri132038758t_real,X0) != hAPP_nat_real(semiri132038758t_real,X1) ) ),
inference(nnf_transformation,[],[f1820]) ).
fof(f1820,plain,
! [X0,X1] :
( hAPP_nat_real(semiri132038758t_real,X0) = hAPP_nat_real(semiri132038758t_real,X1)
<=> X0 = X1 ),
inference(rectify,[],[f247]) ).
fof(f247,axiom,
! [X29,X18] :
( hAPP_nat_real(semiri132038758t_real,X18) = hAPP_nat_real(semiri132038758t_real,X29)
<=> X18 = X29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_of__nat__eq__iff) ).
fof(f8985,plain,
( spl63_283
| ~ spl63_140
| ~ spl63_282 ),
inference(avatar_split_clause,[],[f8981,f8978,f7684,f8983]) ).
fof(f8983,plain,
( spl63_283
<=> ! [X0,X1] :
( min = X0
| one_one_int = X0
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_283])]) ).
fof(f8978,plain,
( spl63_282
<=> ! [X0,X1] :
( number_number_of_int(min) = X0
| one_one_int = X0
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_282])]) ).
fof(f8981,plain,
( ! [X0,X1] :
( min = X0
| one_one_int = X0
| ~ sP7(X0,X1) )
| ~ spl63_140
| ~ spl63_282 ),
inference(forward_demodulation,[],[f8979,f7686]) ).
fof(f8979,plain,
( ! [X0,X1] :
( number_number_of_int(min) = X0
| one_one_int = X0
| ~ sP7(X0,X1) )
| ~ spl63_282 ),
inference(avatar_component_clause,[],[f8978]) ).
fof(f8980,plain,
spl63_282,
inference(avatar_split_clause,[],[f4608,f8978]) ).
fof(f4608,plain,
! [X0,X1] :
( number_number_of_int(min) = X0
| one_one_int = X0
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f3389]) ).
fof(f3389,plain,
! [X0,X1] :
( ( sP7(X0,X1)
| ( ( number_number_of_int(min) != X0
| number_number_of_int(min) != X1 )
& ( one_one_int != X0
| one_one_int != X1 ) ) )
& ( ( number_number_of_int(min) = X0
& number_number_of_int(min) = X1 )
| ( one_one_int = X0
& one_one_int = X1 )
| ~ sP7(X0,X1) ) ),
inference(rectify,[],[f3388]) ).
fof(f3388,plain,
! [X1,X0] :
( ( sP7(X1,X0)
| ( ( number_number_of_int(min) != X1
| number_number_of_int(min) != X0 )
& ( one_one_int != X1
| one_one_int != X0 ) ) )
& ( ( number_number_of_int(min) = X1
& number_number_of_int(min) = X0 )
| ( one_one_int = X1
& one_one_int = X0 )
| ~ sP7(X1,X0) ) ),
inference(flattening,[],[f3387]) ).
fof(f3387,plain,
! [X1,X0] :
( ( sP7(X1,X0)
| ( ( number_number_of_int(min) != X1
| number_number_of_int(min) != X0 )
& ( one_one_int != X1
| one_one_int != X0 ) ) )
& ( ( number_number_of_int(min) = X1
& number_number_of_int(min) = X0 )
| ( one_one_int = X1
& one_one_int = X0 )
| ~ sP7(X1,X0) ) ),
inference(nnf_transformation,[],[f3183]) ).
fof(f3183,plain,
! [X1,X0] :
( sP7(X1,X0)
<=> ( ( number_number_of_int(min) = X1
& number_number_of_int(min) = X0 )
| ( one_one_int = X1
& one_one_int = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f8974,plain,
( spl63_281
| ~ spl63_140
| ~ spl63_280 ),
inference(avatar_split_clause,[],[f8970,f8967,f7684,f8972]) ).
fof(f8972,plain,
( spl63_281
<=> ! [X0,X1] :
( min = X0
| one_one_int = X1
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_281])]) ).
fof(f8967,plain,
( spl63_280
<=> ! [X0,X1] :
( number_number_of_int(min) = X0
| one_one_int = X1
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_280])]) ).
fof(f8970,plain,
( ! [X0,X1] :
( min = X0
| one_one_int = X1
| ~ sP7(X0,X1) )
| ~ spl63_140
| ~ spl63_280 ),
inference(forward_demodulation,[],[f8968,f7686]) ).
fof(f8968,plain,
( ! [X0,X1] :
( number_number_of_int(min) = X0
| one_one_int = X1
| ~ sP7(X0,X1) )
| ~ spl63_280 ),
inference(avatar_component_clause,[],[f8967]) ).
fof(f8969,plain,
spl63_280,
inference(avatar_split_clause,[],[f4607,f8967]) ).
fof(f4607,plain,
! [X0,X1] :
( number_number_of_int(min) = X0
| one_one_int = X1
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f3389]) ).
fof(f8965,plain,
( spl63_279
| spl63_83
| ~ spl63_250 ),
inference(avatar_split_clause,[],[f8817,f8701,f7401,f8962]) ).
fof(f8962,plain,
( spl63_279
<=> sP9(zero_zero_nat,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_279])]) ).
fof(f7401,plain,
( spl63_83
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_83])]) ).
fof(f8701,plain,
( spl63_250
<=> ! [X1] :
( sP9(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_250])]) ).
fof(f8817,plain,
( sP9(zero_zero_nat,min)
| spl63_83
| ~ spl63_250 ),
inference(resolution,[],[f8702,f7403]) ).
fof(f7403,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min))
| spl63_83 ),
inference(avatar_component_clause,[],[f7401]) ).
fof(f8702,plain,
( ! [X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| sP9(zero_zero_nat,X1) )
| ~ spl63_250 ),
inference(avatar_component_clause,[],[f8701]) ).
fof(f8958,plain,
( spl63_278
| ~ spl63_140
| ~ spl63_277 ),
inference(avatar_split_clause,[],[f8954,f8951,f7684,f8956]) ).
fof(f8956,plain,
( spl63_278
<=> ! [X0,X1] :
( min = X1
| one_one_int = X0
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_278])]) ).
fof(f8951,plain,
( spl63_277
<=> ! [X0,X1] :
( number_number_of_int(min) = X1
| one_one_int = X0
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_277])]) ).
fof(f8954,plain,
( ! [X0,X1] :
( min = X1
| one_one_int = X0
| ~ sP7(X0,X1) )
| ~ spl63_140
| ~ spl63_277 ),
inference(forward_demodulation,[],[f8952,f7686]) ).
fof(f8952,plain,
( ! [X0,X1] :
( number_number_of_int(min) = X1
| one_one_int = X0
| ~ sP7(X0,X1) )
| ~ spl63_277 ),
inference(avatar_component_clause,[],[f8951]) ).
fof(f8953,plain,
spl63_277,
inference(avatar_split_clause,[],[f4606,f8951]) ).
fof(f4606,plain,
! [X0,X1] :
( number_number_of_int(min) = X1
| one_one_int = X0
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f3389]) ).
fof(f8947,plain,
( spl63_276
| ~ spl63_140
| ~ spl63_275 ),
inference(avatar_split_clause,[],[f8943,f8940,f7684,f8945]) ).
fof(f8945,plain,
( spl63_276
<=> ! [X0,X1] :
( min = X1
| one_one_int = X1
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_276])]) ).
fof(f8940,plain,
( spl63_275
<=> ! [X0,X1] :
( number_number_of_int(min) = X1
| one_one_int = X1
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_275])]) ).
fof(f8943,plain,
( ! [X0,X1] :
( min = X1
| one_one_int = X1
| ~ sP7(X0,X1) )
| ~ spl63_140
| ~ spl63_275 ),
inference(forward_demodulation,[],[f8941,f7686]) ).
fof(f8941,plain,
( ! [X0,X1] :
( number_number_of_int(min) = X1
| one_one_int = X1
| ~ sP7(X0,X1) )
| ~ spl63_275 ),
inference(avatar_component_clause,[],[f8940]) ).
fof(f8942,plain,
spl63_275,
inference(avatar_split_clause,[],[f4605,f8940]) ).
fof(f4605,plain,
! [X0,X1] :
( number_number_of_int(min) = X1
| one_one_int = X1
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f3389]) ).
fof(f8938,plain,
spl63_274,
inference(avatar_split_clause,[],[f4471,f8936]) ).
fof(f8936,plain,
( spl63_274
<=> ! [X0,X1] :
( abs_abs_int(X0) = one_one_int
| one_one_int != abs_abs_int(times_times_int(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_274])]) ).
fof(f4471,plain,
! [X0,X1] :
( abs_abs_int(X0) = one_one_int
| one_one_int != abs_abs_int(times_times_int(X0,X1)) ),
inference(cnf_transformation,[],[f2482]) ).
fof(f2482,plain,
! [X0,X1] :
( abs_abs_int(X0) = one_one_int
| one_one_int != abs_abs_int(times_times_int(X0,X1)) ),
inference(ennf_transformation,[],[f1645]) ).
fof(f1645,plain,
! [X0,X1] :
( one_one_int = abs_abs_int(times_times_int(X0,X1))
=> abs_abs_int(X0) = one_one_int ),
inference(rectify,[],[f1189]) ).
fof(f1189,axiom,
! [X15,X16] :
( one_one_int = abs_abs_int(times_times_int(X15,X16))
=> one_one_int = abs_abs_int(X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_abs__zmult__eq__1) ).
fof(f8934,plain,
spl63_273,
inference(avatar_split_clause,[],[f4417,f8932]) ).
fof(f8932,plain,
( spl63_273
<=> ! [X0,X1] :
( nat(X0) = X1
| ~ sP3(X1,X0)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_273])]) ).
fof(f4417,plain,
! [X0,X1] :
( nat(X0) = X1
| ~ sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f3339]) ).
fof(f3339,plain,
! [X0,X1] :
( ( ( nat(X0) = X1
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| nat(X0) != X1 ) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f3338]) ).
fof(f3338,plain,
! [X1,X0] :
( ( ( nat(X1) = X0
| ~ sP3(X0,X1) )
& ( sP3(X0,X1)
| nat(X1) != X0 ) )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f3178]) ).
fof(f3178,plain,
! [X1,X0] :
( ( nat(X1) = X0
<=> sP3(X0,X1) )
| ~ sP4(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f8930,plain,
spl63_272,
inference(avatar_split_clause,[],[f4408,f8928]) ).
fof(f8928,plain,
( spl63_272
<=> ! [X0,X1] :
( nat(X0) = X1
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_272])]) ).
fof(f4408,plain,
! [X0,X1] :
( nat(X0) = X1
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3334]) ).
fof(f3334,plain,
! [X0,X1] :
( ( ( nat(X0) = X1
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| nat(X0) != X1 ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f3175]) ).
fof(f3175,plain,
! [X0,X1] :
( ( nat(X0) = X1
<=> sP1(X1,X0) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f8926,plain,
spl63_271,
inference(avatar_split_clause,[],[f4330,f8924]) ).
fof(f8924,plain,
( spl63_271
<=> ! [X0,X1] : number_number_of_int(times_times_int(X0,X1)) = times_times_int(number_number_of_int(X0),number_number_of_int(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_271])]) ).
fof(f4330,plain,
! [X0,X1] : number_number_of_int(times_times_int(X0,X1)) = times_times_int(number_number_of_int(X0),number_number_of_int(X1)),
inference(cnf_transformation,[],[f1550]) ).
fof(f1550,plain,
! [X0,X1] : number_number_of_int(times_times_int(X0,X1)) = times_times_int(number_number_of_int(X0),number_number_of_int(X1)),
inference(rectify,[],[f486]) ).
fof(f486,axiom,
! [X188,X189] : number_number_of_int(times_times_int(X188,X189)) = times_times_int(number_number_of_int(X188),number_number_of_int(X189)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_number__of__mult) ).
fof(f8922,plain,
( spl63_270
| spl63_83
| ~ spl63_248 ),
inference(avatar_split_clause,[],[f8813,f8693,f7401,f8919]) ).
fof(f8919,plain,
( spl63_270
<=> sP3(zero_zero_nat,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_270])]) ).
fof(f8693,plain,
( spl63_248
<=> ! [X1] :
( sP3(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_248])]) ).
fof(f8813,plain,
( sP3(zero_zero_nat,min)
| spl63_83
| ~ spl63_248 ),
inference(resolution,[],[f8694,f7403]) ).
fof(f8694,plain,
( ! [X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| sP3(zero_zero_nat,X1) )
| ~ spl63_248 ),
inference(avatar_component_clause,[],[f8693]) ).
fof(f8917,plain,
spl63_269,
inference(avatar_split_clause,[],[f4329,f8915]) ).
fof(f4329,plain,
! [X0,X1] : number_number_of_int(plus_plus_int(X0,X1)) = plus_plus_int(number_number_of_int(X0),number_number_of_int(X1)),
inference(cnf_transformation,[],[f1549]) ).
fof(f1549,plain,
! [X0,X1] : number_number_of_int(plus_plus_int(X0,X1)) = plus_plus_int(number_number_of_int(X0),number_number_of_int(X1)),
inference(rectify,[],[f153]) ).
fof(f153,axiom,
! [X39,X40] : number_number_of_int(plus_plus_int(X39,X40)) = plus_plus_int(number_number_of_int(X39),number_number_of_int(X40)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_number__of__add) ).
fof(f8913,plain,
spl63_268,
inference(avatar_split_clause,[],[f4328,f8911]) ).
fof(f4328,plain,
! [X0,X1] : number_number_of_int(minus_minus_int(X0,X1)) = minus_minus_int(number_number_of_int(X0),number_number_of_int(X1)),
inference(cnf_transformation,[],[f1548]) ).
fof(f1548,plain,
! [X0,X1] : number_number_of_int(minus_minus_int(X0,X1)) = minus_minus_int(number_number_of_int(X0),number_number_of_int(X1)),
inference(rectify,[],[f496]) ).
fof(f496,axiom,
! [X202,X203] : number_number_of_int(minus_minus_int(X202,X203)) = minus_minus_int(number_number_of_int(X202),number_number_of_int(X203)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_number__of__diff) ).
fof(f8909,plain,
spl63_267,
inference(avatar_split_clause,[],[f4327,f8907]) ).
fof(f8907,plain,
( spl63_267
<=> ! [X0,X1] : number267125858f_real(times_times_int(X0,X1)) = times_times_real(number267125858f_real(X0),number267125858f_real(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_267])]) ).
fof(f4327,plain,
! [X0,X1] : number267125858f_real(times_times_int(X0,X1)) = times_times_real(number267125858f_real(X0),number267125858f_real(X1)),
inference(cnf_transformation,[],[f1547]) ).
fof(f1547,plain,
! [X0,X1] : number267125858f_real(times_times_int(X0,X1)) = times_times_real(number267125858f_real(X0),number267125858f_real(X1)),
inference(rectify,[],[f485]) ).
fof(f485,axiom,
! [X188,X189] : number267125858f_real(times_times_int(X188,X189)) = times_times_real(number267125858f_real(X188),number267125858f_real(X189)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_number__of__mult) ).
fof(f8905,plain,
spl63_266,
inference(avatar_split_clause,[],[f4326,f8903]) ).
fof(f8903,plain,
( spl63_266
<=> ! [X0,X1] : number267125858f_real(plus_plus_int(X0,X1)) = plus_plus_real(number267125858f_real(X0),number267125858f_real(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_266])]) ).
fof(f4326,plain,
! [X0,X1] : number267125858f_real(plus_plus_int(X0,X1)) = plus_plus_real(number267125858f_real(X0),number267125858f_real(X1)),
inference(cnf_transformation,[],[f1546]) ).
fof(f1546,plain,
! [X0,X1] : number267125858f_real(plus_plus_int(X0,X1)) = plus_plus_real(number267125858f_real(X0),number267125858f_real(X1)),
inference(rectify,[],[f154]) ).
fof(f154,axiom,
! [X39,X40] : number267125858f_real(plus_plus_int(X39,X40)) = plus_plus_real(number267125858f_real(X39),number267125858f_real(X40)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_number__of__add) ).
fof(f8901,plain,
spl63_265,
inference(avatar_split_clause,[],[f4325,f8899]) ).
fof(f8899,plain,
( spl63_265
<=> ! [X0,X1] : number267125858f_real(minus_minus_int(X0,X1)) = minus_minus_real(number267125858f_real(X0),number267125858f_real(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_265])]) ).
fof(f4325,plain,
! [X0,X1] : number267125858f_real(minus_minus_int(X0,X1)) = minus_minus_real(number267125858f_real(X0),number267125858f_real(X1)),
inference(cnf_transformation,[],[f1545]) ).
fof(f1545,plain,
! [X0,X1] : number267125858f_real(minus_minus_int(X0,X1)) = minus_minus_real(number267125858f_real(X0),number267125858f_real(X1)),
inference(rectify,[],[f497]) ).
fof(f497,axiom,
! [X202,X203] : number267125858f_real(minus_minus_int(X202,X203)) = minus_minus_real(number267125858f_real(X202),number267125858f_real(X203)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_number__of__diff) ).
fof(f8897,plain,
spl63_264,
inference(avatar_split_clause,[],[f4288,f8895]) ).
fof(f8895,plain,
( spl63_264
<=> ! [X4,X0] :
( hBOOL(hAPP_nat_bool(X0,nat(sK40(X0))))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_264])]) ).
fof(f4288,plain,
! [X0,X4] :
( hBOOL(hAPP_nat_bool(X0,nat(sK40(X0))))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ),
inference(cnf_transformation,[],[f3327]) ).
fof(f8893,plain,
spl63_263,
inference(avatar_split_clause,[],[f4281,f8891]) ).
fof(f8891,plain,
( spl63_263
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ~ hBOOL(hAPP_nat_bool(X0,nat(sK35(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_263])]) ).
fof(f4281,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| ~ hBOOL(hAPP_nat_bool(X0,nat(sK35(X0)))) ),
inference(cnf_transformation,[],[f3317]) ).
fof(f8889,plain,
spl63_262,
inference(avatar_split_clause,[],[f4175,f8887]) ).
fof(f8887,plain,
( spl63_262
<=> ! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
| abs_abs_int(X0) != one_one_int ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_262])]) ).
fof(f4175,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
| abs_abs_int(X0) != one_one_int ),
inference(cnf_transformation,[],[f3261]) ).
fof(f3261,plain,
! [X0] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
| abs_abs_int(X0) != one_one_int )
& ( abs_abs_int(X0) = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ) ),
inference(nnf_transformation,[],[f1460]) ).
fof(f1460,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int))
<=> abs_abs_int(X0) = one_one_int ),
inference(rectify,[],[f1187]) ).
fof(f1187,axiom,
! [X3] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X3),one_one_int))
<=> one_one_int = abs_abs_int(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_zdvd1__eq) ).
fof(f8885,plain,
spl63_261,
inference(avatar_split_clause,[],[f4174,f8883]) ).
fof(f8883,plain,
( spl63_261
<=> ! [X0] :
( abs_abs_int(X0) = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_261])]) ).
fof(f4174,plain,
! [X0] :
( abs_abs_int(X0) = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X0),one_one_int)) ),
inference(cnf_transformation,[],[f3261]) ).
fof(f8881,plain,
spl63_260,
inference(avatar_split_clause,[],[f4029,f8879]) ).
fof(f8879,plain,
( spl63_260
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,times_times_nat(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_260])]) ).
fof(f4029,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,times_times_nat(X0,X0)))),
inference(cnf_transformation,[],[f1364]) ).
fof(f1364,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,times_times_nat(X0,X0)))),
inference(rectify,[],[f874]) ).
fof(f874,axiom,
! [X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),times_times_nat(X15,times_times_nat(X15,X15)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_le__cube) ).
fof(f8877,plain,
( spl63_259
| spl63_83
| ~ spl63_247 ),
inference(avatar_split_clause,[],[f8811,f8689,f7401,f8874]) ).
fof(f8874,plain,
( spl63_259
<=> sP1(zero_zero_nat,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_259])]) ).
fof(f8689,plain,
( spl63_247
<=> ! [X1] :
( sP1(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_247])]) ).
fof(f8811,plain,
( sP1(zero_zero_nat,min)
| spl63_83
| ~ spl63_247 ),
inference(resolution,[],[f8690,f7403]) ).
fof(f8690,plain,
( ! [X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| sP1(zero_zero_nat,X1) )
| ~ spl63_247 ),
inference(avatar_component_clause,[],[f8689]) ).
fof(f8871,plain,
spl63_258,
inference(avatar_split_clause,[],[f3859,f8868]) ).
fof(f3859,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f177]) ).
fof(f177,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,m1),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_mn) ).
fof(f8823,plain,
( spl63_257
| ~ spl63_143
| ~ spl63_153
| ~ spl63_252 ),
inference(avatar_split_clause,[],[f8714,f8710,f7739,f7697,f8820]) ).
fof(f8710,plain,
( spl63_252
<=> plus_plus_int(one_one_int,one_one_int) = hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_252])]) ).
fof(f8714,plain,
( hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)) = minus_minus_int(one_one_int,min)
| ~ spl63_143
| ~ spl63_153
| ~ spl63_252 ),
inference(forward_demodulation,[],[f8712,f8005]) ).
fof(f8712,plain,
( plus_plus_int(one_one_int,one_one_int) = hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat))
| ~ spl63_252 ),
inference(avatar_component_clause,[],[f8710]) ).
fof(f8810,plain,
( spl63_256
| ~ spl63_74
| ~ spl63_140 ),
inference(avatar_split_clause,[],[f8736,f7684,f7346,f8807]) ).
fof(f8807,plain,
( spl63_256
<=> sP7(min,min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_256])]) ).
fof(f7346,plain,
( spl63_74
<=> sP7(number_number_of_int(min),number_number_of_int(min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_74])]) ).
fof(f8736,plain,
( sP7(min,min)
| ~ spl63_74
| ~ spl63_140 ),
inference(superposition,[],[f7348,f7686]) ).
fof(f7348,plain,
( sP7(number_number_of_int(min),number_number_of_int(min))
| ~ spl63_74 ),
inference(avatar_component_clause,[],[f7346]) ).
fof(f8726,plain,
( spl63_255
| ~ spl63_138
| ~ spl63_227 ),
inference(avatar_split_clause,[],[f8607,f8604,f7676,f8724]) ).
fof(f8724,plain,
( spl63_255
<=> ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(one_one_real,abs_abs_real(X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_255])]) ).
fof(f8604,plain,
( spl63_227
<=> ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X0),one_one_real)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_227])]) ).
fof(f8607,plain,
( ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(one_one_real,abs_abs_real(X0))),X0))
| ~ spl63_138
| ~ spl63_227 ),
inference(forward_demodulation,[],[f8605,f7677]) ).
fof(f8605,plain,
( ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X0),one_one_real)),X0))
| ~ spl63_227 ),
inference(avatar_component_clause,[],[f8604]) ).
fof(f8722,plain,
spl63_254,
inference(avatar_split_clause,[],[f6828,f8720]) ).
fof(f8720,plain,
( spl63_254
<=> ! [X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),pls))
| sP9(zero_zero_nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_254])]) ).
fof(f6828,plain,
! [X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),pls))
| sP9(zero_zero_nat,X1) ),
inference(forward_demodulation,[],[f6352,f5608]) ).
fof(f5608,plain,
pls = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(definition_unfolding,[],[f3808,f3772]) ).
fof(f3808,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(cnf_transformation,[],[f322]) ).
fof(f322,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_of__nat__0) ).
fof(f6352,plain,
! [X1] :
( sP9(zero_zero_nat,X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(semiri1621563631at_int,zero_zero_nat))) ),
inference(equality_resolution,[],[f4783]) ).
fof(f4783,plain,
! [X0,X1] :
( sP9(X0,X1)
| zero_zero_nat != X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),hAPP_nat_int(semiri1621563631at_int,X0))) ),
inference(cnf_transformation,[],[f3482]) ).
fof(f8718,plain,
spl63_253,
inference(avatar_split_clause,[],[f6763,f8716]) ).
fof(f8716,plain,
( spl63_253
<=> ! [X0,X1] :
( plus_plus_int(X1,minus_minus_int(X0,X1)) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_253])]) ).
fof(f6763,plain,
! [X0,X1] :
( plus_plus_int(X1,minus_minus_int(X0,X1)) = X0
| ~ is_int(X0) ),
inference(forward_demodulation,[],[f4397,f4311]) ).
fof(f4311,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f1531]) ).
fof(f1531,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(rectify,[],[f378]) ).
fof(f378,axiom,
! [X126,X127] : plus_plus_int(X126,X127) = plus_plus_int(X127,X126),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f4397,plain,
! [X0,X1] :
( plus_plus_int(minus_minus_int(X0,X1),X1) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2425]) ).
fof(f2425,plain,
! [X0,X1] :
( plus_plus_int(minus_minus_int(X0,X1),X1) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1609]) ).
fof(f1609,plain,
! [X0,X1] :
( is_int(X0)
=> plus_plus_int(minus_minus_int(X0,X1),X1) = X0 ),
inference(rectify,[],[f635]) ).
fof(f635,axiom,
! [X302,X303] :
( is_int(X302)
=> plus_plus_int(minus_minus_int(X302,X303),X303) = X302 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_diff__add__cancel) ).
fof(f8713,plain,
spl63_252,
inference(avatar_split_clause,[],[f6501,f8710]) ).
fof(f6501,plain,
plus_plus_int(one_one_int,one_one_int) = hAPP_nat_int(semiri1621563631at_int,plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f6500,f6471]) ).
fof(f6471,plain,
plus_plus_nat(one_one_nat,one_one_nat) = nat(plus_plus_int(one_one_int,one_one_int)),
inference(forward_demodulation,[],[f6470,f6468]) ).
fof(f6470,plain,
plus_plus_nat(one_one_nat,one_one_nat) = nat(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min)))),
inference(forward_demodulation,[],[f5625,f5593]) ).
fof(f5625,plain,
plus_plus_nat(one_one_nat,one_one_nat) = nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min)))),
inference(definition_unfolding,[],[f3842,f3978,f3979,f5578]) ).
fof(f3842,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_semiring__one__add__one__is__two) ).
fof(f6500,plain,
plus_plus_int(one_one_int,one_one_int) = hAPP_nat_int(semiri1621563631at_int,nat(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6499,f6468]) ).
fof(f6499,plain,
number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))) = hAPP_nat_int(semiri1621563631at_int,nat(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5640,f5593]) ).
fof(f5640,plain,
number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))) = hAPP_nat_int(semiri1621563631at_int,nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3861,f3979,f5578,f3978,f3979,f5578]) ).
fof(f3861,plain,
number_number_of_int(bit0(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f180]) ).
fof(f180,axiom,
number_number_of_int(bit0(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_transfer__int__nat__numerals_I3_J) ).
fof(f8708,plain,
( spl63_251
| ~ spl63_22
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7633,f7515,f7116,f8705]) ).
fof(f8705,plain,
( spl63_251
<=> sK62 = number_number_of_int(sK62) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_251])]) ).
fof(f7116,plain,
( spl63_22
<=> is_int(sK62) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_22])]) ).
fof(f7515,plain,
( spl63_109
<=> ! [X0] :
( number_number_of_int(X0) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_109])]) ).
fof(f7633,plain,
( sK62 = number_number_of_int(sK62)
| ~ spl63_22
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7118]) ).
fof(f7118,plain,
( is_int(sK62)
| ~ spl63_22 ),
inference(avatar_component_clause,[],[f7116]) ).
fof(f7516,plain,
( ! [X0] :
( ~ is_int(X0)
| number_number_of_int(X0) = X0 )
| ~ spl63_109 ),
inference(avatar_component_clause,[],[f7515]) ).
fof(f8703,plain,
spl63_250,
inference(avatar_split_clause,[],[f6353,f8701]) ).
fof(f6353,plain,
! [X1] :
( sP9(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(equality_resolution,[],[f6052]) ).
fof(f6052,plain,
! [X0,X1] :
( sP9(X0,X1)
| zero_zero_nat != X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f4782,f3772]) ).
fof(f4782,plain,
! [X0,X1] :
( sP9(X0,X1)
| zero_zero_nat != X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3482]) ).
fof(f8699,plain,
spl63_249,
inference(avatar_split_clause,[],[f6260,f8697]) ).
fof(f8697,plain,
( spl63_249
<=> ! [X0,X3] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ~ sP5(X0,hAPP_nat_int(semiri1621563631at_int,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_249])]) ).
fof(f6260,plain,
! [X3,X0] :
( hBOOL(hAPP_nat_bool(X0,X3))
| ~ sP5(X0,hAPP_nat_int(semiri1621563631at_int,X3)) ),
inference(equality_resolution,[],[f4432]) ).
fof(f4432,plain,
! [X3,X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X3))
| hAPP_nat_int(semiri1621563631at_int,X3) != X1
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3351]) ).
fof(f8695,plain,
spl63_248,
inference(avatar_split_clause,[],[f6253,f8693]) ).
fof(f6253,plain,
! [X1] :
( sP3(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(equality_resolution,[],[f5925]) ).
fof(f5925,plain,
! [X0,X1] :
( sP3(X0,X1)
| zero_zero_nat != X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f4422,f3772]) ).
fof(f4422,plain,
! [X0,X1] :
( sP3(X0,X1)
| zero_zero_nat != X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3341]) ).
fof(f8691,plain,
spl63_247,
inference(avatar_split_clause,[],[f6248,f8689]) ).
fof(f6248,plain,
! [X1] :
( sP1(zero_zero_nat,X1)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(equality_resolution,[],[f5920]) ).
fof(f5920,plain,
! [X0,X1] :
( sP1(X0,X1)
| zero_zero_nat != X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(definition_unfolding,[],[f4413,f3772]) ).
fof(f4413,plain,
! [X0,X1] :
( sP1(X0,X1)
| zero_zero_nat != X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(cnf_transformation,[],[f3337]) ).
fof(f8686,plain,
( ~ spl63_2
| spl63_246 ),
inference(avatar_split_clause,[],[f6222,f8683,f7016]) ).
fof(f7016,plain,
( spl63_2
<=> is_int(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_2])]) ).
fof(f8683,plain,
( spl63_246
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(pls)),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_246])]) ).
fof(f6222,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(pls)),one_one_int))
| ~ is_int(pls) ),
inference(equality_resolution,[],[f5766]) ).
fof(f5766,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| pls != X0
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f4130,f3772]) ).
fof(f4130,plain,
! [X0] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X0)),one_one_int))
| zero_zero_int != X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3244]) ).
fof(f8681,plain,
spl63_245,
inference(avatar_split_clause,[],[f5882,f8679]) ).
fof(f8679,plain,
( spl63_245
<=> ! [X0,X1] : minus_minus_int(plus_plus_int(X0,X0),min) != plus_plus_int(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_245])]) ).
fof(f5882,plain,
! [X0,X1] : minus_minus_int(plus_plus_int(X0,X0),min) != plus_plus_int(X1,X1),
inference(definition_unfolding,[],[f4297,f5578,f3979]) ).
fof(f4297,plain,
! [X0,X1] : bit1(X0) != bit0(X1),
inference(cnf_transformation,[],[f1517]) ).
fof(f1517,plain,
! [X0,X1] : bit1(X0) != bit0(X1),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X21,X31] : bit1(X21) != bit0(X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rel__simps_I50_J) ).
fof(f8677,plain,
spl63_244,
inference(avatar_split_clause,[],[f5760,f8675]) ).
fof(f8675,plain,
( spl63_244
<=> ! [X0] :
( sP0(X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK34(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_244])]) ).
fof(f5760,plain,
! [X0] :
( sP0(X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK34(X0))) ),
inference(definition_unfolding,[],[f4118,f3772]) ).
fof(f4118,plain,
! [X0] :
( sP0(X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK34(X0))) ),
inference(cnf_transformation,[],[f3239]) ).
fof(f3239,plain,
! [X0] :
( ( sP0(X0)
| ( sK34(X0) != X0
& one_one_int != sK34(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK34(X0)),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK34(X0)))
& is_int(sK34(X0)) ) )
& ( ! [X2] :
( X0 = X2
| one_one_int = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ is_int(X2) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f3237,f3238]) ).
fof(f3238,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& one_one_int != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& is_int(X1) )
=> ( sK34(X0) != X0
& one_one_int != sK34(X0)
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK34(X0)),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK34(X0)))
& is_int(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3237,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( X0 != X1
& one_one_int != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& is_int(X1) ) )
& ( ! [X2] :
( X0 = X2
| one_one_int = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X2),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ is_int(X2) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f3236]) ).
fof(f3236,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( X0 != X1
& one_one_int != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
& is_int(X1) ) )
& ( ! [X1] :
( X0 = X1
| one_one_int = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,X1),X0))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f3172]) ).
fof(f8673,plain,
spl63_243,
inference(avatar_split_clause,[],[f5721,f8671]) ).
fof(f8671,plain,
( spl63_243
<=> ! [X0] :
( pls = hAPP_nat_int(power_power_int(pls),X0)
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_243])]) ).
fof(f5721,plain,
! [X0] :
( pls = hAPP_nat_int(power_power_int(pls),X0)
| zero_zero_nat = X0 ),
inference(definition_unfolding,[],[f4052,f3772,f3772]) ).
fof(f4052,plain,
! [X0] :
( zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X0)
| zero_zero_nat = X0 ),
inference(cnf_transformation,[],[f2340]) ).
fof(f2340,plain,
! [X0] :
( ( zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X0)
| zero_zero_nat = X0 )
& ( one_one_int = hAPP_nat_int(power_power_int(zero_zero_int),X0)
| zero_zero_nat != X0 ) ),
inference(ennf_transformation,[],[f1384]) ).
fof(f1384,plain,
! [X0] :
( ( zero_zero_nat != X0
=> zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) )
& ( zero_zero_nat = X0
=> one_one_int = hAPP_nat_int(power_power_int(zero_zero_int),X0) ) ),
inference(rectify,[],[f189]) ).
fof(f189,axiom,
! [X50] :
( ( zero_zero_nat != X50
=> zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),X50) )
& ( zero_zero_nat = X50
=> one_one_int = hAPP_nat_int(power_power_int(zero_zero_int),X50) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_power__0__left) ).
fof(f8669,plain,
spl63_242,
inference(avatar_split_clause,[],[f4716,f8667]) ).
fof(f8667,plain,
( spl63_242
<=> ! [X0,X1] :
( zero_zero_nat = X0
| zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_242])]) ).
fof(f4716,plain,
! [X0,X1] :
( zero_zero_nat = X0
| zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),X1) ),
inference(cnf_transformation,[],[f3442]) ).
fof(f3442,plain,
! [X0,X1] :
( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(X0),X1)
| zero_zero_nat != X0
| zero_zero_nat = X1 )
& ( ( zero_zero_nat = X0
& zero_zero_nat != X1 )
| zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ),
inference(flattening,[],[f3441]) ).
fof(f3441,plain,
! [X0,X1] :
( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(X0),X1)
| zero_zero_nat != X0
| zero_zero_nat = X1 )
& ( ( zero_zero_nat = X0
& zero_zero_nat != X1 )
| zero_zero_nat != hAPP_nat_nat(power_power_nat(X0),X1) ) ),
inference(nnf_transformation,[],[f1800]) ).
fof(f1800,plain,
! [X0,X1] :
( zero_zero_nat = hAPP_nat_nat(power_power_nat(X0),X1)
<=> ( zero_zero_nat = X0
& zero_zero_nat != X1 ) ),
inference(rectify,[],[f431]) ).
fof(f431,axiom,
! [X29,X18] :
( zero_zero_nat = hAPP_nat_nat(power_power_nat(X29),X18)
<=> ( zero_zero_nat = X29
& zero_zero_nat != X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_nat__power__eq__0__iff) ).
fof(f8665,plain,
spl63_241,
inference(avatar_split_clause,[],[f4706,f8663]) ).
fof(f8663,plain,
( spl63_241
<=> ! [X0,X1] :
( is_int(sK50(X0,X1))
| ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_241])]) ).
fof(f4706,plain,
! [X0,X1] :
( is_int(sK50(X0,X1))
| ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ),
inference(cnf_transformation,[],[f3436]) ).
fof(f3436,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(quadRes(X0),X1))
| ! [X2] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
| ~ is_int(X2) ) )
& ( ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK50(X0,X1)),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
& is_int(sK50(X0,X1)) )
| ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f3434,f3435]) ).
fof(f3435,plain,
! [X0,X1] :
( ? [X3] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
& is_int(X3) )
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK50(X0,X1)),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
& is_int(sK50(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3434,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(quadRes(X0),X1))
| ! [X2] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
| ~ is_int(X2) ) )
& ( ? [X3] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X3),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
& is_int(X3) )
| ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ) ),
inference(rectify,[],[f3433]) ).
fof(f3433,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(quadRes(X0),X1))
| ! [X2] :
( ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
| ~ is_int(X2) ) )
& ( ? [X2] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
& is_int(X2) )
| ~ hBOOL(hAPP_int_bool(quadRes(X0),X1)) ) ),
inference(nnf_transformation,[],[f1797]) ).
fof(f1797,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(quadRes(X0),X1))
<=> ? [X2] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X2),number_number_of_nat(bit0(bit1(pls)))),X1),X0))
& is_int(X2) ) ),
inference(rectify,[],[f1149]) ).
fof(f1149,axiom,
! [X29,X3] :
( hBOOL(hAPP_int_bool(quadRes(X29),X3))
<=> ? [X153] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X153),number_number_of_nat(bit0(bit1(pls)))),X3),X29))
& is_int(X153) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_QuadRes__def) ).
fof(f8661,plain,
( spl63_240
| ~ spl63_21
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7631,f7515,f7111,f8658]) ).
fof(f8658,plain,
( spl63_240
<=> sK32 = number_number_of_int(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_240])]) ).
fof(f7111,plain,
( spl63_21
<=> is_int(sK32) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_21])]) ).
fof(f7631,plain,
( sK32 = number_number_of_int(sK32)
| ~ spl63_21
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7113]) ).
fof(f7113,plain,
( is_int(sK32)
| ~ spl63_21 ),
inference(avatar_component_clause,[],[f7111]) ).
fof(f8656,plain,
spl63_239,
inference(avatar_split_clause,[],[f4454,f8654]) ).
fof(f8654,plain,
( spl63_239
<=> ! [X0,X1] :
( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0)
| zero_zero_real = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_239])]) ).
fof(f4454,plain,
! [X0,X1] :
( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0)
| zero_zero_real = X1 ),
inference(cnf_transformation,[],[f2457]) ).
fof(f2457,plain,
! [X0,X1] :
( zero_zero_real != hAPP_nat_real(power_power_real(X1),X0)
| zero_zero_real = X1 ),
inference(ennf_transformation,[],[f1630]) ).
fof(f1630,plain,
! [X0,X1] :
( zero_zero_real != X1
=> zero_zero_real != hAPP_nat_real(power_power_real(X1),X0) ),
inference(rectify,[],[f261]) ).
fof(f261,axiom,
! [X64,X65] :
( zero_zero_real != X65
=> zero_zero_real != hAPP_nat_real(power_power_real(X65),X64) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_field__power__not__zero) ).
fof(f8652,plain,
spl63_238,
inference(avatar_split_clause,[],[f4396,f8650]) ).
fof(f8650,plain,
( spl63_238
<=> ! [X0,X1] :
( minus_minus_int(plus_plus_int(X0,X1),X1) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_238])]) ).
fof(f4396,plain,
! [X0,X1] :
( minus_minus_int(plus_plus_int(X0,X1),X1) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2424]) ).
fof(f2424,plain,
! [X0,X1] :
( minus_minus_int(plus_plus_int(X0,X1),X1) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1608]) ).
fof(f1608,plain,
! [X0,X1] :
( is_int(X0)
=> minus_minus_int(plus_plus_int(X0,X1),X1) = X0 ),
inference(rectify,[],[f633]) ).
fof(f633,axiom,
! [X300,X301] :
( is_int(X300)
=> minus_minus_int(plus_plus_int(X300,X301),X301) = X300 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_add__diff__cancel) ).
fof(f8648,plain,
spl63_237,
inference(avatar_split_clause,[],[f4291,f8646]) ).
fof(f8646,plain,
( spl63_237
<=> ! [X2,X0] :
( is_int(sK41(X0))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_237])]) ).
fof(f4291,plain,
! [X2,X0] :
( is_int(sK41(X0))
| ~ hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(cnf_transformation,[],[f3332]) ).
fof(f8644,plain,
spl63_236,
inference(avatar_split_clause,[],[f4282,f8642]) ).
fof(f8642,plain,
( spl63_236
<=> ! [X0,X3] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| is_int(sK38(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_236])]) ).
fof(f4282,plain,
! [X3,X0] :
( hBOOL(hAPP_int_bool(X0,hAPP_nat_int(semiri1621563631at_int,X3)))
| is_int(sK38(X0)) ),
inference(cnf_transformation,[],[f3322]) ).
fof(f8640,plain,
spl63_235,
inference(avatar_split_clause,[],[f4170,f8638]) ).
fof(f8638,plain,
( spl63_235
<=> ! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_235])]) ).
fof(f4170,plain,
! [X0] :
( zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ),
inference(cnf_transformation,[],[f3259]) ).
fof(f3259,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
| zero_zero_nat != X0 )
& ( zero_zero_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat)) ) ),
inference(nnf_transformation,[],[f1458]) ).
fof(f1458,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),zero_zero_nat))
<=> zero_zero_nat = X0 ),
inference(rectify,[],[f900]) ).
fof(f900,axiom,
! [X18] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),zero_zero_nat))
<=> zero_zero_nat = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_le__0__eq) ).
fof(f8636,plain,
spl63_234,
inference(avatar_split_clause,[],[f4168,f8634]) ).
fof(f8634,plain,
( spl63_234
<=> ! [X0] :
( one_one_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_234])]) ).
fof(f4168,plain,
! [X0] :
( one_one_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ),
inference(cnf_transformation,[],[f3258]) ).
fof(f3258,plain,
! [X0] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
| one_one_nat != X0 )
& ( one_one_nat = X0
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat)) ) ),
inference(nnf_transformation,[],[f1457]) ).
fof(f1457,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),one_one_nat))
<=> one_one_nat = X0 ),
inference(rectify,[],[f1084]) ).
fof(f1084,axiom,
! [X29] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X29),one_one_nat))
<=> one_one_nat = X29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_nat__dvd__1__iff__1) ).
fof(f8632,plain,
spl63_233,
inference(avatar_split_clause,[],[f4135,f8630]) ).
fof(f8630,plain,
( spl63_233
<=> ! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_233])]) ).
fof(f4135,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| zero_zero_nat = X0 ),
inference(cnf_transformation,[],[f2401]) ).
fof(f2401,plain,
! [X0] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0))
| zero_zero_nat = X0 ),
inference(ennf_transformation,[],[f1436]) ).
fof(f1436,plain,
! [X0] :
( zero_zero_nat != X0
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X0)) ),
inference(rectify,[],[f225]) ).
fof(f225,axiom,
! [X16] :
( zero_zero_nat != X16
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_gr0I) ).
fof(f8628,plain,
spl63_232,
inference(avatar_split_clause,[],[f4119,f8626]) ).
fof(f8626,plain,
( spl63_232
<=> ! [X0] :
( sP0(X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK34(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_232])]) ).
fof(f4119,plain,
! [X0] :
( sP0(X0)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(dvd_dvd_int,sK34(X0)),X0)) ),
inference(cnf_transformation,[],[f3239]) ).
fof(f8624,plain,
spl63_231,
inference(avatar_split_clause,[],[f4050,f8622]) ).
fof(f8622,plain,
( spl63_231
<=> ! [X0] :
( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0)
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_231])]) ).
fof(f4050,plain,
! [X0] :
( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0)
| zero_zero_nat = X0 ),
inference(cnf_transformation,[],[f2339]) ).
fof(f2339,plain,
! [X0] :
( ( zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0)
| zero_zero_nat = X0 )
& ( one_one_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0)
| zero_zero_nat != X0 ) ),
inference(ennf_transformation,[],[f1383]) ).
fof(f1383,plain,
! [X0] :
( ( zero_zero_nat != X0
=> zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) )
& ( zero_zero_nat = X0
=> one_one_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X0) ) ),
inference(rectify,[],[f190]) ).
fof(f190,axiom,
! [X50] :
( ( zero_zero_nat != X50
=> zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X50) )
& ( zero_zero_nat = X50
=> one_one_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),X50) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_power__0__left) ).
fof(f8620,plain,
spl63_230,
inference(avatar_split_clause,[],[f4048,f8618]) ).
fof(f8618,plain,
( spl63_230
<=> ! [X0] :
( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0)
| zero_zero_nat = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_230])]) ).
fof(f4048,plain,
! [X0] :
( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0)
| zero_zero_nat = X0 ),
inference(cnf_transformation,[],[f2338]) ).
fof(f2338,plain,
! [X0] :
( ( zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0)
| zero_zero_nat = X0 )
& ( one_one_real = hAPP_nat_real(power_power_real(zero_zero_real),X0)
| zero_zero_nat != X0 ) ),
inference(ennf_transformation,[],[f1382]) ).
fof(f1382,plain,
! [X0] :
( ( zero_zero_nat != X0
=> zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) )
& ( zero_zero_nat = X0
=> one_one_real = hAPP_nat_real(power_power_real(zero_zero_real),X0) ) ),
inference(rectify,[],[f191]) ).
fof(f191,axiom,
! [X50] :
( ( zero_zero_nat != X50
=> zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),X50) )
& ( zero_zero_nat = X50
=> one_one_real = hAPP_nat_real(power_power_real(zero_zero_real),X50) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_power__0__left) ).
fof(f8616,plain,
( spl63_229
| ~ spl63_20
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7630,f7515,f7106,f8613]) ).
fof(f8613,plain,
( spl63_229
<=> sK31 = number_number_of_int(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_229])]) ).
fof(f7106,plain,
( spl63_20
<=> is_int(sK31) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_20])]) ).
fof(f7630,plain,
( sK31 = number_number_of_int(sK31)
| ~ spl63_20
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7108]) ).
fof(f7108,plain,
( is_int(sK31)
| ~ spl63_20 ),
inference(avatar_component_clause,[],[f7106]) ).
fof(f8611,plain,
spl63_228,
inference(avatar_split_clause,[],[f4022,f8609]) ).
fof(f8609,plain,
( spl63_228
<=> ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,abs_abs_real(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_228])]) ).
fof(f4022,plain,
! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,abs_abs_real(X0)))),
inference(cnf_transformation,[],[f1357]) ).
fof(f1357,plain,
! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,abs_abs_real(X0)))),
inference(rectify,[],[f1206]) ).
fof(f1206,axiom,
! [X8] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,abs_abs_real(X8)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_abs__add__one__gt__zero) ).
fof(f8606,plain,
spl63_227,
inference(avatar_split_clause,[],[f4017,f8604]) ).
fof(f4017,plain,
! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X0),one_one_real)),X0)),
inference(cnf_transformation,[],[f1352]) ).
fof(f1352,plain,
! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X0),one_one_real)),X0)),
inference(rectify,[],[f1205]) ).
fof(f1205,axiom,
! [X8] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,plus_plus_real(abs_abs_real(X8),one_one_real)),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_abs__add__one__not__less__self) ).
fof(f8598,plain,
( spl63_226
| ~ spl63_143
| ~ spl63_153
| ~ spl63_217 ),
inference(avatar_split_clause,[],[f8310,f8306,f7739,f7697,f8595]) ).
fof(f8595,plain,
( spl63_226
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),minus_minus_int(one_one_int,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_226])]) ).
fof(f8306,plain,
( spl63_217
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),plus_plus_int(one_one_int,one_one_int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_217])]) ).
fof(f8310,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),minus_minus_int(one_one_int,min)))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_217 ),
inference(forward_demodulation,[],[f8308,f8005]) ).
fof(f8308,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),plus_plus_int(one_one_int,one_one_int)))
| ~ spl63_217 ),
inference(avatar_component_clause,[],[f8306]) ).
fof(f8592,plain,
( spl63_225
| ~ spl63_19
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7629,f7515,f7101,f8589]) ).
fof(f8589,plain,
( spl63_225
<=> sK30 = number_number_of_int(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_225])]) ).
fof(f7101,plain,
( spl63_19
<=> is_int(sK30) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_19])]) ).
fof(f7629,plain,
( sK30 = number_number_of_int(sK30)
| ~ spl63_19
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7103]) ).
fof(f7103,plain,
( is_int(sK30)
| ~ spl63_19 ),
inference(avatar_component_clause,[],[f7101]) ).
fof(f8587,plain,
( spl63_224
| ~ spl63_143
| ~ spl63_153
| ~ spl63_212 ),
inference(avatar_split_clause,[],[f8284,f8280,f7739,f7697,f8584]) ).
fof(f8584,plain,
( spl63_224
<=> plus_plus_nat(one_one_nat,one_one_nat) = nat(minus_minus_int(one_one_int,min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_224])]) ).
fof(f8280,plain,
( spl63_212
<=> plus_plus_nat(one_one_nat,one_one_nat) = nat(plus_plus_int(one_one_int,one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_212])]) ).
fof(f8284,plain,
( plus_plus_nat(one_one_nat,one_one_nat) = nat(minus_minus_int(one_one_int,min))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_212 ),
inference(forward_demodulation,[],[f8282,f8005]) ).
fof(f8282,plain,
( plus_plus_nat(one_one_nat,one_one_nat) = nat(plus_plus_int(one_one_int,one_one_int))
| ~ spl63_212 ),
inference(avatar_component_clause,[],[f8280]) ).
fof(f8564,plain,
( spl63_223
| ~ spl63_143
| ~ spl63_153
| ~ spl63_199 ),
inference(avatar_split_clause,[],[f8221,f8217,f7739,f7697,f8561]) ).
fof(f8561,plain,
( spl63_223
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),minus_minus_int(one_one_int,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_223])]) ).
fof(f8217,plain,
( spl63_199
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,one_one_int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_199])]) ).
fof(f8221,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),minus_minus_int(one_one_int,min)))
| ~ spl63_143
| ~ spl63_153
| ~ spl63_199 ),
inference(forward_demodulation,[],[f8219,f8005]) ).
fof(f8219,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,one_one_int)))
| ~ spl63_199 ),
inference(avatar_component_clause,[],[f8217]) ).
fof(f8559,plain,
( spl63_222
| ~ spl63_18
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7628,f7515,f7096,f8556]) ).
fof(f8556,plain,
( spl63_222
<=> sK29 = number_number_of_int(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_222])]) ).
fof(f7096,plain,
( spl63_18
<=> is_int(sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_18])]) ).
fof(f7628,plain,
( sK29 = number_number_of_int(sK29)
| ~ spl63_18
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7098]) ).
fof(f7098,plain,
( is_int(sK29)
| ~ spl63_18 ),
inference(avatar_component_clause,[],[f7096]) ).
fof(f8526,plain,
( spl63_221
| ~ spl63_17
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7627,f7515,f7091,f8523]) ).
fof(f8523,plain,
( spl63_221
<=> sK28 = number_number_of_int(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_221])]) ).
fof(f7091,plain,
( spl63_17
<=> is_int(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_17])]) ).
fof(f7627,plain,
( sK28 = number_number_of_int(sK28)
| ~ spl63_17
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7093]) ).
fof(f7093,plain,
( is_int(sK28)
| ~ spl63_17 ),
inference(avatar_component_clause,[],[f7091]) ).
fof(f8396,plain,
( spl63_220
| ~ spl63_16
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7626,f7515,f7086,f8393]) ).
fof(f8393,plain,
( spl63_220
<=> sK27 = number_number_of_int(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_220])]) ).
fof(f7086,plain,
( spl63_16
<=> is_int(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_16])]) ).
fof(f7626,plain,
( sK27 = number_number_of_int(sK27)
| ~ spl63_16
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7088]) ).
fof(f7088,plain,
( is_int(sK27)
| ~ spl63_16 ),
inference(avatar_component_clause,[],[f7086]) ).
fof(f8329,plain,
( spl63_219
| ~ spl63_15
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7625,f7515,f7081,f8326]) ).
fof(f8326,plain,
( spl63_219
<=> sK26 = number_number_of_int(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_219])]) ).
fof(f7081,plain,
( spl63_15
<=> is_int(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_15])]) ).
fof(f7625,plain,
( sK26 = number_number_of_int(sK26)
| ~ spl63_15
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7083]) ).
fof(f7083,plain,
( is_int(sK26)
| ~ spl63_15 ),
inference(avatar_component_clause,[],[f7081]) ).
fof(f8314,plain,
spl63_218,
inference(avatar_split_clause,[],[f6571,f8312]) ).
fof(f8312,plain,
( spl63_218
<=> ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),minus_minus_int(X0,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_218])]) ).
fof(f6571,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),minus_minus_int(X0,min))),
inference(forward_demodulation,[],[f4015,f5683]) ).
fof(f4015,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(X0,one_one_int))),
inference(cnf_transformation,[],[f1350]) ).
fof(f1350,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(X0,one_one_int))),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X80] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X80),plus_plus_int(X80,one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__add__one) ).
fof(f8309,plain,
spl63_217,
inference(avatar_split_clause,[],[f6497,f8306]) ).
fof(f6497,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6496,f6468]) ).
fof(f6496,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5635,f5593]) ).
fof(f5635,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3855,f3772,f3979,f5578]) ).
fof(f3855,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
inference(cnf_transformation,[],[f852]) ).
fof(f852,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(f8304,plain,
spl63_216,
inference(avatar_split_clause,[],[f6491,f8301]) ).
fof(f8301,plain,
( spl63_216
<=> pls = hAPP_nat_int(power_power_int(pls),plus_plus_nat(one_one_nat,one_one_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_216])]) ).
fof(f6491,plain,
pls = hAPP_nat_int(power_power_int(pls),plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f6490,f6471]) ).
fof(f6490,plain,
pls = hAPP_nat_int(power_power_int(pls),nat(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6489,f6468]) ).
fof(f6489,plain,
pls = hAPP_nat_int(power_power_int(pls),nat(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5633,f5593]) ).
fof(f5633,plain,
pls = hAPP_nat_int(power_power_int(pls),nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3852,f3772,f3772,f3978,f3979,f5578]) ).
fof(f3852,plain,
zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
zero_zero_int = hAPP_nat_int(power_power_int(zero_zero_int),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zero__power2) ).
fof(f8299,plain,
spl63_215,
inference(avatar_split_clause,[],[f6488,f8296]) ).
fof(f8296,plain,
( spl63_215
<=> zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_215])]) ).
fof(f6488,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f6487,f6471]) ).
fof(f6487,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),nat(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6486,f6468]) ).
fof(f6486,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),nat(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5632,f5593]) ).
fof(f5632,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3851,f3978,f3979,f5578]) ).
fof(f3851,plain,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
zero_zero_nat = hAPP_nat_nat(power_power_nat(zero_zero_nat),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_zero__power2) ).
fof(f8294,plain,
spl63_214,
inference(avatar_split_clause,[],[f6485,f8291]) ).
fof(f8291,plain,
( spl63_214
<=> zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),plus_plus_nat(one_one_nat,one_one_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_214])]) ).
fof(f6485,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),plus_plus_nat(one_one_nat,one_one_nat)),
inference(forward_demodulation,[],[f6484,f6471]) ).
fof(f6484,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat(plus_plus_int(one_one_int,one_one_int))),
inference(forward_demodulation,[],[f6483,f6468]) ).
fof(f6483,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat(number_number_of_int(plus_plus_int(minus_minus_int(pls,min),minus_minus_int(pls,min))))),
inference(forward_demodulation,[],[f5631,f5593]) ).
fof(f5631,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3850,f3978,f3979,f5578]) ).
fof(f3850,plain,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
zero_zero_real = hAPP_nat_real(power_power_real(zero_zero_real),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_zero__power2) ).
fof(f8289,plain,
( spl63_213
| ~ spl63_14
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7624,f7515,f7076,f8286]) ).
fof(f8286,plain,
( spl63_213
<=> sK25 = number_number_of_int(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_213])]) ).
fof(f7076,plain,
( spl63_14
<=> is_int(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_14])]) ).
fof(f7624,plain,
( sK25 = number_number_of_int(sK25)
| ~ spl63_14
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7078]) ).
fof(f7078,plain,
( is_int(sK25)
| ~ spl63_14 ),
inference(avatar_component_clause,[],[f7076]) ).
fof(f8283,plain,
spl63_212,
inference(avatar_split_clause,[],[f6471,f8280]) ).
fof(f8278,plain,
spl63_211,
inference(avatar_split_clause,[],[f6443,f8276]) ).
fof(f8276,plain,
( spl63_211
<=> ! [X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1))
| ~ is_int(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_211])]) ).
fof(f6443,plain,
! [X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1))
| ~ is_int(X1) ),
inference(duplicate_literal_removal,[],[f6293]) ).
fof(f6293,plain,
! [X1] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1))
| ~ is_int(X1)
| ~ is_int(X1) ),
inference(equality_resolution,[],[f4628]) ).
fof(f4628,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3399]) ).
fof(f3399,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f3398]) ).
fof(f3398,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(nnf_transformation,[],[f2684]) ).
fof(f2684,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2683]) ).
fof(f2683,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1761]) ).
fof(f1761,plain,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ) ),
inference(rectify,[],[f747]) ).
fof(f747,axiom,
! [X30,X25] :
( ( is_int(X25)
& is_int(X30) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),X25))
<=> ( X25 != X30
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X30),X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_zless__le) ).
fof(f8274,plain,
spl63_210,
inference(avatar_split_clause,[],[f6250,f8272]) ).
fof(f8272,plain,
( spl63_210
<=> ! [X0] :
( sP3(nat(X0),X0)
| ~ sP4(X0,nat(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_210])]) ).
fof(f6250,plain,
! [X0] :
( sP3(nat(X0),X0)
| ~ sP4(X0,nat(X0)) ),
inference(equality_resolution,[],[f4416]) ).
fof(f4416,plain,
! [X0,X1] :
( sP3(X1,X0)
| nat(X0) != X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f3339]) ).
fof(f8270,plain,
spl63_209,
inference(avatar_split_clause,[],[f6245,f8268]) ).
fof(f8268,plain,
( spl63_209
<=> ! [X0] :
( sP1(nat(X0),X0)
| ~ sP2(X0,nat(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_209])]) ).
fof(f6245,plain,
! [X0] :
( sP1(nat(X0),X0)
| ~ sP2(X0,nat(X0)) ),
inference(equality_resolution,[],[f4407]) ).
fof(f4407,plain,
! [X0,X1] :
( sP1(X1,X0)
| nat(X0) != X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3334]) ).
fof(f8265,plain,
( spl63_208
| ~ spl63_140
| ~ spl63_207 ),
inference(avatar_split_clause,[],[f8259,f8252,f7684,f8262]) ).
fof(f8262,plain,
( spl63_208
<=> one_one_int = abs_abs_int(min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_208])]) ).
fof(f8252,plain,
( spl63_207
<=> one_one_int = abs_abs_int(number_number_of_int(min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_207])]) ).
fof(f8259,plain,
( one_one_int = abs_abs_int(min)
| ~ spl63_140
| ~ spl63_207 ),
inference(forward_demodulation,[],[f8254,f7686]) ).
fof(f8254,plain,
( one_one_int = abs_abs_int(number_number_of_int(min))
| ~ spl63_207 ),
inference(avatar_component_clause,[],[f8252]) ).
fof(f8258,plain,
( ~ spl63_12
| ~ spl63_140
| spl63_206 ),
inference(avatar_split_clause,[],[f8257,f8248,f7684,f7066]) ).
fof(f7066,plain,
( spl63_12
<=> is_int(min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_12])]) ).
fof(f8248,plain,
( spl63_206
<=> is_int(number_number_of_int(min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_206])]) ).
fof(f8257,plain,
( ~ is_int(min)
| ~ spl63_140
| spl63_206 ),
inference(forward_demodulation,[],[f8250,f7686]) ).
fof(f8250,plain,
( ~ is_int(number_number_of_int(min))
| spl63_206 ),
inference(avatar_component_clause,[],[f8248]) ).
fof(f8255,plain,
( ~ spl63_206
| spl63_207 ),
inference(avatar_split_clause,[],[f6216,f8252,f8248]) ).
fof(f6216,plain,
( one_one_int = abs_abs_int(number_number_of_int(min))
| ~ is_int(number_number_of_int(min)) ),
inference(equality_resolution,[],[f4111]) ).
fof(f4111,plain,
! [X0] :
( abs_abs_int(X0) = one_one_int
| number_number_of_int(min) != X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3233]) ).
fof(f8246,plain,
spl63_205,
inference(avatar_split_clause,[],[f5789,f8244]) ).
fof(f8244,plain,
( spl63_205
<=> ! [X0] :
( zero_zero_nat = X0
| pls != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_205])]) ).
fof(f5789,plain,
! [X0] :
( zero_zero_nat = X0
| pls != hAPP_nat_int(semiri1621563631at_int,X0) ),
inference(definition_unfolding,[],[f4166,f3772]) ).
fof(f4166,plain,
! [X0] :
( zero_zero_nat = X0
| zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ),
inference(cnf_transformation,[],[f3257]) ).
fof(f3257,plain,
! [X0] :
( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X0)
| zero_zero_nat != X0 )
& ( zero_zero_nat = X0
| zero_zero_int != hAPP_nat_int(semiri1621563631at_int,X0) ) ),
inference(nnf_transformation,[],[f1456]) ).
fof(f1456,plain,
! [X0] :
( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X0)
<=> zero_zero_nat = X0 ),
inference(rectify,[],[f72]) ).
fof(f72,axiom,
! [X18] :
( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,X18)
<=> zero_zero_nat = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_int__eq__0__conv) ).
fof(f8242,plain,
spl63_204,
inference(avatar_split_clause,[],[f5695,f8240]) ).
fof(f5695,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),times_times_int(X0,X0))),
inference(definition_unfolding,[],[f4014,f3772]) ).
fof(f4014,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X0))),
inference(cnf_transformation,[],[f1349]) ).
fof(f1349,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X0,X0))),
inference(rectify,[],[f563]) ).
fof(f563,axiom,
! [X249] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),times_times_int(X249,X249))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_zero__le__square) ).
fof(f8238,plain,
( spl63_203
| ~ spl63_13
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7623,f7515,f7071,f8235]) ).
fof(f8235,plain,
( spl63_203
<=> sK24 = number_number_of_int(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_203])]) ).
fof(f7071,plain,
( spl63_13
<=> is_int(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_13])]) ).
fof(f7623,plain,
( sK24 = number_number_of_int(sK24)
| ~ spl63_13
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7073]) ).
fof(f7073,plain,
( is_int(sK24)
| ~ spl63_13 ),
inference(avatar_component_clause,[],[f7071]) ).
fof(f8233,plain,
spl63_202,
inference(avatar_split_clause,[],[f5693,f8231]) ).
fof(f8231,plain,
( spl63_202
<=> ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_202])]) ).
fof(f5693,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(definition_unfolding,[],[f4009,f3772]) ).
fof(f4009,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(cnf_transformation,[],[f1344]) ).
fof(f1344,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X0))),
inference(rectify,[],[f813]) ).
fof(f813,axiom,
! [X17] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(f8229,plain,
spl63_201,
inference(avatar_split_clause,[],[f5690,f8227]) ).
fof(f8227,plain,
( spl63_201
<=> ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X0,X0)),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_201])]) ).
fof(f5690,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X0,X0)),pls)),
inference(definition_unfolding,[],[f4003,f3772]) ).
fof(f4003,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X0,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f1338]) ).
fof(f1338,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X0,X0)),zero_zero_int)),
inference(rectify,[],[f792]) ).
fof(f792,axiom,
! [X377] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,times_times_int(X377,X377)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_not__square__less__zero) ).
fof(f8225,plain,
spl63_200,
inference(avatar_split_clause,[],[f5688,f8223]) ).
fof(f8223,plain,
( spl63_200
<=> ! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_200])]) ).
fof(f5688,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),pls)),
inference(definition_unfolding,[],[f4000,f3772]) ).
fof(f4000,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(cnf_transformation,[],[f1335]) ).
fof(f1335,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X0)),zero_zero_int)),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X21] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X21)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_int__less__0__conv) ).
fof(f8220,plain,
spl63_199,
inference(avatar_split_clause,[],[f5627,f8217]) ).
fof(f5627,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,one_one_int))),
inference(definition_unfolding,[],[f3846,f3772]) ).
fof(f3846,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,one_one_int))),
inference(cnf_transformation,[],[f195]) ).
fof(f195,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_zero__less__two) ).
fof(f8215,plain,
spl63_198,
inference(avatar_split_clause,[],[f5304,f8213]) ).
fof(f8213,plain,
( spl63_198
<=> ! [X2,X0,X1] :
( sP15(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_198])]) ).
fof(f5304,plain,
! [X2,X0,X1] :
( sP15(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f3633]) ).
fof(f8211,plain,
spl63_197,
inference(avatar_split_clause,[],[f5303,f8209]) ).
fof(f8209,plain,
( spl63_197
<=> ! [X2,X0,X1] :
( sP15(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_197])]) ).
fof(f5303,plain,
! [X2,X0,X1] :
( sP15(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f3633]) ).
fof(f8207,plain,
spl63_196,
inference(avatar_split_clause,[],[f5297,f8205]) ).
fof(f8205,plain,
( spl63_196
<=> ! [X2,X0,X1] :
( sP14(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_196])]) ).
fof(f5297,plain,
! [X2,X0,X1] :
( sP14(X0,X2,X1)
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f3628]) ).
fof(f8203,plain,
spl63_195,
inference(avatar_split_clause,[],[f5296,f8201]) ).
fof(f8201,plain,
( spl63_195
<=> ! [X2,X0,X1] :
( sP14(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_195])]) ).
fof(f5296,plain,
! [X2,X0,X1] :
( sP14(X0,X2,X1)
| hBOOL(X0)
| hBOOL(X1) ),
inference(cnf_transformation,[],[f3628]) ).
fof(f8199,plain,
spl63_194,
inference(avatar_split_clause,[],[f4702,f8197]) ).
fof(f8197,plain,
( spl63_194
<=> ! [X0,X1] :
( zero_zero_real = X1
| plus_plus_real(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_194])]) ).
fof(f4702,plain,
! [X0,X1] :
( zero_zero_real = X1
| plus_plus_real(X0,X1) != X0 ),
inference(cnf_transformation,[],[f3431]) ).
fof(f3431,plain,
! [X0,X1] :
( ( plus_plus_real(X0,X1) = X0
| zero_zero_real != X1 )
& ( zero_zero_real = X1
| plus_plus_real(X0,X1) != X0 ) ),
inference(nnf_transformation,[],[f1795]) ).
fof(f1795,plain,
! [X0,X1] :
( plus_plus_real(X0,X1) = X0
<=> zero_zero_real = X1 ),
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X81,X5] :
( plus_plus_real(X81,X5) = X81
<=> zero_zero_real = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_add__0__iff) ).
fof(f8195,plain,
spl63_193,
inference(avatar_split_clause,[],[f4697,f8193]) ).
fof(f8193,plain,
( spl63_193
<=> ! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat != plus_plus_nat(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_193])]) ).
fof(f4697,plain,
! [X0,X1] :
( zero_zero_nat = X1
| zero_zero_nat != plus_plus_nat(X0,X1) ),
inference(cnf_transformation,[],[f3428]) ).
fof(f3428,plain,
! [X0,X1] :
( ( zero_zero_nat = plus_plus_nat(X0,X1)
| zero_zero_nat != X1
| zero_zero_nat != X0 )
& ( ( zero_zero_nat = X1
& zero_zero_nat = X0 )
| zero_zero_nat != plus_plus_nat(X0,X1) ) ),
inference(flattening,[],[f3427]) ).
fof(f3427,plain,
! [X0,X1] :
( ( zero_zero_nat = plus_plus_nat(X0,X1)
| zero_zero_nat != X1
| zero_zero_nat != X0 )
& ( ( zero_zero_nat = X1
& zero_zero_nat = X0 )
| zero_zero_nat != plus_plus_nat(X0,X1) ) ),
inference(nnf_transformation,[],[f1793]) ).
fof(f1793,plain,
! [X0,X1] :
( zero_zero_nat = plus_plus_nat(X0,X1)
<=> ( zero_zero_nat = X1
& zero_zero_nat = X0 ) ),
inference(rectify,[],[f241]) ).
fof(f241,axiom,
! [X29,X18] :
( zero_zero_nat = plus_plus_nat(X29,X18)
<=> ( zero_zero_nat = X18
& zero_zero_nat = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_add__is__0) ).
fof(f8191,plain,
( spl63_192
| ~ spl63_7
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7622,f7515,f7041,f8188]) ).
fof(f8188,plain,
( spl63_192
<=> y = number_number_of_int(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_192])]) ).
fof(f7622,plain,
( y = number_number_of_int(y)
| ~ spl63_7
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7043]) ).
fof(f8186,plain,
spl63_191,
inference(avatar_split_clause,[],[f4696,f8184]) ).
fof(f8184,plain,
( spl63_191
<=> ! [X0,X1] :
( zero_zero_nat = X0
| zero_zero_nat != plus_plus_nat(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_191])]) ).
fof(f4696,plain,
! [X0,X1] :
( zero_zero_nat = X0
| zero_zero_nat != plus_plus_nat(X0,X1) ),
inference(cnf_transformation,[],[f3428]) ).
fof(f8182,plain,
spl63_190,
inference(avatar_split_clause,[],[f4681,f8180]) ).
fof(f8180,plain,
( spl63_190
<=> ! [X0,X1] :
( one_one_nat = X1
| one_one_nat != times_times_nat(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_190])]) ).
fof(f4681,plain,
! [X0,X1] :
( one_one_nat = X1
| one_one_nat != times_times_nat(X0,X1) ),
inference(cnf_transformation,[],[f3418]) ).
fof(f3418,plain,
! [X0,X1] :
( ( one_one_nat = times_times_nat(X0,X1)
| one_one_nat != X1
| one_one_nat != X0 )
& ( ( one_one_nat = X1
& one_one_nat = X0 )
| one_one_nat != times_times_nat(X0,X1) ) ),
inference(flattening,[],[f3417]) ).
fof(f3417,plain,
! [X0,X1] :
( ( one_one_nat = times_times_nat(X0,X1)
| one_one_nat != X1
| one_one_nat != X0 )
& ( ( one_one_nat = X1
& one_one_nat = X0 )
| one_one_nat != times_times_nat(X0,X1) ) ),
inference(nnf_transformation,[],[f1787]) ).
fof(f1787,plain,
! [X0,X1] :
( one_one_nat = times_times_nat(X0,X1)
<=> ( one_one_nat = X1
& one_one_nat = X0 ) ),
inference(rectify,[],[f923]) ).
fof(f923,axiom,
! [X18,X29] :
( one_one_nat = times_times_nat(X18,X29)
<=> ( one_one_nat = X29
& one_one_nat = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_894_nat__mult__eq__one) ).
fof(f8178,plain,
spl63_189,
inference(avatar_split_clause,[],[f4680,f8176]) ).
fof(f8176,plain,
( spl63_189
<=> ! [X0,X1] :
( one_one_nat = X0
| one_one_nat != times_times_nat(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_189])]) ).
fof(f4680,plain,
! [X0,X1] :
( one_one_nat = X0
| one_one_nat != times_times_nat(X0,X1) ),
inference(cnf_transformation,[],[f3418]) ).
fof(f8174,plain,
spl63_188,
inference(avatar_split_clause,[],[f4672,f8172]) ).
fof(f8172,plain,
( spl63_188
<=> ! [X0,X1] :
( X0 = X1
| zero_zero_real != minus_minus_real(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_188])]) ).
fof(f4672,plain,
! [X0,X1] :
( X0 = X1
| zero_zero_real != minus_minus_real(X0,X1) ),
inference(cnf_transformation,[],[f3412]) ).
fof(f3412,plain,
! [X0,X1] :
( ( X0 = X1
| zero_zero_real != minus_minus_real(X0,X1) )
& ( zero_zero_real = minus_minus_real(X0,X1)
| X0 != X1 ) ),
inference(nnf_transformation,[],[f1783]) ).
fof(f1783,plain,
! [X0,X1] :
( X0 = X1
<=> zero_zero_real = minus_minus_real(X0,X1) ),
inference(rectify,[],[f622]) ).
fof(f622,axiom,
! [X5,X81] :
( X5 = X81
<=> zero_zero_real = minus_minus_real(X5,X81) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_eq__iff__diff__eq__0) ).
fof(f8170,plain,
spl63_187,
inference(avatar_split_clause,[],[f4587,f8168]) ).
fof(f8168,plain,
( spl63_187
<=> ! [X0,X1] :
( is_int(times_times_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_187])]) ).
fof(f4587,plain,
! [X0,X1] :
( is_int(times_times_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2646]) ).
fof(f2646,plain,
! [X0,X1] :
( is_int(times_times_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2645]) ).
fof(f2645,plain,
! [X0,X1] :
( is_int(times_times_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> is_int(times_times_int(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint) ).
fof(f8166,plain,
spl63_186,
inference(avatar_split_clause,[],[f4586,f8164]) ).
fof(f8164,plain,
( spl63_186
<=> ! [X0,X1] :
( is_int(minus_minus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_186])]) ).
fof(f4586,plain,
! [X0,X1] :
( is_int(minus_minus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2644]) ).
fof(f2644,plain,
! [X0,X1] :
( is_int(minus_minus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2643]) ).
fof(f2643,plain,
! [X0,X1] :
( is_int(minus_minus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> is_int(minus_minus_int(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint) ).
fof(f8162,plain,
spl63_185,
inference(avatar_split_clause,[],[f4585,f8160]) ).
fof(f8160,plain,
( spl63_185
<=> ! [X0,X1] :
( is_int(legendre(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_185])]) ).
fof(f4585,plain,
! [X0,X1] :
( is_int(legendre(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2642]) ).
fof(f2642,plain,
! [X0,X1] :
( is_int(legendre(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2641]) ).
fof(f2641,plain,
! [X0,X1] :
( is_int(legendre(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> is_int(legendre(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Residues_OLegendre) ).
fof(f8158,plain,
spl63_184,
inference(avatar_split_clause,[],[f4468,f8156]) ).
fof(f8156,plain,
( spl63_184
<=> ! [X0,X1] :
( zero_zero_nat = X1
| plus_plus_nat(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_184])]) ).
fof(f4468,plain,
! [X0,X1] :
( zero_zero_nat = X1
| plus_plus_nat(X0,X1) != X0 ),
inference(cnf_transformation,[],[f2478]) ).
fof(f2478,plain,
! [X0,X1] :
( zero_zero_nat = X1
| plus_plus_nat(X0,X1) != X0 ),
inference(ennf_transformation,[],[f1642]) ).
fof(f1642,plain,
! [X0,X1] :
( plus_plus_nat(X0,X1) = X0
=> zero_zero_nat = X1 ),
inference(rectify,[],[f240]) ).
fof(f240,axiom,
! [X15,X16] :
( plus_plus_nat(X15,X16) = X15
=> zero_zero_nat = X16 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add__eq__self__zero) ).
fof(f8154,plain,
spl63_183,
inference(avatar_split_clause,[],[f4395,f8152]) ).
fof(f8152,plain,
( spl63_183
<=> ! [X0,X1] :
( if_int(fTrue,X0,X1) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_183])]) ).
fof(f4395,plain,
! [X0,X1] :
( if_int(fTrue,X0,X1) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2423]) ).
fof(f2423,plain,
! [X0,X1] :
( if_int(fTrue,X0,X1) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1607]) ).
fof(f1607,plain,
! [X0,X1] :
( is_int(X0)
=> if_int(fTrue,X0,X1) = X0 ),
inference(rectify,[],[f1227]) ).
fof(f1227,axiom,
! [X8,X10] :
( is_int(X8)
=> if_int(fTrue,X8,X10) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Int__Oint_T) ).
fof(f8150,plain,
spl63_182,
inference(avatar_split_clause,[],[f4394,f8148]) ).
fof(f8148,plain,
( spl63_182
<=> ! [X0,X1] :
( if_int(fFalse,X0,X1) = X1
| ~ is_int(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_182])]) ).
fof(f4394,plain,
! [X0,X1] :
( if_int(fFalse,X0,X1) = X1
| ~ is_int(X1) ),
inference(cnf_transformation,[],[f2422]) ).
fof(f2422,plain,
! [X0,X1] :
( if_int(fFalse,X0,X1) = X1
| ~ is_int(X1) ),
inference(ennf_transformation,[],[f1606]) ).
fof(f1606,plain,
! [X0,X1] :
( is_int(X1)
=> if_int(fFalse,X0,X1) = X1 ),
inference(rectify,[],[f1228]) ).
fof(f1228,axiom,
! [X8,X10] :
( is_int(X10)
=> if_int(fFalse,X8,X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Int__Oint_T) ).
fof(f8146,plain,
( spl63_181
| ~ spl63_6
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7621,f7515,f7036,f8143]) ).
fof(f8143,plain,
( spl63_181
<=> x = number_number_of_int(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_181])]) ).
fof(f7621,plain,
( x = number_number_of_int(x)
| ~ spl63_6
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7038]) ).
fof(f8141,plain,
spl63_180,
inference(avatar_split_clause,[],[f4323,f8139]) ).
fof(f8139,plain,
( spl63_180
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(X0,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_180])]) ).
fof(f4323,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(X0,X1)),X0)),
inference(cnf_transformation,[],[f1543]) ).
fof(f1543,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(X0,X1)),X0)),
inference(rectify,[],[f937]) ).
fof(f937,axiom,
! [X15,X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,minus_minus_nat(X15,X16)),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_Nat_Odiff__le__self) ).
fof(f8137,plain,
spl63_179,
inference(avatar_split_clause,[],[f4322,f8135]) ).
fof(f8135,plain,
( spl63_179
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_179])]) ).
fof(f4322,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X0,X1))),
inference(cnf_transformation,[],[f1542]) ).
fof(f1542,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X0,X1))),
inference(rectify,[],[f921]) ).
fof(f921,axiom,
! [X16,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),plus_plus_nat(X16,X15))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_892_le__add1) ).
fof(f8133,plain,
spl63_178,
inference(avatar_split_clause,[],[f4321,f8131]) ).
fof(f8131,plain,
( spl63_178
<=> ! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_178])]) ).
fof(f4321,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X1,X0))),
inference(cnf_transformation,[],[f1541]) ).
fof(f1541,plain,
! [X0,X1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),plus_plus_nat(X1,X0))),
inference(rectify,[],[f922]) ).
fof(f922,axiom,
! [X16,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),plus_plus_nat(X15,X16))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_893_le__add2) ).
fof(f8129,plain,
spl63_177,
inference(avatar_split_clause,[],[f4320,f8127]) ).
fof(f8127,plain,
( spl63_177
<=> ! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_177])]) ).
fof(f4320,plain,
! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X0)),
inference(cnf_transformation,[],[f1540]) ).
fof(f1540,plain,
! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X0)),
inference(rectify,[],[f204]) ).
fof(f204,axiom,
! [X22,X23] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X22,X23)),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_not__add__less1) ).
fof(f8125,plain,
spl63_176,
inference(avatar_split_clause,[],[f4319,f8123]) ).
fof(f8123,plain,
( spl63_176
<=> ! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_176])]) ).
fof(f4319,plain,
! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X1)),
inference(cnf_transformation,[],[f1539]) ).
fof(f1539,plain,
! [X0,X1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X0,X1)),X1)),
inference(rectify,[],[f205]) ).
fof(f205,axiom,
! [X23,X22] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,plus_plus_nat(X23,X22)),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_not__add__less2) ).
fof(f8121,plain,
spl63_175,
inference(avatar_split_clause,[],[f4162,f8119]) ).
fof(f8119,plain,
( spl63_175
<=> ! [X0] :
( zero_zero_real = X0
| zero_zero_real != plus_plus_real(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_175])]) ).
fof(f4162,plain,
! [X0] :
( zero_zero_real = X0
| zero_zero_real != plus_plus_real(X0,X0) ),
inference(cnf_transformation,[],[f3255]) ).
fof(f3255,plain,
! [X0] :
( ( zero_zero_real = plus_plus_real(X0,X0)
| zero_zero_real != X0 )
& ( zero_zero_real = X0
| zero_zero_real != plus_plus_real(X0,X0) ) ),
inference(nnf_transformation,[],[f1454]) ).
fof(f1454,plain,
! [X0] :
( zero_zero_real = plus_plus_real(X0,X0)
<=> zero_zero_real = X0 ),
inference(rectify,[],[f119]) ).
fof(f119,axiom,
! [X5] :
( zero_zero_real = plus_plus_real(X5,X5)
<=> zero_zero_real = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_double__eq__0__iff) ).
fof(f8117,plain,
spl63_174,
inference(avatar_split_clause,[],[f4123,f8115]) ).
fof(f8115,plain,
( spl63_174
<=> ! [X0] :
( sP0(X0)
| ~ hBOOL(hAPP_int_bool(zprime,X0))
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_174])]) ).
fof(f4123,plain,
! [X0] :
( sP0(X0)
| ~ hBOOL(hAPP_int_bool(zprime,X0))
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3241]) ).
fof(f8113,plain,
spl63_173,
inference(avatar_split_clause,[],[f4090,f8111]) ).
fof(f8111,plain,
( spl63_173
<=> ! [X0] :
( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_173])]) ).
fof(f4090,plain,
! [X0] :
( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2374]) ).
fof(f2374,plain,
! [X0] :
( hAPP_nat_int(power_power_int(X0),one_one_nat) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1414]) ).
fof(f1414,plain,
! [X0] :
( is_int(X0)
=> hAPP_nat_int(power_power_int(X0),one_one_nat) = X0 ),
inference(rectify,[],[f244]) ).
fof(f244,axiom,
! [X63] :
( is_int(X63)
=> hAPP_nat_int(power_power_int(X63),one_one_nat) = X63 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_power__one__right) ).
fof(f8109,plain,
spl63_172,
inference(avatar_split_clause,[],[f4064,f8107]) ).
fof(f8107,plain,
( spl63_172
<=> ! [X0] :
( fFalse = X0
| fTrue = X0
| ~ is_bool(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_172])]) ).
fof(f4064,plain,
! [X0] :
( fFalse = X0
| fTrue = X0
| ~ is_bool(X0) ),
inference(cnf_transformation,[],[f2347]) ).
fof(f2347,plain,
! [X0] :
( fFalse = X0
| fTrue = X0
| ~ is_bool(X0) ),
inference(flattening,[],[f2346]) ).
fof(f2346,plain,
! [X0] :
( fFalse = X0
| fTrue = X0
| ~ is_bool(X0) ),
inference(ennf_transformation,[],[f1391]) ).
fof(f1391,plain,
! [X0] :
( is_bool(X0)
=> ( fFalse = X0
| fTrue = X0 ) ),
inference(rectify,[],[f1229]) ).
fof(f1229,axiom,
! [X401] :
( is_bool(X401)
=> ( fFalse = X401
| fTrue = X401 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Int__Oint_T) ).
fof(f8105,plain,
spl63_171,
inference(avatar_split_clause,[],[f4016,f8103]) ).
fof(f8103,plain,
( spl63_171
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_171])]) ).
fof(f4016,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,X0))),
inference(cnf_transformation,[],[f1351]) ).
fof(f1351,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),times_times_nat(X0,X0))),
inference(rectify,[],[f873]) ).
fof(f873,axiom,
! [X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),times_times_nat(X15,X15))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_le__square) ).
fof(f8101,plain,
( spl63_170
| ~ spl63_9
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7620,f7515,f7051,f8098]) ).
fof(f8098,plain,
( spl63_170
<=> t = number_number_of_int(t) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_170])]) ).
fof(f7051,plain,
( spl63_9
<=> is_int(t) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_9])]) ).
fof(f7620,plain,
( t = number_number_of_int(t)
| ~ spl63_9
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7053]) ).
fof(f7053,plain,
( is_int(t)
| ~ spl63_9 ),
inference(avatar_component_clause,[],[f7051]) ).
fof(f8096,plain,
spl63_169,
inference(avatar_split_clause,[],[f4013,f8094]) ).
fof(f8094,plain,
( spl63_169
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),plus_plus_nat(X0,one_one_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_169])]) ).
fof(f4013,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),plus_plus_nat(X0,one_one_nat))),
inference(cnf_transformation,[],[f1348]) ).
fof(f1348,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),plus_plus_nat(X0,one_one_nat))),
inference(rectify,[],[f299]) ).
fof(f299,axiom,
! [X80] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X80),plus_plus_nat(X80,one_one_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_less__add__one) ).
fof(f8092,plain,
spl63_168,
inference(avatar_split_clause,[],[f4012,f8090]) ).
fof(f8090,plain,
( spl63_168
<=> ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),plus_plus_real(X0,one_one_real))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_168])]) ).
fof(f4012,plain,
! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),plus_plus_real(X0,one_one_real))),
inference(cnf_transformation,[],[f1347]) ).
fof(f1347,plain,
! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),plus_plus_real(X0,one_one_real))),
inference(rectify,[],[f300]) ).
fof(f300,axiom,
! [X80] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X80),plus_plus_real(X80,one_one_real))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_less__add__one) ).
fof(f8088,plain,
spl63_167,
inference(avatar_split_clause,[],[f4011,f8086]) ).
fof(f4011,plain,
! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X0))),
inference(cnf_transformation,[],[f1346]) ).
fof(f1346,plain,
! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X0,X0))),
inference(rectify,[],[f562]) ).
fof(f562,axiom,
! [X249] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,zero_zero_real),times_times_real(X249,X249))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_zero__le__square) ).
fof(f8084,plain,
spl63_166,
inference(avatar_split_clause,[],[f4007,f8082]) ).
fof(f8082,plain,
( spl63_166
<=> ! [X0] : hAPP_nat_real(semiri132038758t_real,X0) = number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_166])]) ).
fof(f4007,plain,
! [X0] : hAPP_nat_real(semiri132038758t_real,X0) = number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(cnf_transformation,[],[f1342]) ).
fof(f1342,plain,
! [X0] : hAPP_nat_real(semiri132038758t_real,X0) = number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(rectify,[],[f161]) ).
fof(f161,axiom,
! [X41] : number267125858f_real(hAPP_nat_int(semiri1621563631at_int,X41)) = hAPP_nat_real(semiri132038758t_real,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_number__of__int) ).
fof(f8080,plain,
spl63_165,
inference(avatar_split_clause,[],[f4005,f8078]) ).
fof(f4005,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(cnf_transformation,[],[f1340]) ).
fof(f1340,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(rectify,[],[f1188]) ).
fof(f1188,axiom,
! [X15] : hAPP_nat_int(semiri1621563631at_int,X15) = abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_abs__int__eq) ).
fof(f8076,plain,
spl63_164,
inference(avatar_split_clause,[],[f4002,f8074]) ).
fof(f8074,plain,
( spl63_164
<=> ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,times_times_real(X0,X0)),zero_zero_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_164])]) ).
fof(f4002,plain,
! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,times_times_real(X0,X0)),zero_zero_real)),
inference(cnf_transformation,[],[f1337]) ).
fof(f1337,plain,
! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,times_times_real(X0,X0)),zero_zero_real)),
inference(rectify,[],[f791]) ).
fof(f791,axiom,
! [X377] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,times_times_real(X377,X377)),zero_zero_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_not__square__less__zero) ).
fof(f8072,plain,
spl63_163,
inference(avatar_split_clause,[],[f3998,f8070]) ).
fof(f8070,plain,
( spl63_163
<=> ! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X0)),zero_zero_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_163])]) ).
fof(f3998,plain,
! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X0)),zero_zero_real)),
inference(cnf_transformation,[],[f1333]) ).
fof(f1333,plain,
! [X0] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X0)),zero_zero_real)),
inference(rectify,[],[f318]) ).
fof(f318,axiom,
! [X88] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_nat_real(semiri132038758t_real,X88)),zero_zero_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_of__nat__less__0__iff) ).
fof(f8068,plain,
spl63_162,
inference(avatar_split_clause,[],[f3845,f8065]) ).
fof(f8065,plain,
( spl63_162
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_162])]) ).
fof(f3845,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat))),
inference(cnf_transformation,[],[f196]) ).
fof(f196,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),plus_plus_nat(one_one_nat,one_one_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_zero__less__two) ).
fof(f8063,plain,
spl63_161,
inference(avatar_split_clause,[],[f3844,f8060]) ).
fof(f8060,plain,
( spl63_161
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,one_one_real))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_161])]) ).
fof(f3844,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,one_one_real))),
inference(cnf_transformation,[],[f197]) ).
fof(f197,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),plus_plus_real(one_one_real,one_one_real))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_zero__less__two) ).
fof(f8047,plain,
( spl63_160
| ~ spl63_10
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7619,f7515,f7056,f8044]) ).
fof(f8044,plain,
( spl63_160
<=> s = number_number_of_int(s) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_160])]) ).
fof(f7056,plain,
( spl63_10
<=> is_int(s) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_10])]) ).
fof(f7619,plain,
( s = number_number_of_int(s)
| ~ spl63_10
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7058]) ).
fof(f7058,plain,
( is_int(s)
| ~ spl63_10 ),
inference(avatar_component_clause,[],[f7056]) ).
fof(f8029,plain,
spl63_159,
inference(avatar_split_clause,[],[f5582,f8027]) ).
fof(f8027,plain,
( spl63_159
<=> ! [X0] :
( is_int(minus_minus_int(plus_plus_int(X0,X0),min))
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_159])]) ).
fof(f5582,plain,
! [X0] :
( is_int(minus_minus_int(plus_plus_int(X0,X0),min))
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f3749,f5578]) ).
fof(f3749,plain,
! [X0] :
( is_int(bit1(X0))
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2322]) ).
fof(f2322,plain,
! [X0] :
( is_int(bit1(X0))
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( is_int(X0)
=> is_int(bit1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_OBit1) ).
fof(f8025,plain,
spl63_158,
inference(avatar_split_clause,[],[f3751,f8023]) ).
fof(f8023,plain,
( spl63_158
<=> ! [X0,X1] :
( is_int(plus_plus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_158])]) ).
fof(f3751,plain,
! [X0,X1] :
( is_int(plus_plus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2324]) ).
fof(f2324,plain,
! [X0,X1] :
( is_int(plus_plus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2323]) ).
fof(f2323,plain,
! [X0,X1] :
( is_int(plus_plus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> is_int(plus_plus_int(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).
fof(f7987,plain,
( spl63_157
| ~ spl63_8
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7618,f7515,f7046,f7984]) ).
fof(f7984,plain,
( spl63_157
<=> s1 = number_number_of_int(s1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_157])]) ).
fof(f7046,plain,
( spl63_8
<=> is_int(s1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_8])]) ).
fof(f7618,plain,
( s1 = number_number_of_int(s1)
| ~ spl63_8
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7048]) ).
fof(f7048,plain,
( is_int(s1)
| ~ spl63_8 ),
inference(avatar_component_clause,[],[f7046]) ).
fof(f7903,plain,
( spl63_156
| ~ spl63_5
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7617,f7515,f7031,f7900]) ).
fof(f7900,plain,
( spl63_156
<=> m1 = number_number_of_int(m1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_156])]) ).
fof(f7031,plain,
( spl63_5
<=> is_int(m1) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_5])]) ).
fof(f7617,plain,
( m1 = number_number_of_int(m1)
| ~ spl63_5
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7033]) ).
fof(f7033,plain,
( is_int(m1)
| ~ spl63_5 ),
inference(avatar_component_clause,[],[f7031]) ).
fof(f7750,plain,
spl63_155,
inference(avatar_split_clause,[],[f6457,f7747]) ).
fof(f7747,plain,
( spl63_155
<=> one_one_nat = nat(number_number_of_int(minus_minus_int(pls,min))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_155])]) ).
fof(f6457,plain,
one_one_nat = nat(number_number_of_int(minus_minus_int(pls,min))),
inference(forward_demodulation,[],[f5601,f5593]) ).
fof(f5601,plain,
one_one_nat = nat(number_number_of_int(minus_minus_int(plus_plus_int(pls,pls),min))),
inference(definition_unfolding,[],[f3795,f3978,f5578]) ).
fof(f3795,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(cnf_transformation,[],[f175]) ).
fof(f175,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_semiring__numeral__1__eq__1) ).
fof(f7745,plain,
spl63_154,
inference(avatar_split_clause,[],[f5686,f7743]) ).
fof(f7743,plain,
( spl63_154
<=> ! [X0] : pls != plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_154])]) ).
fof(f5686,plain,
! [X0] : pls != plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(definition_unfolding,[],[f3996,f3772]) ).
fof(f3996,plain,
! [X0] : zero_zero_int != plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f1331]) ).
fof(f1331,plain,
! [X0] : zero_zero_int != plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(rectify,[],[f158]) ).
fof(f158,axiom,
! [X17] : zero_zero_int != plus_plus_int(plus_plus_int(one_one_int,X17),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_odd__nonzero) ).
fof(f7741,plain,
spl63_153,
inference(avatar_split_clause,[],[f5683,f7739]) ).
fof(f7737,plain,
spl63_152,
inference(avatar_split_clause,[],[f5676,f7735]) ).
fof(f7735,plain,
( spl63_152
<=> ! [X0] : pls != minus_minus_int(plus_plus_int(X0,X0),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_152])]) ).
fof(f5676,plain,
! [X0] : pls != minus_minus_int(plus_plus_int(X0,X0),min),
inference(definition_unfolding,[],[f3910,f5578]) ).
fof(f3910,plain,
! [X0] : bit1(X0) != pls,
inference(cnf_transformation,[],[f1245]) ).
fof(f1245,plain,
! [X0] : bit1(X0) != pls,
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X31] : pls != bit1(X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rel__simps_I39_J) ).
fof(f7733,plain,
( spl63_151
| ~ spl63_11
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7616,f7515,f7061,f7730]) ).
fof(f7730,plain,
( spl63_151
<=> m = number_number_of_int(m) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_151])]) ).
fof(f7061,plain,
( spl63_11
<=> is_int(m) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_11])]) ).
fof(f7616,plain,
( m = number_number_of_int(m)
| ~ spl63_11
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7063]) ).
fof(f7063,plain,
( is_int(m)
| ~ spl63_11 ),
inference(avatar_component_clause,[],[f7061]) ).
fof(f7728,plain,
spl63_150,
inference(avatar_split_clause,[],[f5586,f7725]) ).
fof(f7725,plain,
( spl63_150
<=> min = minus_minus_int(plus_plus_int(min,min),min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_150])]) ).
fof(f5586,plain,
min = minus_minus_int(plus_plus_int(min,min),min),
inference(definition_unfolding,[],[f3774,f5578]) ).
fof(f3774,plain,
min = bit1(min),
inference(cnf_transformation,[],[f1046]) ).
fof(f1046,axiom,
min = bit1(min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_Bit1__Min) ).
fof(f7723,plain,
spl63_149,
inference(avatar_split_clause,[],[f4611,f7721]) ).
fof(f7721,plain,
( spl63_149
<=> ! [X0,X1] :
( sP8(X0,X1)
| ~ is_int(X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_149])]) ).
fof(f4611,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3185]) ).
fof(f3185,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(definition_folding,[],[f2668,f3184,f3183]) ).
fof(f2668,plain,
! [X0,X1] :
( ( one_one_int = times_times_int(X0,X1)
<=> ( ( number_number_of_int(min) = X1
& number_number_of_int(min) = X0 )
| ( one_one_int = X1
& one_one_int = X0 ) ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(flattening,[],[f2667]) ).
fof(f2667,plain,
! [X0,X1] :
( ( one_one_int = times_times_int(X0,X1)
<=> ( ( number_number_of_int(min) = X1
& number_number_of_int(min) = X0 )
| ( one_one_int = X1
& one_one_int = X0 ) ) )
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1753]) ).
fof(f1753,plain,
! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> ( one_one_int = times_times_int(X0,X1)
<=> ( ( number_number_of_int(min) = X1
& number_number_of_int(min) = X0 )
| ( one_one_int = X1
& one_one_int = X0 ) ) ) ),
inference(rectify,[],[f1058]) ).
fof(f1058,axiom,
! [X29,X18] :
( ( is_int(X18)
& is_int(X29) )
=> ( one_one_int = times_times_int(X29,X18)
<=> ( ( number_number_of_int(min) = X18
& number_number_of_int(min) = X29 )
| ( one_one_int = X18
& one_one_int = X29 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_zmult__eq__1__iff) ).
fof(f7719,plain,
spl63_148,
inference(avatar_split_clause,[],[f4318,f7717]) ).
fof(f7717,plain,
( spl63_148
<=> ! [X0,X1] : plus_plus_real(minus_minus_real(X0,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_148])]) ).
fof(f4318,plain,
! [X0,X1] : plus_plus_real(minus_minus_real(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f1538]) ).
fof(f1538,plain,
! [X0,X1] : plus_plus_real(minus_minus_real(X0,X1),X1) = X0,
inference(rectify,[],[f634]) ).
fof(f634,axiom,
! [X302,X303] : plus_plus_real(minus_minus_real(X302,X303),X303) = X302,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_diff__add__cancel) ).
fof(f7715,plain,
spl63_147,
inference(avatar_split_clause,[],[f4317,f7713]) ).
fof(f7713,plain,
( spl63_147
<=> ! [X0,X1] : minus_minus_nat(plus_plus_nat(X0,X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_147])]) ).
fof(f4317,plain,
! [X0,X1] : minus_minus_nat(plus_plus_nat(X0,X1),X0) = X1,
inference(cnf_transformation,[],[f1537]) ).
fof(f1537,plain,
! [X0,X1] : minus_minus_nat(plus_plus_nat(X0,X1),X0) = X1,
inference(rectify,[],[f733]) ).
fof(f733,axiom,
! [X16,X15] : minus_minus_nat(plus_plus_nat(X16,X15),X16) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_diff__add__inverse) ).
fof(f7711,plain,
spl63_146,
inference(avatar_split_clause,[],[f4316,f7709]) ).
fof(f7709,plain,
( spl63_146
<=> ! [X0,X1] : minus_minus_nat(plus_plus_nat(X0,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_146])]) ).
fof(f4316,plain,
! [X0,X1] : minus_minus_nat(plus_plus_nat(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f1536]) ).
fof(f1536,plain,
! [X0,X1] : minus_minus_nat(plus_plus_nat(X0,X1),X1) = X0,
inference(rectify,[],[f732]) ).
fof(f732,axiom,
! [X15,X16] : minus_minus_nat(plus_plus_nat(X15,X16),X16) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_diff__add__inverse2) ).
fof(f7707,plain,
spl63_145,
inference(avatar_split_clause,[],[f4315,f7705]) ).
fof(f7705,plain,
( spl63_145
<=> ! [X0,X1] : minus_minus_real(plus_plus_real(X0,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_145])]) ).
fof(f4315,plain,
! [X0,X1] : minus_minus_real(plus_plus_real(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f1535]) ).
fof(f1535,plain,
! [X0,X1] : minus_minus_real(plus_plus_real(X0,X1),X1) = X0,
inference(rectify,[],[f632]) ).
fof(f632,axiom,
! [X300,X301] : minus_minus_real(plus_plus_real(X300,X301),X301) = X300,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_add__diff__cancel) ).
fof(f7703,plain,
spl63_144,
inference(avatar_split_clause,[],[f4313,f7701]) ).
fof(f7701,plain,
( spl63_144
<=> ! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_144])]) ).
fof(f4313,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[],[f1533]) ).
fof(f1533,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(rectify,[],[f443]) ).
fof(f443,axiom,
! [X156,X157] : times_times_int(X156,X157) = times_times_int(X157,X156),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f7699,plain,
spl63_143,
inference(avatar_split_clause,[],[f4311,f7697]) ).
fof(f7695,plain,
spl63_142,
inference(avatar_split_clause,[],[f4309,f7693]) ).
fof(f7693,plain,
( spl63_142
<=> ! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_142])]) ).
fof(f4309,plain,
! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(cnf_transformation,[],[f1529]) ).
fof(f1529,plain,
! [X0,X1] : times_times_nat(X0,X1) = times_times_nat(X1,X0),
inference(rectify,[],[f444]) ).
fof(f444,axiom,
! [X156,X157] : times_times_nat(X156,X157) = times_times_nat(X157,X156),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f7691,plain,
spl63_141,
inference(avatar_split_clause,[],[f4307,f7689]) ).
fof(f7689,plain,
( spl63_141
<=> ! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_141])]) ).
fof(f4307,plain,
! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(cnf_transformation,[],[f1527]) ).
fof(f1527,plain,
! [X0,X1] : plus_plus_nat(X0,X1) = plus_plus_nat(X1,X0),
inference(rectify,[],[f379]) ).
fof(f379,axiom,
! [X126,X127] : plus_plus_nat(X126,X127) = plus_plus_nat(X127,X126),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f7687,plain,
( spl63_140
| ~ spl63_12
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7612,f7515,f7066,f7684]) ).
fof(f7612,plain,
( min = number_number_of_int(min)
| ~ spl63_12
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7068]) ).
fof(f7068,plain,
( is_int(min)
| ~ spl63_12 ),
inference(avatar_component_clause,[],[f7066]) ).
fof(f7682,plain,
spl63_139,
inference(avatar_split_clause,[],[f4305,f7680]) ).
fof(f7680,plain,
( spl63_139
<=> ! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_139])]) ).
fof(f4305,plain,
! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0),
inference(cnf_transformation,[],[f1525]) ).
fof(f1525,plain,
! [X0,X1] : times_times_real(X0,X1) = times_times_real(X1,X0),
inference(rectify,[],[f1007]) ).
fof(f1007,axiom,
! [X17,X14] : times_times_real(X17,X14) = times_times_real(X14,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_real__mult__commute) ).
fof(f7678,plain,
spl63_138,
inference(avatar_split_clause,[],[f4304,f7676]) ).
fof(f4304,plain,
! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(cnf_transformation,[],[f1524]) ).
fof(f1524,plain,
! [X0,X1] : plus_plus_real(X0,X1) = plus_plus_real(X1,X0),
inference(rectify,[],[f380]) ).
fof(f380,axiom,
! [X126,X127] : plus_plus_real(X126,X127) = plus_plus_real(X127,X126),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f7674,plain,
spl63_137,
inference(avatar_split_clause,[],[f4303,f7672]) ).
fof(f7672,plain,
( spl63_137
<=> ! [X0,X1] : zero_zero_nat = minus_minus_nat(X0,plus_plus_nat(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_137])]) ).
fof(f4303,plain,
! [X0,X1] : zero_zero_nat = minus_minus_nat(X0,plus_plus_nat(X0,X1)),
inference(cnf_transformation,[],[f1523]) ).
fof(f1523,plain,
! [X0,X1] : zero_zero_nat = minus_minus_nat(X0,plus_plus_nat(X0,X1)),
inference(rectify,[],[f800]) ).
fof(f800,axiom,
! [X16,X15] : zero_zero_nat = minus_minus_nat(X16,plus_plus_nat(X16,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_diff__add__0) ).
fof(f7670,plain,
spl63_136,
inference(avatar_split_clause,[],[f4286,f7668]) ).
fof(f7668,plain,
( spl63_136
<=> ! [X4,X0] :
( is_int(sK40(X0))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_136])]) ).
fof(f4286,plain,
! [X0,X4] :
( is_int(sK40(X0))
| ~ hBOOL(hAPP_nat_bool(X0,X4)) ),
inference(cnf_transformation,[],[f3327]) ).
fof(f7666,plain,
spl63_135,
inference(avatar_split_clause,[],[f4279,f7664]) ).
fof(f7664,plain,
( spl63_135
<=> ! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| is_int(sK35(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_135])]) ).
fof(f4279,plain,
! [X0,X1] :
( hBOOL(hAPP_nat_bool(X0,X1))
| is_int(sK35(X0)) ),
inference(cnf_transformation,[],[f3317]) ).
fof(f7662,plain,
spl63_134,
inference(avatar_split_clause,[],[f4086,f7660]) ).
fof(f7660,plain,
( spl63_134
<=> ! [X0] :
( times_times_int(one_one_int,X0) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_134])]) ).
fof(f4086,plain,
! [X0] :
( times_times_int(one_one_int,X0) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2370]) ).
fof(f2370,plain,
! [X0] :
( times_times_int(one_one_int,X0) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1410]) ).
fof(f1410,plain,
! [X0] :
( is_int(X0)
=> times_times_int(one_one_int,X0) = X0 ),
inference(rectify,[],[f699]) ).
fof(f699,axiom,
! [X333] :
( is_int(X333)
=> times_times_int(one_one_int,X333) = X333 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_mult__1__left) ).
fof(f7658,plain,
spl63_133,
inference(avatar_split_clause,[],[f4082,f7656]) ).
fof(f7656,plain,
( spl63_133
<=> ! [X0] :
( times_times_int(X0,one_one_int) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_133])]) ).
fof(f4082,plain,
! [X0] :
( times_times_int(X0,one_one_int) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2366]) ).
fof(f2366,plain,
! [X0] :
( times_times_int(X0,one_one_int) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1406]) ).
fof(f1406,plain,
! [X0] :
( is_int(X0)
=> times_times_int(X0,one_one_int) = X0 ),
inference(rectify,[],[f746]) ).
fof(f746,axiom,
! [X17] :
( is_int(X17)
=> times_times_int(X17,one_one_int) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_zmult__1__right) ).
fof(f7654,plain,
spl63_132,
inference(avatar_split_clause,[],[f4077,f7652]) ).
fof(f7652,plain,
( spl63_132
<=> ! [X0] :
( plus_plus_int(pls,X0) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_132])]) ).
fof(f4077,plain,
! [X0] :
( plus_plus_int(pls,X0) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2361]) ).
fof(f2361,plain,
! [X0] :
( plus_plus_int(pls,X0) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1401]) ).
fof(f1401,plain,
! [X0] :
( is_int(X0)
=> plus_plus_int(pls,X0) = X0 ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X21] :
( is_int(X21)
=> plus_plus_int(pls,X21) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add__Pls) ).
fof(f7650,plain,
spl63_131,
inference(avatar_split_clause,[],[f4072,f7648]) ).
fof(f7648,plain,
( spl63_131
<=> ! [X0] :
( plus_plus_int(X0,pls) = X0
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_131])]) ).
fof(f4072,plain,
! [X0] :
( plus_plus_int(X0,pls) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2356]) ).
fof(f2356,plain,
! [X0] :
( plus_plus_int(X0,pls) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1396]) ).
fof(f1396,plain,
! [X0] :
( is_int(X0)
=> plus_plus_int(X0,pls) = X0 ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X21] :
( is_int(X21)
=> plus_plus_int(X21,pls) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_add__Pls__right) ).
fof(f7646,plain,
spl63_130,
inference(avatar_split_clause,[],[f4070,f7644]) ).
fof(f4070,plain,
! [X0] :
( minus_minus_int(X0,pls) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2354]) ).
fof(f2354,plain,
! [X0] :
( minus_minus_int(X0,pls) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1394]) ).
fof(f1394,plain,
! [X0] :
( is_int(X0)
=> minus_minus_int(X0,pls) = X0 ),
inference(rectify,[],[f890]) ).
fof(f890,axiom,
! [X21] :
( is_int(X21)
=> minus_minus_int(X21,pls) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_diff__bin__simps_I1_J) ).
fof(f7638,plain,
( spl63_129
| ~ spl63_1
| ~ spl63_109 ),
inference(avatar_split_clause,[],[f7609,f7515,f7011,f7635]) ).
fof(f7011,plain,
( spl63_1
<=> is_int(one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_1])]) ).
fof(f7609,plain,
( one_one_int = number_number_of_int(one_one_int)
| ~ spl63_1
| ~ spl63_109 ),
inference(resolution,[],[f7516,f7013]) ).
fof(f7013,plain,
( is_int(one_one_int)
| ~ spl63_1 ),
inference(avatar_component_clause,[],[f7011]) ).
fof(f7603,plain,
spl63_128,
inference(avatar_split_clause,[],[f6460,f7600]) ).
fof(f7600,plain,
( spl63_128
<=> one_one_int = number_number_of_int(minus_minus_int(pls,min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_128])]) ).
fof(f6460,plain,
one_one_int = number_number_of_int(minus_minus_int(pls,min)),
inference(forward_demodulation,[],[f5604,f5593]) ).
fof(f5604,plain,
one_one_int = number_number_of_int(minus_minus_int(plus_plus_int(pls,pls),min)),
inference(definition_unfolding,[],[f3799,f5578]) ).
fof(f3799,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(cnf_transformation,[],[f54]) ).
fof(f54,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_semiring__norm_I110_J) ).
fof(f7598,plain,
spl63_127,
inference(avatar_split_clause,[],[f6454,f7595]) ).
fof(f7595,plain,
( spl63_127
<=> one_one_real = number267125858f_real(minus_minus_int(pls,min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_127])]) ).
fof(f6454,plain,
one_one_real = number267125858f_real(minus_minus_int(pls,min)),
inference(forward_demodulation,[],[f5598,f5593]) ).
fof(f5598,plain,
one_one_real = number267125858f_real(minus_minus_int(plus_plus_int(pls,pls),min)),
inference(definition_unfolding,[],[f3791,f5578]) ).
fof(f3791,plain,
one_one_real = number267125858f_real(bit1(pls)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
one_one_real = number267125858f_real(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_semiring__norm_I110_J) ).
fof(f7593,plain,
spl63_126,
inference(avatar_split_clause,[],[f6339,f7591]) ).
fof(f7591,plain,
( spl63_126
<=> ! [X1] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_126])]) ).
fof(f6339,plain,
! [X1] : ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X1),X1)),
inference(equality_resolution,[],[f4727]) ).
fof(f4727,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,X0),X1)) ),
inference(cnf_transformation,[],[f3449]) ).
fof(f7588,plain,
( ~ spl63_1
| spl63_125 ),
inference(avatar_split_clause,[],[f6217,f7585,f7011]) ).
fof(f7585,plain,
( spl63_125
<=> one_one_int = abs_abs_int(one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_125])]) ).
fof(f6217,plain,
( one_one_int = abs_abs_int(one_one_int)
| ~ is_int(one_one_int) ),
inference(equality_resolution,[],[f4110]) ).
fof(f4110,plain,
! [X0] :
( abs_abs_int(X0) = one_one_int
| one_one_int != X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3233]) ).
fof(f7583,plain,
spl63_124,
inference(avatar_split_clause,[],[f6206,f7580]) ).
fof(f7580,plain,
( spl63_124
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK62)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_124])]) ).
fof(f6206,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK62)),
inference(definition_unfolding,[],[f5574,f3772]) ).
fof(f5574,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK62)),
inference(cnf_transformation,[],[f3743]) ).
fof(f3743,plain,
( ! [X1] :
( sK62 = X1
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
& hBOOL(hAPP_int_bool(zcong(s1,sK62),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK62),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK62))
& is_int(sK62) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f3171,f3742]) ).
fof(f3742,plain,
( ? [X0] :
( ! [X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
& hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
& is_int(X0) )
=> ( ! [X1] :
( sK62 = X1
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
& hBOOL(hAPP_int_bool(zcong(s1,sK62),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK62),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK62))
& is_int(sK62) ) ),
introduced(choice_axiom,[]) ).
fof(f3171,plain,
? [X0] :
( ! [X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
& hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
& is_int(X0) ),
inference(flattening,[],[f3170]) ).
fof(f3170,plain,
? [X0] :
( ! [X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ is_int(X1) )
& hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
& is_int(X0) ),
inference(ennf_transformation,[],[f2320]) ).
fof(f2320,plain,
? [X0] :
( ! [X1] :
( is_int(X1)
=> ( ( hBOOL(hAPP_int_bool(zcong(s1,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
=> X0 = X1 ) )
& hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
& is_int(X0) ),
inference(rectify,[],[f1112]) ).
fof(f1112,axiom,
? [X152] :
( ! [X153] :
( is_int(X153)
=> ( ( hBOOL(hAPP_int_bool(zcong(s1,X153),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X153),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X153)) )
=> X152 = X153 ) )
& hBOOL(hAPP_int_bool(zcong(s1,X152),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X152),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X152))
& is_int(X152) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s) ).
fof(f7578,plain,
spl63_123,
inference(avatar_split_clause,[],[f5733,f7576]) ).
fof(f5733,plain,
! [X0] :
( is_int(minus_minus_int(X0,min))
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f4066,f3976]) ).
fof(f4066,plain,
! [X0] :
( is_int(succ(X0))
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2350]) ).
fof(f2350,plain,
! [X0] :
( is_int(succ(X0))
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( is_int(X0)
=> is_int(succ(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_Osucc) ).
fof(f7574,plain,
spl63_122,
inference(avatar_split_clause,[],[f5685,f7572]) ).
fof(f7572,plain,
( spl63_122
<=> ! [X0] : hBOOL(hAPP_int_bool(zcong(X0,pls),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_122])]) ).
fof(f5685,plain,
! [X0] : hBOOL(hAPP_int_bool(zcong(X0,pls),X0)),
inference(definition_unfolding,[],[f3994,f3772]) ).
fof(f3994,plain,
! [X0] : hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X0)),
inference(cnf_transformation,[],[f1329]) ).
fof(f1329,plain,
! [X0] : hBOOL(hAPP_int_bool(zcong(X0,zero_zero_int),X0)),
inference(rectify,[],[f1087]) ).
fof(f1087,axiom,
! [X15] : hBOOL(hAPP_int_bool(zcong(X15,zero_zero_int),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_zcong__id) ).
fof(f7570,plain,
spl63_121,
inference(avatar_split_clause,[],[f5670,f7567]) ).
fof(f7567,plain,
( spl63_121
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK26)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_121])]) ).
fof(f5670,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),sK26)),
inference(definition_unfolding,[],[f3894,f3772]) ).
fof(f3894,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK26)),
inference(cnf_transformation,[],[f3219]) ).
fof(f3219,plain,
( hBOOL(hAPP_int_bool(zcong(s1,sK26),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK26),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK26))
& is_int(sK26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f2331,f3218]) ).
fof(f3218,plain,
( ? [X0] :
( hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
& is_int(X0) )
=> ( hBOOL(hAPP_int_bool(zcong(s1,sK26),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK26),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK26))
& is_int(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f2331,plain,
? [X0] :
( hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
& is_int(X0) ),
inference(flattening,[],[f2330]) ).
fof(f2330,plain,
? [X0] :
( hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
& is_int(X0) ),
inference(ennf_transformation,[],[f1239]) ).
fof(f1239,plain,
~ ! [X0] :
( is_int(X0)
=> ~ ( hBOOL(hAPP_int_bool(zcong(s1,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ),
inference(rectify,[],[f1114]) ).
fof(f1114,axiom,
~ ! [X393] :
( is_int(X393)
=> ~ ( hBOOL(hAPP_int_bool(zcong(s1,X393),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X393),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X393)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L) ).
fof(f7565,plain,
spl63_120,
inference(avatar_split_clause,[],[f5659,f7562]) ).
fof(f7562,plain,
( spl63_120
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),s)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_120])]) ).
fof(f5659,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),s)),
inference(definition_unfolding,[],[f3878,f3772]) ).
fof(f3878,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),s)),
inference(cnf_transformation,[],[f1067]) ).
fof(f1067,axiom,
( hBOOL(hAPP_int_bool(zcong(s1,s),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,s),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),s)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_s0p) ).
fof(f7560,plain,
spl63_119,
inference(avatar_split_clause,[],[f5617,f7557]) ).
fof(f7557,plain,
( spl63_119
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_119])]) ).
fof(f5617,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),one_one_int)),
inference(definition_unfolding,[],[f3834,f3772]) ).
fof(f3834,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(cnf_transformation,[],[f810]) ).
fof(f810,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f7555,plain,
spl63_118,
inference(avatar_split_clause,[],[f5615,f7552]) ).
fof(f7552,plain,
( spl63_118
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_118])]) ).
fof(f5615,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),one_one_int)),
inference(definition_unfolding,[],[f3828,f3772]) ).
fof(f3828,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(cnf_transformation,[],[f292]) ).
fof(f292,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_zero__less__one) ).
fof(f7550,plain,
~ spl63_117,
inference(avatar_split_clause,[],[f5612,f7547]) ).
fof(f7547,plain,
( spl63_117
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_117])]) ).
fof(f5612,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),pls)),
inference(definition_unfolding,[],[f3815,f3772]) ).
fof(f3815,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
inference(cnf_transformation,[],[f289]) ).
fof(f289,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_not__one__less__zero) ).
fof(f7545,plain,
spl63_116,
inference(avatar_split_clause,[],[f4393,f7543]) ).
fof(f7543,plain,
( spl63_116
<=> ! [X0,X1] :
( is_bool(hAPP_int_bool(X0,X1))
| ~ is_int(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_116])]) ).
fof(f4393,plain,
! [X0,X1] :
( is_bool(hAPP_int_bool(X0,X1))
| ~ is_int(X1) ),
inference(cnf_transformation,[],[f2421]) ).
fof(f2421,plain,
! [X0,X1] :
( is_bool(hAPP_int_bool(X0,X1))
| ~ is_int(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( is_int(X1)
=> is_bool(hAPP_int_bool(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool) ).
fof(f7541,plain,
spl63_115,
inference(avatar_split_clause,[],[f4302,f7539]) ).
fof(f7539,plain,
( spl63_115
<=> ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_115])]) ).
fof(f4302,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)),
inference(cnf_transformation,[],[f1522]) ).
fof(f1522,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X0),X1)),
inference(rectify,[],[f1153]) ).
fof(f1153,axiom,
! [X21,X15] : hBOOL(hAPP_int_bool(zcong(X21,X21),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_zcong__refl) ).
fof(f7537,plain,
spl63_114,
inference(avatar_split_clause,[],[f4301,f7535]) ).
fof(f7535,plain,
( spl63_114
<=> ! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_114])]) ).
fof(f4301,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)),
inference(cnf_transformation,[],[f1521]) ).
fof(f1521,plain,
! [X0,X1] : hBOOL(hAPP_int_bool(zcong(X0,X1),one_one_int)),
inference(rectify,[],[f1156]) ).
fof(f1156,axiom,
! [X151,X155] : hBOOL(hAPP_int_bool(zcong(X151,X155),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1127_zcong__1) ).
fof(f7533,plain,
spl63_113,
inference(avatar_split_clause,[],[f4300,f7531]) ).
fof(f7531,plain,
( spl63_113
<=> ! [X0,X1] : if_nat(fFalse,X0,X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_113])]) ).
fof(f4300,plain,
! [X0,X1] : if_nat(fFalse,X0,X1) = X1,
inference(cnf_transformation,[],[f1520]) ).
fof(f1520,plain,
! [X0,X1] : if_nat(fFalse,X0,X1) = X1,
inference(rectify,[],[f1231]) ).
fof(f1231,axiom,
! [X8,X10] : if_nat(fFalse,X8,X10) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).
fof(f7529,plain,
spl63_112,
inference(avatar_split_clause,[],[f4299,f7527]) ).
fof(f7527,plain,
( spl63_112
<=> ! [X0,X1] : if_nat(fTrue,X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_112])]) ).
fof(f4299,plain,
! [X0,X1] : if_nat(fTrue,X0,X1) = X0,
inference(cnf_transformation,[],[f1519]) ).
fof(f1519,plain,
! [X0,X1] : if_nat(fTrue,X0,X1) = X0,
inference(rectify,[],[f1230]) ).
fof(f1230,axiom,
! [X8,X10] : if_nat(fTrue,X8,X10) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T) ).
fof(f7525,plain,
spl63_111,
inference(avatar_split_clause,[],[f4121,f7523]) ).
fof(f7523,plain,
( spl63_111
<=> ! [X0] :
( sP0(X0)
| sK34(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_111])]) ).
fof(f4121,plain,
! [X0] :
( sP0(X0)
| sK34(X0) != X0 ),
inference(cnf_transformation,[],[f3239]) ).
fof(f7521,plain,
spl63_110,
inference(avatar_split_clause,[],[f4120,f7519]) ).
fof(f7519,plain,
( spl63_110
<=> ! [X0] :
( sP0(X0)
| one_one_int != sK34(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_110])]) ).
fof(f4120,plain,
! [X0] :
( sP0(X0)
| one_one_int != sK34(X0) ),
inference(cnf_transformation,[],[f3239]) ).
fof(f7517,plain,
spl63_109,
inference(avatar_split_clause,[],[f4069,f7515]) ).
fof(f4069,plain,
! [X0] :
( number_number_of_int(X0) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2353]) ).
fof(f2353,plain,
! [X0] :
( number_number_of_int(X0) = X0
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1393]) ).
fof(f1393,plain,
! [X0] :
( is_int(X0)
=> number_number_of_int(X0) = X0 ),
inference(rectify,[],[f206]) ).
fof(f206,axiom,
! [X21] :
( is_int(X21)
=> number_number_of_int(X21) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_number__of__is__id) ).
fof(f7513,plain,
spl63_108,
inference(avatar_split_clause,[],[f3995,f7511]) ).
fof(f7511,plain,
( spl63_108
<=> ! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_108])]) ).
fof(f3995,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
inference(cnf_transformation,[],[f1330]) ).
fof(f1330,plain,
! [X0] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X0)),
inference(rectify,[],[f477]) ).
fof(f477,axiom,
! [X14] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X14),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_zle__refl) ).
fof(f7509,plain,
spl63_107,
inference(avatar_split_clause,[],[f3993,f7507]) ).
fof(f7507,plain,
( spl63_107
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_107])]) ).
fof(f3993,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(cnf_transformation,[],[f1328]) ).
fof(f1328,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X0),X0)),
inference(rectify,[],[f872]) ).
fof(f872,axiom,
! [X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_le__refl) ).
fof(f7505,plain,
spl63_106,
inference(avatar_split_clause,[],[f3992,f7503]) ).
fof(f7503,plain,
( spl63_106
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_106])]) ).
fof(f3992,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X0)),
inference(cnf_transformation,[],[f1327]) ).
fof(f1327,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X0),X0)),
inference(rectify,[],[f1113]) ).
fof(f1113,axiom,
! [X8] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(dvd_dvd_nat,X8),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_dvd_Oorder__refl) ).
fof(f7501,plain,
spl63_105,
inference(avatar_split_clause,[],[f3991,f7499]) ).
fof(f7499,plain,
( spl63_105
<=> ! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_105])]) ).
fof(f3991,plain,
! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
inference(cnf_transformation,[],[f1326]) ).
fof(f1326,plain,
! [X0] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X0),X0)),
inference(rectify,[],[f1006]) ).
fof(f1006,axiom,
! [X14] : hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_eq_real,X14),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_real__le__refl) ).
fof(f7497,plain,
spl63_104,
inference(avatar_split_clause,[],[f3989,f7495]) ).
fof(f7495,plain,
( spl63_104
<=> ! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_104])]) ).
fof(f3989,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
inference(cnf_transformation,[],[f1324]) ).
fof(f1324,plain,
! [X0] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X0)),
inference(rectify,[],[f899]) ).
fof(f899,axiom,
! [X16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_less__eq__nat_Osimps_I1_J) ).
fof(f7493,plain,
spl63_103,
inference(avatar_split_clause,[],[f3985,f7491]) ).
fof(f7491,plain,
( spl63_103
<=> ! [X0] : hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_103])]) ).
fof(f3985,plain,
! [X0] : hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0,
inference(cnf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X0] : hAPP_nat_nat(power_power_nat(X0),one_one_nat) = X0,
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X63] : hAPP_nat_nat(power_power_nat(X63),one_one_nat) = X63,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_power__one__right) ).
fof(f7489,plain,
spl63_102,
inference(avatar_split_clause,[],[f3983,f7487]) ).
fof(f7487,plain,
( spl63_102
<=> ! [X0] : hAPP_nat_real(power_power_real(X0),one_one_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_102])]) ).
fof(f3983,plain,
! [X0] : hAPP_nat_real(power_power_real(X0),one_one_nat) = X0,
inference(cnf_transformation,[],[f1318]) ).
fof(f1318,plain,
! [X0] : hAPP_nat_real(power_power_real(X0),one_one_nat) = X0,
inference(rectify,[],[f246]) ).
fof(f246,axiom,
! [X63] : hAPP_nat_real(power_power_real(X63),one_one_nat) = X63,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_power__one__right) ).
fof(f7485,plain,
spl63_101,
inference(avatar_split_clause,[],[f3982,f7483]) ).
fof(f7483,plain,
( spl63_101
<=> ! [X0] : nat(hAPP_nat_int(semiri1621563631at_int,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_101])]) ).
fof(f3982,plain,
! [X0] : nat(hAPP_nat_int(semiri1621563631at_int,X0)) = X0,
inference(cnf_transformation,[],[f1317]) ).
fof(f1317,plain,
! [X0] : nat(hAPP_nat_int(semiri1621563631at_int,X0)) = X0,
inference(rectify,[],[f681]) ).
fof(f681,axiom,
! [X16] : nat(hAPP_nat_int(semiri1621563631at_int,X16)) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_nat__int) ).
fof(f7481,plain,
spl63_100,
inference(avatar_split_clause,[],[f3974,f7479]) ).
fof(f7479,plain,
( spl63_100
<=> ! [X0] : one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_100])]) ).
fof(f3974,plain,
! [X0] : one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat),
inference(cnf_transformation,[],[f1309]) ).
fof(f1309,plain,
! [X0] : one_one_int = hAPP_nat_int(power_power_int(X0),zero_zero_nat),
inference(rectify,[],[f319]) ).
fof(f319,axiom,
! [X89] : one_one_int = hAPP_nat_int(power_power_int(X89),zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_power__0) ).
fof(f7477,plain,
spl63_99,
inference(avatar_split_clause,[],[f3973,f7475]) ).
fof(f7475,plain,
( spl63_99
<=> ! [X0] : one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_99])]) ).
fof(f3973,plain,
! [X0] : one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0),
inference(cnf_transformation,[],[f1308]) ).
fof(f1308,plain,
! [X0] : one_one_int = hAPP_nat_int(power_power_int(one_one_int),X0),
inference(rectify,[],[f262]) ).
fof(f262,axiom,
! [X66] : one_one_int = hAPP_nat_int(power_power_int(one_one_int),X66),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_power__one) ).
fof(f7473,plain,
spl63_98,
inference(avatar_split_clause,[],[f3971,f7471]) ).
fof(f7471,plain,
( spl63_98
<=> ! [X0] : one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_98])]) ).
fof(f3971,plain,
! [X0] : one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat),
inference(cnf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X0] : one_one_nat = hAPP_nat_nat(power_power_nat(X0),zero_zero_nat),
inference(rectify,[],[f320]) ).
fof(f320,axiom,
! [X89] : one_one_nat = hAPP_nat_nat(power_power_nat(X89),zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_power__0) ).
fof(f7469,plain,
spl63_97,
inference(avatar_split_clause,[],[f3970,f7467]) ).
fof(f7467,plain,
( spl63_97
<=> ! [X0] : one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_97])]) ).
fof(f3970,plain,
! [X0] : one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0),
inference(cnf_transformation,[],[f1305]) ).
fof(f1305,plain,
! [X0] : one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X0),
inference(rectify,[],[f263]) ).
fof(f263,axiom,
! [X66] : one_one_nat = hAPP_nat_nat(power_power_nat(one_one_nat),X66),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_power__one) ).
fof(f7465,plain,
spl63_96,
inference(avatar_split_clause,[],[f3968,f7463]) ).
fof(f7463,plain,
( spl63_96
<=> ! [X0] : one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_96])]) ).
fof(f3968,plain,
! [X0] : one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat),
inference(cnf_transformation,[],[f1303]) ).
fof(f1303,plain,
! [X0] : one_one_real = hAPP_nat_real(power_power_real(X0),zero_zero_nat),
inference(rectify,[],[f321]) ).
fof(f321,axiom,
! [X89] : one_one_real = hAPP_nat_real(power_power_real(X89),zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_power__0) ).
fof(f7461,plain,
spl63_95,
inference(avatar_split_clause,[],[f3967,f7459]) ).
fof(f7459,plain,
( spl63_95
<=> ! [X0] : one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_95])]) ).
fof(f3967,plain,
! [X0] : one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0),
inference(cnf_transformation,[],[f1302]) ).
fof(f1302,plain,
! [X0] : one_one_real = hAPP_nat_real(power_power_real(one_one_real),X0),
inference(rectify,[],[f264]) ).
fof(f264,axiom,
! [X66] : one_one_real = hAPP_nat_real(power_power_real(one_one_real),X66),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_power__one) ).
fof(f7457,plain,
spl63_94,
inference(avatar_split_clause,[],[f3965,f7455]) ).
fof(f7455,plain,
( spl63_94
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_94])]) ).
fof(f3965,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
inference(cnf_transformation,[],[f1300]) ).
fof(f1300,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),X0)),
inference(rectify,[],[f215]) ).
fof(f215,axiom,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_less__irrefl__nat) ).
fof(f7453,plain,
spl63_93,
inference(avatar_split_clause,[],[f3962,f7451]) ).
fof(f7451,plain,
( spl63_93
<=> ! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_93])]) ).
fof(f3962,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
inference(cnf_transformation,[],[f1297]) ).
fof(f1297,plain,
! [X0] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X0),zero_zero_nat)),
inference(rectify,[],[f232]) ).
fof(f232,axiom,
! [X16] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X16),zero_zero_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_not__less0) ).
fof(f7449,plain,
spl63_92,
inference(avatar_split_clause,[],[f3832,f7446]) ).
fof(f7446,plain,
( spl63_92
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_92])]) ).
fof(f3832,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(cnf_transformation,[],[f434]) ).
fof(f434,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_tpos) ).
fof(f7444,plain,
spl63_91,
inference(avatar_split_clause,[],[f3831,f7441]) ).
fof(f7441,plain,
( spl63_91
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_91])]) ).
fof(f3831,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,min),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_rel__simps_I23_J) ).
fof(f7439,plain,
spl63_90,
inference(avatar_split_clause,[],[f3827,f7436]) ).
fof(f7436,plain,
( spl63_90
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_90])]) ).
fof(f3827,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
fof(f7434,plain,
spl63_89,
inference(avatar_split_clause,[],[f3825,f7431]) ).
fof(f7431,plain,
( spl63_89
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_89])]) ).
fof(f3825,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
inference(cnf_transformation,[],[f1031]) ).
fof(f1031,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_rel__simps_I6_J) ).
fof(f7429,plain,
spl63_88,
inference(avatar_split_clause,[],[f3824,f7426]) ).
fof(f7426,plain,
( spl63_88
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_88])]) ).
fof(f3824,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
inference(cnf_transformation,[],[f293]) ).
fof(f293,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),one_one_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_zero__less__one) ).
fof(f7424,plain,
spl63_87,
inference(avatar_split_clause,[],[f3823,f7421]) ).
fof(f7421,plain,
( spl63_87
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_87])]) ).
fof(f3823,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_n0) ).
fof(f7419,plain,
spl63_86,
inference(avatar_split_clause,[],[f3822,f7416]) ).
fof(f7416,plain,
( spl63_86
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_86])]) ).
fof(f3822,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
inference(cnf_transformation,[],[f200]) ).
fof(f200,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),tn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_tn0) ).
fof(f7414,plain,
spl63_85,
inference(avatar_split_clause,[],[f3821,f7411]) ).
fof(f7411,plain,
( spl63_85
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_85])]) ).
fof(f3821,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
inference(cnf_transformation,[],[f294]) ).
fof(f294,axiom,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),one_one_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_zero__less__one) ).
fof(f7409,plain,
spl63_84,
inference(avatar_split_clause,[],[f3820,f7406]) ).
fof(f7406,plain,
( spl63_84
<=> tn = minus_minus_nat(nat(t),one_one_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_84])]) ).
fof(f3820,plain,
tn = minus_minus_nat(nat(t),one_one_nat),
inference(cnf_transformation,[],[f439]) ).
fof(f439,axiom,
tn = minus_minus_nat(nat(t),one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_tn) ).
fof(f7404,plain,
~ spl63_83,
inference(avatar_split_clause,[],[f3819,f7401]) ).
fof(f3819,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
inference(cnf_transformation,[],[f1038]) ).
fof(f1038,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),min)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_rel__simps_I20_J) ).
fof(f7399,plain,
~ spl63_82,
inference(avatar_split_clause,[],[f3817,f7396]) ).
fof(f7396,plain,
( spl63_82
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_82])]) ).
fof(f3817,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_rel__simps_I2_J) ).
fof(f7394,plain,
~ spl63_81,
inference(avatar_split_clause,[],[f3816,f7391]) ).
fof(f7391,plain,
( spl63_81
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_81])]) ).
fof(f3816,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
inference(cnf_transformation,[],[f1032]) ).
fof(f1032,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),min)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_rel__simps_I3_J) ).
fof(f7389,plain,
~ spl63_80,
inference(avatar_split_clause,[],[f3814,f7386]) ).
fof(f7386,plain,
( spl63_80
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_80])]) ).
fof(f3814,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)),
inference(cnf_transformation,[],[f1041]) ).
fof(f1041,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,min),min)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_rel__simps_I7_J) ).
fof(f7384,plain,
~ spl63_79,
inference(avatar_split_clause,[],[f3812,f7381]) ).
fof(f7381,plain,
( spl63_79
<=> hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_79])]) ).
fof(f3812,plain,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
inference(cnf_transformation,[],[f291]) ).
fof(f291,axiom,
~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,one_one_real),zero_zero_real)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_not__one__less__zero) ).
fof(f7378,plain,
spl63_78,
inference(avatar_split_clause,[],[f5581,f7376]) ).
fof(f7376,plain,
( spl63_78
<=> ! [X0] :
( is_int(plus_plus_int(X0,X0))
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_78])]) ).
fof(f5581,plain,
! [X0] :
( is_int(plus_plus_int(X0,X0))
| ~ is_int(X0) ),
inference(definition_unfolding,[],[f3748,f3979]) ).
fof(f3748,plain,
! [X0] :
( is_int(bit0(X0))
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2321]) ).
fof(f2321,plain,
! [X0] :
( is_int(bit0(X0))
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( is_int(X0)
=> is_int(bit0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_OBit0) ).
fof(f7373,plain,
( spl63_77
| ~ spl63_69
| ~ spl63_76 ),
inference(avatar_split_clause,[],[f7368,f7359,f7324,f7370]) ).
fof(f7324,plain,
( spl63_69
<=> pls = plus_plus_int(pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_69])]) ).
fof(f7359,plain,
( spl63_76
<=> pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_76])]) ).
fof(f7368,plain,
( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(minus_minus_int(minus_minus_int(pls,min),min))))
| ~ spl63_69
| ~ spl63_76 ),
inference(forward_demodulation,[],[f7367,f7326]) ).
fof(f7326,plain,
( pls = plus_plus_int(pls,pls)
| ~ spl63_69 ),
inference(avatar_component_clause,[],[f7324]) ).
fof(f7367,plain,
( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(minus_minus_int(minus_minus_int(plus_plus_int(pls,pls),min),min))))
| ~ spl63_69
| ~ spl63_76 ),
inference(forward_demodulation,[],[f7366,f7326]) ).
fof(f7366,plain,
( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(minus_minus_int(minus_minus_int(plus_plus_int(pls,plus_plus_int(pls,pls)),min),min))))
| ~ spl63_69
| ~ spl63_76 ),
inference(forward_demodulation,[],[f7365,f7326]) ).
fof(f7365,plain,
( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(minus_minus_int(minus_minus_int(plus_plus_int(pls,plus_plus_int(pls,plus_plus_int(pls,pls))),min),min))))
| ~ spl63_76 ),
inference(forward_demodulation,[],[f7364,f4311]) ).
fof(f7364,plain,
( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(minus_minus_int(minus_minus_int(plus_plus_int(pls,plus_plus_int(plus_plus_int(pls,pls),pls)),min),min))))
| ~ spl63_76 ),
inference(forward_demodulation,[],[f7363,f4982]) ).
fof(f7363,plain,
( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(minus_minus_int(minus_minus_int(plus_plus_int(plus_plus_int(pls,pls),plus_plus_int(pls,pls)),min),min))))
| ~ spl63_76 ),
inference(forward_demodulation,[],[f7361,f5687]) ).
fof(f7361,plain,
( pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min)))))
| ~ spl63_76 ),
inference(avatar_component_clause,[],[f7359]) ).
fof(f7362,plain,
spl63_76,
inference(avatar_split_clause,[],[f5579,f7359]) ).
fof(f5579,plain,
pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(minus_minus_int(plus_plus_int(pls,pls),min),minus_minus_int(plus_plus_int(pls,pls),min))))),
inference(definition_unfolding,[],[f3744,f3772,f3978,f3979,f5578]) ).
fof(f3744,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1235]) ).
fof(f1235,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f1234]) ).
fof(f1234,negated_conjecture,
~ ( zero_zero_int != hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) ),
inference(negated_conjecture,[],[f1233]) ).
fof(f1233,conjecture,
zero_zero_int != hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f7353,plain,
spl63_75,
inference(avatar_split_clause,[],[f6570,f7351]) ).
fof(f7351,plain,
( spl63_75
<=> ! [X0] : hAPP_nat_nat(semiri984289939at_nat,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_75])]) ).
fof(f6570,plain,
! [X0] : hAPP_nat_nat(semiri984289939at_nat,X0) = X0,
inference(forward_demodulation,[],[f6569,f3982]) ).
fof(f6569,plain,
! [X0] : nat(hAPP_nat_int(semiri1621563631at_int,X0)) = hAPP_nat_nat(semiri984289939at_nat,X0),
inference(forward_demodulation,[],[f5692,f4006]) ).
fof(f4006,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(cnf_transformation,[],[f1341]) ).
fof(f1341,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,X0) = number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(rectify,[],[f160]) ).
fof(f160,axiom,
! [X41] : hAPP_nat_int(semiri1621563631at_int,X41) = number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X41)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_number__of__int) ).
fof(f5692,plain,
! [X0] : hAPP_nat_nat(semiri984289939at_nat,X0) = nat(number_number_of_int(hAPP_nat_int(semiri1621563631at_int,X0))),
inference(definition_unfolding,[],[f4008,f3978]) ).
fof(f4008,plain,
! [X0] : hAPP_nat_nat(semiri984289939at_nat,X0) = number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(cnf_transformation,[],[f1343]) ).
fof(f1343,plain,
! [X0] : hAPP_nat_nat(semiri984289939at_nat,X0) = number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X0)),
inference(rectify,[],[f159]) ).
fof(f159,axiom,
! [X41] : number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,X41)) = hAPP_nat_nat(semiri984289939at_nat,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_number__of__int) ).
fof(f7349,plain,
spl63_74,
inference(avatar_split_clause,[],[f6282,f7346]) ).
fof(f6282,plain,
sP7(number_number_of_int(min),number_number_of_int(min)),
inference(equality_resolution,[],[f6281]) ).
fof(f6281,plain,
! [X1] :
( sP7(number_number_of_int(min),X1)
| number_number_of_int(min) != X1 ),
inference(equality_resolution,[],[f4610]) ).
fof(f4610,plain,
! [X0,X1] :
( sP7(X0,X1)
| number_number_of_int(min) != X0
| number_number_of_int(min) != X1 ),
inference(cnf_transformation,[],[f3389]) ).
fof(f7344,plain,
spl63_73,
inference(avatar_split_clause,[],[f5682,f7342]) ).
fof(f7342,plain,
( spl63_73
<=> ! [X0] : pls = minus_minus_int(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_73])]) ).
fof(f5682,plain,
! [X0] : pls = minus_minus_int(X0,X0),
inference(definition_unfolding,[],[f3930,f3772]) ).
fof(f3930,plain,
! [X0] : zero_zero_int = minus_minus_int(X0,X0),
inference(cnf_transformation,[],[f1265]) ).
fof(f1265,plain,
! [X0] : zero_zero_int = minus_minus_int(X0,X0),
inference(rectify,[],[f625]) ).
fof(f625,axiom,
! [X294] : zero_zero_int = minus_minus_int(X294,X294),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_diff__self) ).
fof(f7340,plain,
spl63_72,
inference(avatar_split_clause,[],[f5678,f7338]) ).
fof(f5678,plain,
! [X0] : pls = times_times_int(X0,pls),
inference(definition_unfolding,[],[f3926,f3772,f3772]) ).
fof(f3926,plain,
! [X0] : zero_zero_int = times_times_int(X0,zero_zero_int),
inference(cnf_transformation,[],[f1261]) ).
fof(f1261,plain,
! [X0] : zero_zero_int = times_times_int(X0,zero_zero_int),
inference(rectify,[],[f652]) ).
fof(f652,axiom,
! [X310] : zero_zero_int = times_times_int(X310,zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f7336,plain,
spl63_71,
inference(avatar_split_clause,[],[f5674,f7334]) ).
fof(f7334,plain,
( spl63_71
<=> ! [X0] : min != plus_plus_int(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_71])]) ).
fof(f5674,plain,
! [X0] : min != plus_plus_int(X0,X0),
inference(definition_unfolding,[],[f3908,f3979]) ).
fof(f3908,plain,
! [X0] : bit0(X0) != min,
inference(cnf_transformation,[],[f1243]) ).
fof(f1243,plain,
! [X0] : bit0(X0) != min,
inference(rectify,[],[f1042]) ).
fof(f1042,axiom,
! [X31] : min != bit0(X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_rel__simps_I42_J) ).
fof(f7332,plain,
spl63_70,
inference(avatar_split_clause,[],[f5608,f7329]) ).
fof(f7327,plain,
spl63_69,
inference(avatar_split_clause,[],[f5593,f7324]) ).
fof(f7321,plain,
spl63_68,
inference(avatar_split_clause,[],[f5589,f7318]) ).
fof(f7318,plain,
( spl63_68
<=> zero_zero_nat = nat(number_number_of_int(pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_68])]) ).
fof(f5589,plain,
zero_zero_nat = nat(number_number_of_int(pls)),
inference(definition_unfolding,[],[f3781,f3978]) ).
fof(f3781,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_nat__number__of__Pls) ).
fof(f7316,plain,
spl63_67,
inference(avatar_split_clause,[],[f4438,f7314]) ).
fof(f7314,plain,
( spl63_67
<=> ! [X0,X1] :
( sP6(X1,X0)
| ~ is_int(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_67])]) ).
fof(f4438,plain,
! [X0,X1] :
( sP6(X1,X0)
| ~ is_int(X1) ),
inference(cnf_transformation,[],[f3182]) ).
fof(f3182,plain,
! [X0,X1] :
( sP6(X1,X0)
| ~ is_int(X1) ),
inference(definition_folding,[],[f2446,f3181,f3180]) ).
fof(f2446,plain,
! [X0,X1] :
( ( hBOOL(hAPP_nat_bool(X0,nat(X1)))
<=> ( ( hBOOL(hAPP_nat_bool(X0,zero_zero_nat))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) )
& ! [X2] :
( hBOOL(hAPP_nat_bool(X0,X2))
| hAPP_nat_int(semiri1621563631at_int,X2) != X1 ) ) )
| ~ is_int(X1) ),
inference(ennf_transformation,[],[f1622]) ).
fof(f1622,plain,
! [X0,X1] :
( is_int(X1)
=> ( hBOOL(hAPP_nat_bool(X0,nat(X1)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
=> hBOOL(hAPP_nat_bool(X0,zero_zero_nat)) )
& ! [X2] :
( hAPP_nat_int(semiri1621563631at_int,X2) = X1
=> hBOOL(hAPP_nat_bool(X0,X2)) ) ) ) ),
inference(rectify,[],[f846]) ).
fof(f846,axiom,
! [X54,X55] :
( is_int(X55)
=> ( hBOOL(hAPP_nat_bool(X54,nat(X55)))
<=> ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X55),zero_zero_int))
=> hBOOL(hAPP_nat_bool(X54,zero_zero_nat)) )
& ! [X90] :
( hAPP_nat_int(semiri1621563631at_int,X90) = X55
=> hBOOL(hAPP_nat_bool(X54,X90)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_split__nat) ).
fof(f7312,plain,
spl63_66,
inference(avatar_split_clause,[],[f4424,f7310]) ).
fof(f7310,plain,
( spl63_66
<=> ! [X0,X1] :
( sP4(X1,X0)
| ~ is_int(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_66])]) ).
fof(f4424,plain,
! [X0,X1] :
( sP4(X1,X0)
| ~ is_int(X1) ),
inference(cnf_transformation,[],[f3179]) ).
fof(f3179,plain,
! [X0,X1] :
( sP4(X1,X0)
| ~ is_int(X1) ),
inference(definition_folding,[],[f2443,f3178,f3177]) ).
fof(f2443,plain,
! [X0,X1] :
( ( nat(X1) = X0
<=> ( ( zero_zero_nat = X0
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) )
& ( hAPP_nat_int(semiri1621563631at_int,X0) = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ) ) )
| ~ is_int(X1) ),
inference(ennf_transformation,[],[f1619]) ).
fof(f1619,plain,
! [X0,X1] :
( is_int(X1)
=> ( nat(X1) = X0
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> zero_zero_nat = X0 )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
=> hAPP_nat_int(semiri1621563631at_int,X0) = X1 ) ) ) ),
inference(rectify,[],[f770]) ).
fof(f770,axiom,
! [X29,X25] :
( is_int(X25)
=> ( nat(X25) = X29
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X25))
=> zero_zero_nat = X29 )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X25))
=> hAPP_nat_int(semiri1621563631at_int,X29) = X25 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_nat__eq__iff2) ).
fof(f7308,plain,
spl63_65,
inference(avatar_split_clause,[],[f4415,f7306]) ).
fof(f7306,plain,
( spl63_65
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_65])]) ).
fof(f4415,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f3176]) ).
fof(f3176,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ is_int(X0) ),
inference(definition_folding,[],[f2442,f3175,f3174]) ).
fof(f2442,plain,
! [X0,X1] :
( ( nat(X0) = X1
<=> ( ( zero_zero_nat = X1
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) )
& ( hAPP_nat_int(semiri1621563631at_int,X1) = X0
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0)) ) ) )
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1618]) ).
fof(f1618,plain,
! [X0,X1] :
( is_int(X0)
=> ( nat(X0) = X1
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> zero_zero_nat = X1 )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X0))
=> hAPP_nat_int(semiri1621563631at_int,X1) = X0 ) ) ) ),
inference(rectify,[],[f771]) ).
fof(f771,axiom,
! [X25,X29] :
( is_int(X25)
=> ( nat(X25) = X29
<=> ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X25))
=> zero_zero_nat = X29 )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X25))
=> hAPP_nat_int(semiri1621563631at_int,X29) = X25 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_nat__eq__iff) ).
fof(f7304,plain,
spl63_64,
inference(avatar_split_clause,[],[f4117,f7302]) ).
fof(f7302,plain,
( spl63_64
<=> ! [X0] :
( sP0(X0)
| is_int(sK34(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_64])]) ).
fof(f4117,plain,
! [X0] :
( sP0(X0)
| is_int(sK34(X0)) ),
inference(cnf_transformation,[],[f3239]) ).
fof(f7300,plain,
spl63_63,
inference(avatar_split_clause,[],[f4068,f7298]) ).
fof(f7298,plain,
( spl63_63
<=> ! [X0] :
( is_int(number_number_of_int(X0))
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_63])]) ).
fof(f4068,plain,
! [X0] :
( is_int(number_number_of_int(X0))
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2352]) ).
fof(f2352,plain,
! [X0] :
( is_int(number_number_of_int(X0))
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( is_int(X0)
=> is_int(number_number_of_int(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint) ).
fof(f7296,plain,
spl63_62,
inference(avatar_split_clause,[],[f4067,f7294]) ).
fof(f7294,plain,
( spl63_62
<=> ! [X0] :
( is_int(abs_abs_int(X0))
| ~ is_int(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_62])]) ).
fof(f4067,plain,
! [X0] :
( is_int(abs_abs_int(X0))
| ~ is_int(X0) ),
inference(cnf_transformation,[],[f2351]) ).
fof(f2351,plain,
! [X0] :
( is_int(abs_abs_int(X0))
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( is_int(X0)
=> is_int(abs_abs_int(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oabs__class_Oabs_000tc__Int__Oint) ).
fof(f7292,plain,
spl63_61,
inference(avatar_split_clause,[],[f3958,f7290]) ).
fof(f7290,plain,
( spl63_61
<=> ! [X0] : times_times_nat(one_one_nat,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_61])]) ).
fof(f3958,plain,
! [X0] : times_times_nat(one_one_nat,X0) = X0,
inference(cnf_transformation,[],[f1293]) ).
fof(f1293,plain,
! [X0] : times_times_nat(one_one_nat,X0) = X0,
inference(rectify,[],[f927]) ).
fof(f927,axiom,
! [X16] : times_times_nat(one_one_nat,X16) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_nat__mult__1) ).
fof(f7288,plain,
spl63_60,
inference(avatar_split_clause,[],[f3954,f7286]) ).
fof(f7286,plain,
( spl63_60
<=> ! [X0] : times_times_nat(X0,one_one_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_60])]) ).
fof(f3954,plain,
! [X0] : times_times_nat(X0,one_one_nat) = X0,
inference(cnf_transformation,[],[f1289]) ).
fof(f1289,plain,
! [X0] : times_times_nat(X0,one_one_nat) = X0,
inference(rectify,[],[f689]) ).
fof(f689,axiom,
! [X330] : times_times_nat(X330,one_one_nat) = X330,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_mult__1__right) ).
fof(f7284,plain,
spl63_59,
inference(avatar_split_clause,[],[f3950,f7282]) ).
fof(f7282,plain,
( spl63_59
<=> ! [X0] : plus_plus_nat(zero_zero_nat,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_59])]) ).
fof(f3950,plain,
! [X0] : plus_plus_nat(zero_zero_nat,X0) = X0,
inference(cnf_transformation,[],[f1285]) ).
fof(f1285,plain,
! [X0] : plus_plus_nat(zero_zero_nat,X0) = X0,
inference(rectify,[],[f399]) ).
fof(f399,axiom,
! [X131] : plus_plus_nat(zero_zero_nat,X131) = X131,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_add__0) ).
fof(f7280,plain,
spl63_58,
inference(avatar_split_clause,[],[f3946,f7278]) ).
fof(f7278,plain,
( spl63_58
<=> ! [X0] : plus_plus_nat(X0,zero_zero_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_58])]) ).
fof(f3946,plain,
! [X0] : plus_plus_nat(X0,zero_zero_nat) = X0,
inference(cnf_transformation,[],[f1281]) ).
fof(f1281,plain,
! [X0] : plus_plus_nat(X0,zero_zero_nat) = X0,
inference(rectify,[],[f394]) ).
fof(f394,axiom,
! [X130] : plus_plus_nat(X130,zero_zero_nat) = X130,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_add__0__right) ).
fof(f7276,plain,
spl63_57,
inference(avatar_split_clause,[],[f3942,f7274]) ).
fof(f7274,plain,
( spl63_57
<=> ! [X0] : times_times_real(one_one_real,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_57])]) ).
fof(f3942,plain,
! [X0] : times_times_real(one_one_real,X0) = X0,
inference(cnf_transformation,[],[f1277]) ).
fof(f1277,plain,
! [X0] : times_times_real(one_one_real,X0) = X0,
inference(rectify,[],[f697]) ).
fof(f697,axiom,
! [X333] : times_times_real(one_one_real,X333) = X333,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_mult__1__left) ).
fof(f7272,plain,
spl63_56,
inference(avatar_split_clause,[],[f3939,f7270]) ).
fof(f7270,plain,
( spl63_56
<=> ! [X0] : times_times_real(X0,one_one_real) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_56])]) ).
fof(f3939,plain,
! [X0] : times_times_real(X0,one_one_real) = X0,
inference(cnf_transformation,[],[f1274]) ).
fof(f1274,plain,
! [X0] : times_times_real(X0,one_one_real) = X0,
inference(rectify,[],[f682]) ).
fof(f682,axiom,
! [X328] : times_times_real(X328,one_one_real) = X328,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_mult_Ocomm__neutral) ).
fof(f7268,plain,
spl63_55,
inference(avatar_split_clause,[],[f3936,f7266]) ).
fof(f7266,plain,
( spl63_55
<=> ! [X0] : plus_plus_real(zero_zero_real,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_55])]) ).
fof(f3936,plain,
! [X0] : plus_plus_real(zero_zero_real,X0) = X0,
inference(cnf_transformation,[],[f1271]) ).
fof(f1271,plain,
! [X0] : plus_plus_real(zero_zero_real,X0) = X0,
inference(rectify,[],[f406]) ).
fof(f406,axiom,
! [X133] : plus_plus_real(zero_zero_real,X133) = X133,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_add__0__left) ).
fof(f7264,plain,
spl63_54,
inference(avatar_split_clause,[],[f3933,f7262]) ).
fof(f7262,plain,
( spl63_54
<=> ! [X0] : plus_plus_real(X0,zero_zero_real) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_54])]) ).
fof(f3933,plain,
! [X0] : plus_plus_real(X0,zero_zero_real) = X0,
inference(cnf_transformation,[],[f1268]) ).
fof(f1268,plain,
! [X0] : plus_plus_real(X0,zero_zero_real) = X0,
inference(rectify,[],[f392]) ).
fof(f392,axiom,
! [X129] : plus_plus_real(X129,zero_zero_real) = X129,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(f7260,plain,
spl63_53,
inference(avatar_split_clause,[],[f3932,f7258]) ).
fof(f7258,plain,
( spl63_53
<=> ! [X0] : minus_minus_nat(X0,zero_zero_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_53])]) ).
fof(f3932,plain,
! [X0] : minus_minus_nat(X0,zero_zero_nat) = X0,
inference(cnf_transformation,[],[f1267]) ).
fof(f1267,plain,
! [X0] : minus_minus_nat(X0,zero_zero_nat) = X0,
inference(rectify,[],[f658]) ).
fof(f658,axiom,
! [X15] : minus_minus_nat(X15,zero_zero_nat) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_minus__nat_Odiff__0) ).
fof(f7256,plain,
spl63_52,
inference(avatar_split_clause,[],[f3931,f7254]) ).
fof(f7254,plain,
( spl63_52
<=> ! [X0] : minus_minus_real(X0,zero_zero_real) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl63_52])]) ).
fof(f3931,plain,
! [X0] : minus_minus_real(X0,zero_zero_real) = X0,
inference(cnf_transformation,[],[f1266]) ).
fof(f1266,plain,
! [X0] : minus_minus_real(X0,zero_zero_real) = X0,
inference(rectify,[],[f626]) ).
fof(f626,axiom,
! [X295] : minus_minus_real(X295,zero_zero_real) = X295,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_diff__0__right) ).
fof(f7252,plain,
spl63_51,
inference(avatar_split_clause,[],[f3925,f7250]) ).
fof(f7250,plain,
( spl63_51
<=> ! [X0] : pls = times_times_int(pls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_51])]) ).
fof(f3925,plain,
! [X0] : pls = times_times_int(pls,X0),
inference(cnf_transformation,[],[f1260]) ).
fof(f1260,plain,
! [X0] : pls = times_times_int(pls,X0),
inference(rectify,[],[f737]) ).
fof(f737,axiom,
! [X14] : pls = times_times_int(pls,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_mult__Pls) ).
fof(f7248,plain,
spl63_50,
inference(avatar_split_clause,[],[f3924,f7246]) ).
fof(f7246,plain,
( spl63_50
<=> ! [X0] : zero_zero_nat = minus_minus_nat(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_50])]) ).
fof(f3924,plain,
! [X0] : zero_zero_nat = minus_minus_nat(X0,X0),
inference(cnf_transformation,[],[f1259]) ).
fof(f1259,plain,
! [X0] : zero_zero_nat = minus_minus_nat(X0,X0),
inference(rectify,[],[f657]) ).
fof(f657,axiom,
! [X15] : zero_zero_nat = minus_minus_nat(X15,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_diff__self__eq__0) ).
fof(f7244,plain,
spl63_49,
inference(avatar_split_clause,[],[f3921,f7242]) ).
fof(f7242,plain,
( spl63_49
<=> ! [X0] : zero_zero_nat = times_times_nat(zero_zero_nat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_49])]) ).
fof(f3921,plain,
! [X0] : zero_zero_nat = times_times_nat(zero_zero_nat,X0),
inference(cnf_transformation,[],[f1256]) ).
fof(f1256,plain,
! [X0] : zero_zero_nat = times_times_nat(zero_zero_nat,X0),
inference(rectify,[],[f637]) ).
fof(f637,axiom,
! [X304] : zero_zero_nat = times_times_nat(zero_zero_nat,X304),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_mult__zero__left) ).
fof(f7240,plain,
spl63_48,
inference(avatar_split_clause,[],[f3918,f7238]) ).
fof(f7238,plain,
( spl63_48
<=> ! [X0] : zero_zero_nat = times_times_nat(X0,zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_48])]) ).
fof(f3918,plain,
! [X0] : zero_zero_nat = times_times_nat(X0,zero_zero_nat),
inference(cnf_transformation,[],[f1253]) ).
fof(f1253,plain,
! [X0] : zero_zero_nat = times_times_nat(X0,zero_zero_nat),
inference(rectify,[],[f651]) ).
fof(f651,axiom,
! [X310] : zero_zero_nat = times_times_nat(X310,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f7236,plain,
spl63_47,
inference(avatar_split_clause,[],[f3917,f7234]) ).
fof(f7234,plain,
( spl63_47
<=> ! [X0] : zero_zero_nat = minus_minus_nat(zero_zero_nat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_47])]) ).
fof(f3917,plain,
! [X0] : zero_zero_nat = minus_minus_nat(zero_zero_nat,X0),
inference(cnf_transformation,[],[f1252]) ).
fof(f1252,plain,
! [X0] : zero_zero_nat = minus_minus_nat(zero_zero_nat,X0),
inference(rectify,[],[f659]) ).
fof(f659,axiom,
! [X16] : zero_zero_nat = minus_minus_nat(zero_zero_nat,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_diff__0__eq__0) ).
fof(f7232,plain,
spl63_46,
inference(avatar_split_clause,[],[f3916,f7230]) ).
fof(f7230,plain,
( spl63_46
<=> ! [X0] : zero_zero_real = minus_minus_real(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_46])]) ).
fof(f3916,plain,
! [X0] : zero_zero_real = minus_minus_real(X0,X0),
inference(cnf_transformation,[],[f1251]) ).
fof(f1251,plain,
! [X0] : zero_zero_real = minus_minus_real(X0,X0),
inference(rectify,[],[f624]) ).
fof(f624,axiom,
! [X294] : zero_zero_real = minus_minus_real(X294,X294),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_diff__self) ).
fof(f7228,plain,
spl63_45,
inference(avatar_split_clause,[],[f3914,f7226]) ).
fof(f7226,plain,
( spl63_45
<=> ! [X0] : zero_zero_real = times_times_real(zero_zero_real,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_45])]) ).
fof(f3914,plain,
! [X0] : zero_zero_real = times_times_real(zero_zero_real,X0),
inference(cnf_transformation,[],[f1249]) ).
fof(f1249,plain,
! [X0] : zero_zero_real = times_times_real(zero_zero_real,X0),
inference(rectify,[],[f636]) ).
fof(f636,axiom,
! [X304] : zero_zero_real = times_times_real(zero_zero_real,X304),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_mult__zero__left) ).
fof(f7224,plain,
spl63_44,
inference(avatar_split_clause,[],[f3912,f7222]) ).
fof(f7222,plain,
( spl63_44
<=> ! [X0] : zero_zero_real = times_times_real(X0,zero_zero_real) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_44])]) ).
fof(f3912,plain,
! [X0] : zero_zero_real = times_times_real(X0,zero_zero_real),
inference(cnf_transformation,[],[f1247]) ).
fof(f1247,plain,
! [X0] : zero_zero_real = times_times_real(X0,zero_zero_real),
inference(rectify,[],[f650]) ).
fof(f650,axiom,
! [X310] : zero_zero_real = times_times_real(X310,zero_zero_real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f7220,plain,
( ~ spl63_42
| spl63_43 ),
inference(avatar_split_clause,[],[f3883,f7217,f7213]) ).
fof(f7213,plain,
( spl63_42
<=> one_one_int = t ),
introduced(avatar_definition,[new_symbols(naming,[spl63_42])]) ).
fof(f7217,plain,
( spl63_43
<=> is_int(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_43])]) ).
fof(f3883,plain,
( is_int(sK22)
| one_one_int != t ),
inference(cnf_transformation,[],[f3213]) ).
fof(f3213,plain,
( ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(hAPP_nat_int(power_power_int(sK22),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(sK23),number_number_of_nat(bit0(bit1(pls)))))
& is_int(sK23)
& is_int(sK22) )
| one_one_int != t ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f2325,f3212]) ).
fof(f3212,plain,
( ? [X0,X1] :
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
& is_int(X1)
& is_int(X0) )
=> ( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(hAPP_nat_int(power_power_int(sK22),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(sK23),number_number_of_nat(bit0(bit1(pls)))))
& is_int(sK23)
& is_int(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f2325,plain,
( ? [X0,X1] :
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
& is_int(X1)
& is_int(X0) )
| one_one_int != t ),
inference(ennf_transformation,[],[f1236]) ).
fof(f1236,plain,
( one_one_int = t
=> ? [X0,X1] :
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
& is_int(X1)
& is_int(X0) ) ),
inference(rectify,[],[f871]) ).
fof(f871,axiom,
( one_one_int = t
=> ? [X152,X153] :
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(hAPP_nat_int(power_power_int(X152),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X153),number_number_of_nat(bit0(bit1(pls)))))
& is_int(X153)
& is_int(X152) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_) ).
fof(f7211,plain,
spl63_41,
inference(avatar_split_clause,[],[f3806,f7208]) ).
fof(f7208,plain,
( spl63_41
<=> zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_41])]) ).
fof(f3806,plain,
zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat),
inference(cnf_transformation,[],[f324]) ).
fof(f324,axiom,
zero_zero_real = hAPP_nat_real(semiri132038758t_real,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_of__nat__0) ).
fof(f7206,plain,
spl63_40,
inference(avatar_split_clause,[],[f3803,f7203]) ).
fof(f7203,plain,
( spl63_40
<=> one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_40])]) ).
fof(f3803,plain,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
inference(cnf_transformation,[],[f283]) ).
fof(f283,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_transfer__int__nat__numerals_I2_J) ).
fof(f7201,plain,
spl63_39,
inference(avatar_split_clause,[],[f3794,f7198]) ).
fof(f7198,plain,
( spl63_39
<=> one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_39])]) ).
fof(f3794,plain,
one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat),
inference(cnf_transformation,[],[f279]) ).
fof(f279,axiom,
one_one_real = hAPP_nat_real(semiri132038758t_real,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_of__nat__1) ).
fof(f7196,plain,
~ spl63_38,
inference(avatar_split_clause,[],[f6453,f7193]) ).
fof(f7193,plain,
( spl63_38
<=> pls = number_number_of_int(min) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_38])]) ).
fof(f6453,plain,
pls != number_number_of_int(min),
inference(forward_demodulation,[],[f3790,f5594]) ).
fof(f5594,plain,
pls = number_number_of_int(pls),
inference(definition_unfolding,[],[f3786,f3772]) ).
fof(f3786,plain,
zero_zero_int = number_number_of_int(pls),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zero__is__num__zero) ).
fof(f3790,plain,
number_number_of_int(pls) != number_number_of_int(min),
inference(cnf_transformation,[],[f1040]) ).
fof(f1040,axiom,
number_number_of_int(pls) != number_number_of_int(min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_eq__number__of__Pls__Min) ).
fof(f7191,plain,
spl63_37,
inference(avatar_split_clause,[],[f5594,f7188]) ).
fof(f7186,plain,
spl63_36,
inference(avatar_split_clause,[],[f5587,f7183]) ).
fof(f7183,plain,
( spl63_36
<=> zero_zero_nat = nat(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_36])]) ).
fof(f5587,plain,
zero_zero_nat = nat(pls),
inference(definition_unfolding,[],[f3779,f3772]) ).
fof(f3779,plain,
zero_zero_nat = nat(zero_zero_int),
inference(cnf_transformation,[],[f790]) ).
fof(f790,axiom,
zero_zero_nat = nat(zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_nat__0) ).
fof(f7181,plain,
spl63_35,
inference(avatar_split_clause,[],[f4296,f7179]) ).
fof(f7179,plain,
( spl63_35
<=> ! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_35])]) ).
fof(f4296,plain,
! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] : is_bool(hAPP_nat_bool(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
fof(f7177,plain,
spl63_34,
inference(avatar_split_clause,[],[f4295,f7175]) ).
fof(f7175,plain,
( spl63_34
<=> ! [X0,X1] : is_bool(hAPP_real_bool(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_34])]) ).
fof(f4295,plain,
! [X0,X1] : is_bool(hAPP_real_bool(X0,X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] : is_bool(hAPP_real_bool(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__RealDef__Oreal_000tc__HOL__Obool) ).
fof(f7173,plain,
spl63_33,
inference(avatar_split_clause,[],[f3776,f7170]) ).
fof(f7170,plain,
( spl63_33
<=> zero_zero_real = number267125858f_real(pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_33])]) ).
fof(f3776,plain,
zero_zero_real = number267125858f_real(pls),
inference(cnf_transformation,[],[f139]) ).
fof(f139,axiom,
zero_zero_real = number267125858f_real(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_number__of__Pls) ).
fof(f7168,plain,
spl63_32,
inference(avatar_split_clause,[],[f3775,f7165]) ).
fof(f3775,plain,
one_one_nat = nat(one_one_int),
inference(cnf_transformation,[],[f797]) ).
fof(f797,axiom,
one_one_nat = nat(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_transfer__nat__int__numerals_I2_J) ).
fof(f7163,plain,
spl63_31,
inference(avatar_split_clause,[],[f3750,f7161]) ).
fof(f3750,plain,
! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
fof(f7159,plain,
spl63_30,
inference(avatar_split_clause,[],[f6765,f7156]) ).
fof(f7156,plain,
( spl63_30
<=> sP3(zero_zero_nat,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_30])]) ).
fof(f6765,plain,
sP3(zero_zero_nat,pls),
inference(forward_demodulation,[],[f6252,f5608]) ).
fof(f6252,plain,
sP3(zero_zero_nat,hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)),
inference(equality_resolution,[],[f6251]) ).
fof(f6251,plain,
! [X1] :
( sP3(zero_zero_nat,X1)
| hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) != X1 ),
inference(equality_resolution,[],[f4423]) ).
fof(f4423,plain,
! [X0,X1] :
( sP3(X0,X1)
| zero_zero_nat != X0
| hAPP_nat_int(semiri1621563631at_int,X0) != X1 ),
inference(cnf_transformation,[],[f3341]) ).
fof(f7154,plain,
spl63_29,
inference(avatar_split_clause,[],[f6764,f7151]) ).
fof(f7151,plain,
( spl63_29
<=> sP1(zero_zero_nat,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_29])]) ).
fof(f6764,plain,
sP1(zero_zero_nat,pls),
inference(forward_demodulation,[],[f6247,f5608]) ).
fof(f6247,plain,
sP1(zero_zero_nat,hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)),
inference(equality_resolution,[],[f6246]) ).
fof(f6246,plain,
! [X1] :
( sP1(zero_zero_nat,X1)
| hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) != X1 ),
inference(equality_resolution,[],[f4414]) ).
fof(f4414,plain,
! [X0,X1] :
( sP1(X0,X1)
| zero_zero_nat != X0
| hAPP_nat_int(semiri1621563631at_int,X0) != X1 ),
inference(cnf_transformation,[],[f3337]) ).
fof(f7149,plain,
spl63_28,
inference(avatar_split_clause,[],[f6284,f7146]) ).
fof(f7146,plain,
( spl63_28
<=> sP7(one_one_int,one_one_int) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_28])]) ).
fof(f6284,plain,
sP7(one_one_int,one_one_int),
inference(equality_resolution,[],[f6283]) ).
fof(f6283,plain,
! [X1] :
( sP7(one_one_int,X1)
| one_one_int != X1 ),
inference(equality_resolution,[],[f4609]) ).
fof(f4609,plain,
! [X0,X1] :
( sP7(X0,X1)
| one_one_int != X0
| one_one_int != X1 ),
inference(cnf_transformation,[],[f3389]) ).
fof(f7144,plain,
~ spl63_27,
inference(avatar_split_clause,[],[f5583,f7141]) ).
fof(f7141,plain,
( spl63_27
<=> one_one_int = pls ),
introduced(avatar_definition,[new_symbols(naming,[spl63_27])]) ).
fof(f5583,plain,
one_one_int != pls,
inference(definition_unfolding,[],[f3766,f3772]) ).
fof(f3766,plain,
one_one_int != zero_zero_int,
inference(cnf_transformation,[],[f128]) ).
fof(f128,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_int__0__neq__1) ).
fof(f7139,plain,
spl63_26,
inference(avatar_split_clause,[],[f3773,f7136]) ).
fof(f7136,plain,
( spl63_26
<=> is_int(undefined_int(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_26])]) ).
fof(f3773,plain,
is_int(undefined_int(int)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
is_int(undefined_int(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Int__Oint) ).
fof(f7134,plain,
~ spl63_25,
inference(avatar_split_clause,[],[f3769,f7131]) ).
fof(f7131,plain,
( spl63_25
<=> zero_zero_real = one_one_real ),
introduced(avatar_definition,[new_symbols(naming,[spl63_25])]) ).
fof(f3769,plain,
zero_zero_real != one_one_real,
inference(cnf_transformation,[],[f256]) ).
fof(f256,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_one__neq__zero) ).
fof(f7129,plain,
~ spl63_24,
inference(avatar_split_clause,[],[f3764,f7126]) ).
fof(f3764,plain,
one_one_nat != zero_zero_nat,
inference(cnf_transformation,[],[f255]) ).
fof(f255,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_one__neq__zero) ).
fof(f7124,plain,
~ spl63_23,
inference(avatar_split_clause,[],[f3762,f7121]) ).
fof(f7121,plain,
( spl63_23
<=> min = pls ),
introduced(avatar_definition,[new_symbols(naming,[spl63_23])]) ).
fof(f3762,plain,
min != pls,
inference(cnf_transformation,[],[f1044]) ).
fof(f1044,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_rel__simps_I40_J) ).
fof(f7119,plain,
spl63_22,
inference(avatar_split_clause,[],[f5573,f7116]) ).
fof(f5573,plain,
is_int(sK62),
inference(cnf_transformation,[],[f3743]) ).
fof(f7114,plain,
spl63_21,
inference(avatar_split_clause,[],[f3905,f7111]) ).
fof(f3905,plain,
is_int(sK32),
inference(cnf_transformation,[],[f3225]) ).
fof(f7109,plain,
spl63_20,
inference(avatar_split_clause,[],[f3904,f7106]) ).
fof(f3904,plain,
is_int(sK31),
inference(cnf_transformation,[],[f3225]) ).
fof(f7104,plain,
spl63_19,
inference(avatar_split_clause,[],[f3901,f7101]) ).
fof(f3901,plain,
is_int(sK30),
inference(cnf_transformation,[],[f3223]) ).
fof(f7099,plain,
spl63_18,
inference(avatar_split_clause,[],[f3900,f7096]) ).
fof(f3900,plain,
is_int(sK29),
inference(cnf_transformation,[],[f3223]) ).
fof(f7094,plain,
spl63_17,
inference(avatar_split_clause,[],[f3898,f7091]) ).
fof(f3898,plain,
is_int(sK28),
inference(cnf_transformation,[],[f3221]) ).
fof(f3221,plain,
( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) = plus_plus_int(hAPP_nat_int(power_power_int(sK27),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(sK28),number_number_of_nat(bit0(bit1(pls)))))
& is_int(sK28)
& is_int(sK27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f2333,f3220]) ).
fof(f3220,plain,
( ? [X0,X1] :
( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) = plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
& is_int(X1)
& is_int(X0) )
=> ( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) = plus_plus_int(hAPP_nat_int(power_power_int(sK27),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(sK28),number_number_of_nat(bit0(bit1(pls)))))
& is_int(sK28)
& is_int(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f2333,plain,
? [X0,X1] :
( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) = plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
& is_int(X1)
& is_int(X0) ),
inference(flattening,[],[f2332]) ).
fof(f2332,plain,
? [X0,X1] :
( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) = plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls)))))
& is_int(X1)
& is_int(X0) ),
inference(ennf_transformation,[],[f1240]) ).
fof(f1240,plain,
~ ! [X0,X1] :
( ( is_int(X1)
& is_int(X0) )
=> times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) != plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) ),
inference(rectify,[],[f868]) ).
fof(f868,axiom,
~ ! [X152,X153] :
( ( is_int(X153)
& is_int(X152) )
=> times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) != plus_plus_int(hAPP_nat_int(power_power_int(X152),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X153),number_number_of_nat(bit0(bit1(pls))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A) ).
fof(f7089,plain,
spl63_16,
inference(avatar_split_clause,[],[f3897,f7086]) ).
fof(f3897,plain,
is_int(sK27),
inference(cnf_transformation,[],[f3221]) ).
fof(f7084,plain,
spl63_15,
inference(avatar_split_clause,[],[f3893,f7081]) ).
fof(f3893,plain,
is_int(sK26),
inference(cnf_transformation,[],[f3219]) ).
fof(f7079,plain,
spl63_14,
inference(avatar_split_clause,[],[f3891,f7076]) ).
fof(f3891,plain,
is_int(sK25),
inference(cnf_transformation,[],[f3217]) ).
fof(f3217,plain,
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK25),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& is_int(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f2329,f3216]) ).
fof(f3216,plain,
( ? [X0] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& is_int(X0) )
=> ( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(sK25),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& is_int(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f2329,plain,
? [X0] :
( hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))
& is_int(X0) ),
inference(ennf_transformation,[],[f1238]) ).
fof(f1238,plain,
~ ! [X0] :
( is_int(X0)
=> ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) ),
inference(rectify,[],[f1068]) ).
fof(f1068,axiom,
~ ! [X390] :
( is_int(X390)
=> ~ hBOOL(hAPP_int_bool(zcong(hAPP_nat_int(power_power_int(X390),number_number_of_nat(bit0(bit1(pls)))),number_number_of_int(min)),plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4) ).
fof(f7074,plain,
spl63_13,
inference(avatar_split_clause,[],[f3889,f7071]) ).
fof(f3889,plain,
is_int(sK24),
inference(cnf_transformation,[],[f3215]) ).
fof(f3215,plain,
( plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),sK24)
& is_int(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f2328,f3214]) ).
fof(f3214,plain,
( ? [X0] :
( plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),X0)
& is_int(X0) )
=> ( plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),sK24)
& is_int(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f2328,plain,
? [X0] :
( plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),X0)
& is_int(X0) ),
inference(ennf_transformation,[],[f1237]) ).
fof(f1237,plain,
~ ! [X0] :
( is_int(X0)
=> plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),X0) ),
inference(rectify,[],[f1005]) ).
fof(f1005,axiom,
~ ! [X388] :
( is_int(X388)
=> plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),X388) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976__096_B_Bthesis_O_A_I_B_Bt_O_As_____A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_) ).
fof(f7069,plain,
spl63_12,
inference(avatar_split_clause,[],[f3761,f7066]) ).
fof(f3761,plain,
is_int(min),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
is_int(min),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_OMin) ).
fof(f7064,plain,
spl63_11,
inference(avatar_split_clause,[],[f3760,f7061]) ).
fof(f3760,plain,
is_int(m),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
is_int(m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_m) ).
fof(f7059,plain,
spl63_10,
inference(avatar_split_clause,[],[f3759,f7056]) ).
fof(f3759,plain,
is_int(s),
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
is_int(s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_s____) ).
fof(f7054,plain,
spl63_9,
inference(avatar_split_clause,[],[f3758,f7051]) ).
fof(f3758,plain,
is_int(t),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
is_int(t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_t____) ).
fof(f7049,plain,
spl63_8,
inference(avatar_split_clause,[],[f3757,f7046]) ).
fof(f3757,plain,
is_int(s1),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
is_int(s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_s1____) ).
fof(f7044,plain,
spl63_7,
inference(avatar_split_clause,[],[f3756,f7041]) ).
fof(f3756,plain,
is_int(y),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
is_int(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_y____) ).
fof(f7039,plain,
spl63_6,
inference(avatar_split_clause,[],[f3755,f7036]) ).
fof(f3755,plain,
is_int(x),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
is_int(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_x____) ).
fof(f7034,plain,
spl63_5,
inference(avatar_split_clause,[],[f3754,f7031]) ).
fof(f3754,plain,
is_int(m1),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
is_int(m1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_m1____) ).
fof(f7029,plain,
spl63_4,
inference(avatar_split_clause,[],[f3753,f7026]) ).
fof(f7026,plain,
( spl63_4
<=> is_bool(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_4])]) ).
fof(f3753,plain,
is_bool(fFalse),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
is_bool(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fFalse) ).
fof(f7024,plain,
spl63_3,
inference(avatar_split_clause,[],[f3752,f7021]) ).
fof(f7021,plain,
( spl63_3
<=> is_bool(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl63_3])]) ).
fof(f3752,plain,
is_bool(fTrue),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
is_bool(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fTrue) ).
fof(f7019,plain,
spl63_2,
inference(avatar_split_clause,[],[f3746,f7016]) ).
fof(f3746,plain,
is_int(pls),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
is_int(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_OPls) ).
fof(f7014,plain,
spl63_1,
inference(avatar_split_clause,[],[f3745,f7011]) ).
fof(f3745,plain,
is_int(one_one_int),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
is_int(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32 % Computer : n020.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 23:15:32 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (6364)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.40 % (6367)WARNING: value z3 for option sas not known
% 0.16/0.41 % (6371)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.41 % (6366)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.41 % (6370)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.41 % (6368)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.41 % (6369)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.41 % (6367)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.42 % (6365)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.25/0.63 % (6369)First to succeed.
% 1.73/0.67 % (6369)Refutation found. Thanks to Tanya!
% 1.73/0.67 % SZS status Theorem for theBenchmark
% 1.73/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 1.73/0.69 % (6369)------------------------------
% 1.73/0.69 % (6369)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.73/0.69 % (6369)Termination reason: Refutation
% 1.73/0.69
% 1.73/0.69 % (6369)Memory used [KB]: 6823
% 1.73/0.69 % (6369)Time elapsed: 0.260 s
% 1.73/0.69 % (6369)Instructions burned: 541 (million)
% 1.73/0.69 % (6369)------------------------------
% 1.73/0.69 % (6369)------------------------------
% 1.73/0.69 % (6364)Success in time 0.36 s
%------------------------------------------------------------------------------